This dissertation has been microfilmed exactly as received bo—15,075
CHERRY, Jr., Robert Homer, 1931- AZEOTROPIC BEHAVIOR IN THE CRITICAL REGION: THE SYSTEM ACETONE—n-PENTANE
The Ohio State University, Ph.D., 1966 Engineering, chemical
University Microfilms, Inc., Ann Arbor, Michigan AZEOTROPIG BEHAVIOR IN THE CRITICAL REGION:
THE SYSTEM ACETONE— n-PENTANE
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University
By
ROBERT HOMER CHERRY, JR., B.S., M.S.E,
The Ohio State University 1966
Approved by;
Adviser Department of Chemical Engineering ACKNOWLEDGMENTS
The author takes this opportunity to express his sincere thanks to Professor Webster B. Kay for his guidance, patience, and understanding.
To the Department of Chemical Engineering, and to
Professor Joseph H. Koffolt, in particular, are due thanks for providing the Linde Postgraduate Fellowship in Chemical
Engineering (1958-59 and 1960-61); and the DuPont Postgraduate
Teaching Assistantship (1959-80).
The National Science Foundation is thanked for grants covering the period of this research, and for the
National Science Foundation Summer Teaching Fellowship, i960.
ii CONTENTS Page
ABSTRACT ...... 1
INTRODUCTION ...... 3
RELATED LITERATURE ...... 7
EQUIPMENT AND PROCEDURE ...... 10
RESULTS 17
Phase Behavior ...... 17
Volumetric Behavior ...... 17
PRECISION AND ACCURACY...... 26
Temperature...... 26
Volume ...... 27
P r e s s u r e ...... 28
Composition...... 29
DISCUSSION OP THE R E S U L T S ...... 32
Phase B e h a v i o r ...... 32
Reproducibility of Dew and Bubble Points . 32
Dew Line for Sample 2 5 ...... 32
Correlation of Critical Properties .... 3^
The Azeotropic Locus ...... 37
Volumetric Behavior ...... ^0
DEVELOPMENT OF AN ENERGY PARAMETER...... ^9
CONCLUSIONS ...... 6l
RECOMMENDATIONS...... * '64
iii CONTENTS— (Continued)
Page
APPENDIX...... 65
I PREPARATION OF PURE COMPONENTS...... 66
Source and Preparation...... 66
Degassing Procedure ...... 66
II VOLUME CALIBRATION...... 69
III CALCULATION OF SAMPLE COMPOSITION ...... 77
IV DETAILS OF EXPERIMENTAL P R O C E D U R E ...... 83
Determination of a Border Curve ..... 85
Dew P o i n t ...... 85
Bubble Point ...... 86
Critical P o i n t ...... 87
Determination of an Isotherm...... 88
V CALCULATION OF TEMPERATURE, VOLUME AND
PRESSURE ...... 90
Temperature...... 91
V o l u m e ...... 91
Pressure...... 9^
Dead-weight G a g e ...... 9^
Bourdon Gauge ...... 95
Mercury Legs ...... 95
Capillarity ...... 96
Mercury Vapor Pressure ...... 97
Absolute Pressure ...... 98
Sample Calculation ...... 98
iv CONTENTS— (Cont inued)
Page
VI EFFECT OF MERCURY ON THE OBSERVED PRESSURE. 104-
VII EXPERIMENTAL DA T A ...... 109
BIBLIOGRAPHY ...... l4l
' AUTOBIOGRAPHY ...... 1^5
v FIGURES Figure Page
1 Experimental T u b e ...... 11
2 Apparatus...... 12
3 Vacuum Loading Train ...... 1^
k Pressure-Temperature Border Curves .... 19
5 Density-Temperature Border Curves ...... 20
6 Critical Temperature-Composition Locus . . 21
7 Critical Pressure-Composition Locus .... 22
8 Critical Volume-Composition Locus ...... 23
9 Isotherms for Sample 22(80.03mole^ n - p e n t a n e ) ...... 2^
10 Isotherms in the Low-density Region, Sample 22 (80.03 mole$ n-pentane) ...... 25
11 Azeotropic Locus on the P-x P l a n e ..... 36
12 Azeotropic Locus on the log P-log x Plane . 39 -
13 Azeotropic Locus: Dependence of P and x upon T ...... ^1
1^ Z - Tr Isochors for Sample 2 2 ...... 51
15 Energy Derivative as a Function of Reduced, Density ...... 55
16 A£(x) as a Function of Reduced Energy . . . 57
17 Energy Parameter as a Function of Composition at Constant Reduced Density . . 60
18 Calibration of Glass Capillary Tube .... 72
19 Schematic Diagram of Mercury Heads .... 92
20 Estimated Correction for the Effect of Mercury on the Sample Pressure ...... 108
vi TABLES
Table Page
1 Critical Properties for the System Acetone— n-Pentane ...... 18
2 Critical Properties of Purified Acetone S a m p l e ...... 31
3 Duplicate Measurements of Dew and Bubble P o i n t s ...... 33
4 Correlation of the Critical Properties . . . 35
5 Azeotropic Locus for the Acetone— n- Pentane S y s t e m ...... 38
6 Least-Squares Constants for the Isotherms: Sample 21 (51*41 Mole Percent n-Pentane) . . 43
7 Least-Squares Constants for the Isotherms: Sample 22 (80.03 Mole Percent n-Pentane) . . 44
8 Least-Squares Constants for the Isotherms: Sample 23 (64.90 Mole Percent n-Pentane) . . 45
9 Least-Squares Constants for the Isotherms: Sample 24 (59*87 Mole Percent n-Pentane) . . 46
10 Least-Squares Constants for the Isotherms: Sample 25 (71*88 Mole Percent n-Pentane) . . 47
11 Least-Squares Constants for the Isotherms: Sample 26 (54.30 Mole Percent n-Pentane) . . 48
12 Calculated Values of the Energy Derivative . 54
13 Calculated Values of the Function . . . 56
14 Calculated Values of the Integral Energy P a r a m e t e r ...... 58
15 Values of Volume Calibration Constants . . . 76
16 Calculated Values of the Loading Parameters. 81
17 Composition of the Six Mixtures of Acetone— n-Pentane ...... 82
vii ABSTRACT
The pressure-volume isotherms and phase behavior
were determined for the binary system acetone— n-pentane
at six compositions from 51*^1 to 80.03 mole$ n-pentane over
a pressure range from 75-1000 psia, and a temperature range
from 130-230°C. The critical pressures and temperatures were
correlated with composition by a quadratic in which an
interaction parameter was assigned as the arithmetic mean
of the values for the six mixtures. The critical volume
locus appeared to be composed of two curves which intersect
near the composition of the critical azeotrope.
The system acetone— n-pentane forms a positive
azeotrope in the critical region. The azeotropic locus
was established by applying the Gibbs-Konawalow criteria to
the P - x isotherms. The azeotropic locus does not inter
sect the critical locus at its point of minimum temperature.
An energy derivative based on the thermodynamic
equation of state was evaluated along the border curve for
all six mixtures and for pure n-pentane. Values of this
energy derivative at the critical point were nearly constant
for the mixtures' and for pure n-pentane; the maximum
deviation from the mean of the seven values was about 1
percent.
An integral energy parameter calculated from the energy derivative showed a weak maximum with respect to composition at constant reduced density. This weak maximum appeared to follow the trend in the azeotropic locus. However, the existence of a unique configuration at the azeotropic composition remains in doubt. Direct measurement of the isochors (rather than isotherms) within a volume accuracy of one part in ten thousand will probably be required to settle this question. CHAPTER I
INTRODUCTION
One of the most common examples of non-ideality
in liquid solutions is the formation of a constant boiling
mixture. Such a mixture is known as an azeotrope and is
characterized by the fact that the composition of the liquid
and vapor in equilibrium are identical. So far as is known,
Dalton (1) in 1802 was the first to report the existence of
constant boiling mixtures. However, the extent to which
azeotropes form was not realized until 1918 when Lecat (2)
published his first monograph of azeotropic data in which
some 6000 - 7000 binary azeotropic systems were reported.
Since that time, through the efforts of Lecat (3)»
Sweitoslawski (^) (5) (6), and others, thousands of additional azeotropic systems have been examined. Horsley’s latest
compilation (7) lists some 17,000.
Almost without exception these experimental studies were concerned with the examination of the systems in the region at atmospheric pressure. Around 1950 Kay and his
students (8) (9) (10) at Ohio State University started a systematic study of azeotropic systems covering a pressure range from atmospheric to the critical pressure. As a result of these studies it was found that systems which form azeotropes in the critical region exhibit much greater diversity in their phase behavior than systems that do not form azeotropes. This diversity manifests itself in the form of the P-T critical locus curve of the system. In nonazeotrope-forming systems the critical locus may vary
from a straight line to a convex curve with a maximum
pressure point, whereas in systems that form positive
azeotropes the critical locus curve may possess a minimum
temperature point and maximum and minimum pressure points.
This work showed that the phase behavior of azeotrope- forming systems is complex. During this same period,
Kreglewski (11) (12) (13)» at the Polish Academy of Science at Warsaw, attempted to define mathematically the conditions
■under which an azeotrope can form in the critical region.
The formation of azeotropes in a mixture is a manifestation of the deviation of the solution from the
ideal solution law. This is due to the interaction of the molecules of the solution. Each molecule is characterized by a force field which interacts with the force field of its neighbor molecules; the difference in interaction between like and unlike molecules determines to some unknown extent the properties of the mixture. If, therefore, one could determine the effect of size, molecular shape, and type on ? the magnitude of the intermolecular forces then one might predict the extent to which a solution would deviate from ideal solution behavior.
For mixtures of relatively simple molecules, the behavior of real gases and gas mixtures has been described by the methods of statistical mechanics. This approach is essentially an intuitive one in which a model for the interaction is proposed and analyzed and its worth evaluated
on the basis of a comparison with experimental results. One
such model is that derived by Lennard-Jones and modified
subsequently in various ways by Kihara, Stockmayer and
others, so as to make it applicable to molecules of both
spherical and non-spherical shape. These models have been
partially successful over limited temperature ranges and at densities well below the critical density. They represent, however, only a beginning in the solution of a very complex
problem.
While thermodynamics, per se, deals with the macroscopic properties of the liquid state and not with the properties of the individual molecules, it is concerned with the overall effect of the attractive and repulsive forces between large groups of molecules. Therefore, the rigorous thermodynamic equation (i) (3E/dv)T = T(dP/ar)v - p is applicable to the exploration of the properties of azeotropic systems. The internal pressure may ^e regarded as the average isothermal rate of change of the internal energy of the system as the volume (which is related to the distance between molecular centers) is changed. Hildebrand (1^) thought of T<£p/a-r\, as a kind of thermal pressure related to the kinetic energy of the molecules. The external pressure P is the pressure one measures with a pressure gauge. Determination of the P-T isochors of a binary system would permit evaluation of foE /9V)*r in accordance with equation (1).
Hildebrand and coworkers (14) have applied equation
(1) to liquids at pressures below 3-^ atmospheres, but made no attempt to include the^igher pressures in the critical region. Rowlinson (15) has shown that the association of a minimum critical temperature with positive azeotropy and a maximum critical temperature with negative azeotropy has a / simple theoretical basis. It would seem, therefore, that a determination of in the critical region of a binary azeotrope might yield significant information on the energy of interaction of two unlike molecules. The present study of the acetone— n-pentane system was undertaken to explore this possibility. CHAPTER II
RELATED LITERATURE
Aside from the use of the excess thermodynamic properties, classical thermodynamics has contributed1' directly very little to the elucidation of the nature of the interaction of molecules, since the latter is the sum of the contributions of many kinds of forces. However, with the use of the basic thermodynamic equation of state (equation 1), a method is provided Ttfhereby information can be obtained on the change in the internal energy as the distance between the molecules varies and as the kind and numbers of molecules vary around a given molecule.
