THE VAPOR PRESSURE OF TITANIUM TETRACHLORIDE
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University
By
HOMER CLYDE WEED, JR., B.S., M.S.
** «*
The Ohio State University 1957
Approved by:
// / 'Adviser Jepartment of Chemistry ACKNOWLEDGMENTS
The author wishes to thank Dr. George E. MacWood for the helpful guidance and encouragement given by him throughout the course of the research.
Professor P. M. Harris and Professor W. J. Taylor have generously lent equipment essential for the ex perimental workj the thanks of the author go to them also.
The cell compartment used in the spectrophoto- metric measurements was constructed by Messrs. P. G.
Laverack and Roy Morris of the Chemistry Department
Instrument Shopj their cooperation and their sugges tions concerning the mechanical design are appreciated.
The author is indebted to Mrs. Carl G. Kauffmann for her efforts in connection with the arrangement of the dissertation and fer her execution of a difficult typing assignment.
Financial support for this research was provided by the Office of Naval Research under Contract No.
NONR-495(06). This support is hereby acknowledged.
-ii TABLE OF CONTENTS
Page
I. INTRODUCTION...... 1
A. Statement of Problem...... 1
B. Survey of Relevant Investigations 2
II. EXPERIMENTAL...... 9
A. Apparatus...... 10
Transfer Systems...... 10 System for Absolute Vapor Pressure Measurements...... 13 System for Spectrophotometric Measurements...... 17
B. Operating Procedures...... 20
Sample Transfer...... 20 Absolute Vapor Pressure Measurements.. 20 Spectrophotometric Measurements 22 Calibration of Thermocouples..... 23
III. ANALYSIS OF DATA...... 25
A. Reduction of Observations...... 25
Time...... 25 Temperature...... 26 Pressure...... 46 Absorbance, Wave Length and 7r ...... 55
B. Thermodynamic Functions...... 84
Theory...... 84 Least Squares Analysis, Absolute Measurements...... 87 Numerical Expressions for the Heat, Free Energy and Entropy of Vaporisation...... 88 Numerical Expressions for the Heat, Free Energy and Entropy of Sublimation...... 90
-iii- TABLE OF CONTENTS, eont.
Pag£
C. Spectrophotometric Functions...... 90
The ory...... 91 Calculation of A Q for the 50 mm Cell.. 92 The Cell Constants K*...... 93 The Molar Absorbancy Index ajj...... 96
D. Tabulated Thermal Functions...... 99
Spectroscopic Values for the Gas...... 99 Tabular Differences from Vapor Pressure Results ...... 107 Thermal Functions of Condensed Phases...... 118
E. Estimation of Errors...... 119
Time...... 119 Temperature...... 119 Pressure...... 122 Absorbance, Wave Length, and t c ...... 123 Thermal Functions...... 124- Molar Absorbancy Index...... 129
IV. RESULTS AND CONCLUSIONS...... 131
A. Vapor Pressures...... 131
B. Heats and Entropies of Vaporization... 133
C. Molar Absorbancy Index a^...... 135
BIBLIOGRAPHY...... 136
AUTOBIOGRAPHY...... 139
-iv- LIST OF TABLES
Table Number Page * . I. (R^./R0) v s . Temperature...... 2S
II. Bridge Temperature Correction Factors.. 32
III. Self-Consistency Corrections...... 33
IV. EMF vs. Temperature for the Copper- Constantan Thermocouple Above 273.16°K...... 37
V. Calibration Data for the Copper- Constantan Thermocouple from 0°C to 30°C...... 39
VI. Corrections on Absolute Temperatures Above 273.16 K for the Copper-Constan- tan Thermocouple...... 4.0
VII. Calibration Data for the Copper- Constantan Thermocouple below 0°C...... 4.2
VIII. EMF vs. Temperature for the Chromel- Alumel Thermocouple...... 4-3
IX. Calibration Data for the Chromel- Alumel Thermocouple...... 4-7
X. Correction do for Thermal Expansion of Scale...... 51
XI. Capillary Depression d. of the Mercury Meniscus in a Fyrex Tube,...... 53
XII. Correction for Thermal Expansion of Mercury...... 54
XIII. The Vapor Pressure of Liquid Titanium Tetrachloride: Absolute Manometric Data...... 56
XIV, A 0 vs. T' for the l.mm Cell...... 60
XV. The Vapor Pressure of Liquid Titanium Tetrachloride: Data for the 1 Mm Cell. 6l LIST OF TABLES, cont. Table Humber Page.
XVI, A 0 vs, T1 for the 5 mm Cell,,,.,...... 63
XVII, The Vapor Pressure of Liquid Titanium Tetrachloride: Data for the 5 mm Cell.. 64.
XVIII. Calculated Values of A for the 50 mm C e l l , ...... 68
XIX. The Vapor Pressure of Solid and Liquid Titanium Tetrachloride: Data for the 50 mm Cell...... 69
XX. A 0 vs. T 1 for the 50 mm Cell...... 74
XXI. Wave Length Calibration...... 76
XXII. The Molar Absorbancy Index aM for Titanium Tetrachloride Vapor from 980 to 200 mmu...... 78
XXIII. Summary of Results for Absorption Constants...... 95
XXIV. Comparison of Molar Absorbancy Index Values . 100
XXV. Calculated or Graphically Interpolated Corrections for Thermal Functions of Titanium Tetrachloride in the Ideal Gaseous State...... 104
XXVI. Fundamental Vibration Frequencies and Degeneracies for Titanium Tetra chloride Gas...... 106
XXVII. Thermal Functions for Titanium Tetra chloride in the Ideal Gaseous State.... 108
XXVIII. Calculation of ...... Ill
XXIX. Thermal Functions for Titanium Tetra chloride Solid and Liquid .....* 113
XXX. Tabular and Interpolated Values of Thermal Functions...... 116
-vi- LIST-OF TABLES, cont. Table Humber Paae
XXXI. Comparison of Thermal Functions at 200°K...... 127
XXXII, Comparison of Experimental Vapor Pressures of Schaefer and Zeppernick with Calculated Vapor Pressures from This Investigation,.,...... 132
-vii- LIST OF ILLUSTRATIONS
Figure Number Pa^je
1. Vacuum System for Filling Optical Cells...... 12
2. Measuring System and Vacuum System for Absolute Manometry...... 15
3. Cell Compartment for Absorbance Measurements with Beckman DU Spectrophotometer...... 19
4. Absorption Coefficient of Titanium Tetrachloride vs WaveLength...... 102
-viiil- I. INTRODUCTION
A.. Statement of the Problem
In connection with an investigation of the thermo dynamic properties of titanium halides, particularly titanium chlorides, it became apparent that the vapor pressure of solid titanium tetrachloride had not been measured experimentally and that there were discrep ancies between the results of the previous investi- (12 3) gators * * who had measured values for liquid
(1) Kimio Arii, Bulletin of the Institute for Physical Chemical Research (Tokyo), 714.-718 (i929).
(2) Kimio Arii, Science Reports, Tohoku Imperial University, First Series, 22, 182-199 (1933).
(3) Harold Schaefer and Friedrich Zeppernick, Zeitschrift fhr anorganische und allgemeine Chemie, 222, 274. (1953). titanium tetrachloride. The work of this dissertation was undertaken in order to check on these results and to extend the range of measurement far enough to obtain experimental vapor pressure values for solid titanium tetrachloride, so that related thermodynamic properties such as heat and entropy of vaporization and sublimation could be calculated. Spectrophotometric methods ap peared suitable for most of the temperature and pressure range to be explored; in connection with their use, the absorption spectrum of titanium tetrachloride vapor was determined over the visible and ultraviolet wave-length range since it was not known with precision at that time.
B. Survey of Relevant Investigations (1 2 Although the results of Arii * ) were quite self consistent they could not be verified by Schaefer
(4.) K. K. Kelley, Contributions to the Data of Theoretical Metallurgy, III. The Free Energies of Vaporization and Vapor Pressures of Inorganic Substances. Bureau of Mines Bulletin 3S3, Washington (1935), p. 106.
(3) and Zeppernick, who found that their measured vapor pressures were consistently lower than those of Arii in the same temperature range and attributed this differ ence to the presence of residual inert gas in the measuring cell of Aril's apparatus. Aril's measurements O 0 covered the range from 4-08.16 K to 293.16 K: Schaefer and Zeppernick1s from 359.56°K to 312.76°K. The dis crepancy between the two sets of results and the lack of data below 293.16°K made it desirable to check both sets over at least a part of their temperature range and to obtain further information for temperatures below
293.16°K. (5) The experimental work of Latimer on the specific 3
(5 ) W* M s La timer, Journal of the American Qhest eal Society, 90-97 (1922).
heat capacity of solid and liquid titanium tetrachloride
and on the heat of fusion of the solid has been used by
Skinner in calculating values of thermal functions
(6 ) Gordon Skinner, Charles E. Beckett and H. L. Johnston, Titanium and Its Compounds. Herrick L. Johnston Enterprises, Columbus, Ohio (1954)> p. 108.
for solid titanium tetrachloride from 50°K to the
melting point and for liquid titanium tetrachloride
from the melting point to the normal boiling point.
There have been no other specific heat capacity deter
minations reported on the solid or the liquid since those
of Latimer.
Skinner has calculated heat capacities and other
(6 ) op. cit.. p. 109.
thermal functions for titanium tetrachloride in the
ideal gaseous state from 50°K to 3000°K, later recalcu- (n) lating some of the high temperature values w / to allow
(7) Gordon Skinner, Journal of Physical Chemistry, JL2» 113 (1955). for vibrational anhsrmonicities and rotation-vibration
interaction in the titanium tetrachloride molecule.
Similar calculations have been performed by Hawkins
-and Carpenter for the range 10Q°K to 500°K, using
(8 ) N. J. Hawkins and D. R. Carpenter, Journal of Chemical Physics, Z2, 1700 (1955).
a slightly different value (2.ISA) for the Ti-Cl bond
distance than those quoted by Skinner (2.21^0.05A
and 2.18+0.04A). At 150°K and above, Skinner's cal
culated heat capacity values are about 0.04 cal/mol°K
higher than those of Hawkins and Carpenter, with cor
responding differences in the values for the other
thermal functions. There is substantial agreement
regarding the infra-red and Raman vibration frequen
cies used in the calculations.
There have been two direct calorimetric determina
tions of the heat of fusion of solid titanium tetra
chloride: one by Latimer on material of unspecified (9) purity; and one by the National Bureau of Standards
(4) W. M. Latimer, o p . ci t .
(9) Private communication at Office of Naval Research Conferenoe, November 14-16, 1955.
on highly purified material prepared and carefully (.10) W. Stanley Clabaugh, Robert T. Leslie and Raleigh Gilchrist, Journal of Research of the National Bureau of Standards, ££, 261 (1955). RP 2628.
11 analyzed ( ) by them. Their value was higher than
(11) Raleigh Gilchrist, R. B. Johannesen, C. L. Gordon and J. E. Stewart, Journal of Research of the National Bureau of Standards, 22» 197 (1954). BP 2533.
Latimer's: 2330 cal/mol as compared with 2233 cal/mol.
On the assumption that their experimental methods were
at least as accurate as Latimer's their value was con
sidered the more reliable on account of the high purity
of the material used.
The melting temperature of the solid has also been
determined by Latimer (24S.0°K) and by Furukawa
( 4 ) W. M. Latimer, on. cit.
(12) Private communication, Inorganic Chemistry Section, Division of Chemistry, National Bureau of Standards, Washington, D. C. February 8 , 1954.
(249.045^0.015°K). Furukawa1s value was determined by
extrapolatiaaof the melting curve on highly purified
material and was therefore considered the more reliable
of the two values.
No data have been reported on the absorption spec trum of solid titanium tetrachloride. The absorption spectrum of the pure liquid from 2-15 mu has recently (n ) been reported by Gilchrist and co-workers*' ' As
(11) Raleigh Gilchrist, at al.. o p . cit.
one result of their investigation they believed that
the titanium tetrachloride used in the only previously- (1 1 ) reported work was impure. On the basis of their
(13) H. H. Marvin, Physical Review, 24, 161-186 (1912).
frequency assignments for the infra-red bands which
they observed, they were able to obtain what they con
sidered to be good agreement between the frequencies
observed by them and those which they calculated from
Raman data reported by several previous investigators.
The most recently reported infra-red absorption
data on titanium tetrachloride vapor were obtained by (8 ) Hawkins and Carpenter ' 1 over the wave-length range
(8 ) N. J. Hawkins and D. R. Carpenter, op. cit.
6-22 mu. Although they observed two questionable ab
sorption bands at their highest operating temperature
(125°C) they considered that these were probably due to impurities. They reported good agreement between observed frequencies and those which they calculated -7- on the basis of their frequency assignments, using ex perimental Raman frequencies from previous investigators.
In connection with their work on the tetrachlorides of carbon, silicon, tin and titanium, Dutta and Saha
(14) A. K. Dutta and M. N. Saha, Bulletin of the Academy of Sciences of the United Provinces of Agra and Oudh, India, 1, 19-25 (1931-32). reported a long-wave-length absorption limit of 336 mmu for titanium tetrachloride vapor but did not investigate the continuum in detail for shorter wave lengths than this. The results of such an investigation in the region from 240 mmu to 360 mmu have recently been reported by (15) Mason and Vango, who found a maximum in the absorbancy
(15) David M. Mason and Stephen P. Vango, Journal of Physical Chemistry, ^0, 622 (1956). at 230 mmu and a molar absorbancy index at this wave length of 7.29 x 10^ l/mol cm. Since they used Arii's (4) data as recalculated by Kelley for vapor pressure
(4 ) K. K. Kelley, op. cit. values corresponding to their observed absorbancies, the pressure may have been too high, and the calculated molar absorbancy values therefore too low. This point is discussed further in Section IV. -8-
Although heats of vaporization have been calculated from vapor pressure data. no direct calorimetric
(4) K. K. Kelley, op.cit.
(3) Harald Schaefer and Friedrich Zeppernick, £.41»
(6 ) Gordon Skinner, op. cit.. p. 47. determinations have been reported. No values for the heat of sublimation of titanium tetrachloride have been reported either from vapor pressure measurements or direct calorimetry.
It thus appeared that the vapor pressure should be further investigated, especially if the measurements could be extended to sufficiently low temperatures to yield information on the sublimation equilibrium for solid titanium tetrachloride. II. EXPERIMENTAL WORK
Three types of experiments were performed: absolute vapor pressure measurements above 10 mm Hg; relative spectrophotometric measurements at 279*3 mmu over the
10 to 0.01 mm Hg range; and spectrophotometric measure- ) ments at constant pressure over the wave length range from 200 to 930 mmu.
Because of the high reactivity of titanium tetra chloride, sealed systems were used for storage, transfer and vapor pressure measurement of the high-purity material used in this investigation.
(16) Precautions for Handling Ampoules Containing Titanium Tetrachloride of High Purity Prepared by the National Bureau of Standards. Private communication, Inorganic Chemistry Section, Division of Chemistry, National Bureau of Standards, Washington, D.C., Febru ary 8 , 1954*
The experience of Sanderson and MacWood had indi cated that the sensitivity of available spoon gauges was (17) about 0.03 mm, using the gauge as a null indicator.
(17) Benjamin S. Sanderson and George E. MacWood, Journal of Physical Chemistry, £2, 316-319 (1956).
Absolute vapor pressure measurements were therefore made with a spoon gauge, a large-bore H-type mercury manometer being used to measure the pressure in the reference system. -10-
Preliminary absorbance measurements on titanium tetra chloride vapor together with the vapor pressure results of Arii^^ showed that relative vapor pressures could be
(l) Arii, op. cit. measured near the melting point with cells of 50 mm optical path. The spectrophotometric measurements were therefore begun at this path length; cells of 5 mm and
1 mm path length were used later in order to extend the spectrophotometric measurements up to the range of the absolute measurements.
A. Apparatus.
Transfer Systems.
Conventional systems were used in transferring titanium tetrachloride from the NBS storage ampoules as shown in Fig ure 1. Excepting for the optical cells F, which were of fused silica with Vycor sidearms, the systems were made of
Pyrex. The sidearms of the 1 mm and 5 mm optical cells were attached to the manifold at G by means of graded Vycor-to-
Pyrex seals.
The system used for filling the 50 mm optical cells was similar to that shown in Figure 1, except that it had no sample holders, storage bulb, nor hot-air ovens. The cells were attached at G by means of standard taper 12/5 spherical joints, sealed with a thin layer of Apiezon black wax and kept cool during torching of the system by Figure 1, Vacuum System for Filling Optical Cells
A. High Vacuum Section: Pumps, Liquid Nitrogen Trap and Ionization Gauge
B. Manifold for Transferring Titanium Tetrachloride
C. Capillary for Sealing-Off the Manifold
D. Glass-Coated Iron Slug
E. Bulb Containing Titanium Tetrachloride
F. Optical Cells
G. Graded Seals Joining Cells to Manifold
H. Laboratory Ampoules with Breakoff Tips
I. Laboratory Storage Bulb
J. Gas-Heated Ovens
-11- A B
“ 1
QJ
Figure I. - 1 3 -
means of plugs of absorbant cotton moistened with water*
The high vacuum section A included a Welsh DuoSeal
forepump, a two-stage water-cooled mercury diffusion
pump, a liquid nitrogen trap, and a VG-l-A ionization
gauge.
System for Absolute Vanor Pressure Measurements-
The apparatus is shown in Figure 2. Provision was in
cluded for the following operationss evacuation of the
system by the high vacuum section A of Figure 1, or
isolation from A; adjustment and measurement of the press
ure in reference section R, or isolation of the mercury
manometer from R; evacuation of the reference arm of the
mercury manometer; isolation of either side of the spoon
gauge 0 from,the reference section; determination of the
null position of the spoon gauge; admission of titanium
tetrachloride vapor to the sample section S; measurement
and control of the temperature of the vapor and of the
liquid in S.
The H-type mercury manometer, was of conventional de
sign, with reference and working arms of 17.25 t 0.1 mm
ID, The mercury menisci were illuminated from the rear
through two horizontal sharp-edged slits which could be adjusted to define the images of the menisci. The mano meter was read with a single-telescope cathetometer (Wild,
OSU Serial No. 24-2709), the readings being referred to a standard half-meter bar (Gaertner M 1012, Serial No. 259) Figure 2
Apparatus for Absolute Vapor Pressure Measurements
R. Reference Section
A. Stopcock to High Vacuum Section A of Figure 1
B, C, D, Vacuum Stopcocks for Connection to Auxiliary Vacuum, Mercury Manometer, and Dry Argon Supply
E. Reference Section Manifold
F. Ion Gauge
G. Vacuum Stopcock for Connection to Reference Arm of Mercury Manometer
I, J. Vacuum Stopcocks for Iaolation of the Spoon Gauge
K. Seal-Off Capillary, 2 mm ID x 5 cm
L. Reference Bulb of Spoon Gauge
M. Adjustable Reference Pointer
N* 4-OX Gaertner Microscope
S. Sample Section
0, Spoon Gauge and Movable Pointer
P. Heating Mantle
Q* Glass-Coated Iron Slug
T. Platinum Resistance Thermometer
H. Sample Holder with Break-Off Tip
U. Pyrex Dewar, 15 cm ID x 34 cm
-1 4 -15-
R s JL- _A_
u
Figure 2 -16-
suspended between the reference and working arms of the
manometer. The temperature of the manometer and bar
was read from a thermometer suspended inside the glass
fronted wooden case in which the manometer was housed.
The null position of the spoon gauge pointer was
determined with a 40X Gaertner microscope (OSU Serial
No. 234&92)using diffuse illumination from the rear.
The temperature of the spoon gauge and of the titan
ium tetrachloride vapor in the sample section was
measured at points "xn (Figure 2) with iron-constantan
thermocouples and a portable potentiometer (L&N, Model
8662, OSU Serial No. 189235). The gauge thermocouple was also used as the sensing element for a controller
(Foxboro, Model 4041-5, OSU Serial No. I69648) and relay to regulate the temperature.