A search of the literature discloses that
Hildebrand, Westwater, Frantz and Carter (16) (17) (18) obtained values of OE^SV)^- for a series of liquids at relatively low pressures (up to about 4 atmospheres) and at temperatures considerably below the critical point. He found that at pressures below the normal boiling point that (2) (aE/av)^ = t(3P/2>t)v = a,/v* ^ aev/v where "a" approximates the value of "a" in the Van der Waals equation and is related to the energy of vaporization,AEy.
Hildebrand has shown (19) that (AEy/V)^/2 serves as an important parameter for the correlation of solubility data.
Nothing appears to have been done to apply the thermodynamic equation to binary systems in their critical region. 8 The acetone— n-pentane system has heen examined in the critical region by Brown (20), who obtained P-T-x data to show the existence of a minimum point in the critical locus curve. The coordinates of the point were estimated to be 19^.5°C, and 528 psia, at 80 rnole^ n-pentane. The coordinates of the critical azeotrope were not determined.
Pennington and Kobe (21) measured the vapor pressure of pure acetone from the standard boiling point to the critical point, and also reported data on the second virial coefficients for the vapor. Bottomley and Spurling (22),
Brown and Smith (23), Lambert and coworkers (2J+), and
Leverett (25) have also reported second virial coefficients for pure acetone.
Young and coworkers (26), (27), (28) made a very s < complete study of the P-V-T relations of n-pentane. This work includes isotherms, isochors, vapor pressure, saturated liquid and vapor densities, and heats of vaporization. These data on n-pentane still remain among the most extensive and reliable available. Second virial coefficients for n-pentane have been reported by Beattie et al. (29), McGlashan and
Potter (30), Garner and McCoubrey (31), mnd Leverett (25).
The effect of the presence of mercury on observed critical properties is discussed by Jepson and Rowlinson (33).
Methods of approximating interaction virial coefficients are discussed by Rowlinson, Sumner and Sutton (3^)* The apparatus and methods used in this study are essentially those of Kay and Rambosek (35)> and Kay and
Donham (36).
Certain general references have been most useful.
The collection of physical properties by Timmermans (37) is appreciated. Hirschfelder, Curtiss, and Bird (38) have presented a great mass of material on the theory of equilibrium and transport properties. The monograph on the solubility of non-electrolytes by Hildebrand and Scott (14) includes the work on the solubility parameter concept of
Hildebrand and his students. CHAPTER III
EQUIPMENT AND PROCEDURE
The equipment and technique employed in this work, except for minor modifications, have been perfected by Kay and his students (35) (36). Simplicity of operation, direct visual observation of the sample by the experimenter, and use of a small, highly purified sample (approximately 0.5 mg.-mole in this work) are some important advantages of this technique.
The sample is confined over mercury in a calibrated precision-bore capillary; dimensions of this sample tube are given in Figure 1. A small steel ball placed inside the tube with the sample is moved vigorously with a large permanent magnet to provide stirring to assure rapid attainment of equilibrium.
Figure 2 is a schematic representation of the- apparatus. The calibrated sample tube (T) is maintained at constant temperature by a vapor bath consisting of jacket (J), boiling flask (L), heater (F), vacuum ballast (VB) and vacuum pump (VAC). The double-walled jacket (J) is silvered except for diametrically opposed longitudinal viewing slits; the annular space is evacuated. The desired bath temperature is adjusted and maintained by regulation of the pressure in ballast (VB) over the range 20-76 cm. Hg absolute. The resistance of the calibrated platinum resistance thermometer
(R) is measured at (K) by a calibrated precision recording 10
I; 11
I * ALL DIMENSIONS IN CENTIMETERS, NO SCALE j MATERIAL - 7740 Pyrex
OlDl * 1.0 56.5 I.D. =0.46
66
9.5
f 10/30
Figure !• Experimental Tube 12
bleed r —W—N-
high- pressure PB
MAN
VAC calibration
bleed CV
Figure 2. Apparatus 13 Wheatstone bridge or alternately measured (without recording) by a calibrated Mueller bridge.
Sample tube (T) is held firmly in a rubber shock mounting at the top of compressor block (C) which is connected through check valve (GV) to the backleg chamber (B).
The bore of the sample tube (except for the volume of the trapped sample and stirring ball) and the lower portion of the backleg chamber are completely filled with freshly distilled mercury. The upper end of the backleg chamber connects directly to the high-pressure manifold (M).
Stability in the high-pressure manifold is provided by ballast tank (PB). The calibrated bourdon gauge (H) is used as a pilot pressure indicator; during a run, pressure is measured by primary-standard dead-weight piston gauge (DWG). Pressure in the manifold system is raised by admitting high-pressure nitrogen gas into the manifold through the double-valve trap, or lowered by bleeding nitrogen to atmosphere through the double-valve bleed trap.
The experiment consists of maintaining simultaneously a constant temperature and a constant pressure on the sample.
After the attainment of equilibrium, a precision cathetometer is used to measure the length of capillary occupied by the sample in tube (T), so that the sample volume may be calculated from the volume calibration.
Figure 3 is a schematic representation of the high- vacuum glass loading train used to load a binary mixture into DP
VAC
Figure 3* Vaouum Loading Train the sample tube. Sample tube (T) is connected, to the vacuum train through a mercury-sealed, standard.-taper joint.
The assembly is brought to operating condition by starting vacuum pump (VAC) and diffusion pump (DP). With trap (N)
immersed in liquid nitrogen, the entire system, except for
reservoirs (A) and (B), is pumped for an hour after McLeod
gage (G) first indicates stick vacuum (for this McLeod gage an absolute pressure less than 10"^mm. mercury). The two
components, n-pentane and acetone, are stored in flasks
(A) and (B) respectively; both are maintained at the temper ature of an acetone/dry ice bath and are shielded from direct
light by glass wool and aluminum foil. The safety manometer
(P) may be used to measure vapor pressure. The contents of flask (B) are distilled into reservoir (E) and then back to
(B), a standard degassing operation taken as a precautionary measure. A small amount of the lower-boiling component
(acetone) is distilled from flask (B) into the calibrated loading capillary (C), then into sample tube (T), and finally
into cold trap (N). This flushing operation is repeated at least twice, after which the system is again pumped to ensure stick vacuum. The desired amount of acetone is then distilled from (B) into (C), where the length of liquid column at the ice point is carefully measured with a precision cathetometer. The acetone sample, now of known mass, is transferred from (C) into sample tube (T), where it
is frozen with liquid nitrogen. 16
The n-pentane in flask (A) Is degassed, the flushing operation is repeated (except for tube (T)), the sample of predetermined size is measured in (C), then transferred and frozen into (T) in a manner analogous to that for the acetone. The transfer from (C) into (T) is accomplished quantitatively in less than 30 minutes. Liquid mercury from reservoir (H) is introduced through a hair capillary into the bore of the sample tube, trapping the frozen sample in the closed end of (T). The sample tube is then carefully removed from the loading train and installed in compressor block (C), Figure 2.
Further details of the procedures described above and of the necessary calibrations are given in Appendixes
I, II, III and IV. CHAPTER IV
RESULTS
The pressure-volume isotherms and phase behavior were determined for the binary system acetone— n-pentane at six compositions from 51-80 mole$ n-pentane over a pressure range from 75-1000 psia, and temperature range from 130-230°C.
A complete tabulation of the data is given in Appendix VII.
Phase behavior
The border curve or boundary of the region in which two phases may coexist in equilibrium, includes the dew and bubble curves, which coincide at the critical point. These data are presented graphically by the pressure-temperature and density-temperature curves of Figures ^ and 5» Data for the variation of critical properties with composition are given
in Table 1, and plotted in Figures 6 to 8. All pressures were measured with the precision dead-weight gage as stated in Chapter III except for Sample 21, for which the calibrated bourdon gauge was used. The dew, bubble and critical pressures for Sample 21 are accurate and precise to +1.0 psi and +0.5 psi respectively, excluding the effects of mercury.
Volumetric behavior
Typical behavior for the compressibility factor- density isotherms is shown for Sample 22 (80.03 mole$ n-pentane) in Figure 9* An enlargement of the low-density region is given in Figure 10; the solid curves are computed from a polynomial determined by least squares. The volumetric behavior and the least-squares procedure are discussed in detail in Chapter VII. 17 18
TABLE 1
CRITICAL PROPERTIES FOR THE SYSTEM ACETONE— n-PENTANE
Critical Critical Critical Mole fraction temp. pressure volume Sample n-pentane °C psia 1/mole
— 0 234.44 677.8 0.213*
21 0.5141 199.83 576.43 0.2716
26 0.5430 198.15 569.19 0.2720
24 0.5967 196.65 560.65 0.2730
23 0.6490 195.50 549.97 0.2785
25 0.7188 194.26 538.71 0.2926
22 0.8003 193.91 524.8 0.300
* 1.0 196.6 489.5 0.311
#Kobe and Lynn PRESSURE, psia 400 440 480 380 420 460 360 500 560 560 520 540 Figure 4. Pressure-Temperature Border Curves Border Pressure-Temperature 4. Figure 170 ii i* 15 14 E EAUE *C PERATURE, TEM 160 M OLE FRACTION FRACTION OLE M RENTANE N A T N E -R n O B I I B O 41 190 CIIA LOCUS 'CRITICAL 200 19 DENSITY, moles/liter Figure 5» Density-Temperature Border Curves Border Density-Temperature 5» Figure 170 ArI n-*EKTA»e SAfrVIC CAL POI T IN O P L A tC r m C 22 23 4 2 9 2 9 2 TEMPERATURE. 180 C ° 190 200 CRITICAL TEMPERATURE 240 200 190 220 230 210 0 Figure 6. Critical Temperature-Composition Loous Temperature-Composition Critical 6. Figure , OE RCIN n-PENTANE FRACTION MOLE X, 0.2 0.4 calculated - — AEOE (40) ACETONE O BON (20) BROWN V A p-PENTANE (40) (40) p-PENTANE A TI WORK THIS O 0.6 8 0 21 U) CRLTICAL PRESSURE, psia 0 0 6 0 0 5 0 0 4 700 Figure 7. Crltioal Pressure-Composition Loous Pressure-Composition Crltioal 7. Figure — calculated — ACETONE(40) O A n-PENTANE (4 0 ) ) 0 (4 n-PENTANE A TI WORK THIS O X 2 0 L FATO n-PENTANE FRACTION OLE 04 6 0 0.8 22 CRITICAL VOLUME, liters/mole 8 2 0 0.32 0.22 0l30 0.24 020 6 02 f / * / Figure 8. Critical Volume-Compos Volume-Compos Critical it 8. ion Locus Figure /
/ a ' V / / / . • , OE RCIN n-PENTANE FRACTION MOLE X, 2 0.8 6 0 4 0 02 f /
/ /■ ------< L TI WORK THIS 0 / n - i AC > / / si ated estim calculated i ear lin ✓ / PFN ETOI . A /
-i / OO'y > m y\rr % / / r(40) D) - Y ~ s s ' t / / / / / ' / f ' / . V * * 3 2 \ 10 00 OS Figure 9» Isotherms for Sample 22 (80.03 Mole Percent n-Pentane) Percent (80.03Mole 22 Sample for Isotherms 9» Figure Z ■ PV/RT 4 0 02 20 EST, otes/liter m DENSITY, 30 40 90 0 8 COMPESSIBIUTY FACTOR, Z-PV/RT Q80 Q95 0.85 Q90 0.75 100 105 O Sample 22 (80.03 Mole Percent n-Pentane) Percent (80.03Mole Region, 22 Sample intheLow-density Isotherms 10. Figure 0.2 EST, moles/liter DENSITY, 04 Q 6
CHAPTER V
PRECISION AND ACCURACY
Estimates of the precision and accuracy of the physical measurements are presented in this chapter. The details of the volume calibration procedures are given in
Appendix II. The methods used to calculate true values of pressure, volume and temperature from the raw data are described in Appendix V, which also includes a complete sample calculation.
Temperature
The temperature of the vapor bath (at the top of the sample tube) was measured with a precision platinum resistance thermometer calibrated by the National Bureau of
Standards. Resistance values were taken from a precision recording Wheatstone bridge. The thermometer/recorder system was calibrated and checked against the ice point and against the freezing points of high-purity samples of tin and zinc.
These freezing points were certified by the National Bureau of Standards. To check the technique, the freezing points were measured with a second precision resistance thermometer and Mueller bridge, both calibrated by the National Bureau of Standards. These measurements agreed with certified freezing points of the tin and zinc samples within 0.001 and
0.01°C, respectively.
The ice point resistance was checked periodically over the time that data were taken. Twenty-four hour stability tests were made to check the effect of changes in
26 27 ambient temperature on recorder stability. The maximum observed variation in the resistance indicated by the recorder was always less than +0.002 ohm, equivalent to
+0 .02°cT
The liquids used in the vapor jacket were heart- cuts taken from a series of vacuum distillations. J Consequently, the vertical temperature gradient on the sample probably does not exceed 0.01°C.
The error caused by radiation of the hot platinum resistance element through the sighting slits in the silvered vapor jacket was measured by measuring the change in indicated temperature upon Insertion of an aluminum radiation shield. This error was less than -0.02°C for the maximum temperature difference, i.e., a vapor bath temperature of
230°C and an ambient temperature of 23°C.
The temperature measurements are precise to within +0.01°C, and accurate to within +0 .05°C. Volume
The accuracy of the volume measurement is directly related to the uncertainty in the calibration constants, which are expressed as 95% confidence limits given in
Appendix II. The precision of the volume measurement depends almost entirely upon the precision of the one-meter cathetometer used in the experiment. This precision was experimentally determined to be +0.002 cm. per reading, so that any length measurement was reproducible to within 28
+0.005 cm. On this basis, the lowest measured, densities are estimated to be accurate to +0 .06$ and precise to +0 .0^$.
The highest values of density are accurate and precise to within about +0 .3$.
Pressure
The primary-standard dead-weight pressure gage is precise within +0.05 psi at pressures above 120 psig.
Below this pressure, precision decreases approximately linearly to + 0.2 psi at the minimum pressure (60 psig) measured during this experiment. The absolute accuracy of the gage is probably very close to the values for precision.
The sum of the errors in estimating pressure corrections for the mercury legs, the effect of capillarity at the mercury interface, and barometric pressure totals less than +0.05 psi. This figure includes the precision of the estimate of mercury vapor pressure for sample pressures below 150 psia. The accuracy of the calculated sample pressure above 150 psia suffers from the assumption that the true sample pressure is given by subtracting the vapor pressure of mercury (corrected for the Poynting effect) from the observed pressure. This is a consequence of ignoring the mercury— acetone and mercury— n-pentane interactions in the organic phase; these interactions increase in magnitude above 150 psia, and reach about one pound per square inch at the critical density. A detailed discussion of this effect is given in Appendix VI. 29 Dew, bubble and critical points were reproducible to within +0.05 psi. A measure of the accuracy was obtained by making measurements across the two-phase region between the visually observed dew and bubble points. The result was a linear pressure-volume isotherm which intersected the liquid and vapor isotherms within +0.05 psi of these visually observed dew and bubble points. On the basis of this result, it is probable that the accuracy of the visual location of the border curve is within +0.1 psi for all points.
In summary, the precision of the reported pressures in the single phase region is claimed to be +0.25 psi, with an accuracy of +O.30 psi, exclusive of mercury effects.
For points on the border curve, the precision is +0.30 psi, while accuracy is estimated to be +0.35 psi. The effect of mercury is estimated to be approximately +1.0 psi at the critical density.
Composition
The accuracy of the determination of the masses of the pure components depends primarily on the uncertainty in the calibration constants for the loading capillary and on the precision of a length measurement made with the
10-cm. Gaertner cathetometer. The calibration constants were established by the least-squares procedure described in Appendix II; the precision of the cathetometer was experimentally determined to be + 0.001 cm. On this basis, 30 the accuracy of the sample mass is within +0 .05$ for all samples.
The actual sample composition, calculated, from the masses of the two components loaded, into the sample tube, depends on the purities of the acetone and n-pentane.
The Phillips research grade n-pentane, as received, was
99*84 mole$ n-pentane, with isopentane the major impurity.
In view of the purification treatment described in detail in Appendix I, the purity of n-pentane as loaded is claimed to be 99*95 mole$ or better. The trace of isopentane would not affect to a detectable extent either the average molecular weight or the behavior of the sample*
Water is believed to be the major impurity in the acetone. The primary measure of acetone purity was taken as the difference between the dew and bubble pressures, which was 1.6 psi at a reduced temperature of O.96. This small deviation from isobaric vaporization indicates a highly-purified sample. The measured critical point of the acetone is compared to the measurement of McAdams (39) and the values chosen by Kobe and Lynn (40) in Table 2.
The rather large uncertainty given by Kobe and Lynn probably is caused by varying amounts of water in the acetone used by the experimenters whose data were examined. It is claimed that the purification of the acetone, described in Appendix I, removed all but traces of water from the sample used in this work. This conclusion is supported by the fact that the 31 critical properties given in Table 1 fall at the low end of the range given by Kobe and Lynn.
TABLE 2
CRITICAL PROPERTIES OP PURIFIED ACETONE SAMPLE
Critical Critical Pressure Temperature psia °C
This work 677.8 234. *J4
McAdams (39) 677-5 23^.^7
Kobe and Lynn (^0) 685 ±9 235.5 ±1
The values of sample composition listed in
Appendix III are claimed to be accurate within +0.05 mole$. CHAPTER VI
DISCUSSION OF THE RESULTS
Phase behavior
Reproducibility of dew and bubble points. During the course of the experimental work, it became obvious that the very narrow two-phase regions exhibited by this system placed a considerable strain on the ability of the ex perimenter to locate the border curve accurately and re- producibly. Multiple observations were made for five different dew and bubble points for three of the samples.
The first of each set of repeated observations shown in
Table 3 were made by the author; the second and third observations were made by another experienced observer, who made a completely independent approach to the two-phase region. The agreement among the pressures for these multiple observations is within the precisions specified in Chapter v.
The rather large volume disagreement for Sample 24 is difficult to explain.
Dew line for sample 25. The dew line for
Sample 25 (71.88 mole# n-pentane) is anomalous, although the critical properties and bubble line are quite reasonable when compared with the other samples. The dew pressure at the critical temperature was checked by an independent observer and found to agree within 0.02 psi. It is highly unlikely that during the experiment this sample became contaminated by a heavy impurity, which would have tended to lower the dew pressure. Furthermore, a heavy impurity would 32 33 tend to produce a greater lowering of the dew pressure at lower temperatures than near the critical, whereas just the reverse was actually observed. Two other rationalizations are: first, that the effect is produced by unexpectedly large interactions of the dissolved mercury with acetone and pentane, and second, that for this particular composition at temperatures near the critical, some reversible reaction takes place which produces a heavy molecule. It was not feasible to test these two rationalizations, either by detailed calculation or by experimental means.
TABLE 3
DUPLICATE MEASUREMENTS OF DEW AND BUBBLE POINTS
Type of Temperature Pressure, Volume Sample point psia l/mole
22* bubble 193.89 524.92 0.2725 524.85 0.2721
24 bubble 195.40 549.4? 0.2612 549.39 0.2558
2k dew 190.02 503.85 0.5073 503.81 0.5077 504.00 0.5065
25 dew 194.26 535.39 0.3917 535.37 0.3919
25 bubble 170.04 370.77 0.1623 370.82 0.1624
*The second measurement was also made by the author four hours after the first. 3k
Correlation of critical properties. The critical pressures and temperatures were correlated with composition by the quadratic relationship
(3) <3C = % Ck,„ + 2x(l-x)Qc,u + 0-xf oCi3z where Qq stands for either critical pressure or critical temperature of the mixture, x is the mole fraction of component 1 (n-pentane), and the subscripts 11, 1 2 , and
22 refer to pentane-pentane, pentane-acetone, and acetone- acetone interactions, respectively.
For the critical temperatures, the interaction parameter Tq was taken as the arithmetic mean of the values calculated from equation (3) for each of the six mixtures. This mean value gives an adequate correlation, as shown by the solid curve on the Tc - x plot, Figure 6 .
Deviations of the individual critical temperatures from the calculated curve are given in Table *]-. The maximum deviation is 0.6°C. The minimum temperature (193«8°C) in the
Tq - x locus, as calculated from the correlation, occurs at
79*7 mole$ n-pentane.