Coarse control of the temperature of the water bath was accomplished by means of a mercury-in-glass thermo regulator, electronic relay (Fisher-Serfass) and 125-watt heater. Temperatures were read at a thermometer current of 2.0 ma with a platinum resistance thermometer (L&N,
Thermohm, Serial No. 723009), Mueller bridge (Rubicon,
Serial No. 46826) and box galvanometer (Rubicon, Type
3404-H)- An auxiliary 125-watt heater and manually- operated Variac were used for precise temperature control during runs. -17-
Svstem for Spectrophotometric Measurements.
A Beckman DU spectrophotometer (Serial No. 30563) was modified for the measurements by installation of the cell compartment shown in Figure 3. This figure shows a side view of the outer case together with a section through the center line of the sample cell. Provision was in cluded in the system for measurement and control of temperature T of the coondensed phase in the sidearm and
T* of the vapor phase in the optical cell; for positioning the sample or reference cell in the beam; and for calibra tion of the thermocouples in situ relative to the plati num resistance thermometer mentioned above.
EMF’s of the copper-constantan and ehromel-alumel thermocouples were measured with a K-2 potentiometer,
Rubicon Type 3404-2 galvanometer, and Eppley standard cell (OSU Serial No. 130307). In order to avoid flexure of the thermocouple leads as the optical cells were moved perpendicular to the light beam, the leads were brought out to the K-2 through the center of the slide handle D.
Temperatures below 0°G were obtained with a trichloro- ethylene or calcium-chloride-water bath cooled by packing solid carbon dioxide between the Dewar P and an outer case
(not shown in the figure). Above 0°C, the bath was cooled by circulating water between copper coils in it and in an ice bath. Heat was supplied by a 125-watt blade heater, thyratron circuit, and mercury-in-glass thermoregulator. Figure 3
Cell Compartment for Spectrophotometric Measurements
A. Beckman DU Monochromator and Photocell Compartment
B. Aluminum Outer Case, 20 cm x 16.5 cm x 14 cm
C. Aluminum Inner Case with Heating Elements, 14*5 cm x 10 cm x 7 cm (Flexible Leads Not Shown)
D. Slide Handle with Concentric Tube for Thermocouple Leads
E. Kinematic Mounting and Mechanical Linkage to Slide Handle
F. Cell Holder, 6 cm x 6*4 cm x 3.9 cm
G. Bottom Half of Cell Holder (Aluminum)
H. Removable Top Half of Cell Holder (Copper)
I* Spring, Positioning Stop, and Cell Spacers
J. Fused Silica Sample Cell, 5 mm Optical Path, with Sidearm 27*3 cm x 0.8 cm 0D
K. Bakelite Insulating Block
L. Thin-Walled Copper Enclosure for Sidearm, 20.5 cm x 11 cm x 2.8 cm
M. Heat-Transfer Liquid (jj-Propyl or ^-Amyl Alcohol)
N, Copper Thermocouple Block, 7 cm x 2.5 cm x 1 cm x Location of Copper-Constantan Thermocouple Junction
+ Location of Chromel-Alumel Thermocouple Junction
P. Unsilvered Dewar
-1 8 -1 9 -
V-
Figure 3 -20-
The optical cells had fused silica bodies and win dows j the long sidearms of the sample cells were made of Vycor. The short sidearms of the 1 mm and 5 mm reference cells were fused shut under vacuum before the cells were used; the standard taper sidearm of the 50 mm reference cell was closed with a stopper.
B . Operating Procedures.
Sample Transfer.
The system for the 50 mm cells was held at 1.3x10“^ mm Hg or less for 4 hours, torched intermittently for
2.5 hours, and then cut off at C from the vacuum section
A (Figure l). After transfer the filled 50 mm cells were removed from the manifold by fusing the sidearms closed about 5 cm below the joints. The same procedure was used for the 1 and 5 mm cells F and ampoules H and I except —5 o that the system was held at about 1x10 mm Hg and 370 C for 13 hours before it was cut off from A. The filled am poules were sealed off after the cells had been removed.
Absolute Vapor Pressure Measurements.
The sample section was held at a pressure of 5x10*"-’ mm
Hg or less for about 35 hours; during this period the tem perature of the tubing near K (Figure 2) was about 22 5°C and the thermocouples on the spoon gauge bulb L and sample holder H read about 360°G. The sample section was then isolated fromthe reference section by sealing it off at
K, and the sample admitted. -21-
Before each run, the zero resistance and resistance ratio of the fixed armsviere checked on the,Mueller bridge.
Operations during the run were recorded vs. time, which was read to the nearest second from a continuously- running tenth-second electric timer.
After the temperature of the bath had been adjusted, the sequence of operations was as follows; reading of the bridge temperature and bridge resistance; balancing of the spoon gaugej isolation of the reference manometerj reading of bridge temperature and resistance; reading of the manometer and manometer temperature; reopening of the manometer to the manifold; reading of the vapor phase thermocouples. The sequence was repeated twice at each temperature, the balance point of the spoon gauge being approached alternately from the direction of high and low pressure. Since the average drift rate was about
0.001°G/min, the bath temperatures usually varied less o than 0.03 C during each sequence.
The zero reading for the spoon gauge was determined at intervals by freezing out the sample with liquid nitrogen and evacuating the reference section to a pressure of 5 x 10~** mm Hg or less, with the mercury manometer closed off at C (Figure 2).
The zero reading for the mercury manometer was similarly determined with the spoon gauge balanced and then isolated from the manifold at I (Figure 2). -22-
Data were taken from 298.5 to 319.1°K in order to
overlap the data of Schaefer and Zeppernick starting at
312.8°K.
Spectrophotometric Measurements.
After the adjustment of the bath temperature, the fol
lowing sequence of operations was used for the runs at a
constant wave length of 279.8 mmu: reading of the EMF
of the cell thermocouplej reading of the EMF of the side-
arm thermocouplej balancing of the spectrophotometer for
100$ transmission of the reference cell and reading the
absorbance of the sample cellj reading of the sidearm
thermocouple EMFj alternate spectrophotometer and sidearm
thermocouple readings until from 2 to 5 spectrophotometer
readings had been obtainedj reading of the EMF of the cell
thermocouple. The EMF and absorbance readings were re
corded vs. time as in the procedure for absolute vapor
pressure measurements. The average drift rate of the
cell and sidearm temperatures was about 0.02°c/minj
runs at each temperature lasted about 8.5 min.
The absorbance of the empty sample cell vs. the-
reference cell was determined in the same way as des
cribed above except that liquid nitrogen was used as the bath and heat transfer liquid so that the titanium tetra
chloride was frozen out in the sidea_rm. The temperature
of the cell was varied over a range wide enough to include the range of temperature variation during the runs. In the determination of the absorbance of the empty
1 mm sample cell vs. the reference cell over the wave length range from 980 to 200 mmu, the range was covered from long to shorter wave lengths. The sample was frozen out in the sidea-rm as described above.
The absorbance of the sample cell and vapor was measured as a function of the wave length at a pressure o of 13.7 mm Hg and a sidearm temperature of 302.6 K; the cell temperature varied between 312°K and 318.5°K. The operating sequence for these measurements was the same as described above for the runs at 279.8 mmu.
Calibration of Thermocouples.
Both thermocouples were calibrated in situ. The copper-constantan sidearm thermocouple was fastened by its thread suspension to a small wire loop inside the cell compartment and the sidearm replaced with a platinum re sistance thermometer. Below 0°C the bath temperatures were stabilized by operating at the freezing points of chloro form (-63.5°C), ethylene dichloride (-36°C), carbon tetra chloride (-22.9°C) and tertiary amyl alcohol (-12°C).
The Mueller bridge readings and thermocouple EMF readings were recorded vs. time as described above. The average drift rates were about 0.0064°C/min for the thermocouple and 0.0048°C/min for the resistance thermometer.
The chromel-alumel cell thermocouple was calibrated by substituting a cylindrical aluminum block for the -24-
sample cell, with the resistance thermometer inserted in a hole along the longitudinal axis of the block* The average drift rates were about 0.0043°C/min for the thermocouple and about 0,0028°C/min for the resistance thermometer. III. ANALYSIS OF DATA
After reduction of the instrument readings to values
of pressure, temperature, absorbance, etc., the absolute
vapor pressures were analyzed by the method of least
squares to obtain values for the constants in the vapor
pressure equations for the liquid and for the solid.
These equations were then used together with the spectro-
photometric data to obtain the molar absorbancy index of
the vapor, first at 279.8 mmu and then over the range
from 200 to 980 mmu. Tables of thermal functions for
the gas and the solid liquid were calculated using the
vapor pressure results of this and one other investiga
tion.
The details of the analysis, including an estimation
of errors, are given below.
A. Reduction of Observations.
Time.
Instrument readings were recorded to the nearest
second as functions of time, which was considered as the
independent variable for purposes of initial reduction
of data. For a particular kind of experiment, instrument readings corresponding to one of the variables were used directly and simultaneous readings for the other variables involved in the experiment were obtained by linear inter polation with respect to time. Graphical plots of EMF -26- vs. time for some of the early spectrophotometric data
indicated that for time intervals up to about 300 sec the deviation from linearity was small. Most of the
interpolations were therefore performed arithmetically.
For absolute measurements, the time at which the
spoon gauge was balanced and the mercury manometer locked was recorded and the corresponding Mueller bridge readings
obtained by interpolation. The temperature of the mano meter was also recorded vs. time} its interpolated value was used in the formulas for reduction of manometric readings to pressures. Usually this was the same as the average value for the period during which the readings were being taken on the locked manometer.
For spectrophotometric measurements, directly ob served values of the absorbance were used and the corres ponding cell and sidearm thermocouple EMF values obtained by interpolation.
EMF values obtained during thermocouple calibration experiments were used directly} the corresponding Mueller bridge readings for the platinum resistance thermometer were interpolated.
Resl.sta.nce thermome try.
The absolute temperature T(°K) was calculated from
(1) T=t + 273.16.
Numerical values of t (°C) were obtained by linear -27-
interpolation of experimental values of (H^/Rq) in
Table I of (R^./R0) v s , t, calculated for integral values
of t from the formula
(2) (R+/R )=1 + At + Bt2 - lOOCt3 + Ct4, for t » 0 (18). u O G=0
(18) H, F. Stimson, Journal of Research, National Bureau of Standards, 42* 209 (1949)*
In this formula
(3) A ■ a(l + 10-2$) = 0.003983033
B = -10“4a5 = -5.85532x10“^
C = -10"8ap « -4.3366x10*"12 and the values of a, (and approximate R 0) were de termined for the resistance thermometer (Thermohm No,
723009) by NBS calibration^19^.
(19) National Bureau of Standards Certificate 3.1/G-18939, February 7, 1956:; a=0.00392448; R 0= 25.558 absolute ohms. National Bureau of Standards Certificate 3.1/115245 NBS 1051, October 8, 1948: a=0.00392474? R0=25.551 absolute ohms? S =1.492} (3=0.1105.
Mueller bridge readings were reduced to values of
R-k, R0 and (R^/R0) according to the following equation:
(4) [(D - Z)K + £ c ] c = R.
R(Rt> R 0) is the resistance of the thermometer (at temperature t°C, 0°C).
D is the mean of the normal (N^) and reversed (Rj) -23-
Table I
(R^./R0) va. Temperature, Thermohm No. 723009. Fundamental Temperature Scale for This Investigation
t, °c (dR/k0dt, °C"1 ) x 107
— 65 .7384325 40636 -64 .7425011 40671 -63 .7465682
-37 .8517961 40284 -36 .8558245
-23 .9080740 40103 -22 .9120843
-16 .9361195 40016 -15 .9401211
0 1.0000000
3 1.0318268 39731 9 1.0357999 39718 10 1.0397717 39709 11 1.0437426 39695 12 1.0477121 39683 13 1.0516804
17 1.0675424 39625 18 1.0715049
23 1.0913001 39554 24 1.0952555 3954-3 Table 1 (cont.)
t, °C (dR/R dt, °C"1 ) x 107
25 1.0992098 39533 26 1.1031631 39519 27 1.1071150 39508 28 1.1110658 394-98 29 1.1150156 39484 30 I.II8964O 39473 31 1.1229113 39462 32 1.1268575 39450 33 1.1308025 39439 34 1.1347462 39425 35 1.1386889 39415 36 1.1426304 39402 37 1.1465706 39392 38 1.1505098 3 9 3 7 9 39 1.1544477 39367 40 1.1583844 39357 41 1.1623201 39344 42 1.1662545 39333 43 1.1701878 39321 44 1.1741199 39309 45 1.1780508 39297 Table I (cont.)
t, °C R+/Rt' o (dR/R dt, °C“1 ) x 107
4.6 1.1819805 39287 47 1.1859092
57 1.2251305 39157 58 1.2290462 39145 59 1.2329607 39134 60 1.2368741
131 1.5117290 38291 132 1.5155581
134 1.5232126 38256 135 1.5270382 readings of the Mueller bridge at the operating tempera
ture tg.
Z is the mean of four readings (N^, R^, Ng, Rg)
bridgej it corresponded to the "zero resistance" of
the bridge and usually had a value of about -0.0003 abs
ohms.
K is the temperature correction factor converting the
resistance of the bridge coils at the operating tempera
ture tg to their resistance at 35°C. This factor was
calculated assuming the coils to have the same resistance-
temperature coefficient as that cited by Mueller
(Table II).
(20) E. F. Mueller, in Temperature. Its Measure ment and Control in Science and Industry, Reinhold Publishing Corp., New York (194-1), p. 69.
to is the sum of the self-consistency corrections for (21) the coils, determined experimentally for the bridge
(21) Notes to Supplement Resistance Thermometer Certificates, National Bureau of Standards, January 1, 1949, pp. 10-15.
(Rubicon, Ser. No. 4-6826) used in this investigation.
It was tabulated as a function of the temperature-correct
ed bridge readings (Table III).
C Is the conversion factor from "bridge units" to abs ohms.
It had the numerical value 0.9995789 abs/ohms/bridge unit, —32"»
Table II
Bridge Temperature Correction Factors from tg to 35°C
tg,°c (K-l)xlO7 (K-l)xlO7 tB ,°c (K-l)x: ♦ b A 24.0 720 27.7 384 31.4 144 .1 708 .8 376 .5 140 .2 696 .9 368 .6 136 .3 684 28.0 360 .7 132 •4 672 .1 352 .8 128 .5 660 .2 344 .9 124 • 6 648 .3 336 32.0 120 .7 636 .4 328 .1 116 .8 624 .5 320 .2 112 .9 612 .6 312 .3 108 25.0 600 .7 304 .4 104 .1 592 .8 296 .5 100 .2 584 .9 288 .6 096 .3 576 29.0 280 .7 092 .4 568 .1 272 .8 088 .5 560 .2 264 .9 084 .6 552 .3 256 33.0 080 .7 544 .4 248 .1 076 .8 536 .5 240 .2 072 .9 528 .6 232 .3 068 26.0 520 .7 224 •4 O64 .1 512 .8 216 .5 060 .2 504 .9 208 .6 056 .3 496 30.0 200 .7 052 • 4 488 .1 196 .8 048 .5 480 .2 192 .9 044 .6 472 .3 188 34.0 040 .7 464 .4 184 .1 036 .8 456 .5 180 .2 032 .9 448 .6 176 .3 028 27.0 440 .7 172 .4 024 432 .8 168 .5 020 .2 424 *9 164 .6 016 .3 416 31.0 160 .7 012 •4 408 .1 156 .8 008 .5 400 • 2 152 .9 004 .6 392 .3 148 35.0 33-
Table III
Self-Consistency Corrections c for Rubicon Mueller Bridge, Serial No. 4-6826
Dial Designation M W V V p lated xlO xl x.l x.01 x.001 x.0001 t .0 °C c X 106
0 0 0 0 0 0 0
1 3360 100 -101 40 -1 0
2 6710 100 -251 30 -2 0
3 10170 -48 -452 20 -3 0
4 13620 -98 -452 10 -4 0
5 16980 99 -5 03 0 -5 0 H H 6 20540 198 -554 1 -6 0
7 199 -654 -21 -7 0
8 155 -705 -31 -8 0
9 255 -756 -41 -9 0
X 456 -857 -51 -10 0 -34- determined by measurement of a standard 10-ohm resistor
(22) Leeds and Northrup Go. Certificate for Stan dard Resistor, Serial No. 613883, Catalog No. 4025s R=10.OOOl/25°C International ohms, correct within 1 part in 104- as of January 1946. Smithsonian Physical Tables.. 9th rev. ed., Smithsonian Institution, Washington (1954), PP* 19, 20, Table 5i 1 mean International ohm=l.00049 absolute ohm.
with the bridge.
Since the experimental value R 0 =* 25.55855 I 0.00003
abs ohms obtained in this investigation was in satis
factory agreement with the NBS approximate value of
25*558 abs ohms, the temperature scale of this investi
gation was based on Equations (l), (2) and (3) using the
corresponding (newer) value of a = 0.00392448, and the
old values of p and <5.
Temperature.
Thermocouple Me a s urerne nts.
Precise knowledge of the temperature of the vapor phase was not required for the absolute manometric ex periments, except that the temperature of the vapor phase should always be greater than that of the liquid. The
EMF values of the iron-constantan thermocouples were therefore recorded to the nearest microvolt and the vapor phase temperatures calculated from them by linear inter polation in standard tables (23). No calibration curves
(23) Leeds, and Northrup Standard Conversion Tables, No. 31031, p. 8. were used in the calculation, and the temperatures were not tabulated. They were approximately 15°C greater than the bath temperatures.
For the spectrophotometric work, it was necessary to have fairly precise knowledge of the temperature of both the condensed phase in the sidearm (T) and the vapor phase in the optical cell (T>). The general re duction scheme was to use tables of EMF vs. temperature for approximate temperature calculations from experimental
EMF values obtained during the runs. The approximate temperatures were adjusted by means of large scale devia tion plots to the temperature scale used in the absdute measurements. Data for the deviation plots were obtained during calibration experiments on the thermocouples; mean values of the data were plotted.
Above the ice point, for the copper-constantan thermocouple, the following EMF-temperature relation was used:
(5) 6s = -7145.264.7 + 13*865610 + .04500To2, T q¥ 273.16, obtained from
(6) 6s = 38»450t + .04500t2, t* 0, and
(7) t = T - 2 7 3 . It was tabiated at integral
(24-) Vm. F. Roeser and H. T. Wensel, in Temperature, Its Measurement and Control in Science and Industry, Rein hold Publishing Corp., New York (194-1) pp. 303-304. -3 6 - values of T (Table IV),
Values of £s the standard EMF were calculated from
the experimental EMF values and the relation:
(8) £ s » ^ + A 3 £ + (^s -£)
where A was read from a deviation plot of A vs.£, This
plot was based on mean values of A and £ from the cali
bration data of Table V. In this table the£s values
were calculated from resistance thermometer temperatures
(t,°C) by Equation (2) above. The temperature scale
differed from the final scale owing to: (l) a calcula
tion error of about +0.10°C for one value at 8°C; and
(2) the use of values of a and different from the o final ones and affecting the scale systematically by
0.01°G or less.
Approximate temperatures (T0) were calculated from values of £s by linear Interpolation in Table IV. Once
calculated, the approximate temperatures were corrected to the temperature scale of the absolute measurements by the relation:
(9) T = T0 + AT * where A T was read from a plot of AT vs« T0 . This plot was prepared from the mean values of T0 and AT shown in
Table VI, and included corrections for the calculation error and the use of old values of a and R0 mentioned above. As expected, the corrections were largest for
T0 - 281,5°K. -37-
Table IV
EMF vs. Temperature for the Copper-Constantan Thermocouple Above 273.16 °K
T0,°K 6g, muV (d€/dT0,auV/°K) x 10*
273.16 0.00 384877 274 32.33 385706 275 70.90 386606 276 109.56 387506 277 148.31 388406 278 187.15 389306 279 226.08 390206 280 265.10 391106 281 304.21 392006 282 343.41 392906 283 382.71 393806 284 422.09 394706 285 461.56 395606 286 501.12 396506 287 540.77 397406 288 580.51 398306 289 620.34 399206 290 660.26 400106 291 700.27 401006 292 740.37 401906 293 780.56 402806 -38- Table jv (cont.)