The interaction critical pressure PCji2 was also taken as the arithmetic mean of the values calculated for each of the six mixtures. The calculated P - x curve shown in Figure 7 is nearly linear. The maximum deviation from the calculated curve is 1.7 psi (Table 4); this value is not much greater than the estimated effect (+1 psi) of mercury on the critical pressures. 35
TABLE 4
CORRELATION OP THE CRITICAL PROPERTIES
CRITICAL PARAMETERS
(11) (12) (22) n-pentane acetone— n-pentane acetone
Tc , °K 469.8(d >°) 456.5(b) 508.8 Po, psia 489.5 ^ 571.3(8 ) 684.8(°) V 0 j l/mole 0 .31l(°) (0.2894) 0 .213(°) Mole fraction ^ T c , A P C, Av ,(a) Sample n-pentane K psia 1/mole 21 0 .5141 +O.63 +0.05 -0.0055 26 0.5430 -0.03 +1.69 -0.0078 24 0.5967 +0.06 -0.01 -0.0117 23 0.6490 +0.11 +0.86 -0.0106 25 O .7188 -0.09 -0.70 - -0.0019 22 0.8003 -0.04 -1.31 o(a ) (a) In the case of critical volume the interaction parameter V^2 Is taken as the observed critical volume for Sample 22 (80.03 mole% n-pentane),... (b) Arithmetic mean of Values for the six mixtures. Kobe and Lynn (40) Beattie, Levine and Douslin (4l) PRESSURE, psia the oritical pressure loous.) pressure oritical the (The corresponding temperatures are marked along marked are temperatures corresponding (The /^ m ?Ure ^h® Azeotropio Locus on the P-x Plane P-x the on Locus Azeotropio ^h® /^m?Ure 700 0 0 6 0 0 4 0 0 5 200 0 0 3 , OE RCfN n-PENTANE FRACTfON MOLE X, 2 6 OB Q6 4 0 02 RTCL RSUE LOCUS PRESSURE CRITICAL , TI WORK THIS 0,0 a BROWN AZEOTROPES LOCUS OF OF LOCUS 19426 180 36 * 37 The quadratic relationship was applied to the critical volumes, although it is recognized that the V_c - x locus is not quadratic. The value of Vc 12 was taken as the observed critical volume for Sample 22 (80.03 mole$ n-pentane). As shown in Figure 8 the V„ - x locus appears to be composed of two smooth curves which intersect at 62-63 mole$ n-pentane, that is, at about the same composition at which the critical locus intersects the azeotropic locus. No simple scheme appears feasible for establishing a quantitative relationship between volume and composition. The azeotropic locus. The pressure and composition of the azeotrope at a given temperature was located by applying the Gibbs-Konowalow law: for both the dew and bubble lines on a P - x plot, the slopes (dP/0x)T must be zero at the value (P,x) at which the azeotrope forms at a given temperature. The P - x plot with temperature as the parameter is shown in Figure 11, along with the critical pressure locus. The dew lines show the maxima characteristic of a positive azeotrope, while the bubble lines tend to collapse toward the dew lines at these maxima. The azeotropic composition is taken as the point of zero slope of the dew line; the azeotropic pressure is taken as the mean of the dew and bubble pressures. Values of temperature, pressure, and composition so determined are given in Table 5* Othmer and Ten Eyke (^2) showed that the azeotropic locus can be correlated by plotting the logarithm of azeotropic pressure against the logarithm of the composition. As shown in Figure 12, this correlation produces a straight- line plot on which is also shown the critical pressure- composition locus. The solid point at 0.797 mole fraction n-pentane corresponds to the minimum in the Tq - x locus. Thus, for the system acetone— n-pentane, the azeotropic locus does not intersect the critical locus at the composition of minimum critical temperature. In the past, there has been some confusion in this regard, possibly stemming from Rowlinson's (4-3) valid observation that, although not a thermodynamic necessity, "...positive critical azeotropy is generally associated with a minimum in the critical temperature on a (Tc ,x) graph..." This is an observation on the probable existence of a positive azeotrope, but does not serve to establish its location. TABLE 5 THE AZEOTROPIC LOCUS FOR THE ACETONE— n-PENTANE SYSTEM Temperature, Pressure, x, mole fraction °C psia n-pentane 196-196.2a 556 0.621 195 54-7 0.623 192.5 526 0.625 190 507 0.629 185 470 0.635 180 4-34- 0.64-0 175 4-00 0.64-6 170 370 0.652 aEstimated for Intersection of azeotropic locus with critical pressure locus. 39 700 6 0 0 critical locus 5 0 0 p azeotropic locus 400 300 2Q0I 150 10 0 9 0.8 0,7 0.6 0 5 0 4 X, MOLE FRACTION n-PENTANE Figure 12. The Azeotropic Loous on the log P— log x Plane* (The solid point at 0*8 mole fraction n-pentane is the minimum point in the T0-x locus.) 40 The linear correlation, which has the same form as the Clapeyron equation for a one-component system, is shown in the plot of the logarithm of pressure against reciprocal absolute temperature, Figure 13. Obviously, then, a plot of the logarithm of composition against reciprocal absolute temperature should also be linear, as shown in the bottom portion of Figure 13. In summary, therefore, it has been established that the system acetone— n-pentane forms an azeotrope in the critical region, and that the azeotropic locus does not intersect the critical locus at its point of minimum temperature. Volumetric behavior The experimental pressure-volume isotherms have been smoothed by computing by least-squares the coefficients of the polynomial -m, • W Z - PV/ET = 0 The choice of the order m of polynomial used to represent a given set of data rests with the experimenter. This choice is quite beyond the theory of least squares, and so is somewhat arbitrary. The following considerations entered into the final choice of polynomial for each isotherm. All the data were plotted in order to remove obviously bad points caused by mistakes in observation. The IBM 7094 computer was programmed to produce in succession the least-squares polynomials for orders from zero through ten. In examining these fits, the order was considered too I LOG X LOG Patm. 19 .1 0 18 .1 0 020 Q21 150 Dependence of P and x upon- x P and of Loousi Dependence TheT Azeotropic 13* Figure 10/ - 2 - ) (1000/T .3 0 low If there was a marked trend in the deviations (observed- calculated values). For example, such a trend would result if a linear polynomial were fitted to a set of data which followed a quadratic physical law. The-order was considered too high if the sample estimate of the variance of the fit was not significantly lower than that for the next-lowest- order polynomial. In other words, one chooses the lowest order polynomial that gives an adequate fit. For the first two isotherms measured in this work, the best fits were more complex than required by the physical situation. These two isotherms were discarded as a matter of judgment because of excessive noise in the data sets. The experimental procedure was adjusted, with subsequent improvement in the results. The constants in the polynomials for the isotherms for each mixture are presented in Tables 6 through 11. The polynomials serve only as an interpolation device; extrapolation does not have any physical meaning. The constants for a given polynomial do not bear any necessary relationship to the virial coefficients or to constants in any other equation of state. TABLE 6 LEAST-SQUARES CONSTANTS FOR THE ISOTHERMS: SAMPLE 21 (51.41 MOLE PERCENT n-PENTANE) Type Vapor Vapor Crit. Crit. Fluid Fluid Fluid Vapor liquid t,°C 190.02 195.02 199.83 199.83 205.04- 215.00 230.02 ao 1.02492 1.02568 1.02587 0.58272 1.024-96 1.0224-8 1.02354- ”al 0 .3860? 0.37379 0.36547 0.17200 0.35168 0.33065 0.31526 a2xl01= 0.49379 0.46805 0.4-3309 0.57002 0.34-729 0.334-85 0.4-5779 a^xl02= — — 0.30852 -1.3134-2 0.86156 0.7054-5 -0.204-37 a^xl02= —— -0.08164 0.11214- -0.25666 -0.21823 — i — — a^xlo3= — — 0.19903 0.17551 s2xl0+8 18.7 9.7 6.0 16.9 23.2 14-.3 20.4 s xlO^ 4.3 3.1 2.4 4-.1 4.8 3.8 4.5 2s xlO^ 8.6 6.2 4. 8 8.2 10.6 7.6 9.0 Vj O TABLE 7 LEAST-SQUARES CONSTANTS FOR THE ISOTHERMS: SAMPLE 22 (80.03 MOLE PERCENT n-PENTANE) Type Vapor Vapor Crit. Crit. Fluid Fluid Fluid vapor liquid o ■p o \ # 180.05 190.02 193.91 193.91 205.04 215.00 230.02 ao 1.00539 1.00504 1.00534 1.12981 1.00307 1.00421 1.00068 "al 0 .40409 0.38496 0.37244 0.68350 0.34369 0.32812 0.29541 a2xl0 0.51144 0.50590 0.40805 2.34968 0.26913 0.27313 0.19304 a3Xl02 — \ 0.54679 -4.18226 1.37916 1.23044 1.14129 a^xlQ2 —— -0.11421 0.29484 -0.38972 -0.35841 -0.20828 a^xlO-^ ——— — 0.32356 0.30699 — s2xl08 14.0 3.5 17.0 25.6 10.9 26.7 6.7 s xlO^ 3-7 4.1 5.1 3.3 5.2 2.6 2s xlO^ 7*4 3.8 8.2 10.2 6.6 10.4 5.2 -r TABLE 8 LEAST-SQUARES CONSTANTS FOR THE ISOTHERMS: SAMPLE 23 (64.90 MOLE PERCENT n-PENTANE) Type Vapor Vapor Vapor Crit. Fluid Fluid Fluid vapor t, °c 130.02 170.01 190.02 195.50 200.03 215.00 230.03 ao 1.01772 1.01802 1.01772 1.01741 1.01650 1.01740 1.01697 “al 0.53479 0.42785 0.38686 0.37816 0.36057 0.34213 0.31541 a2Xl01= 0.51761 0.54037 0.54445 0.56324 0.41100 0.53849 0.47276 a^xlO^= — -0.15524 -0.24136 0.59361 -0.40710 -0.21254 a^xl02= — .— — — -0.20157 — — a^xl(P= — — — — 0.16016 —— s2xl08 4.1 3.1 10.0 2.6 13.5 18.7 9.8 s xlO^ 2.0 1.8 3.2 1.6 3.7 4.3 3.1 2s xlO^ 4.0 3.6 6.4 3.2 7.4 8.6 6.2 -P- 46 TABLE 9 LEAST-SQUARES CONSTANTS FOR THE ISOTHERMS: SAMPLE 24 (59*67 MOLE PERCENT n-PENTANE) Type Vapor Vapor Crit. Fluid vapor t, °C 130.02 170.00 196.65 230.02 ao 1.01959 1.01871 1.01931 1.01995 0.31548 "al 0.54236 0.42477 0.37197 a 2X10'1' 0.68581 0.52848 0.53067 0.47417 a^xlO2 — -0.18879 -0.22426 s^xlO^ 2.7 9.6 32.6 2.2 s xlO^ 1.7 3.1 5.7 1.5 2s xlO^ 3.4 6.2 11.4 3.0 ^7 TABLE 10 LEAST-SQUABES CONSTANTS FOR THE ISOTHERMS: SAMPLE 25 (?1.88 MOLE PERCENT n-PENTANE) Type Vapor Vapor Crit. Fluid vapor t, °C 129.98 170.04 194.26 230.01 ao 1.02297 1.02145 1.02095 1.02177 ’al 0.55442 0.43625 0.38312 0.32200 a2xl01 0.73084 0.57582 0.54147 0.49364 a-^xlO2 — — -0.14170 -0.23223 s2xlO® 3.0 8.4 7.7 3.7 s xlO^ 1.7 2.9 2.8 1.9 2s xlO^ 3.4 5.8 5.6 3.8 il-8 TABLE 11 LEAST-SQUARES CONSTANTS FOR THE ISOTHERMS: SAMPLE 2 6 (5^.30 MOLE PERCENT n-PENTANE) Type Vapor Vapor Crit. Fluid vapor t, °C 130.00 170.00 198.15 230.00 ao 1.03038 1.02905 1.028*1-3 1.02937 "al 0.568^3 0.^087 0. 37^88 0.32119 a£XlO+1= 1.0125 0.7167^' 0.52868 0.48^97 a^xl02= ■ 0.16669 •0.23907 s2 xlO8 1.8 5.6 15.8 17.8 s xlO^ 1.^ 2.k J+.O ^.2 2s xlO^ 2.8 k.Q 8.0 8.^ CHAPTER VII DEVELOPMENT OF AN ENERGY PARAMETER The differential of the energy of a system of constant mass and constant composition which is subjected to no external forces other than pressure is given by (5) oLE = T**5> - Pd.V For an isothermal process at constant composition, (6) (3E/av)T = T (d s /3 v)T - p The Maxwell relation derived from the differential "work function dA = -SdT - pdV is (?) ( a s / 8 v )r - O p / b t ) v Combination of (6) and (7) results in the so-called i thermodynamic equation of state: (6) Cze/ z>v ) t = t Cz p / z t ) * - p Equation (8) may be put in dimensionless form by multiplying both sides by (V/RT), and rearranging, to give (9) 560 = (d(E/er)/a£*vV)T + £ - (v/iz)@P/dT)v The function £(x) depends on the composition of the particular mixture to which it is applied. The right side can be expressed in terms of compressibility factor, Z= PV/RT. d-i ' (2x/dv)P>TM * Cdi/dP)Tyd.P + fa /d r)^ d r <10> (di/di)^ - Oi/»r)Ti„ (zp/ar)', + (V//Zr)(2p/2r)v - z / r Hence, (11) 5T)v - £ + t (2z/2>tX k 9 50 j Equation 11 may be written in terms of reduced temperature (Tr = T/Tc ) and reduced density (Dr = D/Dc): (12) EM ~ H (d2/dT«,)D^ If the slopes of the Z - Tr isochors are evaluated at the point of intersection of the isochor with the saturation line, then Z and Tr assume saturation values: (13) 2 ^ , 6 0 = The slopes of the Z - T^jr isochors at the intersections with the border curve are required for calculation of the energy derivative. Figure (1^) shows the Z - Tr isochors for Sample 22 (80.03 mole^ n-pentane), as an example of the relations found for each of the mixtures. Plots for all six mixtures and for pure n-pentane were constructed as follows. A. value of reduced density for a particular isochor was chosen. The value of the saturation compressibility factor Z_ was read from a large-scale plot of Zg vs. Drg. The value of Trg corresponding to the value of Zs was read from the Zg - Trg border curve. Values of Z in the single-phase regionjwere taken either from computer tabulations calculated from the least-squares fits for the isotherms, or from large-scale plots of the Z - D isotherms which were prepared from the least-squares fits. In Figure (1^), the isochors at reduced densities greater than 1.5 appear to cross into the two-phase region enclosed by the Z - Tr border curve, and also appear to / i COMPRESSIBILITY FACTOR, Z*PV/RT 0.0 06 Q.4 1.0 line — line bubble, bubble, Figure Z - Tr1^. 9 1.05 095 (80*03 Hole Peroent n-Pentane) Peroent Hole (80*03 EUE TMEAUE T/Tc TEMPERATURE, REDUCED o BORDER CURVE, ex p e rim e n ta l points points l ta n e rim e p ex CURVE, BORDER o a 1.00 SCOE, acltd points calculated ISOCHORES, Isoohors for Sample Sample for Isoohors h ^15 13— 11.6 11.6 22 07 0.3 08 09 ca A O 06 05 ___ 51 1.10 52 intersect isochors of lower density. This behavior has been verified by calculating Z and Tr from a large-scale plot of the P - T isochors, none of which intersect other isochors or appear to cross the two-phase region. This behavior arises because the isochors and border curve are the projections onto the Z - Tr plane of curves which are actually on a multidimensional surface. The isochors for pure n-pentane also behaved in this manner. Young, (26) and Hose-Innes and Young, (2?) published extensive measurements of the border curve and isotherms of pure n-pentane. Included in this work were the isochors, obtained by cross-plotting the isotherms. These authors used an experimental apparatus similar to that used for the present work. The data of Rose-Innes and Young for n-pentane were taken for the pure reference component. These data were treated in a fashion identical to the method, used for the six binary mixtures of acetone— n-pentane. For each isochor, the coefficients of a quadratic polynomial were computed by solving three simultaneous equations of the form: ( i k ) 2 * & o + + 4 -a T f t The slope of the isochor is calculated from the quadratic: (15) = The point on the border curve (Z-jT*,-,)o X o was always taken as one of the three points used to calculate the constants in equation (1*0. The Z - Tr isochors at and near the critical 53 density for samples 21 and 22 are linear within the experi mental error. For samples 23j 25 and 26, the isochors were assumed to be linear in the critical region, because only two widely-separated points were available. For sample 2^, the isochors above a reduced density of 0.75 are not available. Values of the energy derivative £(x) given in Table 12 were calculated from equation (13). The maximum deviation of the values of the energy derivative at the critical density from the mean value 1.9^ is about one percent. Figure 15 is a smoothed plot of these calculated values for the six mixtures and for pure n-pentane. An integral energy parameter was calculated from the energy derivative, ^.(x). Integration is a linear operation, so that (l6) = E(*) where A€(x)= EO) is the energy derivative for pure n-pentane. The calculated values of Ag(x) are given in Table 13> and are plotted in Figure 16. The integrals for A£(x) and m were calculated by applying Simpson's rule over a succession of small increments of the independent variable, Dr . Values of the integral energy parameter £ 60 ' calculated from equation 17 are given for the six mixtures in Table 1^+. It is remarkable that although the border curves for the six binary mixtures, Figures k and 5* vary widely, 54 TABLE 12 CALCULATED VALUES OF THE ENERGY DERIVATIVE Sample 21 26 24 23 25 22 Mole % 51.^1 54.30 59.67 64.90 71.88 80.03 100. n-pentane Dr ENERGY DERIVATIVE, S(x) 0.1 1.183 1.290 1.290 1.214 1.192 1.176 1.116 0.2 1.361 1.521 1.521 1.416 1.377 1.342 1.328 0.3 1.533 1.687 1.687 1.607 1.552 1.502 1.481 0.4 1.700 1.821 1.821 1.792 1.715 1.653 1.627 0.5 1.857 1.934 1.934 1.962 1.873 1.793 1.767 0.55 1.933 1.960 1.960 2.044 1.903 1.849 1.827 0.6 2.010 1.942 1.942 2.109 1.868 1.896 1.876 0.-65 2.072 1.890 1.890 2.130 1.820 1.931 1.912 0.7 2.110 1.859 1.859 2.112 1.802 1.952 1.937 0.75 2.121 1.860 1.860 2.072 1.803 1.961 1.948 0.8 2.093 1.867 - 2.026 1.820 1.962 1.951 0.85 2.038 1.886 - 1.990 1.847 1.960 1.950 0.9 1.985 1.905 - 1.960 1.878 1.950 1.945 0.95 1.963 1.925 - 1.940 1.901 1.938 1.940 1.0 1.946 1.947 - 1.930 1.920 1.930 1*935 I .05 1.950 1.963 _ 1.930 1.930 1.930 1.932 1.1 1.963 1.982 - 1.950 1.940 1.940 1.942 1.15 1.985 2.018 - 1.986 - 1.955 1.960 1.2 2.027 - - 2.033 - 1.980 2.000 1.3 2.140 -- 2.160 - 2.078 2.117 1.4 2.296 - - 2.320 - 2.230 2.272 1.5 2.490 -- - - 2.425 2.465 1.6 2.715 -- - - 2.657 2.693 Energy Derivative»6 (x) ■ £ 4 + "I**, [Cae/aTJ] 2.0 1.0 1.6 22 IB Figure 15* Energy Derivative as a Function of Reduced Density Reduced of a Function as Derivative Energy 15* Figure * Pentane 4 0 6 0 23 25 eue est, D. Density, Reduced Reduced OB 24 ends 24 1.0 25 ends 25 .2 1 a ple Sam 21 22 TCPSrtdrSrx/22 n-Pentane 1.6 Mole % 56 TABLE 13 CALCULATED VALUES OP THE FUNCTION A £(*) Sample 21 26 24 23 25 22_ . Mole % 51.41 54.30 59.67 64.90 71.88 80.03 n-pentane Dr A"6(x) = &(*) - £(l) 0.1 0.017 .124 .124 .048 .026 .010 0.2 .033 .193 .193 .088 .049 .014 0.3 .052 .206 .206 .126 .071 .021 0.4 .073 .194 .194 .165 .088 .026 0.5 .090 .167 .167 .195 .106 .026 0.55 .106 .133 .133 .217 .076 .022 0.6 .134 . 066 .066 .233 -.008 .020 0.65 .160 -.022 -.022 .218 -.092 .019 0.7 .173 -.078 -.078 .175 --*135 .015 0.75 .173 -.088 -.088 .124 -.145 .013 0.8 .142 -. 064 - .075 -.131 .011 0.85 .088 -.040 - .040 -.103 .010 0.9 .040 -.015 - .015 -.067 .005 0.95 .023 .012 - 0 -.039 -.002 i-n 0 0 0 0 1 1 • 1.0 .011 .031 - • -.015 1.05 .018 .040 -.002 -.002 -.002 1.1 .021 .058 - .008 -.002 -.002 1.15 .025 ' - - .026 - -.00 5 1.2 .027 - - .033 - -.020 1.3 .023 - - .043 - -.039 1.4 .024 - - .048 - -.042 1.5 .02 5 - - -- -.040 1.6 .022 - - - - -.036 -02 a - A5. ■ £ ( ) - SCO .1 0 02 CX1 iue1. ^() saFnto fRdcdDniy (h sml composi sample (The Density. Reduced of Function a as A^»(x) 16. Figure in i oepretnpnaeaea flos 2, 1^$ 2, 80.03$, 22, 51.^1$, 21, follows: as are n-pentane percent mole in tions 3 61*.90$;23, 02 2k, 59'. 5 2 67 $; 25, 71.88$; and and 71.88$; 25, $; eue est, Dr Density, Beduced OJa i .8 0 23 ends 25 26 , 1.0 5k. 30$). 1^4 23 1.6 22 j\ V ->3 58 TABLE 14 CALCULATED VALUES OF THE INTEGRAL ENERGY PARAMETER, £(x) Sample 21 26 24 23 25 22 Mole % 51.41 54.30 59.67 64.90 71.88 80.03 100 n-pentane Dr g(x) • f 0 0 0 0 0 0 0 0 0.1 0.11 0.12 0.12 0.11 0.11 0.11 0.11 0.2 .24 .26 .26 .24 .24 .24 .23 0.3 .38 .42 .42 •39 • 38 .38 .37 0.4 .54 .59 .59 .56 .55 .53 .53 0.5 .72 .78 .78 .75 .73 .71 .70 0.6 .91 .98 .98 .95 .92 .89 .88 0.7 1.12 1.16 1.16 1.17 1.10 1.08 1.07 0.8 1.33 1.35 - 1.37 1.28 1.28 1.27 0.9 1.54 1.54 - 1.57 1.46 1.48 1.46 1.0 1.73 1.73 - 1.77 1.65 1.67 1.66 1.1 1.93 1.93 - 1.96 I .85 1.86 1.85 1.2 2.13 — - 2.16 - 2.06 2.05 1.3 2.33 - - 2.37 - 2.26 2.25 1.4 2.56 - - 2.59 - 2.48 2.47 1*5 2.79 - - - ' - 2.71 2.71 1.6 3.05 - - - - 2.96 2.96 1.7 -—— -- 3.24 3.25 1.8 3.55 3.56 59 there is not a correspondingly large variation in the energy parameter with composition at constant reduced density, as shorn in Figure 17. For the curve at Dp =1.0, a weak maximum appears to exist in the neighborhood of the azeotropic composition (62.1 mole,^ n-pentane). This weak maximum tends toward lower n-pentane composition as the density decreases, so that the location of the maximum appears to follow the trend of the azeotopic locus. In addition, the size of the maximum decreases with decreasing density. It is not possible to estimate the location of the maximum above the critical isochor (Dr = 1.0). On the basis of these calculations, there may be a unique configuration at the azeotropic composition. Because of the uncertainty in the volume measurement, which is amplified by the need to compute derivatives of isochors calculated from the measured isotherms, the uncertainty in the calculated values of the energy parameter £(A is probably of the same order of magnitude as the trend in the curve at Dr = 1.0. It appears that volume measurements one to two orders of magnitude more precise than those made in this—work will be necessary to provide a definitive answer to this question. Integral Energy Parameter, E(x) .o 2.0 1.0 0.5 Composition at Constant Reduced Density Reduced Constant at Composition Figure 17. Energy Parameter as a Function of Function a as Parameter Energy 17. Figure -o- 0.6 -o . oe rcin n-pentane fraction Mole x. . 0.8 0.7 a ! ' 0.9 1.0 .2 0 4 40.7 .9 0 4 40.8 .0 1 4 41.1 412 O Os CHAPTER VIII CONCLUSIONS The pressure-volume isotherms and phase behavior were determined for the binary system acetone— n-pentane at six compositions from 51*^1 to 80.03 mole percent n- pentane. Pressures varied between 75-1000 psia, for corresponding temperatures between 130-230°C. The temperatures are accurate to +0.05°C, while the pressures are claimed to be at least as accurate as +0.35 psi for all data, exclusive of the effects of mercury. The effect of mercury on the observed pressure was estimated to be approximately +1.0 psi at the critical density. The dew and bubble points for all mixtures were located with demonstrated reproducibility. The bubble lines and critical points follow a trend, as do all the dew lines except that for the mixture at 71*88 mole percent n-pentane. This anomalous dew line was verified. The critical temperatures and pressures are correlated with composition by a quadratic function in which an interaction critical property was given,an arithmetic mean value. The calculated minimum in the critical tempera ture locus occurs at 79*7 mole percent n-pentane at 193•8°C. The critical pressure locus does not display an extreme value. The critical volume-composition locus is composed of two curves which appear to intersect at the composition of the critical azeotrope. 61 62 The system acetone— n-pentane forms an azeotrope in the critical region. Furthermore, the azeotropic locus does not intersect the critical locus at its point of minimum temperature. The pressure-volume isotherms were smoothed by computing the least-squares coefficients of a polynomial for compressibility factor as a function of density. These polynomials were used for purposes of interpolation; the coefficients do not bear any necessary relationship to virial coefficients or to the coefficients in any other equation of state. An energy derivative based on the thermodjmamic equation of state was evaluated along the border curve for all six mixtures and for pure n-pentane. Values of this dimensionless energy derivative at the critical point are nearly constant for the six mixtures and for the pure component n-pentane; the maximum deviation from the mean of the seven values is about one percent. An integral energy parameter, calculated from the energy derivative, showed a weak maximum with respect to composition at constant reduced density. Furthermore, this weak maximum tends toward lower concentrations of n-pentane as the density decreases, that is, the maximum appears to follow the azeotropic locus. Because of the uncertainty in the volume measurement, which is amplified by the procedure for calculating the integral energy parameter, the existence of a unique configuration at the azeotropic composition remains in doubt. Volume measurements one to two orders magnitude more precise than those made in this work will be required to settle this question. CHAPTER IX RECOMMENDATIONS The existence of a maximum value of the energy parameter coinciding with the locus of a positive azeotrope is still in doubt. An improved experiment will be required to settle the question. Isochors should be measured directly in an apparatus that does not contain mercury. Elimination of the mercury would remove the largest single source of inaccuracy in the pressure measurement. Measurement of the isochors directly would eliminate the uncertainty caused by calculating the isochors from measured isotherms, as was done in this work. Volume measurements accurate to within one part in ten thousand are recommended rather than the three parts per thousand accuracy of volumes at the highest densities measured in this work. It is recommended that an azeotrope other than one. containing either acetone or an alcohol be investigated in the initial attempt at high-accuracy measurement of isochors in the critical region. Mixtures of paraffin hydrocarbons with the perfluoro-hydrocarbon derivatives are suggested, since for such a system both components would be highly stable at the necessarily high temperatures and pressures. 