Is, *uV (d6/dT0,muV/°K) x 10* T0»°K
402806 294 820.84 403706 295 861.21 404606 296 901.67 405506 297 942.22 406406 298 982.86 407306 299 1023.59 408206 300 1064.42 409106 301 1105.33 410006 302 1146.33 410906 303 1187.42 411806 304 1228.60 412706 305 1269.87 -39-
Table V
Calibration Data for the Copper-Constantan Thermocouple from 0°C to 30°C
Deviations* Experimental Data* Mean Values* (v x 10)
t,°C 6 S £ A «= £ A i s £ A
0.0 0.0 0.0 0 0 0 8.323 323.1 302.4 20.7 2 -9 11 8.343 323.9 302.9 21.0 322.9# 303.3 1 9 .6# 10 -4 14 8.289# 321.8# 304.7 17.1# -11 14 -25
12.423 484.6 454.2 30.4 -11 -11 1 12.452 485.7 455.2 30.5 485.7 455.3 30.5 0 -1 0 12.481 486.9 456.4 30.5 12 11 0
17.679 693.8 650.1 43.7 0 -6 6 17.698 694.6 650.7 43.9 693.8 650.7 43.1 8 0 8 17.675 693.1 651.3 41.8 -7 6 -13
23.169 915.0 857.8 57.2 -2 -1 1 23.173 915.2 857.9 57.3 915.2 857.9 57.3 0 0 0 23.178 915.4 858.1 57.3 2 2 0
29.692 1181.3 1107,4 73.9 -4 -7 3 29.645 1179.4 1106.6 72.8 -23 -15 -8 29.651 1179.6 1106.0 73.6 1181.7 1108.1 73.6 -21 •-21 0 29.752 1183.8 1109.7 74.1 21 16 5 29.762 1184.2 1110.6 73.6 25 25 0
i v ^ 26.63 22.09 13.11 m 17 17 17 1.66 1.38 .82 € 2 0.10 0.03 0.05 € 0.3 0.3 0.2
* EMF values in microvolts # Miscalculated value of t. Table VI
Corrections on Absolute Temperatures Above 273.16°K for the Copper-Constantan Thermocouple
Experimental Values Mean Values '
T, T0, Jot A* x 3 T To & h PK °K xlO3 °K K xlO
273.160 273.160 0 0 0 0
8.321 281.481 281.483 -2 281.509 281.478 31 — 28 5 -33 8.341 281.501 281.503 -2 -8 25 -33 8.386 281.546 281.449 97 37 -29 66
12.420 285.580 285.583 -3 285.608 285.612 -4 -28 -29 1 12.447 285.607 285.612 -5 -1 0 -1 12.476 285.636 285.641 “5 28 29 -1
17.678 290.838 290.839 -1 290.841 290.844 -3 -3 -5 2 17*694 290.854 290.858 -4 13 14 «1 17.672 290.832 290.835 -3 -9 -9 0
23.161 296.321 296.329 -8 296.325 296.333 -8 -4 -4 0 23.165 296.325 296.333 -8 0 0 Q 23.170 296.330 296.338 —8 5 5 0
29.682 302.842 302.852 -10 302.850 302.860 -10 -8 -8 0 29.635 302.795 302.805 -10 -55 -55 0 29.641 302.801 302.811 -10 -49 -49 0 29.741 302.901 302.912 -11 51 52 -1 29.752 302.912 302.922 -10 62 62 0
Zv2 0.016 0.016 0.006543 a 0 17 17 17 t»2 0.001 0.001 0.000409 £?xl03 0.059 0.059 0.024 € 0.008 0.008 0.004 All values of T for the 1 mm cell and those for the
5 mm cell above the ice point were calculated in this way. ( oc) Below the iee point, the table of Sanderson
(25) R. T. Sanderson, Vacuum Manipulation of Volatile Comnounds. John Wiley and Sons, Inc., New York (1948) p. 121. was used for the relationship between s the standard
EMF and t (°C) the temperature of the copper-constantan thermocouple•
Two deviation plots of & vs.6 were used in the re duction of 6 to 6s: one for the range from 0°C to
-36.2°C and one from -36.2°C to -63.5°C. They were pre pared from the calibration data of Table VII for which the ■temperature scale differed from the final resistance thermometer scale by ,004°C or less in the range 0°C to
-36.2°C, and was the same as the final scale from -36.2°C to -63.5°C.
Values of t were calculated from 6s by linear inter polation in Sanderson's table. T was then calculated from Equation (7) above.
This procedure was used to obtain T values for all
5 mm cell data below the ice .point and for all 50 mm cell data.
For the chromel-alumel thermocouple, Table VIII was calculated from the EMF—temperature equations Table VII
Calibration Data for the Copper-Constantan Thermocouple Below 0°C
Deviations Mean Values Experimental Data (v x 10)
t, € s, e, £a, e, G muV muV A muV auV L * A
0.0 0.0 0.0 0 0 0 -15.104 570.5 535.1 35.4 -15.100 570.3 534.8 35.5 570.3 534.9 35.4 0 -1 1 -15.094 570.1 534.8 35.3 -2 -1 -1
-22.876 855.6 802,9 52.7 -8 2 -10 -22.874 855.5 802.8 52.7 -9 1 -10 -22.885 855.9 802.6 53.3 856.4 802.7 53.7 — 5 -1 -4 -22.919 857.2 802.7 54.5 8 0 3 -22.920 857.2 802.7 54.5 8 0 8 -22.918 857.1 802.7 54.4 7 0 7
-36.165 1329.4 1245.2 84.2 0 0 0 -35.165' 1329.4 1245.2 84.2 1329.4 1245.2 84.2 0 0 0 —36.166 1329.4 1245.2 84.2 0 0 0
-64.045 2264.8 2119.5 145.3 —1 0 -1 -64.045 2264.9 2119.5 145.4 2264.9 2119.5 145.4 0 0 0 -64.046 2264.9 2119.5 145.4 0 0 0 tv2 3.6 0.12 3.96 15 15 15 € 2 0.2 0.01 0.28 e2 0.02 0.001 0.02 € 0.1 0.02 0.1 -4-3~ Table VIZI
EMF vs. Temperature for the Chromel-Alumel Thermocouple from 273.16 °K to 408 °K
T 0f> °K ^SmuV (dg*/dT«,muV/0K) x 102
273.16 0.00
287 552.74 4008 288 592.82 4010 289 632.92
294 833.68 4021 295 873.89 4023 296 914.12 4025 297 954.37 4027 298 994.64 4029 299 1034.93 4030 300 1075.23 4033 301 1115.56 4034 302 1155.90 4036 303 1196.26 4038 304 1236.64 4040 305 1277.04 4042 306 1317.46 4044 307 1357.90 4046 308 1398.36 4046 309 1438.82 4050 -44~ Table VIII(cout.)
V , °K g«, auV (d6*/dT«,auV/°K) x 102
4050 310 1479.32 4051 311 1519.83 4054 312 1560.37
330 2293.18 4089 331 2334.07 4091 332 2374.98 4093 333 2415.91 4095 334 2456.86 4097 335 2497.83 4098 336 2538.81 4101 337 2579.82 4102 338 2620.84 4105 339 2661.89 4106 340 2702.95 4108 341 2744.03 4109 342 2785.12 4112 343 2826.24 4114 344 2867.38
367 3818.76 4160 368 3860.36 -45-
Table VIII (cont*)
V . °K £*, muV (dg'/dT*,nraV/°K) x 1 0 2
407 5497.18 4235 408 5539.53 (10) g»= -10167.8612 + 34.3694 T» + .00945857 T*2,
T*^ 273.16. o This equation was obtained from least-squares analysis of calibration data for the thermocouple. The calibra tion data were also used to prepare a deviation plot of
£ T l vs. T*jj these data and the mean values used for the plot were tabulated iTable IX). They were based on the same temperature scale as that for absolute manometry.
Experimental values of £ ’, obtained by interpolation with respect to time from the spectrophotometric runs, were reduced to values of T£ by linear interpolation in Table VIII. Final values of T* were obtained from
T£ and the relations
T* - T»0 + AT*, where &T* was read from the deviation plot.
This procedure was employed for all the values of
T* in the spectrophotometric work.
Pressure*
Because the manometrio readings were taken for one downward and one upward traverse of the cathetometer, each reading discussed below was the mean of the two readings obtained during the traverses. The reduction ( 26 ) scheme was based on that of Beattie et al. '
(26) James A. Beattie et al. Proceedings of the American Academy of Arts and Sciences, 7Af.344-370 (1941)* Table IX
Calibration Data for the Ghromel-Aluael Thermocouple ftoa 273»16°£ to 407,26°K
Experimental Data Mean Values Deviations (v x 103) t, Tf, ft, T * AT* T t *p * at * n * o * & i T* °c °K muV og ' ?103 K o| xl03 1 T 0 * AT* 273.16 273.16 0 0 0 0
29.195 302.355 1164.4 302.211 144 -293 -297 6 29.195 302.355 1164.4 302.211 144 302.648 302.508 138 -293 -297 6 29.773 302.933 1188.5 302.808 125 285 300 -13 29.788 302.948 1188.6 302.810 138 300 302 0
57.407 330.567 2319.4 330.641 -74 -670 -667 -3 57.420 330.580 2318.9 330.629 -49 -657 -679 22 57.427 330.587 2318.6 330.622 -35 331.237 331.308 -71 -650 -686 36 59.054 332.214 2387.4 332.303 -89 977 995 -18 59.077 332.237 2389.2 332.347 -110 1000 1039 -39
134.091 407.251 5507.6 407.246 5 -6 0 -6 134.094 407.254 5507.6 407.246 8 407.257 407.246 11 -3 0 -3 134.100 407.260 5507.6 407.246 U 3 0 3 134.101 407.261 5507.6 407.246 15 -4 0 4
2v2 3.601 3.804 0.003945 n 13 13 13 € 2 0.300 0*317 0.000329 €z 0.023 0.024 0.000025 € 0.152 0,156 0.005 -48-
The difference in elevation between the crowns of the mercury menisci in the reference arm (l) and the working arm (2) of the manometer was given by:
(11) H = - (D2+M2-S2 ).
M-^Mg) is the reading on the scale of the cathetometer when the image of the cross hair was set on the crown
of the meniscus in the reference (working) arm.
®1^®2^ reading of the nearest millimeter mark on the standard l/2-m bar when the cross hair was set on the crown of the meniscusj this reading was obtained from the scale numbers engraved on the bar.
Si(S2) is the reading on the scale of the cathetometer when the image of the cross hair was set on the milli meter mark D^(Dg).
NiCNg) is the reading on the cathetometer scale when the image of the cross hair was set on the bottom of the meniscus in the reference (working) arm of the manometer.
(12) h±»Mi-H1 (ini, 2) where hj(h2 ) is the height of the mercury meniscus in the reference (working) arm of the manometer.
The pressure on the reference side of the spoon gauge was the pressure p in the working arm (2) of the manometer.
(13) P-Pj-pJ.
P* is the mean of the zero point readings taken before -49- ancl after a data sequence and therefore averaged over the secular variation of the zero point for the spoon gauge and manometer. (U) pj-BUslalill, it is the mean of the corrected pressures obtained by approaching the spoon gauge halance point from the high pressure (p5(b)) and low pressure (p*(l)) directions.
(15) p l= [(H+Hd1+Hd2+Hd3)+d4 ] d5d6d7 where
Hid]^ is the correction for the ruling error of the scale on the standard 1/2-m bar, assuming the ruling error to be uniformly distributed over the nominal length 1**500 mm.
The true length 1=500.0015 mm was determined by calibra tion to a temperature t s =20.0°C,
(27) Certificate, December 1948, from the Techni cal Laboratory, Gaertner Scientific Corp., for M1012 Stainless Steel Scale, Serial No, 259*
(16) Hd-t - Hi|--£■■■"•),
Hd2 is the correction for thermal expansion of the bar when used at a temperature t£ different than tg the calibration temperature. It was assumed that t'=t_ the s m temperature of the manometer.
(17) Hd2 = Hos (tJ - tg) where is the mean thermal expansion coefficient with the values of 1.03xl0“^/°C*(27) vs^ ^ Shown
(27) Ibid.
in Table X.
Hd^ is the correction for gravitational stretching of
the bar (density p and Young's Modulus E) when suspended
vertically from its upper endj tie) Ha3 = aaiggi J 2E
where (E+2D )=440 mm was very nearly constant for the
U-tube (constant-mass) manometer used in this investiga
tion, but would vary with H in the case of a constant— (26) volume manometer such as used by Beattie et al. The
(2 6 ) op_._cit_.
-•3 3 density and Young's Modulus had the values 7«7SslO g/mm
and l*9305xl0^^dynes/mm^ respectively.
(28) Metals Handbook. 194-8 Edition, The American Society for Metals., Cleveland (194.8), p. 553, Table IV. d^ is the correction for capillary depression of the mercury menisci of heights h^Chg) in the manometer reference (working) arms of inside diameter d=17.25*0.1 mm
(1 9 ) a, - M S t i a l * H 2 7 The numerical value of (k/d2 )=.04-54. was obtained from a *- 51**
Table X
Correction d2 for Thermal Expansion of Gaertner M1012 Scale, Serial Number 259, at Temperature tB°C
tm , °C d2 x 105 tm , °C d2 x 105
26.0 6 30.0 10 .1 6 .1 10 .2 6 .2 11 .3 6 .3 11 .4 7 .4 11 .5 7 .5 11 .6 7 *6 11 .7 7 .7 11 *8 7 .8 11 .9 7 .9 11 27.0 7 31.0 11 .1 7 .1 11 .2 7 .2 12 .3 8 12 • A 8 .4 12 .5 8 .5 12 .6 8 .6 12 .7 8 .7 12 .8 8 .8 12 .9 8 .9 12 28.0 8 32.0 12 .1 8 .1 12 .2 8 .2 13 .3 9 .3 13 •A 9 *4 13 .5 9 .5 13 .6 9 .6 13 .7 9 .7 13 .8 9 .8 13 .9 9 .9 13 29*0 9 33.0 13 .1 9 .1 13 .2 10 .2 14 .3 10 .3 14 10 .5 10 .6 10 .7 10 .8 10 .9 10 -52- graphical plot of k vs. d using the results of Cawood ( 29 ) and Patterson.'
(29) W, Cawood and H, S. Patterson, Transactions of the Faraday Society, 514 (1933).
(2 0 ) d4 = ,0454(h1-h2 )=d4 l-d42
Values of d^j: vs. are given in Table XI, dj is the correction for thermal expansion of mercury from
0°C to the temperature t of the manometer.
(2 1 ) d5 = (l+atj-1
and it is 0 given as a function of t m in Table XII. This table was obtained by linear interpolation in a similar table prepared for integral values of t by Beattie
(30) James A. Beattie et al.f Proceedings of the American Academy of Arts and Sciences, 2k> 371-388 (1941), Table XII.
<36 is the correction for the compressibility of mercury; (22) where {3 the mean cubical compressibility coefficient has the calculated value of 4*0xl0”^/atm or 5.27xl0“9/mm at 29*5°C#^°^ and p* is less than or equal to 30 mm.
(30) Ifeia., p. 380 Table XI
Capillary Depression d/ of the Mercury Meniscus in a Pyrex Tube of Inside diameter 17.25-0.1 mm
BDKSBBSSSS h ^ h±* h±* hi* d4i‘ hi* d4i* d4i* d4i* d4i* *01 .000 .29 .013 .57 .026 .85 .039 1.13 .051 ,02 .000 .30 .014 .58 .026 .86 .039 1.14 .052 .03 *001 .31 .014 .59 .027 .87 .040 1.15 .052 .04 .002 .32 .015 .60 .027 .88 .040 1.16 .053 .05 .002 .33 .015 .61 .028 .89 .040 1.17 .053 .06 .003 .62 .028 .90 .041 1.18 .054 .07 .003 .34 .015 .63 .029 .91 .041 1.19 .054 .08 .004 .35 .016 .64 .029 .92 .042 1.20 .055 .09 .004 .36 .016 .65 .030 .93 .042 1.21 .055 .10 *005 .37 .017 .66 .030 .94 .043 1.22 .056 .11 .005 .38 .017 .67 .031 .95 .043 1.23 .056 .12 .005 .39 .018 • 68 .031 .96 .044 1.24 .056 .13 .006 .40 .018 .69 .031 .97 .044 1.25 .057 .14 .006 .41 .019 .70 .032 .98 .045 1.26 .057 .15 .007 .42 .019 .71 .032 .99 .045 1.27 .058 .16 .007 .43 .020 .72 .033 1.00 .045 1.28 .058 .17 .008 .44 .020 .73 .033 1.01 .046 1.29 .059 .18 .008 .45 .020 .74 .034 1.02 .046 1.30 .059 .19 .009 .46 .021 .75 .034 1.03 .047 1.31 .060 .20 .009 .47 .021 .76 .035 1.04 .047 1.32 .060 • 21 .010 .48 .022 .77 .035 1.05 .048 1.33 .061 .22 .010 .49 .022 .78 .035 1.06 .048 1.34 .061 .23 .010 .50 .023 .79 .036 1.07 .049 1.35 .061 .24 .011 .51 .023 .80 .036 1.08 .049 1.36 .062 .25 .011 .52 • 024 .81 .037 1.09 .050 1.37 .062 .26 .012 .53 .024 .82 .037 1.10 .050 1.38 .063 .27 .012 .54 .025 .83 .038 1.11 .050 1.39 .063 .28 .013 .55 .025 .84 .038 1.12 .051 1.40 .064 .56 .025
* d^£ is the capillary depression in mar“Eg, rounded to the nearest 0*001 mm and h^ is the height of the meniscus in mm* -54'
Table XIX
Correction d<- for the Thermal Expansion of Mercury from 0°C to tm°C
t * °c d * m* V V °C 5
26.0 .99530 29.7 .99463 • .1 28 .8 62 .2 26 .9 60 .3 24 30.0 .99458 .4 23 .1 56 .5 21 .2 54 .6 .99519 .3 53 .7 17 .4 51 .8 16 .5 .99449 .9 14 .6 47 27.0 12 .7 45 .1 10 .8 44 .2 .99508 .9 42 .3 07 31.0 40 •4 04 .1 .99438 .5 03 .2 36 .6 01 .3 34 .7 .99499 .4 33 .8 98 .5 31 .9 96 .6 .99429 2 8 ,0 , 94 .7 27 .1 92 .8 26 .2 9® .9 24 *3 .99489 32.0 22 .4 87 .1 20 .5 87 .2 .99418 .6 83 .3 17 .7 81 .4 14 .8 80 .5 13 .9 .99478 .6 11 29.0 76 .7 .99409 .1 76 .8 08 .2 72 .9 06 .3 71 33.0 04 .4 .99469 .1 02 .5 67 .2 00 • 6 .99465 .3 .99399
*dc ia the ratio of the density of mercury at tm°C and 1 atm to the density of mercury at 0°C and 1 atm* -55— d7 is the correction for the local value of the gravita tional constant g^=980.092 cm/sec^ to the standard value gn=980„665 cm/sec^*^l)
(31) Smithsonian Physical Tablesf 9th rev. ed., Smithsonian Institution, Washington, D. C. (1954), p. 716, Table 805.
(23) d7 = (gi/gj,).
Substituting numerical values for d^_, d^> d^, and d^,
(2 4 ) p* = [h(1 + 3xl0"6 + d2 + 8 *66xl(T8) + d^] d5
x (1 - 2.53x10-9)(0.9994157)*
Neglecting quantities of 10"^ or less compared with unity,
(25) p* s [h(1 + d2 ) + d4] d5 (0 .9994157)*
Equations (13), (14) and (25) were used in order to reduce the manometric readings to experimental values for the vapor pressure. These values are tabulated in
Table XIII. The equations were derived on the basis that effects due to gravitational stretching of the bar, ruling errors of the scale, and compressibility of the mercury in the manometer could be neglected*
Absorbance, Wave Length and XT*
The absorbance of the vapor (A) was calculated from • experimentally measurable variables by the following relations (26) A = A ^ T , T 1, X , s) -A.0 (T»,X, s). Table XIII
The Vapor Pressure of Liquid Titanium Tetrachloride:
Absolute Manometric Data
T, °K p, mm Hg - I obs v ^ l O 4
319.08 31.306 101.4832 181 319.08 31.152 4734 83 319.07 31.266 4802 164 319.07 31.193 4755 118 319.07 31.230 4779 142 319.07 31.388 4879 242 319.06 31.214 4764 131 318.09 29.883 3434 170 318.09 29.845 3409 144 317.10 28.361 1921 53
317.11 28.282 1870 -12 316.03 27.119 0516 166 316.02 27.045 101.0457 121 315.03 25.743 100.8998 77 315.03 25.753 9006 84 315.02 25.698 8959 52 315.01 25.701 8956 63 314.02 24.561 7574 105 314.01 24.536 7549 94 313.52 23.994 6868 120
313.51 24.020 6884 152 313.04 23.403 6138 87 313.02 23.352 6085 63 312.03 22.331 4714 133 33-2.02 22.349 4724 158 311.05 21.218 3218 73 311.03 21.171 3164 48 309.53 19.709 1004 104 309.53 19.691 0986 85 309.04 19.124 0163 -8
309.03 19.128 100.0163 6 308.04 18.240 99.8728 50 308.04 18.232 8719 42 308.03 18.157 8632 -30 308.03 18.192 8671 8 307.03 17.286 7159 0 -57-
Table XIII (cont.)