6l\ APPENDIX I PREPARATION OF PURE COMPONENTS 65 66 PREPARATION OF PURE COMPONENTS Source and preparation Phillips Research-grade normal-pentane (Phillips Petroleum Company, Bartlesville, Oklahoma), lot number 6, was used in this study. The stated purity was 99*8^ mole%, with isopentane (2-methyl butane) the major impurity. This material was distilled through a fresh silica-gel column to remove traces of water and oxidation products. The column effluent was collected in an evacuated glass bulb which was sealed off in vacuo, so that no contact with the atmosphere was possible. The glass bulb was then sealed directly to the vacuum loading train before the seal was broken. Reagent-grade acetone, conforming with American Chemical Society Code 100^, was purified by vacuum distillation at a reflux ratio of 9:1 in a four-foot tower packed with 1 /k in. glass helices. A heart-cut consisting of 15% of the initial still-pot charge was collected. Timmermans (37) has stated that distillation of acetone over CaCl2 is ineffective as a dehydrating procedure. Consequently, a portion of the freshly distilled heart-cut was immediately charged into flask (E), Figure 3» on the vacuum loading train. Degassing Procedure The "degassing" of a liquid sample held in the vacuum loading train is described in great detail by Skaates (^). The following description is given with Figure 3 as a basis. 67 The freshly distilled acetone was immediately charged to removable flask (E) on the loading train. The loading capillary (G) and sample tube yoke, (H) and (T), were shut off the manifold during this procedure. Manifold (M) was evacuated to stick vacuum with the valves at (E), (B) and (A) remaining closed. With a dry-ice/acetone bath under the freshly installed liquid acetone at (E) and the valve at the left of the manifold open to vacuum, the valve at (E) was opened for 15-30 seconds, then closed again. The light impurities and dissolved gases were the first to distill from flask (E) to the liquid nitrogen trap (N). The valve to the vacuum pump was closed to permit transfer of the acetone into (B). During the first few distillations, the first material to condense was a slushy solid, which was then distilled to trap (N). The last few drops of liquid in (E), which presumably contain heavy impurities, were distilled to trap (N) for discard. This procedure was repeated, transferring the liquid from (B) to (E), until a liquid remained which did not form a ‘•slushy" phase on first condensing and which vaporized smoothly and quietly without bumping. After 25 to 30 transfers, approximately half of the initial charge remained. This purified liquid acetone was stored in flask (B) which was always immersed in a dewar of crushed dry ice in acetone. Aluminum foil was used to shield the liquid from direct light. 68 The degassing of the n-pentane was the same as for the acetone, with the following exceptions: 1) The sealed ampoule of purified--n-pentane was welded to the right end of manifold (M), Figure 3» before the break-seal was fractured. 2) No slushy material was formed during initial condensation. The purified liquid n-pentane was stored in flask (A) in a dry-ice/acetone bath. Flask (A) was shielded from light with aluminum foil. APPENDIX II VOLUME CALIBRATION "s 69 70 VOLUME CALIBRATION It was essential to this experiment to have accurate volume calibrations for two precision-bore pyrex glass capillary tubes: (1) the loading capillary, used to estimate the mass of each component, and (2) the experimental tube, in which the binary mixture was confined during the experiment. The calibration procedure was the same for both tubes. The capillary was first cleaned carefully with chromic acid cleaning solution, followed by a water rinse, an alcoholic-KOH rinse, a distilled-x^ater rinse, an acetone rinse, and a final rinse with fresh, reagent-grade ethyl ether. The capillary was then installed on the vacuum loading train (Figure 2), pumped down to stick vacuum, then filled with freshly distilled mercury; evacuation before filling prevented entrapment of tiny air bubbles between the mercury column and the tube wall. The cleaning and filling operations were repeated until a continuous, mirror-like column of mercury filled the bore of the capillary. The tube was then clamped in a vertical position, as shown in Figure 18, closed end down. The distance, H, between the outer surface of the closed end of the tube and the high point of the mercury meniscus, at the longitudinal axis of the capillary, was measured with a high-precision ten- centimeter cathetometer (Gaertner Company, Model M9L0-3^2 with Ml01At microscope), which gave reproducible readings to within +0.0002 cm. At the same time, the height of the mercury meniscus, Hm in Figure 18, was measured. These measurements were performed in a windowless room maintained at constant temperature and constant humidity. Ambient temperature was read from a mercury thermometer hanging next to the capillary being calibrated. It was necessary to maintain invariant lighting conditions for reproducible measurements of the length of mercury column. A flourescent lamp, covered with green cellophane, and placed directly behind the tube, permitted the most consistant readings. A small amount of mercury was carefully removed from the capillary into a clean, tared weighing bottle. The bottle was weighed on a beam-rider analytical balance, sensitive and reproducible to less than 0.05 The above process of measuring the height of the mercury column, removing mercury and weighing was repeated until all the mercury had been removed. The final weighing represented the total mass of mercury present when the height of column was first measured at the start of the process. The result was a coordinated set of readings of height, H; meniscus height, Hm ; mass of mercury, W; and ambient temperature. These data were used to compute the level volume, VL , defined as the actual volume of the mercury present plus the volume of the mercury meniscus complement, V_.c The latter was taken as the volume between a plane perpendicular 72 m Figure 18. Calibration of Glass Capillary Tube 73 to the longitudinal capillary axis and tangent to the highest point on the meniscus, and the concave (downward) mercury surface, as shown in Figure 18. The shape of the mercury surface appeared in all cases to be a section of a sphere, with a contact angle of approximately 1^0°. For a precision-bore capillary, the level volume is nearly a linear function of distance: (17) VL = a + bH = VHg + V0 where constants a and b are determined by a least-squares procedure. The volume complement is given by the relationship: (18) where 7Zr = b, the mean cross-sectional area of the tube bore. Combining and rearranging equations (17) and (18) gives the following result: (i9) Cv^ - tc u £ / t > ) = The dependent variable (VHg - HmV 6 ) is linear in.the independent variable (H - Iim/2). The advantage gained by fitting this particular form lies in avoiding an a priori estimate of the meniscus volume complement, which depends on the (unknown) value of the mean cross-sectional area of the tube. The volume of liquid mercury, VHg , was computed from the density-temperature relationship given in (4-5)* Constants a and b were calculated by a least-squares procedure on an IBM 1620 digital computer. The program in FORTRAN language is available for use. For the sample tube, the value of H exceeded the 10-cm. range of the precision cathetometer, so that it was necessary to compute H by slimming a set of distances between reference marks less than 10 cm. apart. The computed results showed a slight trend in the deviations of the single measurements from the least-squares linear fit. Except for the lower (large-bore) section of the sample tube, this trend was masked by the uncertainty inherent in the experiment for which the calibration was used. A small calibration correction was applied to the large-bore section of the sample tube. The calculated values of constants a and b for equation (19) are presented in Table 15 for the loading capillary and for the upper and lower sections of the experimental tube. The estimates of the confidence limits for both a and b show the interval within which repeated sets of measurements of a and b would tend to fall 19 times in every 20. The variance, proportional to the mean-square error, is a measure of the internal consistency, or noise-level, of a given set of data; standard deviation (the square root of the variance) is the root-mean-square error. Some investigators define the precision of a cali bration as being twice the standard deviation. In the region where the upper and lower sections of the experimental tube were welded together, neither calibration holds, so that no volume may be computed. The calibration of the upper (small-bore) section holds for values of H from 3 to 1^.9 cm.; for the lower (large-bore) section, the calibration holds for H from 18.2 to 33 cm. 76 TABLE 15 VALUES OF THE VOLUME-CALIBRATION CONSTANTS VL = a + bH, cm3 Loading Experimental Tube Capillary small-* large-** bore bore section section value of a -0.002179 -0.01353 -2.10617 {95%) +0..000008 +0.00012 +0 .00134 value of b 0.007805 0.031021 0.162393 (95%) +0.000003 +0.000021 +0.000051 variance, s^ 49 x 10”12 1 x 10“8 7 X 10"8 standard 1, 11 deviation, s 7 x 10 ° 1 x 10“4 3 x 10-^ precision,, 2s lk x 10“6 2 x lO"1*' 6 x 10-2* The calibration for the small-bore section of the experimental tube holds for values of H between 3 and 1^.9 om. **The calibration of the large-bore section of the experimental tube holds for values of H between 18.2 and 33 om* APPENDIX III CALCULATION OF SAMPLE COMPOSITION 77 78 CALCULATION OF SAMPLE COMPOSITION The calculation of the composition of the acetone-- n-pentane mixtures was arranged so that during the loading procedure the experimenter could make minor adjustments to approach some preselected composition. Reference is made to Figure 3j the schematic diagram of the loading train. The mass of component trapped in loading capillary (C) is the sum of the masses of liquid and vapor; (20) * m ( l) + n i (g) where (L) and (g) indicate liquid and vapor, and n is gram- moles of component i. Now (21) n where v is volume, d is density, M is molecular weight. For the vapor, (22) yii (g) * (v c -vt (Pi) ( pi /r t ) where K is the total volume of the loading capillary enclosed by the two stopcocks, p^ is the vapor pressure of the liquid at the ice point, and T is the temperature of the vapor, assumed to be the ambient temperature. For convenience, let Tfci • pi Ir .T <«> M = C a / m ) * Kl * 7l| + Tlj, Then, (2*0 Xikl* n<; = (K.