T, °K p, am Hg ▼ xl()4 ” ^ o b a a
307.02 17.241 7102 -42 306.03 16.433 5654 9 306.03 16.406 99.5622 -24 305.04 15.592 4116 -22 305.04 15.612 4141 4 304.02 14.793 2558 -15 304.02 14.772 2530 -43 303.04 14.024 1003 -57 303.04 14.039 1024 —36 302.56 13.686 0276 -40 302.56 13.689 0280 -35 302.53 13.582 0109 -160
302.52 13.600 99.0131 -123 302.24 13.411 98.9711 -107 302.11 13.318 9507 -109 302.02 13.250 9359 -116 302.03 13.249 9363 -128 301.84 13.125 9080 —114 301.84 13.106 9051 -144 301.53 12.884 8554 -156 301.52 12.870 8528 -167 301.19 12.626 7980 -198
301.18 12.653 8017 -145 301.03 12.556 7788 -139 301.03 12.611 7874 -52 301.01 12.618 7876 -20 301.00 12.646 7914 34 299.03 11.240 4567 -200 299.03 11.248 4581 -186 298.92 11.192 4426 -166 298.86 11.138 4299 -198 298.55 10.951 3804 -199 298.54 10.943 98.3784 -203
I -58-
A i s the measured absorbance of the sample cell con
taining titanium tetrachloride vapor, relative to the
reference cell. A Q is the measured absorbance of the
sample cell, relative to the same reference cell, with
the vapor frozen out in the sidearm of the sample cell
by cooling the sidearm with liquid nitrogen.
X is the wave length in millimicrons (mmu) of the radiant
energy passing through the sample or reference cell from
the monochromator.
A]_ and A 0 were calculated for the same value of T', X ,
and s the slit width reading on the spectrophotometer.
For reduction of the vapor pressure data an opti
cally measurable variable was defined which is proportional
to the pressure of an ideal gas. This variable is
(27) 7t = AT* = (A1-A0)T«
T* , A]:, A 0 and 7T were tabulated as a function of T for
a constant wave length of 279.80 mmu.
Experimental values of A-^ for the 1 mm, 5 mm and
50 mm cells were used directly and the corresponding
values of T and T* obtained by interpolation as indi
cated in the section "Temperature11 above.
Graphical plots of A c vs. T* were made for the 1 mm,
5 mm, and 50 mm cells from direct experimental values of
A.0 and interpolated values of T*. For each value of A^
at T, T', the corresponding value of A 0 at the same value
of T* was read from the plot for the same cell as A^. For the 1 mm cell, experimental and plotted values
of A Q and T* are given in Table XIV. Values of JT , cal
culated by Equation (27) and using A Q values read from
the plot, were tabulated as a function of T (Table XV).
A 0 vs. T1 plots for the 5 mm cell were prepared from the experimental data given in Table XVI. These plots were used with equation (27) to calculate the values shown as a function of T in Table XVII.
The experimental data for the 50 mm cell included those for both vaporization and sublimation equilibria, in Connection with the thermodynamic treatment of these data, a mean value of A Q was calculated which was con
sistent with them and with a calorimetric value for the heat of fusion. The relation used was Equation (80), derived in the section on "Thermodynamic Functions".
The calculation is given in some detail in Table
XVIII. After rejection of 7 of the data on account of a secular trend, the mean value A 0 = 0.0l6l±0.00030 was obtained. It was used to reduce all experimental Aj_ values for the 50 mm cell:
(2 8 ) T«(AX - 0 .0 1 6 1 ) =yr.
The values of jt given in Table XIX as a function of T were calculated from this equation.
Values of A0 determined experimentally as a function of T* are given in Table XX. Sublimation data calculated from these experimental A G values showed curvature on a —60—
Table XIV
A Q vs. T* for the 1 mm Cell at a Slit Width of 0.250 mm
Experimental Data Plotted Values Deviations, v T*,°K A^xlO4 T«,°K A xlO4- A 0xlO* T* o
284.49 150 288.95 145 5 4.46 293.38 140 -5 -4.43
326.67 120 -4 -4.08 326.67 120 -4 —4 *• 08 327.62 125 1 -3.03 328.00 123 330.75 124 -1 -2.75 328.53 120 -4 -2.22 329.31 125 1 -1.44 330.45 125 1 -.30 330.91 120 -4 .16 332.17 125 1 1.42
343.16 138 343.89 134 4 -.73 344.13 130 -4 .24
358.28 120 11 -.24 358.37 110 1 -.13 358.46 110 358.50 109 1 -.04 358.49 100 -9 -.01 358.53 105 -4 .03
371x10“8 99.35
22x10"8 5.84 12x10-9 0.32 11x10“* 0.57
* A 0 is the absorbance of the empty 1 mm sample cell, relative to the 1 mm reference cell. —61—
Table XV
The Vapor Pressure of Liquid Titanium Tetrachloride: Spectrophotometric Data for the 1 mm Cell. =*2.57256'
T, °K T f, °K 7t VXl 0‘ AxlO* ° 2.
302.24 342.62 5295 132 176.89 14 302.21 342.58 5290 132 176.70 18 302.20 342.54 5280 132 176.34 3 301.51 342.15 5090 132 169.64 -20 301.51 342.16 5100 132 169.99 1 301.50 342.16 5075 132 169.13 -45 298.95 338.81 4490 130 147.72 -29 298.95 338.80 4510 130 148.39 17 298.95 338.79 4510 130 148.39 17 296.99 341.40 4020 131 132.77 -22
296.99 341.44 4016 131 132.65 -31 296.99 341.46 4013 131 132.55 -38 296.05 333.29 4160 125 134.48 183* 296.83 333.33 4160 125 « 296.82 333.35 4160 125 * 295.45 338.09 3740 129 122.08 8 295.44 338.11 3750 129 122.43 29 295.44 338.12 3750 129 122.43 29 295.08 337.80 3680 129 119.95 24 295.06 337.76 3682 129 120.01 42
295.05 337.72 3695 129 120.43 82 293.99 338.30 3450 129 112.35 -17 293.97 338.34 3460 129 112.70 26 293.97 338.39 3463 129 112.82 38 292.99 342.45 3205 132 105.23 103* 292.99 342.47 3210 132 105.41 -86 292.98 342.49 3225 132 105.93 -31 292.17 339.04 3120 130 104.37 -8 292.13 339.08 3125 130 101.55 33 292.09 339*13 3116 130 101.26 29
290.77 342.30 2850 132 93.037 -57 290.77 342.30 2850 132 93.034 -45 290.75 342.28 2846 132 92.895 -61 290.05 339.15 2775 130 89.705 -1 Table IV (cont.)
T, °K T», °K Tt rxlO4 & o * 5*0*
290.01 339.16 2760 130 89.199 -36 289.99 339.16 2760 130 89.199 -24 288.70 340.41 2530 131 81.664 146* 288.71 340.45 2565 131 82.866 -10 288.70 340.37 2570 131 83.016 17 287.99 339.00 2470 130 79.326 -17 287.93 339.00 2463 130 79.089 -13 287.90 339.00 2463 130 79.089 6 286.90 340.26 2305 131 73.973 -66 286.87 340.23 2300 131 73.796 -73
286.85 340.18 2300 131 73.785 -59 286.03 337.63 2216 129 70.463 -29 286.02 337.64 2210 129 70.263 -50 286.02 337.64 2224 129 70.736 17 284.87 337.45 2085 128 66.039 29 284.82 337.39 2070 128 65.521 -20 284.02 337.80 1985 129 62.696 29 284.02 337.72 1975 129 62.343 29 284.01 337.76 1985 129 62.688 33 282.90 336.23 1873 127 58.706 63
282.90 336.24 1875 127 58.775 75 282.90 336.27 1873 127 58.713 65 282.10 339.60 1755 130 55.185 -57 282.10 339.55 1760 130 55.347 -29 282.09 339.66 1760 130 55.365 -17 279.94 335.00 1573 127 46.441 3 279.87 335.03 1570 127 46.345 26 279.83 335.06 1566 127 277.90 336.55 1393 128 42.574 19 277.85 336.45 1395 128 42.628 65 277.85 336.49 1400 128 42.802 105*
* Rejected on statistical grounds* -63-
Table XVI A.q v s * T : for the 5 mm Cell at Various Slit Widths
Slit Width Slit Width Slit Width Mean 0 *24-0 mm 0.250 mm 0.260 mm Values A qx104* vx104 A qXIO^ v x 104 A qx 104 vxlO4
70 -7 80 2 75 -3 80 3. 78 0 78 0 80 3 80 2 80 2 75 -2 80 2 78 0 75 -2 75 -3 80 3 A.X10* 77 78 78 T?,°K 284. 9 284.9 285.0
70 -4 78 1 78 1 75 1 80 2 76 -1 74- 0 75 -2 80 3 78 4 75 -2 75 -2 A 0xlo4 74 77 77 T* ,°K 302. 0 301.3 300.7
95 11 80 -1 76 -7 80 -4 80 -1 80 -3 78 -6 82 2 88 5 84 0 74 -6 88 5 77 -7 90 6 L 90 6 A oxl0 84 81 83 T*,OK 311. 3 ' 311.3 311.3
80 -2 70 -9 80 -1 83 1 80 1 80 -1 83 1 80 1 80 -1 83 1 84 5 83 2 80 -1 A 0xlO^ 82 79 81 T« ,°K 333. 1 332.5 332.2 Iv 2 382x10“® 220x10”8 144 n 20 20 20 e*2 20x10”® 12xl0"8 76x10“9 & 1x10“® 58x10"}° 38x10“J° € lxl0”4 76x10“° 62x10"°
* A 0 is the absorbance of the empty 5 mm sample cell, relative to the 5 mm reference cell. -64
Table XVII
The Vapor Pressure of Liquid Titanium Tetrachloride: Spectrophotometric Data for the 5 bus Cell* K2“4.19491
T, °K T», °K Tt ▼xlO '&**
285.17 303.68 11270 76 339.94 8 285.16 303.65 11240 76 339.00 -13 285.15 303.61 11220 76 338.34 -27 285.11 303.43 11240 78 338.69 8 285.10 303.40 11300 78 340.48 67 285.09 303.35 11155 78 336.02 -59 285.05 303.19 11205 78 337.36 5 285.05 303.15 11260 78 338.98 54 285.04 303.07 11145 78 335.41 -48 281.69 305.83 9010 80 273.11 -32
281.68 305.82 9010 80 273.10 -25 281.67 305.79 9010 80 273.07 -20 281.66 305.71 9040 79 273.95 17 281.65 305.67 9000 79 272.69 -22 281.65 305.65 9000 79 272.67 -22 281.64 305.51 9000 78 272.58 -21 281.64 305.48 9020 78 273.16 1 281.64 305.45 9000 78 272.52 -22 278.45 306.92 7350 80 223.13 -2 278.43 307.05 7310 81 221.97 -32
278.42 307.07 7310 81 221.98 -25 278.41 306.95 7590 81 230.49 * 278.40 307.08 7310 81 221.99 -13 278.37 306.98 7250 81 220.07 -80 278.35 307.01 7250 81 220.10 -66 278.33 307.04 7310 81 221.96 31 278.33 307.14 7280 79 221.17 -4 278.32 307.15 7280 79 221.18 3 278.30 307.16 7260 79 220.57 -11 278.26 307.21 7210 79 219.07 -55
278.25 307.25 6900 79 209.58 * 278.24 307.29 7220 79 219.44 -25 278.24 307.55 7210 80 219.28 -29 278.23 307.53 7230 80 219.88 3 278.22 307.34 7240 79 220.09 19 278.22 307.50 7200 80 218.94 40 278.22 307.48 7260 80 220.77 49 Table XVIl(eont.)
T, »K T», °K vxlO' llo* xfo* Jt
278s21 305.90 7310 79 221.20 74 278.19 307.17 7190 81 218.37 -41 278.17 307.16 7180 81 218.05 -43 278.16 307.15 7190 81 218.35 -22 273.97 304.71 5540 77 166.46 21 273.96 304.72 5540 77 166.47 28 273.95 304.73 5540 77 166.47 35 273.93 304.76 5525 78 166.00 21 273.93 304.76 5525 78 166.00 21 273.93 304.78 5525 78 166.01 21
273.90 304.81 5520 79 165.85 31 273.90 304.82 5520 79 165.85 31 273.90 304.82 5510 79 165.55 15 270.64 308.46 4340 82 131.34 -84 270.59 308.47 4390 82 132.89 67 270.57 308.77 4370 81 132.43 47 270.56 308.75 4360 81 132.11 31 270.56 308.75 4360 81 132.11 31 270.55 308.73 4360 81 132.11 35 270.55 308.48 4340 81 131.38 -20
270.54 308.71 43 40 81 131.48 -4 270.53 308.49 4360 81 132.00 42 270.51 308.63 4460 80 135.18 * 270.50 308.60 4280 80 129.61 * 270.50 308.58 4320 80 130.84 -27 270.49 308.56 4360 80 132.06 74 270.10 309.65 4220 82 127.82 17 270.10 309.65 4210 82 127.82 17 270.09 309.65 4210 82 127.82 24 270.08 309.64 4190 82 127.20 -18
270.06 309.59 4210 80 127.86 49 270.06 309.59 4210 80 127.86 49 270.05 309.58 4190 80 127.24 8 270.04 309.56 4175 80 126.77 -22 270.03 309.55 4180 80 126.92 —4 269.94 309.49 4100 82 124.35 « 269.91 309.48 4120 82 124.97 -75 269.87 309.46 4120 82 124.96 * 266.59 309.96 3300 82 99.745 10 266.58 309.96 3290 82 99.435 -15 -6 6 - Tabla X7Il(cont.)
T, °K T», °K 7T vxlO4 & 0 * t*0*
266.5^ 309.96 3285 82 99.280 -32 266.57 309.95 3285 82 99.277 -25 266.52 309.91 3270 80 98.861 -29 266.51 309.91 3270 80 98.861 -22 266.51 309.93 3270 80 98.868 -22 266.47 309.92 3270 80 98.865 5 266.45 309.91 3290 82 98.489 -18 266.45 309.88 3265 82 98.635 -4 266.45 309.87 3260 82 98.477 -21 266.44 309.86 3250 82 98.164 -43 263.23 310.10 2590 83 77.742 -43 263.21 310.10 2585 83 77.587 -50 263.1S 310.10 2585 83 77.587 -27 263.16 310.10 2580 83 77.432 -32 263.08 310.08 2560 80 76.900 -43 263.06 310.08 2550 80 76.590 -68 263.04 310.07 2550 80 76.587 -55 263.03 310.07 2546 80 76.463 -61 262.99 310.10 2546 83 76.378 -43 262.98 310.12 2546 83 76.383 -36 262.97 310.14 2546 83 76.388 -29 262.97 310.16 2540 83 76.206 -52 261.80 309.91 2350 82 70.288 10 261.80 309.91 2340 82 69.978 -36 261.77 309.92 2340 82 69.980 -13 261.75 309.92 2338 82 69.918 -6 261.73 309.93 2330 80 69.734 -18 261.72 309.93 2330 80 69.734 -11 261.69 309.91 2330 80 69.730 12 261.69 309.91 2330 80 69.730 12
261.65 309.96 2320 82 69.369 -11 261.65 309.98 2310 82 69.064 -55 261.63 310.00 2312 82 69.130 -32 261.62 310.02 2310 82 69.073 -32 258.43 303.73 1880 79 54.702 56 258.41 303.73 1880 79 54.702 72 258.39 303.73 1875 79 54.550 60 258.36 303.73 1875 78 54.760 * 258.35 303.74 1875 78 54.762 « 258.34 303.74 1875 78 54.762 « 258.31 303.74 1870 76 54.670 * -67-
Table 2VII (cont • )
T, °K T*!, °K 7t vxlO* tloA Axl©4 ° L 258.31 303.74 1870 76 54.670 « 258.31 303.74 1850 76 54.061 31 252.54 305.30 1200 77 34.285 44 252.53 305.28 1200 77 34.283 51 252.51 305.25 1190 77 33.974 -22 252.45 305.16 1195 78 34.086 58 252.44 305.14 1195 78 34.084 65 252.41 305.10 1192 78 33.988 63 252.37 305.03 1190 79 33.889 65 252.35 305.00 1185 79 33.733 35 252.33 304.96 1188 79 33.820 79
* Rejected on statistical grounds. -6 8 - Table XVIII
Calculated Values of A for the 50 mm Cell at a Slit Width of 0.250 mm
Sublimation Data Vaporization Data rx vx AjxlO^. T«,°K T,°K A-jOclO^- T*,°K T,°K 103 & 104
6270 295.01 245.46 23800 301.51 261.95 3952 333 « 6270 295.13 245.46 18940 301.72 258.90 3138 343 * 4880 299.42 243.19 18550 301.72 258.79 4027 365 « 4840 299.49 243.06 18660 301.72 258.74 4070 338 * 3450 296.59 240.06 16670 301.74 257.25 4997 142 -19 3455 297.48 239.96 16670 301.74 257.23 5060 200 « 3485 297.49 239.95 14620 301.68 255.71 4498 301 * 3445 297.48 239.90 14500 301.69 255.60 4483 271 * 3350 296.69 239.69 13640 301.62 254.74 4277 210 49 2723 300.91 237.94 13030 301.57 254.16 5046 176 16 2738 300.92 237.94 13030 301.56 254.12 5031 184 23 2730 300.91 237.93 12910 301.53 254.01 4992 180 19 2305 300.47 236.43 12760 301.50 253.94 5887 166 5 2310 300.47 236.41 12280 301.18 253.36 5638 160 -1 1938 302.33 234.97 11160 301.33 252.19 6095 128 -33 1934 302.32 234.85 11100 301.35 252.14 6156 156 -6 1930 302.30 234.84 10450 301.40 251.41 5804 156 -6 1940 298.69 234.81 10000 300.93 250.81 5486 143 -18 1905 298.71 234.59 9995 300.95 250.75 5601 147 -14 1550 302.90 232.74 9200 299.93 249.74 6523 I64 3 1540 302.90 232.72 9160 299.70 249.70 6522 160 -1 1530 302.89 232.71 9120 299.85 249.66 6504 151 -10 1524 302.89 232.69 8330 300.84 248.60 5946 148 -13 1150 303.61 229.85 8270 300.84 248.50 8334 179 18 1130 303.61 229.84 8210 300.84 248.38 8261 154 -7 1136 303.61 229.80 8170 300.84 248.33 8266 167 6 823 303.41 226.76 8040 300.84 248.16 11890 160 -1 800 303.39 226.67 7070 298.90 246.53 10530 127 -34 820 303.41 226.67 6925 298.91 246.28 10310 164 3 655 302.17 224.17 6720 298.67 245.99 13800 181 20 645 302.16 224.13 5895 299.57 244.43 12070 171 10 633 302.14 224.08 4445 300.20 241.18 9075 161 0 628 302.13 224.06 4359 300.38 240.98 8930 158 -3 543 301.22 222.56 3485 296.63 238.25 8534 153 -8 530 301.23 222.26 3342 300.40 238.02 8581 159 -2 520 301.2$ 221.95 3330 300.41 237.96 8890 164 3 515 301.25 221.84 3330 300.41 237.92 8987 163 2 * Rejected because of secular trend. -69-
Table XIX
The Vapor Pressure of Liquid and Solid Titanium Tetra chloride: Spectrophotometric Data for the 50 mm Cell. A 0 - 0.0161 (Calculated). K3 = 6.49576.
T,°K T*,°K AjxlO^ 7T vxlO5
Normal Liquid
262.21 301.45 24800 742.75 27744* 262.02 301.47 23050 690.04 -5507* 261.95 301.51 23800 712.74 556 261.93 301.52 23770 711.86 582 261.90 301.58 22880 685.16 -3018* 261.89 301.55 23160 693.53 -1729* 261.89 301.56 22650 678.18 -3967* 259.11 301.65 18660 558.03 -2466* 258.95 301.72 18940 566.59 281 258.90 301.72 18940 566.59 664
258.87 301.68 18480 552.65 -1597* 258.84 301.72 18910 565.69 966* 258.80 301.70 18800 562.34 678 258.79 301.72 18550 554.83 -590 258.77 301.71 18580 555.72 -276 258.76 301.72 18730 560.26 614 258.74 301.72 18810 562.67 1198* 258.74 301.72 18660 558.15 391 258.74 301.72 18600 556.34 66 257.28 301.74 16600 496.03 -126
257.25 301.74 16670 498.14 531 257.23 301.74 16670 498.14 687 255.82 301.67 14770 440.71 -516 255.79 301.72 14680 438.06 -884 255.75 301.67 14820 442.22 377 255.71 301.68 14620 436.20 -678 255.66 301.72 14560 434* 44 -687 255.66 301.68 14580 435.00 -559 255.62 301.71 14520 433.23 -651 255.60 301.69 14500 432.60 -638
255.60 301.72 14520 433.23 -493 254.78 301.61 13700 408.35 96 254.75 301.64 13650 406.88 -26 -70-
Table XIX(cont.)
T,°K T*,°K AjXlO* 7r vxlO^
254.74 301.62 13640 406.56 -25 254.72 301.63 13550 403.86 -532 254.26 301.58 13170 392.33 243 254.16 301.57 13030 388.09 -43 254.12 301.56 13030 388.08 274 254.10 301.55 12950 385.66 -191 254.06 301.55 12970 386.26 285 254.02 301.54 12880 383.53 -103 254.01 301.53 12910 384.42 209 253.98 301,52 12910 384.41 447
253.98 301.52 12880 383.51 373 253.94 301.51 12770 380.18 -339 253.94 301.50 12760 379.86 -423 253.92 301.48 12980 386.47 1462* 253.92 301.47 12780 380.44 -110 253.91 301.47 12830 381.94 363 253.36 301.18 12280 365.00 252 253.27 301.19 12180 362.00 153 253.19 301.22 12080 359.03 -25 252.30 301.35 11220 333.27 -251
252.19 301.33 11160 331.44 95 252.14 301.35 11100 329.65 -38 251*45 301.37 10465 310.54 -363 251.42 301.39 10465 310.56 -110 251.41 301.40 10450 310.11 -173 251.40 301.42 10360 307.42 -962* 250.91 300.91 10055 297.92 -133 250.84 300.92 10045 297.43 347 250.81 400.93 10000 296.09 143 250.77 300.96 9995 295.97 433
250.77 300.94 9995 295.95 433 250.76 300.97 9995 295.98 519 250.75 300.95 9995 295.96 594 249.83 299.73 9240 272.12 -167 249.76 299.79 9220 271.58 219 249.75 299.96 9160 269.93 -308 249.74 299.93 9200 271.11 212 -71- Table Z1X (cont.)
T,°K t *,°k A-jxlO* 7T ▼xlO^
2*9.71 299.89 9110 268.37 -554 249.70 299.70 9160 269.70 24 249.68 299.81 9125 268.75 -161 249.66 299.85 9120 268.64 -36 249.39 298.36 9330 274.10 4234* 249.36 298.43 9020 264.91 1074* Metastable Liquid
24S.93 300.88 8600 253.92 444 246.84 300.88 8520 251.51 249 246.64 300.89 8360 246.70 2 246.60 300.84 8330 245.76 -42 246.56 300.84 8280 244.25 -489 246.58 300.84 8350 246.36 371 246.55 300.84 8280 244.25 -237 246.53 300.84 8330 245.76 548
246.52 300.84 8280 244.25 17 246.51 300.84 8330 245.76 717 246.50 300.84 8270 243.95 63 246.50 300.84 8280 244.25 186 246.47 300.90 8250 243.40 90 246.43 300.84 8210 242.15 -87 246.36 300.84 8210 242.15 335 246.33 300.84 8170 240.95 262 246.33 300.91 8160 240.70 158 246.25 300.84 8080 238.24 -193
246.22 300.84 8080 238.24 61 248.16 300.84 8040 237.03 59 243.16 300.84 8010 236.13 -321 248.15 300.91 8005 236.04 -274 248.02 300.92 7925 233.64 -194 246.53 298.90 7070 206.51 187 246.48 299.00 7040 205.68 214 246.46 299.07 7025 205.28 -211 246.41 299.03 6950 203.01 -490 246.28 298.81 6925 202.11 186 -72-
Table H I (cont.)
T,°K T*,°K AjxlO^ TC vxlO5
246.18 298.77 6860 200.14 69 246.15 298.75 6830 199.23 -128 246.12 298.72 6840 199.51 272 245.99 298.67 6720 195.89 -436 244.43 299.57 5895 171.77 11 244.31 299.53 5825 169.65 -178 244.23 299.50 5740 167.09 -995* 241.18 300.20 4445 128.61 41 241.14 300.18 4420 127.85 -189 241.09 300.17 4395 127.09 -333
241.06 300.23 4380 127.75 457 240.98 300.38 4359 126.10 -118 240.97 300.40 4355 125.99 -114 240.95 300.39 4345 125.68 -114 238.36 296*63 3480 98.451 -799 238.25 296.63 3485 98.599 376 238.21 296.63 3485 98.599 749 238.06 300.41 3360 96.101 -419 238.03 300.41 3410 97.603 1412* 238.02 300.40 3342 95.557 -613
237.97 300.41 3335 95.350 —364 237.96 300.41 3330 95.200 -427 237.93 300.41 3330 95.200 -147 237.92 300.41 3330 95.200 -54 Solid
245.46 295.01 6270 180.22 2674* 245.46 295.13 6270 180.30 2719* 243.19 299.42 4880 141.30 2706* 243.06 299.49 4840 140.13 3284* 240.06 296.59 3450 97.548 73 239.96 297.48 3455 97.989 1640* 239.95 297.49 3485 98.826 2603* 239.90 297.48 3445 97.692 2007* 239.69 296.69 3350 94.614 1154* 237.94 300.91 2723 77.093 419 -73- Table XIX(cont.)
T,°K t *,°k AjxlO* 7T vxlO5
237.94 300.92 2738 77.547 1007* 237.93 300.91 2730 77.304 807 236.43 300.47 2305 64.421 -242 236.41 300*47 2310 64.571 221 234.97 302.33 1938 53.724 -1447* 234.85 302.32 1934 53.601 -272 234.84 302.30 1930 53.476 -388 234.81 298.69 1940 53.137 -673 234.59 298.71 1905 52.095 -74 232.74 302.90 1550 42.072 452
232.72 302.90 1540 41.769 -33 232.71 302.89 1530 41.465 -643 232.69 302.89 1524 41.283 -843 229.85 303.61 1150 30.026 1696* 229.84 303.61 1130 29*419 -223 229.80 303.61 1136 29.601 884 226.76 303.41 823 20.085 -37 226.67 303.39 800 19.386 -2479* 226.67 303.41 820 19.994 647 244.17 302.17 655 14.927 3425*
224.13 302.16 645 14.624 1893* 224.08 302.14 633 14.261 28 224.06 302.13 628 14.109 -784 222.56 301.22 543 11.506 -1579* 222.26 301.23 530 11.115 -1081* 221.95 301.24 520 10.814 272 221.84 301.25 515 10.664 332
* Rejected on statistical grounds* -74-
Table XX
A 0 v s . T* for the 50 mm Cell at a Slit Width of 0.240 mm
Experimental Values Plotted Values Deviations, v T»,°K A xlO*# T*,°K A qx 10^ T»xl02 Aoxl05 o
288.28 138 288.33 134.5 -5 35 288.33 128 0 -65 288.38 132 5 -25 288.40 140 7 55
366.40 126 -95 5 367.27 117 367.35 121 8 -4 368.13 120 78
Iv2 1.527 133x1(3® n 7 7
€»2 0.2545 22.0x10** to -t € 0.0364 3.14x10' € 0.191 1.77x10'
# A is the absorbance of the empty 50 mm sample cell, relative to the 50 mm reference cell* - 7 5 - plot of log Tf vs. l/T as well as a temperature trend which was not consistent with the vaporization data and an in dependent calorimetric value for the heat of fusion*
The calculated value of A Q = 0.0161 was finally
used since in addition to being consistent with the ealori-
metric heat of fusion, it removed the low-temperature
curvature from the log 7T vs, l/T plot for the sublima
tion data without appreciably changing the temperature
trend previously established for the vaporization data.
During the runs at variable wave length and slit
width for the absorption spectrum of the vapor in the
1 mm cell, both T* and T were held approximately con
stant. For this reason, the values of T* and T corres
ponding to direct experimental values of A-j_ and A 0
were obtained by linear interpolation of the temperature
(not the thermocouple EMF) with respect to time.
Observed wave length readings X. from the spectro-
photometer were corrected to the true wave lengths X by
the relation
(29) X= X e + ax.
A X was read from a deviation plot of A X VS. X £• The
calibration data of Table XXI were used for this plot.
Wave length values for the Hg lamp used in the calibration
were taken from Brode,^^
(32) Wallace R. Brode, Chemical Spectroscopy. 2d ed., John Wiley and Sons, Inc., New York (1943), p. 520. - 7 6 -
Table XII
Wave Length Calibration of Beckman DU Spectrophotometer
s,# AX» mmu mmu mm mmu
1128.7 1034 1014.0 .32* -20.0 - 772.92 - - - 690.75 - w e - 623.44 - mm 584.2 579.07 .22 -5.13 - 576.96 -- 551*5 546.07 .0575 -5.43 438.4 435.83 .035 -2.57 406.7 404.66 .047 -2.04 366.6 365.01** .094 -1.59 335.25 334.15** .784 -1.10 314.1 313.15** .132 -.95 302.9 - 1.0 - 297.4 296.76** .435 — •64 265.7 265.2 1.65 — .5 254.1 253.6 .057 -.5
* Instrument balanced using the 0.1 position of the selector switch.
*• Taken from Brode, Chemicals SnectroscoDV.
# s is the slit width reading from the spectro photometer.
Light source: mercury vapor lamp (Beckman M-1341). -77«*
Spectral band width values were calculated from true wave length values and slit width readings by means of a nomograph.'(33) '
(33) H. M. Haendler, Journal of the Optical Society of America, 4.17-4-19 (1948).
Values of A 0 (T’) were calculated from the relation
(30) A 0 (T«) = A 0 (T") + (dAo/dT,)(T' - T")
= A 0 (T") - 3.97x 10“5(t « - Tw).
TH was the cell temperature at which A Q was measured and T* the temperature at which the corresponding value of A^ was measured. The value of the derivative was obtained from the A Q vs. T* plot for the 1 mm cell at a wave length of 279.80 mmu and a slit width of 0.250 mm.
It was assumed to be independent of wave length and slit width, a reasonable approximation since (T* - Tn) was always less than 10°K and the correction on A Q therefore correspondingly small.
Values of A^ and k 0 and of the slit width and spectral bandwidth were tabulated as functions of wave length
(Table XXII), Table XXII
The Molar Absorbancy Index for Titanium Tetrachloride Vapor from 980 to 200 mmu
X>a * mmu ■A1 •Ao T,°K . T«, °K . s,*mm . X, mmu a2/mol. B*
1000 to 981.2 to 330 328.9 0 329 .0145 .0138 302.57 312.86 .260 327.9 .9703 15.3 328 .0150 .0138 302.57 312.86 .260 326.9 1.663 15.1 327 .0180 .0138 302.57 312.86 .280 325.9 5.822 16.0 326 .0190 .0138 302.57 312.86 .280 324.9 7.208 15.8 325 .0195 .0138 302.57 312.86 .280 323.9 7.901 15.7 325 .0215 .0115 302.60 317.38 .250 323.9 13.99 14.3 324- .0200 .0148 302.57 312.86 .300 322.9 7.208 16.6 324 .0215 .0115 302.60 317.41 .250 322.9 14.00 14.0
323 .0210 .0133 302.57 312.86 .310 322.0 9.980 17.0 323 .0235 .0110 302.60 317.42 .250 322.0 17.50 13.8 322 .0230 .0138 302.57 312.87 .320 321.0 12.75 17.3 322 .0240 .0105 302.60 317.44 .250 321.0 18.90 13.7 321 .0260 .0138 302.57 312.87 .330 320.0 16.86 17.5 321 .0260 .0115 302.60 317.47 .250 320.0 20.30 13.6 320 .0285 .0128 302.57 312.87 .342 319.0 21.69 18.0 320 .0295 .0110 302.60 317.48 .250 319.0 25.90 13.4 319 .0305 ► 0115 302.60 317.58 .250 318.0 26.61 13.4
318 .0340 .0105 302.60 317.61 .250 317.0 32.91 317 .0380 .0115 302.60 317.63 .250 316.0 37.12 316 .0420 .0115 302.59 317,66 .250 315.0 42.74 315 .0470 .0115 302.59 317.68 .250 314.0 49.76 314 .0501 .0105 302.59 317.80 .250 313.0 55.52 Table XXIl(cont.)
Xe,aau Al *0 T,°K T*, °K s,*nua X^suau ajj, m2/aol B*
313 .0560 .0107 302.59 317.85 .250 312.0 63.52 312 .0600 .0107 302.60 317.88 .250 311.0 69.10 311 .0660 .0107 302.60 317.91 .250 310.1 77.52 310 .0710 .0113 302.60 317.93 .250 309.1 83.69 12.1 309 .0793 .0113 302.61 318.06 .250 308.1 95.32 308 .0870 .0115 302.60 318.10 .250 307.1 105.9 307 .0950 .0110 302.60 318.12 .250 306.1 117.8 306 .1050 .0113 302.60 318.15 .250 305.1 131.4 305 .1130 .0115 302.59 318.18 .250 304.1 142.5 11.6 304 .1265 .0115 302.59 318.26 .250 303.1 161.5
303 .1400 .0115 302.59 318.28 .250 302.1 180.4 302 .1525 .0113 302.60 318.29 .250 301.1 198.2 301 .1685 .0115 302.60 318.32 .250 300.2 220.4 300 .1870 .0105 302.60 318.35 .250 299.2 247.8 11.0 299 .2045 .0116 302.60 318.34 .250 298.2 270.8 298 .2260 .0116 302.60 318.33 ♦250 297.2 300.9 297 .2485 .0116 302,60 318.31 .250 296.2 332.5 296 .2715 .0116 302.59 318.30 .250 295.2 365.0 295 .2980 .0116 302.59 318.29 .250 294.2 402.2 10.4
294 .3260 .0116 302.59 318.19 .250 293.2 441.4 293 .3570 .0116 302.59 318.16 .250 292.2 484.8 292 .3842 .0116 302.59 318.13 .250 291.2 523.0 291 .4140 .0114 302.59 318.11 .250 290.2 565.0 290 .4430 .0116 302.60 318.08 .250 289.3 605.1 9.9 289 .4740 .0116 302.60 318.00 .250 288.3 648.4 288 .4980 .0116 302.59 317.97 .250 287.3 682.3 Table XXII(cont.)
X^,amU A 1 A q T, °K T*, °K s,*iaia X, nuau aM» a^/mol B* 287 .5280 .0116 302.59 317.95 .250 286.3 724.4 286 .5510 .0114 302.59 317.92 .250 285.3 756.8 285 .5700 .0116 302.90 317.90 .250 284.3 783.6 9.3 234 .5950 .0117 302.60 316.35 .250 283.3 813.7 283 .6010 .0100 302.60 316.35 .250 282.3 823.4 282 .6070 .0117 302.60 316.35 .250 281.3 830.4 281 .6070 .0120 302.60 316.35 .250 280.3 829.0 8.9 281 .6070 .0127 302.59 316.32 .250 280.3 829.4 8.9 280.75 .6070 .0120 302.59 316.34 .250 280.05 829.4 8.8 280.75 .6070 .0127 302.59 316.30 .250 280.05 829.3 8.8
280.50 .6060 .0120 302.59 316.34 .250 279.80 828.0 8.8 280.50 .6040 .0127 302.59 316.29 .250 279.80 825.1 8.8 280.25 .6020 .0117 302.59 316.34 .250 279.55 823.8 8.8 280.25 .6025 .0117 302.59 316.28 .250 279.55 824.4 8.8 280 .6000 .0117 302.59 316.34 .250 279.3 821.0 8.7 280 .6000 .0117 302459 316.27 .250 279.3 820.8 8.7 279 .5930 .0113 302.59 316.23 .250 278.3 811.5 278 .5740 .0128 302.59 316.23 .250 277.4 783.0 277 .5540 .0131 302.59 316.22 .250 276.4 754.6
276 .5280 .0137 302.59 316.21 .260 275.4 717.5 8.6 275 .4980 .0137 302.59 316.21 .260 274.4 675.6 274 .4680 .0137 302.59 316.20 .260 273.4 633.7 273 .4350 .0137 302.60 316.21 .300 272.4 587.4 8.3 273 .4360 .0137 302.60 316.22 .300 272.4 588.8 9.5 272 .4020 .0133 302.60 316.23 .300 271.4 542.0 271 .3665 .0130 302.60 316.24 .300 270.4 491.7 Table XXIl(cont,)
A 1 T, °K T», o r s,*mm X, mmu aft, m^/mol B '
270 .3330 .0138 302.61 316.25 .300 269.4 444.9 9.2 269 .3010 .0128 302.61 316.29 .300 268.4 401.7 268 .2710 .0133 302.60 316.30 .300 267.4 359.4 267 .2435 .0133 302.60 316.31 .300 266.4 321.1 266 .2170 .0138 302.60 316.33 .300 265.4 283.4 265 .1965 .0133 302.59 316.35 .300 264.5 255.7 8.6 264 .1795 .0138 302.60 316.27 .300 263.5 231.1 263 .1640 .0133 302.60 316.27 .300 262.5 210.2 262 .1520 .0133 302.60 316.28 .300 261.5 193.4 261 .1460 .0138 302.59 316.29 .300 260.5 184.5
260 .1420 .0128 302.59 316.29 ,300 259.5 180.3 8.1 259 .1410 .0138 302.59 316.30 .300 258.5 177.5 258 .1425 .0138 302.59 316.30 .300 257.5 179.6 257 .1480 .0133 302.60 316.30 .300 256.5 187.9 256 .1570 .0128 302.60 316.30 .300 255.5 201.1 255 .1680 .0125 302.60 316.30 .300 254.5 216.7 7.6 254 .1835 .0118 302.60 316.30 .300 253.5 239.5 253 .2000 .0118 302.59 316.31 .350 252.5 262.6 8.5 252 .2200 .0088 302.59 316.31 .350 251.6 294.7 251 .2430 .0118 302.59 316.32 .350 250.6 322.6
250 .2690 .0113 302.58 316.32 .350 249.6 359.8 8.2 249 .2980 .0117 302.59 316.32 .350 248.6 399.5 248 .3280 .0107 302.59 316.32 .350 247.6 442 • 8 247 .3700 .0113 302.59 316.32 .350 246.6 500.6 246 .3960 .0107 302.60 316.32 .350 245.6 537.4 245 .4320 .0107 302.60 316.32 .350 244.6 587.6 7.9 244 .4660 .0102 302.60 316.32 .350 243.6 635.7 Table XXIl(cont.)