- ^ A))T- + Zi Vi A) = KTi- (Zc-WiXvUO) 79 The volume of liquid, v^(L), is the sum of the level volume (obtained from the capillary calibration and the measured height of the liquid column, E) and the-volume of the liquid meniscus: (25) K; 3 (a+'H’ft) + yc ' (&+ Vo)i +4-Hi - a/+4 Hi where a and b are the constants in the calibration, and Vq is the meniscus volume. Combining equation (25) with (2^). gives •*W * [KTi - CdU -T,-)] - [4 (ic -ir^] Hi (2 6 ) = Qi - U Hi =• For a desired sample size (N) and mole fraction (x^) for the first component, the desired height of liquid column, is given by (27) Ha, - CQ/L>)a, The actual value of H„ measured during the loading procedure, Si I Ha , is rarely exactly equal to Hs . The moles of component a actually present becomes (28) 71 (29) H f r c u * where n^ is the moles of component b which will yield the desired composition in a sample of N moles total. Therefore the desired height of liquid column for component b is (30) % = - (xi./xa.) (n i /u^) 80 Again, the actual value rarely coincides with the desired value H"b, so that the actual moles of component b are given by (31) = Q jr - Finally, the actual total moles of mixture N', and the actual mole fractions are given by s j * tlq, yi/<£ ° 2) Xo,-- K / h J ; Xir- /hi In order to compute the constants Qj_ and one assumes an ambient temperature of 25°C; any actual room temperature in the range 20-30°C is within the experimental error. The results of this calculation are summarized in Table (16). The computed sample sizes and mole fractions for the six mixtures studied in this work are given in Table (17). 81 TABLE 16 CALCULATED VALUES OP THE LOADING PARAMETERS Volume Calibration: K = O.8893 cm3 a = -0.002179 ±0.000008 at 95% confidence level b = +0.007805 +0.000003 at 95% confidence level acetone n-pentane Physical Properties: V„, meniscus volume, cm3 0.000120 0.000156 d , gm/cm3 0.81250 0.64539 M, molecular weight 58.08 72.15 d = d/M 0.013989 O.OO8945 TT = P0/RT, 25°C 3.72X10"6 9.855x10“' Ktt 3.35xl0"6 8 .86xl0"6 rr - d -0.013985 -0.0089360 Loading Parameters: a* = a + VG -0.002050 -0.002062 a* ( t t - d) +2.8669x10“3 +1.8426x10 Q = Krr ■ a'(tr - d) -2.532x 10"3 -0.9563x10 U = b (tt - d) 10.915x 10“3 -6.97^5*10 TABLE 17 COMPOSITIONS OP THE SIX MIXTURES OP ACETONE— n-PENTANE --N x 103, mole percents mixture mg-moles acetone n-pentane 21 .5025 4-8.59 51.4-1 22 .5154- 19.97 80.03 23 .4953 35.10 64-.90 24- .4760 4-0.33 59.67 25 .4-873 28.12 71.88 26 .3704- 4-5.70 54-. 30 APPENDIX IV DETAILS OF EXPERIMENTAL PROCEDURE 83 DETAILS OF EXPERIMENTAL PROCEDURE The apparatus shown schematically in Figure 2 was used to determine dew, bubble and critical points as well as to establish the P - V isotherms. Determination of volumes both of the saturated states and of the superheated vapor at low pressures, in a single sample loading, required a dual-bore experimental tube as shown in Figure 1. With this- tube, a sample of approximately one-half milligram-mole j permitted the phase behavior to be determined in the upper 2 mm. section, while pressures down to approximately six atmospheres were accomodated by the lower 5 nun* section. The pure materials used in the vapor jacket to maintain constanti temperature at a given level were diethyl oxalate (130°C), naphthalene (170° - 215°C), and diphenyl ether (230°C). These materials were chosen because the vapor jacket could be operated smoothly from 20 cm. Hg absolute up to atmospheric pressure. After the startup period required to adjust the vapor bath, the sample was expanded until a pressure was obtained about 5-10 psi below the pressure desired for the first point to be measured. Vigorous stirring was required to attain equilibrium with respect both to temperature and to saturation of the sample with mercury; 30 - 60 minutes was usually sufficient. In general, the points were taken in increasing order of pressure at a given temperature, and of increasing temperature. 85 After the desired conditions for a particular point were established, a set of readings were taken which permit calculation of pressure, volume, and temperature; details are given in Appendix V. Determination of a border curve Establishment of the boundary of the region in which two phases may coexist in equilibrium involves visual determination of dew, bubble and critical points. Visual determination means that for each of the three types of points there exists a specific, reproducible physical configuration which is visible to the observer; in addition, two experienced observers tend to agree on the temperature and pressure (usually within 0.1 psi and 0.01°C) required to produce this recognizable configuration. Vigorous stirring of the sample was essential; sufficient time had to be allowed for the sample to reach equilibrium after any small change in pressure or temperature. Dew point. The dew point, or point at which condensed liquid first appeared in the vapor sample at a given temperature, was always approached from the single phase (vapor) region. Pressure was increased in small increments (usually 0.1 psi). Between increments, the sample was stirred vigorously. When a tiny black speck of liquid was just visible (with a magnifying glass) between the stirring ball and tube wall, the dew point was established, provided this configuration was reproducible and that a pressure decrease of no more than 0.1 psi was sufficient to cause the speck to vanish. In general, the determination of the dew point required several passes, as well as patience and experience; two hours were sometimes required to locate a single dew point. Since the pressure had to be increased to reach a dew point, best results were obtained when first a rough estimate of dew pressure was made, so that the pressure at the start of the search was near the true dew point. Nonetheless, more time was required to reach a true equilibrium dew point than a bubble point, which was located by decreasing the pressure. Bubble point. The bubble point, or point at which vapor first appeared in the liquid sample at a given temperature, was^always approached from the single-phase / / (liquid) region. Pressure was decreased in increments of 0.1 psi or less, with interspersed periods of stirring as for the dew point. The bubble point was defined as the pressure which will maintain the smallest bubble visible (with a magnifying glass) at the top of the sample tube provided that this configuration was reproducible and that a pressure increase of less than 0.1 psi, and usually less than 0.05 psi, would cause the bubble to vanish. While the determination of the bubble point usually required several passes, the process was faster than for a dew point, while at the same time the resulting bubble*’ line showed less scatter than the corresponding dew line. Critical point. The critical point is defined, in this laboratory to be the conditions of temperature and pressure which exist when the meniscus separating the liquid phase from the vapor phase first disappears, so that the resulting fluid seems to be entirely uniform and without the lines of optical refraction which indicate local density variations. These conditions invariably were accompanied by the "critical opalescence," viz., the sample takes on a hazy, foggy appearance as though the sample space were occupied by smoke. The color of the opalescent material varied from reddish-brown to pearl gray, depending upon the lighting conditions and the sample composition. The conditions by which the experimenter visually established the critical point were not as sharply defined as those for a dew or bubble point. For this reason, the location of the critical point appeared to depend on the manner in which it was approached, and also on the experience and finesse of the experimenter. In this laboratory it is standard procedure to approach the critical point from within the two-phase region. The approach to critical temperature was signaled by a marked flattening of the liquid-vapor phase boundary (meniscus) as the interfacial" tension decreased. Opalescence began within about a half degree centigrade of the critical temperature, and became more pronounced as temperature approached the critical. The final approach to critical conditions required making small increases in temperature, 88 0.01°C or less, while the pressure was carefully adjusted to maintain equality between the volume of the vapor phase and the volume of the liquid phase. Thus, the 50% quality line was followed until the smallest obtainable increment in pressure at the final temperature causes the phase boundary to vanish. The conditions of temperature and pressure found in this manner were reproducible to within 0.01°C and 0.1 psi, respectively. Another experienced experimenter was usually able to duplicate the location of the critical point within the same limits. This procedure gave reproducible results, whereas an approach to the critical point from outside the two-phase retion did not. Furthermore, much stirring was required. Since the specific heat at constant volume tends to increase sharply near the critical point, and reaches a large (but presumable finite) value at the critical point, sufficient time must be allowed to establish thermal and diffusional equilibrium. Volume equilibrium appeared to be quite slow and often lagged the disappearance of the meniscus by 5 to 10 minutes. Three or four hours was sometimes required to locate a critical point, particularly in the region near the point of intersection of the azeotropic locus with the critical locus. Determination of an isotherm The general statements made at the beginning of Appendix IV apply as well to the measurement of points on a 89 pressure-volume isotherm. The desired temperature was established and maintained. Manifold pressure x-jas regulated so that the dead-weight gage balanced at the desired pressure. Vigorous stirring of the sample hastened the approach to the equilibrium volume; this approach was followed by recording the level of the top of the mercury meniscus until the differences in a few successive readings show no further trend. The usual reading were taken to permit calculation of pressure, volume and temperature. Pressure was then slowly raised to the value desired for the next point. APPENDIX V CALCULATION OF TEMPERATURE, VOLUME AND PRESSURE 90 CALCULATION OF TEMPERATURE, VOLUME AND PRESSURE During the experiment the following were recorded for each point: run and' sample identification numbers; resistance of the resistance thermometer; five cathetometer levels (L-l through L^, Figure 19); pressure indicated by both the dead-weight gage and the bourdon gauge; cylinder temperature and residual oil head of the dead-weight gage; ambient temperature; and barometric pressure. The true values of temperature, volume, and pressure of the sample were calculated by the methods outlined below. A complete sample calculation is presented at the end of this appendix. Temperature The value of resistance taken from the recorder was converted to temperature by referring to a resistance- temperature table computed for an interval of 0.01°C. This table was calculated on the IBM 70^4- computer from the quadratic Callendar equation, using the three calibration constants. Volume The volume occupied by the sample consisted of the “level volume," VL , plus the volume complement of the mercury meniscus, minus the volume of the steel stirring ball. Since the calibration of the experimental tube was performed at room temperature and atmospheric pressure, the calibration was corrected for the effects of pressure and temperature distortions. Pressure stresses on a closed cylinder were sample v, mercury Figure 19* Sohematio Diagram of Meroury Heads 93 computed from the relationships presented by Comings (46), using the physical property data for 7740 Pyrex glass taken from Shand (47). At an internal pressure of 1000 psi, the volume strain for the experimental tube was on the order of 3 parts in 