^ e i 1 A, T, °K T«, °K s,*mm A, mmu »M>
243 5050 .0107 302.61 316.32 .400 242.6 689.1 242 5433 .0117 302.61 316.32 .400 241.6 741.1 241 5820 .0117 302.60 316.32 .400 240.6 795.5 24' 6160 .0122 302.60 316.32 .400 239.7 842.2 239 6470 .0113 302.61 316.32 .400 238.7 886.2 238 6800 .0118 302.61 316.32 .400 237.7 931.5 237 7020 .0128 302.61 316.32 .400 236.7 960.8 236 7230 .0128 302.61 316.32 .400 235.7 990.0 235 7420 .0128 302.62 316.32 .400 234.7 1016. 234 7520 .0128 302.62 316.32 .400 233.7 1030
233 7570 .0128 302.61 316.32 .450 232.7 1037 232 7570 .0138 302.60 316.32 .450 231.7 1037 231 7500 .0128 302.60 316.32 .450 230.7 1028 230 7370 .0133 302.60 316.32 .450 229.8 1009 229 7180 .0128 302.59 316.32 •450 228.8 984.1 228 6930 .0133 302.60 316.32 .500 227.8 948.0 227 6660 .0138 302.61 316.32 .500 226.8 909.2 226 6330 .0138 302.61 316.32 .500 225.8 863.2 225 6000 .0133 302,61 316.32 .500 224.8 817.9 224 5640 .0138 302.62 316.33 .550 223.8 766.6
223 5290 .0139 302.61 316.33 .550 222.8 718.1 222 4920 .0133 302.61 316.33 .600 221.8 667.4 221 4590 .0148 302.60 316.34 .600 220.8 619.6 220 4260 .0148 302.60 316.34 .650 219.8 573.6 219 3950 .0143 302.59 316.35 .700 218.8 531.3 218 3660 .0143 302.60 316.35 .750 217.8 490.6 217 3420 .0148 302.60 316.35 .760 216.8 456.4 TableXXIl(cont.)
3 ^ , mmu T , °K T«, °K s,#mm SM , m 2/mol B* H A o ^ m m u
216 • 3210 .0148 302.60 316.35 .820 215.9 427.1 11.8 215 .3080 .0148 302.61 316.35 .880 214.9 408.8 12.3 214 .2890 .0158 302.61 316.35 .950 213.9 380.9 13 . a 213 .2770 .0168 302.60 316.36 1.050 212.9 363.0 14.0 212 .2700 .0158 302.60 316.36 1.150 211.9 354.6 15.0 211 .2640 .0183 302.59 316.37 1.275 210.9 342.9 .16.6 210 .2600 .0193 302.59 316.37 1.400 209.9 336.0 17.7 209 .2585 .0198 302.60 316.37 1.600 208.9 332.2 208 .2585 .0208 302.60 316.38 1.800 207.9 331.6 16.4 207 .2629 .0218 302.60 316.38 1.450 206.9 336.3 16.9
206 .2674 .0243 302.61 316.39 1.700 205.9 339.0 15.0 206 .2674 .0257 302.61 316.39 1.700 205.9 337.0 15.0 205 .2758 .0257 302.61 316.39 2.00 205.0 348.7 17.4 205 .2716 .0257 302.62 316.40 1.250 205.0 342.7 14.5 204 .2799 .0274 302.61 316.40 1.500 204.0 352.1 17.0 203 .2967 .0294 302.61 316.41 1.850 203.0 372.7 15.5 202 .2967 .0330 302.60 316.41 1.850 202.0 367.9 15.5 201 .3373 .0330 302.60 316.42 1.500 201.0 424.6 16.0 200 .3646 .0330 302.59 316.42 2.000 200.0 462.9 16.1
* B is the spectral band width in A and s is the slit width reading in mm* -84-
B. Thermodynamic Functions.
Theory.
The relevant equilibria are:
(31) TiGl^(l) - TiCl^g);
(32) TiCl4 (s) = TiCl4 (l)j
(33) TiCl4 (s) = TiCl^g).
The vaporization process was investigated by absolute
and by spectrophotometric methods, and the sublimation
process by the spectrophotometric method. Ho experi
mental investigation was made of the fusion equilibrium.
The molal Gibbs free energy F is the same for all
phases at equilibrium; for each phase
(34) » Vdp - SdT
where V and S are the molal volume and molal entropy,
respectively. For the liquid and vapor phase,
(35) do .S* - S1 dT " VS - Vi
Two approximations are now made: is neglected relative to VS; and the vapor is considered ideal so
that (36) VS = RT/p.
The first approximation makes the denominator in (35) too large by about 112 cm^/22400 crn-^ or 5/1000. The second approximation can be estimated to make the de- nominator too large by at most 4/10 in the pressure and temperature range of this investigation, with its effect decreasing rapidly as the temperature is lowered. Since the vaporization process is reversible and isobaric,
<37> M = AS; using this and the two approximations above in Equa tion (35),
(33) a In u = AH = Hg - a 1 dT r t 2 g p Since the vapor is assumed to behave ideally, and since
Hr^ changes with pressure by less than 4 eal/mol in the range from p up to 1 atm at constant temperature,
(39) Hg - a1 ■ E0g - Ho1 = A K ° .
Here, AH° is the heat of vaporization when the vapor and the liquid are in .their respective standard states:; ideal gas at a pressure of 1 atm and theequilibrium temperature Tj and liquid at a pressure of 1 atm and the equilibrium temperature T. Then for the vapor pressure of the liquid:
(4d The corresponding vapor pressure equation for the solid is (41) fl .Ifl-.p = Ag°s dT kT2 in which the effect of pressure up to 1 atm on &s at constant temperature is neglected. The standard state for the solid is the solid at the equilibrium tempera ture T and a pressure of 1 atm. -36- The molal heat capacities at a constant pressure of 1 atm were assumed to have the form (4.2) C° = a + bT - P = 17.950 + 0.01615 T (gas, T « 24-9.045-350) = 14.938 + 0.0278 T (gas, T = 200-249.045) = 25.55 + 0.026875 T (solid, T = 200-249.045) = 34.515 + 0.007115 T (liquid, T = 249.045 - 350). The values of a and b for the liquid and solid were (6) calculated from Skinner's tabulated heat capacities. (6 ) Skinner, op. cit.T p. 108. Values of a and b for the gas were calculated from the (8) tabular values of Hawkins and Carpenter for the (8 ) Hawkins and Carpenter, o p . cit. vapor in the ideal gaseous state at 1 atm. The corresponding ACp is givenibys (43) AC ° ■ As + A*>T = -16.665 + 0.0090346 T (vaporization) = -10.612 + 9.25x10“^ T (sublimation)• The standard heat and free energy of vaporization and of sublimation were used in calculating a table of thermal functions} they are (44) A H 0 = A H 0 +AaT + (Ab/2)T2 2 (45) -AF° = RT In p = -AH + AaT In T + - IT 0 2 where A^o an<* i are integration constants. -87- Least Squares Analysis. Absolute Mea suremanta. The numerical values of AHo and I for the vapori zation process were determined by a least-squares analysis of the absolute vapor pressure data for the liquid (Table XIII). The function used was (46) 2 = £Ho + I * -R In p + &a In T + rj» * (4 ) Kelley, op. cit,. p. 3. The details of the analysis are as follows. For a set of n data, the deviation Vi of the i/th datum is (47) Vi » Z c - I obg = 1 + TTj; ~ I 0bs where numerical values of Z obg were obtained from the p, T data and the right hand side of Equation (4 6 ) above. Minimizing the sum of the squares of the deviations with respect to £H0 and I leads to the normal equations (48) | (I/T + aho/t2 - ZobaA ) = 0> t v. = 0. These equations were solved by the method of Doolittle ( 3/.) which also gives the relative weights Wg and wj (34) 0. M. Leland, Practical Least Squares, McGraw-Hill Book Co., Inc., New York (1921). of &R0 ®n<* The precision indices are given for a measurement of unit weight find for the Unknowns by: -38- (4-9) € * 2 = £ v 2/( n-m)j (50) € 2 = €»2/Whj (51) e\ = e*2/wi. The numerical results for n = 69 data and m = 2 unknowns are: (52) £v2 = 0,009326j 6 * = 0.011798; (53) AH0 “ 14221.3 eal/molj €jj =s 20.07cal/molj (54) I » -146.0349 cal/mol°Kj €j * 0.0651 cal/mol°K. This value of I is for p in mm Hgj for p in atm, (55) I = -146.0349 + R In 760 = -132.8532 cal/mol°K = I . a Table XIII gives the values of £obs ant* deviations. No data were rejected on statistical grounds. Numerical Expressions for the Heatr Free Energy and E„ntippy._ of._yaP-Qy ig.a ti ,oa. The corresponding numerical expressions for the heat, free energy, and entropy of vaporization are: (56) AH°y = 14221.3 - 16.665 T + 0.0045173 T2j (57) -AF°v = -14221*3 - 16.665 T In T + 0.0045173 T2 + 132.8532 Tj (58) AS% ■ A«(l + In T) + Ab T - Ig = -16.665(1 + In T) + 0.0090346 T + 132.8532. The calculated vapor pressure of the liquid was compared with the spectrophotometric results in order to estab lish the numerical value of the molar absorbancy index aM* -89- (59) In p = L + B/T + C In T + D T » 73.4877801 - - 8.386171 In T + 0.0022732 T (p in M Eg), where (6C& L = -I/Rj B a -AH0/R} c a Aa/Rj D « A6/2R. The calculated vapor pressure of the solid was obtained from the vapor pressure of the liquid and a calorimetrie value for the heat of fusion AHf : (61) In p^ = Lj + Bj/T + C-j_ In T + T j (62) In pB « Lg + B s/T + Cs In T + D g T where the subscripts ws" and "I" refer to the sublima tion and vaporization values respectively. At the triple point Tm, two conditions may be imposed on the vapor pressure equations: (63) In Pi(Tm ) = In pg (Tm) j and (64) A Hf = A H°e (Tjn) - A H°y (Tm.)* In terms of the heat of fusion and the vapor pressure constants, (65) Bs = -AHf/R + Bx + (Cs - C1) Tm + (Da - Dx) Tm2. Eliminating In p in Equations (61) and (62) and sub stituting the value for Bg from Equation (65), (66) L. - + A«£A T m + (0^ - Cs) (1 + la I„) * 2 (B1 - ».) V Using the NBS value of 2330 cal/mol for AHf at Tm * 249.045°K and the numerical values for the vapor pressure constants which correspond to the A c °p expressions for sublimation and vaporization in Equation (43), -90- (67) B s = -7696.935; AH - 15295.3 cal/molj 08 (68) Lg = 59.3594; Is ■ -117.95909 eal/mol°K for p in mm Hg. (69) Lg = 52.72612; Is = -104.77736 cal/mol°K for p in atm. The calculated vapor pressure of the solid was used to establish the numerical value of a^ for the spectro photometric sublimation data: (70) In ps = 59.3594 - - 5.340177 In T + 0.0002327 T (ps in mm Hg). Humerieal Expressions for the Heatr Free Energy and Entropy of Sublimation. The following numerical expressions for the heat, free energy, and entropy of sublimation were used in calculating a table of thermal functions for the tem perature range 200°K to 249.045°K: (71) = 15295.3 - 10.612 T + 4.625xl0“4 T2j (72) Asg » -10.612 In T + 9.25xl0“4 T + 94.1654; (73) -AF° « -15295.3 - 10.612 T In T + 4.625xl0~4 T2 8 + 104.7774 T. C. Spectrophotometric Functions. The comparison of the spectrophotometric results with vapor pressures calculated from the absolute mano- metric measurements not only established a numerical value for the molar absorbancy index aji for the vapor, but also provided an independent check on the extrapolation -91- of the absolute results from room temperature to lower temperatures. This comparison was effected as follows. The vapor was treated as a homogeneous, ideal gas, confined at a concentration c and temperature T1 between plane, parallel windows defining an optical path of effective length b. Then (74) A . abc , = (Ax - Alr) -(A0 - Aor) where the absorbancy index a has a numerical value de pending on the units used for b and c, or b, R, and p. (35) (35) Kasson S, Gibson, Suectrophotometrvf 200 to l f000 Millimicrons. National Bureau of Standards of Standards Circular 4#4> September 15, 1949, A,, and A are the absorbances of the filled and i. o empty sample cell respectively, measured relative to the reference cell. In the operation of the Beckman spectro photometer used in this investigation, balancing the instrument for 100$ transmission with reference cell in the beam had the effect of setting k^r and AQr equal to zero each time that a measurement was made, but regard less of their numerical value, they were assumed to be equal since the optical properties of the reference cell were assumed to remain the same at all times. Since (AT1) is proportional to the pressure, it was defined as (75) 7Ts at* = (aMb/R) p « (AL - A0)T«j with p in mm Hg, b in cm, and R = 62363.1 cm^mm Hg/mol°K, ajj is given in cm^/mol. (76) = In p + In aM + In bj - In R = In p + Kj (J » 1, 2, 3) where the index j is equal tq 1 for the 1 mm cell, 2 for the 5 mm cell, and 3 for the 50 mm cell. The difference between the nominal value bj and the effective value bj for the optical path of the j/th cell is called Pj: (77) bj = b.j * Pj Values of 7?vs, T for the 1 mm and 5 mm cells were calculated using experimental value of A0 as shown in the section on reduction of observations. The value of A 6 used for the 50 mm cell data was calculated as follows Calculation of A Q for the 50 mm Cell, Using the subscripts "I” and "s" for vaporization data and sublimation data respectively, the values of 7Tare related to the calculated vapor pressures by (78) 7t^ = — A q ) T 1^ = (a^b/R) P^ (•*■]_) (79) jrs - (Als - A0) T-s - ( ,MbA ) p s (Ts ). Here, A Q and (a^b/iR) are the same for both sets of dataj eliminating (a^b/R), (80) A » A 11 " rAls, r » plT 1s ° (1 - r) PsT'i * The ratio P^/p s Is calculated from Equations (59) and (70) for the vapor pressure of the liquid and of the -93- solid and is therefore consistent with the value 2330 cal/mol for the heat of fusion. Table XVIII gives the value of A0 calculated for each of the 37 sublimation data. The values of A^ appearing in the fourth column of this table were selected at random over the whole tem perature range for normal and metastable liquid in order to give approximately the same fractional variation in Aj for both sets of data. As indicated by the asterisks, 7 of the sublimation data were rejected because of secular trend and therefore did not contribute to the calculated mean value of 0.0161 for A 0. This trend is believed to be due to sticking of the cell-holder slide of the spectrophotometer during the last three runs with the 50 mm cell, which caused partial cutoff of the beam by the edge of the oven in which the optical cells were positioned and abnormally large instrument readings for A^. The Cell Constants Kj. Numerical values of the were obtained by least squares analysis of the 7f, T data (Tables XV, XVII, XIX) as follows: (81) xi3 = - m Pi(Ti) where is the value of the cell constant for the i/th datum and j/th cell, and In p^(T^) is the calculated value of In p for the datum at T^ from Equation (59) or (70). The deviation of from the least-squares -94- value K.j is (82) v±J = - K^. O Minimizing ^v * with respect to and solving for K ^, (83) K = I K ij ni where nj is the number of data in the set for the i/th. cell. The statistical weight Wj, the precision € ! of a measurement of weight unity, and the precision index €■ are given by: (34) Wj = n^j e] =Zv2/Ur l); €? = €'d/nr In order to base the final values of Kj on data having essentially Gaussian distribution, data were rejected from the original set to leave successively smaller sets. When a smallest set was found for which the number of rejectable data agreed reasonably well with that calcu lated for Gaussian distribution, K. was calculated from v the data left in this set. For n data, (0.0455 n) is the number rejectable from the set, assuming Gaussian distribution and / v ^ / > 2 € ’ as a basis for the rejection of a datum*^ 4 ) (34) Leland, pp. cit.f p. 230. Table XXIII summarizes the results of this rejection -95- Table XXIII Summary of Results for Absorption Constants at 279*8 mmu Number Basis for Set n 0 .0455 n Rejected Rejection* 1 mm Cell; K1 = 2.57256 1 0.00049: 58 data 1 65 3 3 /▼/ > 4 h/ 2 62 3 4 /v/>2 €* 3 58 3 0 1 0.00036: 5 mm Cell: K2 = 4.19491 118 data 1 129 6 3 /v/ >4/v/ 2 126 6 8 /v/> 2€» 3 118 5 0 50 mm Cell; k 3 = 6.49576 1 0.00034: 134 data 1 165 8 13 /v/ > 2 e* 2 152 7 10 Same 3 142 6 8 Same 4 134 6 0 * /v/ is the absolute value of the deviation v and /v/ is the average of the absolute values of the deviations. -96- scheme. The relatively large number of rejections for the 50 mm cell is due to the secular trend in the last 11 data (9 sublimation and 2 vaporization) obtained with this cell* The precision of the final Kj values is high: (35) ^ = 2.57256; = 0.00049; nx = 58; K2 = 4.19491; €2 = 0.00036; n2 = 113; K3 = 6.49576; €3 = 0.00034; n3 = 134. The precision indices were calculated from the deviations in Tables XV, XVII, XIX and Equation (84). The Molar Absorbancy Index aM . In the calculation of ajy[ for the vapor, once the Kj are known one can use the nominal b* values given on the J sample cells and obtain a value of ajj for each cell corresponding to that particular cell. In principle, however, a$j should be the same for all cells, and if the Kj are known with sufficiently high precision, the limit ing factor influencing the precision of aM will be the precision with which the nominal cell depths are known. A single value of aM, independent of j, was therefore calculated in term3 of pj. For any two cells, from Equation (76) (86) ^ - Kj = In (bj/bj) a In u±J., i^j. then (87) b j 3 3 “i3 * exp ( K l ' Kj>’ and -97- (88) p± = uijb^ - b»± + ttijPj. For j = 2 and i =1, 3: (89) fij, = uls^ - 4 * ^ ^ 2 P3 u32b2 ■ b3 + u32^2 and the value of p2 should be chosen so as to give physically reasonable values for all (3^. Then the effective cell depths b.. can be calculated and In aM determined from Equation (76). This was done with the following numerical results for b* = 0.1001 cm, b l5 = 0.5001 cm, and b* * 5.003 cm. . v (90) p± = b« exp (Kx-K2) - b£ + p2 exp(K^-K^) « (0 ,5001) (0 .1974.36) - (0.1001) + 0.197436 p2, P3 = (0.5001)(9.98271) - (5.003) + 9.98271 p2. From a plot of p]_ and p3 vs. p2, the value p2 = 0.00050 cm gave physically reasonable values for (3-j_ and p^: (91) p1 = -0.00126 cm P2 = 0.00050 cm @2 ■ -0.00566 cm. The corresponding values for bj are: (92) b1 - 0.09884} b2 = 0.50060} b3 = 4.99734. From Equation (76) for j = 2 (93) log aM = MK2 - log b2 + log R = 1.8218252 - log 0.50060 + 4.7949277 * 6.6167529. (94) an * 8*26536x10^ cm^/mol for a wave length of 279.8 mmu* - 98- The choice of Pg 3 0.00050 cm corresponds to the tolerance limits of (*0.0005 cm) of nominal length (36) stated by the manufacturerv ' of the 5 mm and 1 mm (36) Scientific Instrumentst Catalog 4 8 , American Instrument Co., Silver Spring, Md. (194-8) p. 128. cells, and is about 1/1000 of the nominal length. The corresponding value of -0.00126 cm for Pj_ is about 2.5X as large as the stated tolerance limit, but this and the fractional error of 12/1000 of the nominal length might well be expected considering the small path length and highly re-entrant construction of the cell. The 50 mm cell was made by a different manufacturerj since its tolerance limits are not stated and since the value -0.00566 cm for represents a difference of about 1/1000 of the nominal length, this value also appears reasonable. numerical values of Sjj throughout the wave length range 200 to 980 mmu were calculated in terms of ajj ** 8.26536x10^ cm^/mol at 279.8 mmu in order to make them consistent with it and with the effective cell depth b^ a 0.09884 cm. In the equations which follow, the subscript "280" indicates variables corresponding to a wave length of 279#8 mmuj variables which correspond to other wave lengths carry no subscript. - 99- (96) a - (ap/7r)280(7r/p) = 6.0595xl05 (71/p) = a^(X-) in cm^/mol. The vapor pressures p and P28O were calculated from Equation (59). The results are given in Table XXII as a function of the true wave length. They were also plotted on a large scale for the location of maxima, minima, and the long-wave-length limit of absorptionj the results of this plot are given in Table XXIV and in Figure U for comparison with those of Mason and Vango, ^5) (15) Mason and Vango, op. cit. d , M a i a % a.4 -Tfee.i:aa.i...Lvnsligas Spectroscopic Values for the Gas. Tabulated spectroscopic values for thermal functions of the gas were taken from the calculations of Hawkins (a) and Carpenter for the vapor In the ideal gaseous (&) Hawkins and Carpenter, o p . cit. state at 1 atm. Since tteir values were calculated at a relatively small number of temperatures, the following procedure was employed in order to interpolate in their - 100- Table XXIV Comparison of Molar Absorbancy Index Values X ,aH log aM A mmu m /mo1 This This Work Mason Work Mason 360 .0 340 3.2 0.505 328.9 0 325 5.4 0.732 320 19.7 19.0 1.294 1.279 .015 315 42.5 1.628 310 78.7 1.896 305 129.8 2.113 300 226.0 188.0 2.354 2.274 .080 295 371.3 2.570 290 573.0 497.0 2.758 2.696 .062 285 769.5 2.886 280.9 830.6 2.919 280 828.2 729.0 2.918 2.863 .055 275 697.2 2.843 270 473.5 410.0 2.675 2.613 .062 265 271.2 2.433 260 181.2 154.0 2.258 2.188 .176 258.3 177.4 2.249 255 208.0 2.318 250 345.2 292.0 2.538 2.465 .073 245 568.6 2.755 340 820.3 719.0 2.914 2.857 .057 235 1009.3 3.004 232.2 1038 3.016 230 1012.6 3.006 225 824.4 2.916 220 582.7 2.765 215 406.0 2.609 210 336.6 2.527 208.2 331.4 2.520 205 3 4 4 . 6 2.537 200 462.9 2.665 Figure A The Molar Absorbancy Index of Titanium Tetrachloride Vapor as a Function of Wave Length Plotted Values, Mason and Vango ------ Resuits of This Investigation ------ -101- - 102- 30 20 2 O O' o Q 0 - 200 220 240 260 280 300 320 Wove Length (m/i) Figure 4 table. For some thermal function of the gas, X®, (97) XS = X» + S where (98) 5 = X" - X« and is a correction-term calculated at the temperatures used by Hawkins and Carpenter in their table, and ob tained at other temperatures in this range by linear interpolation or extrapolation. Calculated and graphi cally interpolated values of & vs. T are given in Table XXV, In the equations above, X” is the value of the thermal function from the table of Hawkins and Carpente X* is given by (99) X* = Xy + Xe. X^c is the translational and rotational contribution to the thermal function assuming that for temperatures greater than 200°K the translational and rotational de grees of freedom of the molecule are fully excited. Xv is the vibrational contribution to the thermal function (100) = £ gix ir where g^ is the degeneracy of the ith normal mode of vibration of frequencyV±, and Xi is the contribution for one degree of freedom of a harmonic oscillator of this frequency. For the titanium tetrachloride molecule, there are 9 vibrational degrees of freedom and 4 fundamental - 104 - Table XXV Calculated or Graphically Interpolated Corrections for Thermal Functions of Titanium Tetrachloride in the Ideal Gaseous State at 1 atm Pressure C ■ _ t T ok CpO [-H.5r.H8j *30 2 0 0 0 553 0 -548 * 220 1 317 -247 -566 240 2 83 -495 -571 24« 2 -11 -594 -576 249*045 2 -23 -607 -576 250 2 —34 -619 -577 * 260 -18 -32 -601 -562 273 -45 -28 -578 -542 273.16 -44 -28 -578 -542 280 -12 -24 -581 -549 298 74 -12 -586 -566 « 298.16 73 -12 -586 -566 300 63 -16 -591 -568 320 9 -49 -644 -586 335 -36 -74 -684 -600 340 -51 -83 -697 —604 350 -81 -100 -723 -613 * 360 -64 -88 -699 -601 380 -31 -62 -652 -578 400 3 -38 -603 -554 408*66 18 -27 -582 -554 409*66 19 -26 -580 -543 ^Calculated and plotted; all other valnes read from the plots by linear interpolation or extrapolation* frequenciesj the frequencies and corresponding degenera cies are given in Table XXVI along with values of (37 ) (hc/k)Z^. Then the vibrational contribution is (37) Values of h, c, k from Smithsonian Physical TablesT 9th rev. ed„, Smithsonian Institution, Washing ton (1954) P» 54> Table 28. (101) Xv = 1 Xx (xx) + 2 X2 (x 2 ) + 3 X3 (x3) + 3 *4(*4) where the x^ depend on the temperature: (102) x± = (hc^/kT). The vibrational contribution for the heat capacity, enthalpy function, free energy function, and entropy are as follows: 2 xi (103) X., = R 9 for C°_ij 1 (exi - l )2 p (104) X± = R x-j/Ce - 1) for T / TjiQ n o \ (105) X i = R ln(l~exi) for 1----- 5 J . (106) X i = R x i/(exi - l) - In (l - exi) for S°. Values of (X^/fct) were obtained from tables of (X^/R) v s * Xj; after calculation of the x^ as functions of T from Equation (102). (38) Herrick L. Johnston, Lydia Savedoff, and Jack Belzer, Contributions to the Thermodynamic Functions by a Planck-Einsteln Oscillator in One Degree of Freedom. N^vexos P-646, Office of Naval Research, Washington (1949). -106- Table XXVI Fundamental Vibration Frequencies and Degeneracies for Titanium Tetrachloride Gas i V ., cm"1 (hc/k)l/ * i Si 1 1 388 1 558.3 2 119 2 171.2 3 498.5 3 717.3 4 139 3 200.0 * Values of h, c, k from Smithsonian Physical Tables. 9th rev. ed., Smithsonian Institution, Wash ington (1954), P. 54, Table 28. The translational and rotational contribution for the heat capacity, enthalpy function, entropy, and free energy function were calculated from (107) (108) S° » S°00 - 4 R In 200 + 4R In T; q O qi| q 200 200 “ v200 where is the value at 200°K from the table of Haw- kins and Carpenter, and Sy200 was obtained from Equation (100) above* (109) I— ° J = 4R - S°0Q + 4R in 200 - 4R In T. c The function (H° - Hq ) was calculated from (110) after values of the enthalpy function had been obtained vs* T. In the calculation of thermal functions for the gas, the value R = 1.987 cal/mol°K was used since it appeared that this value had been used by Hawkins and Carpenter in preparing their table. The results of this calculation appear in Table XXVII. Tabular Differences from Vanor Pressure Results. In order to establish the tabular difference between Xg a thermal function for the vapor, and X*" or Xs the same thermal function for the liquid or solid at the same temperature as the vapor, Table XXVII Thermal Functions for TlCl^ In the Ideal Gaseous State R = 1.987 cal/(mol °K); = 14,108.4 cal/mol. eo (h°"Hq) (S!=5S) .(E^S) cal/(mol °K) cal/mol cal/(mol °K) cal/(mol °K) cal/(mol °K) 200 20.498 2991 14.956 75.525 60.569 220 21.119 3404 15.473 77.488 62.015 240 21.650 3827 15.945 79.326 63.381 24 8 21.842 3999 16.124 80.030 63.906 249.045 21.876 4021 16.144 80.113 63.969 801 250 21.888 4042 16,167 80.203 64.036 260 22.106 4261 16.390 81.061 64.671 273 22.367 4551 16,669 82.149 65.480 273.16 22.369 4-554 16.672 82.163 65.491 280 22.501 4708 16.813 82.716 65.903 298 22.819 5116 17.169 84.134 66.965 298.16 22.821 5120 17.171 84.141 66.970 300 22.849 5161 17.204 84.276 67.072 320 23.140 5621 17.564 85.761 68.197 335 23.331 5968 17.816 86.822 69.006 340 23.389 6084 17.894 87.163 69.269 Table XXVII (cont. ) (EO-H8) T °K (h °-h ®) S° &P cal/fmol °K) cal/mol cal/(mol °K) cal/(mol °K) cal/(mol °K) 350 23.503 6319 18.054 87.849 69.795 360 23.619 6554 18.205 88.501 70.296 380 23.811 7029 18.498 89.794 71.296 400 23.987 7508 18.771 91.027 72.256 408.66 24.057 7717 18.884 91.548 72.664 409.66 24.064 7741 18.896 91.604 72.708 ,109 -110- (111) xe - x1 = a x was calculated from the vapor pressure results of this investigation in the range from 200°K to 249.045°K for the sublimation process, and from 249«045°K to 335°K for the vaporization process. tfinJ A H°, AF°, an<3 A^ 0 Jr were calculated from Equations (43), (56), (57), (58) for vaporization and Equations (43), (71), (73), (72) for sublimation. In order to have a basis for cal culating the functions which involved Hg directly, a mean value of A^o wafl calculated from (112) a h °t = -A(H° - h£)t +a h £ - (H° - Hg) 8 or 1 - (H° - Hg)^ + AHj Here, (H° - Hg)^ was taken from the tabular values for the vapor and AH0 was calculated from Equations (56) and (71). The value for liquid or solid was based on Skinner's tabular value for the solid at 200°Kj (113) (H° - Hg)| or 1 « (H° - H°)®qo + r TC° ® °r 1 dT ^200P T + l A H t 200 s or 1 where (H° - H®)8 = 3903 cal/mol, (C° ) is given o goo P by Equation (42) for the solid and liquid, and one transition is involved: fusion at 249.045°K with AHf * 2330 cal/mol. Numerical details are given in Table XXVIIIj the result is -111- Table XXVIII Calculation of for Titanium Tetrachloride . (Hi0 - H§) 0 0 P V > % T,°K Gas* Solid or 0 Liquid 200 2991.2 3903*0** 13191.4 14103.2 -5.2 250 404.1.7 7816.6 10337.3 14H2.2 3.8 273 4550.6 8653.3 10008.5 14111.2 ^ 8 298 5116.4 9566.9 9656.3 14106.8 -1.6 2 v 2 51.88 n 4 € ’2 17.29 €2 4.32 £ 2.08 * Values from Hawkins and Carpenter ** Value for the solid at 200°K from Skinner’s table -112- (114.) = 14-108.4 1 2 . 1 cal/mol. The values of (H° - Hg) shown in Table XXVIII for solid and liquid agree with those in Skinner’s table only at 200°K because of the linear approximation (Equation (42)) for the molal heat capacity and the use of a value of 2330 cal/mol for the heat of fusion instead of the value 2233 cal/mol used by Skinner. Neither do the values for solid and liquid in Table XXVIII agree exactly with those in the final Table (Table XXIX), b ecause the final values were calculated from the spectroscopic values for the gas, the vapor pressure values for AH°, and the mean value of A**g = 14108.4 cal/mols (115) (H° - Hg)1 or s (H° — Hg)* -A (H° - Hg) - (H° - Hg)S - AH° + AHg The differences are small, well within the limits of experimental error. This method of "calculating down ward” from the values for the gas was used in order to ensure consistency between the tabular values from 200°K to 320°K and the vapor pressure results of this investigation. The change in (H° - Hg) for vaporization and sub limation was calculated from Equations (56), (71) and (114): (116) A(H° - Hg) - AH° - AHg * AH° - 14108.4 cal/mol The change in the enthalpy function was calculated Table XXIX Thermal Functions for TiCl/ Solid and Liquid R » 1.9872 cal/(mol °K); * 14,1°8.4 cal/mol c» te*2> (5^28) -(£!^p cal/(mol °K) cal/mol cal/(mol °K) cal/(mol °K) cal/(mol °K) Solid 200 30.925 3908 19.541 37.400 17.859 220 31.527 4529 20.588 40.356 19.768 240 32.040 5160 21.501 43.099 21.598 248 32.224 5415 21.835 44.144 22.309 ■113 249.045 32.258 5448 21.875 44.270 22.395 Liquid 249.045 36.291 7778 31.230 53.626 22.396 250 36.294 7813 31.251 53.771 22.520 260 36.422 8176 31.446 55.193 23.747 273 36.566 8651 31.687 56.976 25.289 273.16 36.566 8656 31.690 56.998 25.308 280 36.636 8907 31.810 57.902 26.092 298 36.792 9569 32.109 60.196 28.087 298.16 36.792 9574 32.110 60.210 28.100 300 36.804 9641 32.137 60.431 28.294 320 36.914 10316 32.238 62.618 30.380 335 10800 32.239 64.075 31.836 340 10956 32.224 64.525 32.301 Table XHX(cont*) 0 (h °-h J) S° T K - m cal/(mol °K) cal/mol cal/(mol °K) cal/(mol °K) cal/(mol °K) 350 11276 32.217 65.441 33.224 360 11596 32.211 66.320 34.109 330 12238 32.205 68.045 35.840 400 12868 32.170 69.659 37.489 408.66 13168 32.222 70.405 38.183 409.66 - U 2 0 3 32.237 70.496 38.259 - 1 x 7 , -115- from Equation (116) and the relation (117) A s 2 A(hq - h°)t Equations (57) and (73) for &F° were used to calculate the change in the free energy functions (118) A (** - HS ) V T /T T T A large-scale plot was made of the enthalpy and free energy functions vs. T and vs. 1/T from 280°K to 335°K in order to extend the table of thermal functions up to the normal boiling point of titanium tetrachloride at 409»66°K by using the vapor pressure results of Schaefer and Zeppernick,^) The tabular values used in (3) Schaefer and Zeppernick, on. cit. this plot are given in Table XXX under the heading "This Work". The corresponding values from Schaefer and Zeppernick1s vapor pressure results were calculated for the range 280°K to 409.66°K as follows. The change in the free energy function was calculated using the value AH® = 14108.4 as in Equation (118) above, and A®,q/T fr om (119) -AF°/T = (r /m )(log Pmm - log 760) fchere (r / m ) has the value 4.5756971 and (120) log Pmm = 25.1289 - 2919.3 - 5.7877 log T Table XXX Tabular and Interpolated Values of Thermal Functions ^ ©K ______Tabular Interpolated -a(2!^S) -a (J£=52) -a(£^I)-a(5!t5S) as* -a (h»-h | ) This This ■------Work Schaefer Work Schaefar 280 39*8109 39.6737 14.9968 14.1820 39.8109 14.9968 24.8141 4199.1 300 38.7786 38.7015 14.9333 14.0033 38.7786 14.9333 23.8453 4480.0 320 12 *116.9. 37.8029 13.8469 37.8168 14.8666 22.9502 4757.3 335 37.1371 w : v m 14.8146 13.7419 37.1709 14.674 22.4969 4915.8 •911 340 36.9677 13.7089 36.9677 14.547 22.4207 4946.0 350 36.5712 13.6459 36.5712 14.207 22.3642 4972.4 360 36.1876 13.5863 36.1876 13.852 22.3356 4986.7 380 35.4560 13.4766 35.4560 13.4766 21.9794 5121.1 400 34.7673 13.3778 34.7673 13.3778 21.3895 5351.1 408.66 34.4812 13.3380 34.4812 13.3380 21.1432 5450.7 409.66 34.4486 13.3336 34.4486 13.3336 21.1150 5462.2 -117' from the vapor pressure results of Schaefer and Zepper- nick assuming a value of -11.5 cal/mol°K for The P plot was then smoothed graphically from 320°K to 335 K to give the interpolated values shown in Table XXX. The change in the enthalpy function was calculated r and was plotted vs. T for 280°K to the boiling point. The plotted values and those obtained by interpolation after graphical smoothing of the plot are given in Table XXX under the ’’Tabular, Schaefer” and "Interpolated” headings respectively. The values of &S° shown in the eighth column of Table XXX were calculated from the interpolated values for the free energy and enthalpy functions in the sixth and seventh columns: The change in (H° - H°), calculated from the enthalpy function values in the seventh column by the relation (123) is shown as a function of temperature in the last column of Table XXX. Although they were not tabulated, values of A h ° were calculated from (124) AH° = A(H° - h °)t + a h ° = A(H° - O t + 14.108.3 cal/mol at a few temperatures. Thermal Functions of Condensed Phases. Values of thermal functions X^* or s for the liquid or solid were "calculated downward" from the values for the gas and the vapor pressure results of this investi gation and of Schaefer and Zeppernick: (125) X1 0r 0 ■ X g - a x . The calculated values were then plotted as a function of T| since the plots for all functions excepting the free energy function for the solid and liquid showed inflection above 320°K, they were smoothed graphically between 320°K and 4-09.66°K in order to obtain the tabu lar values given in Table XXIX. The smoothing operation is equivalent to the use of the following relations:: (126) ~ Hp) ~ 32.2 cal/mol°K, 320 4 T « 4-09.66°K. ' T T (127) ( a 0 - (H° - H°)^oo + 32.2 T, 3 0 0 «T 4 409.66°K. (128) S<£ = (H ‘° - ^o)1 - - H°jX where _ /F° - H®\ h ° - H/P° " H° \ -119- and the gas and vapor pressure values on the right hand side are calculated from Equations (97) and (118), o1 No experimental values are available for C P above 300°K. Values calculated from the spectroscopic values for the gas and ^Cp = -11.5 cal/mol°K are not consistent with the smoothed values of (H° - H°)^j and those calculated by numerical differentiation of (H° - H§j^ show a broad, flat minimum from 330°K to 380°K which appears to be at least U cal/mol°K too low. It seems improbable that the calculated values give an adequate indication of the heat capacity behavior of the liquid in this temperature range:-, therefore they are not tabulated for temperatures above 320°K. E . Estimation of Errors. U s a . During the course of the experimental measurements the time ('I') was recorded to the nearest second. Since some delay would be expected to occur in the recording process, the error in the time is estimated to be (130) 6^ = 2 sec. Temperature. The error in the temperatures measured during the absolute manometric experiments is taken as the minimum error in the temperature scale of this investigation. From the relations (131) T - t + 273.16j t * t(R,K0)j R = R(?r ) -120- the mean square error in the absolute temperature € ^ is (132) e\ =£2 = (3t/0R)2£ 2 + (9t/9R0)2€^ o where € is the mean square error in the Centigrade t temperature of the resistance thermometer and €-.6,, K R q are the mean square errors in the resistance at tempera ture t°C, 0°C respectively. Because of the temperature drift of the bath with time, mm£\ — A (133) ® 1.69x10“ ohms/sec x 2 sec = 3.38x10“ ohms. it From the constants of the thermometer, (134) Ot/SR) s -Ot/9R0) * 250/25.56 = 9.78°C/ohm. The error in R 0 is between 0.3x10“^ and 8.5x10"^ ohms, the upper bound being the average deviation obtained from measurements of R Q over a period of about 1 year, and the lower bound from the final determination of the ' value of R 0 used in all calculations. Then€y can be calculated to be between 2.95x10“^ and 8.3xl0~^°K. As a final estimate, which allows for the occurrence of small temperature gradients between the surface of the - resistance thermometer and the liquid titanium tetra chloride in the sample bulb, (1 35) e T = 0.01°K. The average drift rate of the bath during the absolute manometric measurements was 1.65xlO“’5oQy/gQC or 9,92xl0”^°c/ min. During calibration of the copper-constantan thermo couple, the bath drifted in temperature, the average -121- drift rate being 6.42xlO“3°c/min for the thermocouple and 4»’76xlO~3°C/min for the platinum resistance ther mometer. During spectrophotometric runs the mean drift rate was 0.0l8°C/min for the thermocouple. The minimum error in reading EMF values from the K-2 potentiometer was 0.1 muV, both during the calibration experiments and the runs. Considering this and the error of 0.01°K above in the fundamental temperature scale of this investigation, the error € ^ is estimated as (136) € T = 0.015°K for the temperature T of the solid or liquid measured during the spectrophotometric experiments. From the calibration data for the copper-constantan thermocouple (Tables V, VI, VII) the relative error within the scale for the thermocouple is estimated as 0.2 muV or 0.004.°C, The minimum error in T* the cell temperature is estimated as 0.106°K on the basis of similar considera tions of the 0.01°K error in the resistance thermometer temperatures, the reading error of 0.1 muV for the EMF of the chromel-alumel thermocouple, and the error arising from drift of the optical cell temperature during cali bration and during the runs. From the calibration data (Table IX) the minimum relative error for the chromel- alumel thermocouple is 0.006°K, but the actual error arising from the use of the calibration plot is somewhat larger since the data in the region 330,6°K to 332.6°K -122- were represented by a single point on the plot. In order to make allowance for this, the error in T' is estimated to be (137) €t, = 0.02°K. From the relations | f U ) j , « | /"I \ (138) p = Pi-P^J P± » — --- » p*» [H(l+d2)+djd5 x (0.9994157) used in the reduction of experimental manometric data, the mean square error in the pressure is given by (139) €*••»■€* + £ 2 , + € 2 P pi p0» g where (140) £ , = €„ = 0.01 mmj p • xt (141) ^ p i Q = 3.76x10"^ mmj (142) € - 0.04 mm, o The error in p* is determined by the reading error for the scale of the cathetometer, on which distances can be read to the nearest 0.05 mm and estimated to the nearest 0.01 mm. The error in pQ* is the mean square error in the zero-point determination, calculated for 27 data. The error £_ occurs because of the use of the e spoon gauge as a null-indicating instrument to balance the pressure of the titanium tetrachloride vapor against the pressure in the reference system and manometer. Since a 40X ^microscope was used to view the movable -123- and reference pointers of the gauge, and since the tip of the movable pointer was about 0.03 mm wide, the minimum detectable deflection of the pointer is esti mated to be 0.01 mm. From this and the experimentally determined gauge sensitivity 4 mm Hg/mm deflection, 6^ is estimated to be 0.04 mm Hg. From Equations (139) to (142 ), the error in the experimentally measured pressures is estimated to be (143) € p = 0.041 mm Hg and is determined mostly by the error of the spoon gauge. Since the pressures are between 10 and 32 mm Hg, the fractional error is between 1*3/1000 and 4/1000. Absorbancer Wave Length, and Tf. From the relation for 7f (144) AT* = (A-l - A 0)T« the mean square error in 6 ^ , is (145) V * = T*2 6 ^ + T*2 € 2o + A2 € For the measurements at 279.8 mmu. the error in A is o estimated as (146) € Aq = 5xlo“‘S T* € = 300x5x10"^ = 0.15. This is based in the €A values from Tables XIV, XVI, ans XX, and on the value £. = 3x10”^ in the calculated "O A 0 for the 50 mm cell. Errors in A^ were estimated from the relation (1*7) S A1 - . 8.6^x10“^(10^1) -124- where t is the transmittance of the sample cell relative -3 to the reference cell and E^ = 2x10 is the estimated error in reading the transmittance scale of the spectro photometer. Then for the 1 mm, 5 mm, and 50 mm cells, from Equations (145), (146) and (147), (148) 0.14-SA^* 0.53, 0.404-€n 40.89 (l mm cell)j 0.11 4 A-^ 1.12, 0 . 3 7 4 ^ * 3 . 4 2 (5 mm cell); 0.05^4-^ 2.48, 0.334^*78.3 (50 mm cell). These estimates are based on 0,02°K as the estimated error in T1 the cell temperature. In the measurements from 200 mmu to 980 mmu on the 1 mm cell, A Q varied between 0.014 at 330 mmu and 0.033 at 200 mmu. The error Is estimated as (149) €. = O.OOlj T* €. = 0.3. " O iio Since A^ varied between 0.0145 and 0,7570, the error in Aj was estimated from Equation (147) to be between 8.94x10“^ and 49.4x10“^. Then from Equations (145) and (149) (150) 0.40*6^4 1 .42 . The error in the wave length is estimated as 0.1 mmu. In the following estimation of errors in thermal functions, it is assumed that errors in the thermal functions X® for the gas (Table XXVII) are so small that they can be neglected; -125- (151) X1 or 3 = X« — ^Xj 6 X1 or 3 = For the range from 409.66°K to 320°K , where the tabular values for the free energy function correspond to vapor pressure results of Schaefer and Zeppernick (Equation (120)), the errors in In p and in T are esti mated as (152) € la = 0 ,05j € t = 0.1°K. At a temperature of 360°K the corresponding error in the free energy function (CL53) a (F-1 li«) T T is given by (154) € 2 = (H€lnp)2 + ( ^ o / T ) 2 + (£H°€ t /t 2)2 = (1,987x0.05)2 + (2.08/360)2 + (14108/12960)2 x (0.01)} €f = 0 .1465. Estimates of (155) € a h° * ^ (Ho _ Ho) = 400 cal/yolj 6^so = € ^ Ho - h o o V ^ = 1.1 cal/mol°K appear reasonable since this the largest discrepancy to be expected between values of ^H° and &S° calculated from tables XXVTI and XXIX, and calculated directly from the vapor pressure (Equation (120)). The values of the thermal functions for the liquid are consistent among themselves. The tabular values of the free energy function for liquid and gas, together with A1*0 = 14-108*3 cal/mol are consistent with Equation (120) for the vapor pressures,! since they were calculated from it. In the range from 320°K to 24-9»045°K the tabular values of the thermal functions for the liquid are con sistent within themselves and with the vapor pressure results of this investigation. The mean square errors in the heat capacity constants are estimated as (156) = 0.517 cal/mol°Kj = 0.0016 cal/mol(°K)2 assuming that has an error of 2% and a value of 36.5 cal/mol°K at 320°K. The errors in the heat capa city terms determine the upper bounds for the errors in other thermal functions; in the case of A**0 and A S 0, (157) 20*3 * € ^ 0 *167; 0.065^€^s o $3.24-. Here the lower bounds are determined by the mean square errors in A H 0 and I, respectively. In view of the good agreement (Table XXXI) between the entropy of the solid at 200°K from this investigation and that calculated by Skinner from Latimer’s heat capacity data, it seems probable that the upper bound is much too large and that the actual error is close to the lower bound. Therefore the estimates which follow are for the minimum error. (15S) € 2a (H°-H°) s + £ 2 0 3 4-16 + 4.3 = 4-20.3; o eA(HO-H“) = 2 ° ' 6 °al/BOl; -127- Table XXXI Comparison of Thermal Functions for the Solid at 20Q°K Value at 200°K Function A This Work Skinner* o 30.9250 30.93 -0.0050 W W o 3908.2 3903 5.2 r _H8) 19.5410 19.52 0.0210 s ° 37.4003 36.99 0.4103 f ? : ) 17.8593 17.47 0.3893 * Reference (6), p. 108 -128- € = 20.6/320 = 0.064- cal/mol°K for A ^H° ~ Ho) €lnps €L + ^ B/T)2 + (b€t/!I?)2 = (0.0327)2 + (10.2/320)2 + (7156x0.01/10120)2 = 20.88x10~A €inp= 0.0456. For the free energy function, (159) € F = H £ lnp » 0.091 cal/mol°Kj and for the free energy, (160) €^,0 = 0.091 x 320 = 29.0 cal/mol. The overall precision with which Equations (59) and (70) reproduce the vapor pressure data of this investigation is (161) £*2 =IvV(n-l) = 70.07xl0"V(377-l) = I8.63xl0~6 lnp e* = 0.00431. lnp Here the sum is taken over the absolute data and spectro photometric data together. The use of the calorimetric value of 2330 cal/mol for the heat of fusion to obtain expressions for thermal functions for the sublimation process introduces an additional error estimated as 23 cal/molt (162) e 2 = e 2 + € 2 = (20.3)2 + (23)2 J AHg AHf f Q = 30.8 cal/mol. AHf Corresponding errors in other thermal functions are: (163) € = 0.104 cal/mol°K for AS° and A ^H ° ~ 11 oj . € = 0.147 cal/mol°K for the free energy function? (164) £ ^ f o = 0.147 x 225 = 33.1 cal/mol. From 320°K to 200°K the error contribution from the mean square error in the temperature scale is negligible compared with that from the mean square error in the pressure. Molar _Abs_orbency Index. The mean square error in In a^ at 279.8 mmu is the weighted mean of the errors for the 1 mm, 5 mm, and 50 mm cells, considering all the spectrophotometric data as a single set: (165) € lna * » 3 - 1, 2. 3 M n(n-l) where, from Equations (76) and (88), the error for the j/th cell is (166) £? = egj + = Uj2€ p2. Assuming that €p2 is 5.0x10 ^ cm, and using the numeri cal values of b^ and 6^ in Equations (92) and (85), (167) (Cp/b^. = 0.001, j = 1 , 2, 3. Then for n = 310 data, (168) £2 = 41.3x10“®j € = 6.425x10”^ in aji (169) € a , = aM€,„ a. = 8.26536x10^x6.425x10”^ M M ln aM = 5310 cm2/mol. Then at 279*8 mmu (170) ln aM = 15.2356366 Z 0,00064.25? aM = (8.26536 ± 0.00531)xl06 cm2/mol. For other wave lengths, from Equation (96), (171) £ 2 s (£2 + £ + £ 2 ) + €-, Ina^ In rx lnp 280 lnrr lnp = (0.413 + 36.9 + 18.6)xl0**6 + /7t)2 + I8.6xl0“6. At 327.9 mmu, the error ln aM is 1.66 and tends to increase without bound as ajj approaches zero. At 279.8 mmu, the error in ln aM is 0.0074 rather than 0.00064 because the precision of the data for the absorption spectrum corresponds to that of a measurement of unit weight rather than of weight n = 310. The errors for the minimum at 258.5 mmu and the second maximum at 231.7 mmu are 0.014 and 0.010 respectively. IV. RESULTS AND CONCLUSIONS A. Vapor Pressures. The vapor pressure of TiCl has been investigated 4 in the temperature range from 320°K to 237°K for the normal and metastable liquid and 249.045°K to 222°K for the solid. Vapor pressure equations have been ob tained which reproduce the experimental data with an overall precision of 4*3 parts/1000. These vapor pressure results are in good agreement (o) with those of Schaefer and Zeppernick in the range (3) Schaefer and Zeppernick, o p . cit. from 312°K to 320°Kj letting ps and Tg represent the experimental vapor pressures and temperatures of Schaefer and Zeppernick, and In p the natural logarithm of the vapor pressure at Tg as calculated from Equation (59) of the section "Analysis of Data", the deviation is (172) v± = ln pgi - ln p± . Prom Table XXXII, for n = 14 data, the precision of agreement is 2.39 parts/1000. The vapor pressures of Arii ( ' "L ' ) in the range from -131- -132- Table XXXIX Comparison of Experimental Vapor Pressures of Schaefer and Zeppernick with Calculated Vapor Pressures from This Investigation ■P" ps , mm °K < w H O 23.0 312.76 6 23.0 313.16 -138 23.5 313.16 27 23.5 313.41 -95 23.5 313.45 -118 24.0 313.56 44 25.5 315.06 -70 26.5 315.56 76 30.0 318.01 162 29.5 318.16 -76 30.0 318.46 -47 30.5 318.66 25 31.5 319.46 -23 31.5 319.56 -69 Z V2 0.001118 n 14 €‘2 0.00007987 €2 0.0000057 € 0.00239 -133- 293.16°K to 323.l6°K are from 9 to 20% higher than those of this investigation, presumably on account of residual gas in the vapor phase within his system. B , Heats and Entropies of Vaporization. At 320°K, the heats and entropies of vaporization are (173) = 9351 cal/mol} = 22.95 cal/mol°K for this investigation, and (174-) " 9677 cal/molj AS° = 23.96 cal/mol°K from the constants in the vapor pressure equation of Schaefer and Zeppernick (Equation (120), Analysis of Data)} their heat and entropy of vaporization are higher by 326 cal/mol and 1.01 cal/mol°K, respectively. Considering that their expression was intended to apply up to the boiling point at 4-09.66°K, and that their value for AH0 is essentially an average over the range from 312°K to 356°K, the agreement is about as good as could be expected. The temperature trend of the absolute measurements of this investigation is confirmed by the spectrophoto metric results: consistent values of the molar absorljancy index for all three optical cells could not be obtained if the calculated vapor pressures (Equations (59) and (70), Analysis of Data) were not correct. The results of a check on the entropy and other ther mal functions are shown in Table XXXI. Values in the -134- column “This Work"were calculated along the path; solid at 0°K, ideal gas at 0°K, ideal gas at 29S.l6°K, liquid at 298.16°K, liquid at 2 4 9 . 0 4 5 % solid at 2 4 9 . 0 4 5 % solid at 200°K. Values in the coluran“Skinner“ were calculated along the path; solid at 0°K, solid at 200°K. The entropy discrepancy at 200°K is 0.41 cal/mol°K, the cycle failing to close by this amount. This represents a considerable im- (6) provement over the situation described by Skinner an (6) Skinner, op. cit. which the discrepancy between the calorimetric and spectro scopic entropy for the gas at 29S.16°K was 2.53 cal/mol°K. The improvement is mostly due to the use of a higher value for the entropy of fusion (9.36 cal/mol°K, NBS, vs. 9.01 cal/mol°K) and an entropy of vaporization at 298.16°K (23.931 cal/mol°K) which is calculated from the vapor pressure results of this investigation. The 0.41 cal/mol°K discrepancy in the entropy of the solid at 2 00°K may be due to a transition below 87°K (the lowest experimental temperature), bit it seems more probable that it arises from the particular procedure employed in fitting the heat capacity curve to the data. Considering this and the precision with which the vapor pressure values and the spectroscopic values for the gas are now known, it seems very desirable to have the heat capacities redeter mined in the range from 20°K to 300°K and then extended as near as possible to the normal boiling point at 409.66°K. -135- C. Molar Absorbancy Index a^. The results of this investigation agree with those (15) of Mason and Vango . on the location of the maximum in (15) Mason and Vango, op. cit. a^ at 280,9 mmu, but not on the minimum at 258.3 mmu (Table XXIV and Figure 4); they obtain a corresponding minimum at about 260.2 mmu. Their value for the long- wave-length limit of absorption is 360 mmu vs. 328.9 mmu from this investigation; this difference is not surprising since the wave length of the absorption limit is sensitive to small errors in the measurement of absorbance, and they give no indication of the procedure which they used in de termining the absorbance of their empty sample cell. For all wave lengths from 24-0 mmu to 320 mmu, their values of log ajj are lower than those obtained in this investigation and there does not seem to be any systematic trend with wave length. They used the vapor pressure equation of Arii in calculating the pressure of the (l) Arii, o p . c i t . TiCl^ vapor in the sample cell of their spectrophotometer: since pressures calculated from his equation are too high, one would expect the resulting values of log ajj to be consistently lower than those from this investigation. BIBLIOGRAPHY (1) Kimio Arii, Bulletin of the Institute for Physical Chemical Research (Tokyo), 8, 714-718 (1929). (2) Kimio Arii, Science Reports, Tohoku Imperial Uni versity, 1st Series, 22, 182-199 (1933). (3) Harald Schaefer and Friedrich Zeppernick, Zeit- schrift fttr anorganische und allgemeine Chemie, 222., 274 (1953). (4) K. K. Kelley, Contributions to the Data of Theoret ical Metallurgy. III. The Free Energies of Vaporization and Vapor Pressures of Inorganic Substances. Bureau of Mines Bulletin 383, Washington (1953), p. 106. (5) W. M. Latimer, Journal of the American Chemical Society, ^4, 90-97 (1922). (6) Gordon Skinner, Charles E. Beckett and H. L. Johnston, and Its Compounds. Herrick L. Johnston Enterprises, Columbus, Ohio (1954), p. 108. (7) Gordon Skinner, Journal of Physical Chemistry, 22, H3 (1955). (8) N. J. Hawkins and D. R. Carpenter, Journal of Chemical Physics, 22, 1700 (1955). (9) Private communication at Office of Naval Research Conference, November 14-16, 1955. (10) W. Stanley Clabaugh, Robert T. Leslie and Raleigh Gilchrist, Journal of Research of the National Bureau of Standards, ££, 261 (1955). RP 2628. (11) Raleigh Gilchrist, R. B. Johannesen, C. L. Gordon and J. E. Stewart, Journal of Research of the National Bureau of Standards, 22, 197 (1954). R.P. 2533. (12) Private communication, Inorganic Chemistry Section, Division of Chemistry, National Bureau of Standards, Washington, D. C. February 8, 1954 (13) H. H. Marvin, Physical Review, 2L, 161-186 (1912). -136- -137- (14) A. K. Dutta and M. N. Saha, Bulletin of the Academy of Science of the United Provinces of Agra and Oudh, India, 1, 19-25 (1931-32). (15) David M. Mason and Stephen P. Vango, Journal of Physical Chemistry, 60, 622 (1956). (16) Private communication, Inorganic Chemistry Section, Division of Chemistry, National Bureau of Standards, Washington D. C., February 8, 1954. (17) Benjamin S. Sanderson and George E. MacWood, Jour nal of Physical Chemistry, 60, 316-319 (1956). (18) H. F. Stimson, Journal of Research, National Bur eau of Standards, ,4£, 209 (1949). (19) National Bureau of Standards Certificate 3.1/G-18939, February 7, 1956} Certificate 3.l/ll5245 NBS 1051, October 8, 194^. (20) E. F. Mueller, in Temperaturer Its Measurement and Control in Science and Industry, Reinhold Publish ing Corp., New York (1941), p. 69. (21) Notes to Supplement Resistance Thermometer Certifi cates, National Bureau of Standards, January 1, 1949, pp. 10-15. (22) Leeds and Northrup Co. Certificate for Standard Resistor, Serial No. 613883, Catalog No. 4025: January, 1946} Smithsonian Physical Tables, 9th rev. ed., Smithsonian Institution, Washington, D. C. (1954), PP. 19-20, Table 5. (23) Leeds and Northrup Standard Conversion Tables, No. 31031, p. 8. (24) Wm. F. Roeser and H. T. Wensel, Temperature,. Its Measurement and Control in Science and Industrvf Reinhold Publishing Corp., New York (1941), pp. 303-304. (25) R. T. Sanderson, Vacuum Manipulation of Volatile Compoundsr John Wiley and Sons, Inc., New York (1948) p. 121. (26) James A. Beattie et al. Proceedings of the American Academy of Arts and Sciences, 74. 344-370 (1941). -138- Certificate, December 1948, from the Technical Laboratory, Gaertner Scientific Corp., for M1012 Stainless Steel Scale, Serial No. 259. Metals Handbook. 1948 Edition, The American Society for Metals, Cleveland (1948), p. 553, Table IV. W. Cawood and H. S. Patterson, Transactions of the Faraday Society, 23, 514 (1933). James A. Beattie at al. Proceedings of the Ameri can Academy of Arts and Sciences, 2A, 371-388 (1941), Table III. Smithsonian Physical Tables, 9th rev. ed., Smithsonian Institution, Washington, D. C. (1954), p. 716, Table 805. Wallace R. Brode, Chemical Spectroscopy. 2d ed., John Wiley and Sons, Inc., New York (1943), p. 520. H. M. Haendler, Journal of the Optical Society of America, 417-419 (1948). 0. M. Leland, Practical Least Squares, McGraw- Hill Brok Co., Inc., New York (1921). Kasson S. Gibson, Spectrophotometryf 200 to l f000 Millimicrons. National Bureau of Standards Circu lar 484, September 15, 1949. Scientific Instruments, Catalog 4 8 , American In strument Co., Silver Spring, Md. (|.948) p. 128. Values of h, c, k from Smithsonian Physical Tablesf 9th rev. ed., Smithsonian Institution, Washington, D. C. (1954), P. 54, Table 28. Herrick L. Johnston, Lydia Savedoff and Jack Belzer, Contributions to the Thermodynamic Functions by a Planck-Einsteln Oscillator in One Degree of Freedom. Navexos P-646, Office of Naval Research, Washington (1949). AUTOBIOGRAPHY I, Homer Clyde Weed, Jr., was born in Sun City, Kansas, March 30, 1920. I received my secondary school education in the public schools of Bisbee, Arizona, and my undergraduate training at the Uni versity of Arizona, which granted me the Bachelor of Science degree in 19-42. In 194# The Ohio State University granted me the Master of Science degreej during the period 1946-4# 1 served as a graduate assistant in the Department of Chemistry and as a research assistant on Project 291 under the direc tion of Professor Wallace R. Brode. From 194# to 1957 I served as a graduate assistant in the Department of Chemistry and as a research assistant on OSU Research Foundation Projects 360, 266, and 553 while completing the requirements for the degree Doctor of Philosophy under the direction of Dr. G. E. MacWood., -139