100,000; consequently this effect was ignored. The form of the volume calibration at room temperature is: (33) Vo - fro +'f r o H In the experimental apparatus at some elevated temperature t, (3^) l£ - <2* * -k H where is the length actually observed by the experimenter. Assuming glass to be an isotropic solid, we have / u = 1+u.e os) - 4 / A Cu/Lo)*' «*/&o where oC is the temperature coefficient of linear expansion for the glass, 9 is the temperature difference and L is any linear dimension. Thus equation 34 may be written: (36) vi|if «. - [ a * H t A similar relationship holds for the change of volume with temperature of the steel stirring ball: (3?) vs i / v 9tt> » ( l + / . s 6 ? The meniscus appeared to be a spherical segment, so that the meniscus volume complement at the mercury-organic phase interface is given by (38) Vc = ( x / C / z ) - ( t / 6 ) h £ U- 9^ The mean tube cross-section at t°C is given by b^. = bQ(l +*£9)^ so that (38) becomes (39) v0 = f a / z - G 'szit* J Therefore, the sample volume is (4*0) V = VL + vc - Vs, cm. 3 Pressure In this experiment a precision dead-weight piston gage (Ruska Instrument Corporation, Houston, Texas; Type 2^00 HL) was used as the primary means of measuring pressure of the nitrogen gas in manifold (M), Figure 2. A calibrated bourdon gauge (Heise Bourdon Tube Company, Newtown, Connecticut) was used to indicate the approximate manifold pressure. Calculation of the true absolute pressure on the sample involved: correcting the pressure indicated on the Ruska gage for temperature, pressure, residual oil heads in the gage, and local gravity; accounting for the effects of the mercury heads H^, Hc and in Figure (19); correcting for the pressure differences (due to surface tension) across the mercury interfaces in the experimental tube and the backleg chamber; correcting for the presence of the mercury vapor in the sample; and adding the local barometric pressure to the computed gage pressure. Dead-weight gage. The manufacturer*.s directions furnished with the dead-weight gage agreed with procedures presented by Johnson et al. (^8) and Gross (^9)» The pressure indicated by the Ruska gage, Pj_, is given by < 4 1 ) P£« ( tp ' + ?„) (A A' ) /gb 95 where P' is the.sum of the face values of the weights, PQ is the no-load pressure of the gage, (A0/A0 *) is an area ratio, g^ and gs are the local and standard values of gravitational acceleration. This indicated pressure was corrected for gage deformations caused by pressure and temperature, as well as for any residual oil head in the gage itself: (te) P= R; D- r > p<;Ui-Pr^-zo)l + w0 where P is the corrected gage pressure in psi, t is the temperature of the gage piston in °C, HQ is the residual oil head in psi, and P^. and F are constants dependent on the gage construction. No correction for the buoyancy of the weights was applied because introduction of an error of 1 part in 100,000 would require a change in barometric pressure of 6 cm. Hg. Corrections for the surface tension of the oil were accounted for in the design of the gage. Bourdon gauge. A calibration graph for the bourdon gauge was prepared by comparing it with the dead weight gage. Mercury legs. Correction was made for the column of mercury standing above the reference level (L^) shown in Figure 19. The hot zone at the vapor-bath temperature extends from upward; the cold zone at ambient temperature extends downward from L^. A step-function change in temperature was assumed to occur at L^; the error introduced by this assumption is within the accuracy limits specified in Chapter V. (i*3) H*,' , H e * L4 - i-5 + L H mercury level in backleg chamber (B) from the position at sample loading (H-f,) to the actual position for the present sample volume. The volume difference A v divided by the cross sectional area of the backleg chamber gives this change in level. Hence, the pressure difference between L 2 and the mercury surface in the backleg chamber is given by (iu+) APl = -k, CH+, tl-LHccUl where d^ and dQ are mercury densities in the hot and cold zones, and k^ is the factor for converting grams mass/cm.^ to psi at local gravity. Mercury densities were taken from the Handbook of Chemistry and Physics (^5) » a Lagrange interpolation formula was used. Capillarity. When.any interface between two liquid phases is curved, the curvature must be produced and main tained by a pressure difference normal to the curved surface. Adamson (50).shox\rs that for a spherical segment, this pressure difference is given by (if 5) APC = f i / R . where / is the interfacial tension and R is the radius of curvature of the spherical segment. The meniscus height, Hm and the tube radius r are related to E by constant, and T^X = T/Tc , the reduced temperature. Thus, A P ~ c is given by combining equations (^5) through (^7 ): (H-8) APc = -kx [AHn/C^/ic + )][7a0-7i)n/41 where kg is a factor for conversion of units to psi. Adamson (50) states that the higher pressure exists on the concave side of a curved interface provided the principle radii of curvature have the same sign; since for a spherical meniscus, the principle radii are identical, correction must be subtracted from the observed pressure. There was a very small pressure correction due to the curved mercury surface in backleg chamber (B). Interpolation in the Smithsonian tables (52) gave a value of 0.003 psi. Mercury vapor pressure. Data on the vapor pressure of mercury were taken from Douglass et al. (53)• A standard Lagrange interpolation procedure was used. The vapor pressure of mercury is enhanced by the pressure of the second component, the so-called Poynting effect: where PQ is the vapor pressure for liquid mercury in contact with pure mercury vapor, p the actual vapor pressure at total 98 pressure P, and v(L) is the molar volume of liquid mercury at temperature T. The corrected vapor pressure, p, is subtracted from the observed total pressure to give the actual pressure of the sample. A detailed discussion of the effect of the mercury on the pressure of the organic phase is given in Appendix VI. Absolute pressure. A mercury barometer was read to the nearest 0.01 cm. and corrected for ambient temperature, capillarity, and local gravity. Let barometric pressure be P^: (50) & where Islj is the factor required to convert inches of Hg to psi at local gravity. The true absolute sample pressure, P s , may be expressed by combining equations (A-2), (W-) , (^8), and (^9 ) for the force balance: (51) R, -f APl +APc + = P+ 0.003 + P+ so that (52) Ps P- APU -APc. + 0.003 -j? + P4. Sample calculation A complete sample calculation is presented in outline form for the point at lowest pressure of the super critical (230°C) isotherm of Sample 26. The actual calculations were performed on an IBM 7090 computer. SAMPLE CALCULATION DATA run identification 0100 sample/isotherm 26o4 resistance thermometer ohms ^J-8.200 sample temperature, t, °C 230.00 Cathetometer readings, cm level L-, 68.iKL0 Lo 39.236 L 3 39.127 Ln 26.000 L5 17.720 Ruska dead-weight gage P^, face values of weights, psi 70.000 tr , cylinder temperature, °c 2^.8 H0 , residual oil head, psi -0.037 Heise bourdon gauge indicated pressure, psi 75*0 corrected pressure, psi 76.0 Ambient conditions tr , room temperature, °C 2^.8 B, local barometer, in. Hg. 29.^1 PHYSICAL CONSTANTS Acceleration of gravity locals gj. = 980.09^7 cm/sec2 standard: gs = 98O.665 cm/sec ratio: gL/gs = 0.999^18 Temperature coefficients of linear expansion, 77^0 Pyrex glass, 3.2 x 10”^/°C mild steel, 3^*5 x 10"°/°C Surface tension of liquid mercury, 'io - 527 dynes/cm PHYSICAL PARAMETERS FOR APPARATUS Tube calibration large-bore section aQ = -2.10617 cc bQ = 0.162393 cc Volume of stirring ball at 25°C Vs ,o = 0.00209 cc Sample volume at loading vL0AD = °*°39 cc Backleg chamber, at loading Cross-sectional area, A-u =-3*87 cm2 depth of mercury, = 9*^50 cm Ruska dead weight gage F-n = -^.7 x 10“^/psi f£ = +2.^ x 10-5/Oc pQ = 5.997 psi at standard gravity (A0/Aq) = (5-0000/5.0011)= 0.999780 FACTORS FOR CONVERSION OF UNITS (basis: local gravity) Convert (gm mass/cm2) to psi: = (0.014223) (0.99942) = 0.014215 Convert (dynes/cm2) to psi: k2 = (1.450** x 10"5) (0.99942) = 1.4496 x 10“5 Convert in. Hg to t>si: k3 = (0.99942) (14.696)/( 29.921) = 0.49088 PRELIMINARY CALCULATIONS Compute quantities which depend on the temperature. Units = psi, liters, °K, gram-moles gas constant, R = 1.2058? Sample temperature T°K = 273.16 + t°C = 503.l6°K RT - 606.75 e = t°c - 25 = 205.00 Properties of liquid mercury Densities, molar volume dh = 13.0442 gm/cc d« = 13.5345 gm/cc V(L) = 0.20061/13.0442 = 0.1538 /mole Vapor pressure at 230°C p = 0.832 psi Surface tension at 230°C , t = 527 (1 - 503/1172) 13-/9 t = 267 dynes/cm Temperature corrections to tube calibration: (1 +*©) = (1 + 205(3.2 x 10-6)) = 1.00066 (1 +49)2 = 1.00132 (1 +4P )3 = 1.00198 at = a 0 (1 + ‘69)2 = -2.IIO3 cc bt = bo d + 4©)2 = +0.16261 bt/TC = r2 = 0.05176 cm2 Volume of stirring ball at t°C (1 + 4©) steel = 1.0071 Vs = 0.00209 (1.0071) = 0.00210 cc 102 VOLUME Sample length H = Lx - L 2 = 6 8 . ^ 1 0 - 39.236 = 29.17^ cm Meniscus height Hm = L 2 - L 3 = 39.236 - 39.127 = 0.109 cm Hm 2 = 0.0119 cm2 Correction to large-bore tube calibration A V oal = 0 . 0 0 0 2 cc Level volume at 230°C V L = (at + A v cal) + btH = (-2.1103 + 0.0002) + ~ b T l626l (29.17*0 = 2.6337 CC Meniscus volume complement Vc = Hm (bt/2 - 0.5236 Hm2) = (0.109) (o.16261/2 - 0.5236X (0.0119)) = 0 . 0 0 8 1 8 cc Sample volume V = VL + Vc - Vs = 2.6337 + 0.00818 - 0.00210 = 2.6^00 cc ABSOLUTE PRESSURE (RUSKA GAGE) Indicated pressure: P± = (70.000 + 5-997) (0.99978) (0.999^2) = 75.991 psi Correction factors: (1 - F^P, ) = 1 . + it-.7 x 1 0 - 8 (7 5 .9 9 1 ) = 1 . 0 0 0 0 0 (1 - Ft (t - 20)) = 1 + 2 . x 1 0 - 5 (2k.Q - 20) = 1.00012 Corrected pressure: P = Pi(l - FpPiJd - FT (t - 20)) - H0 = 75.991 (1.00000) (1.00012) - 0.037 = 75.963 Psi 103 Correction for Mercury legs: Hh = L2 - = 39.236 - 26.000 = 13.236 cm AV.= VL - VL0AD = 2.64-0 - 0.039 = 2.601 cc V/Ab = 2.601/3.87 = 0.672 cm H = Lk - L 6 + Hb - V/Ab H0 = 26.000 - 17.720 + 9.4-50 - 0.672 = 17.059 cm Hhdh = 13.326 (13.04-4-2) = 172.653 gm/cm2 Hcdc = 17.059 (13.534-5) = 230.885 gm/cm2 PL = k, (Hhdh + H„d ) ^ = 0:014213 (172.553 + 230.885) = 5*736 psi Correction for Capillarity H = (bt/lC + H™2)/2Hm = (0.0518 + 0.01191/(2(0.109)) = 0.2922 cm Pc = k2( 2 /R) = (1.4-5 x 10-5) (2 x 267/0.2922) = 0.026 psi Barometric Pressure Pf = k3B = 0.4-9088 (29.4-4-1) = 14-.4-51 psi Approximate Absolute Sample Pressure P£ = P - PL - PG + 0.003 + Pb '= 75.963 - 5.736 - 0.026 + 0.003 + 14-.4-51 = 84-.655 psia Poynting Effect true mercury vapor pressure: p = p exp (V(L) Pg/RT) \ p = 0.832 exp (0.01538 x 84-.66/606.8) =. 0.834 psi True absolute sample pressure ps = p« - p = 84.655 - 0.834 Ps = 83.82 psia SUMMARY t = 230.00°C ■ V = 2.6400 cc P = 83.82 psia APPENDIX VI- EFFECT OF MERCURY ON THE OBSERVED PRESSURE 104 105 EFFECT OF MERCURY ON THE OBSERVED PRESSURE Rowlinson and co-vrorkers (32) (33) (3^) have shown that the effect of the mercury on gas compressibility measurements may be quite large at higher densities and temperatures. Their reasoning and methods of calculation for propane and butane will be extended here to estimate the magnitude of the effect on acetone— n-pentane mixtures. In the following derivations, let subscripts 1, 2 and 3 denote acetone, n-pentane and mercury respectively; let np be the moles of component i in the organic phase; let v be the observed organic phase volume at measured total pressure P when mercury is present. If (np + n 2) moles of organic phase (in the absence of mercury) are confined in a volume v at temperature T, then the pressure Pp2 is given by: 3 Rx /R.T- t* )/V + B (T,iut)7t*)/Vz-+ C(T,yu/t jv*+ " " " ( 53) 6„(t ) + 2 * fa d,2 (t) + H i & ^ C t) C Cr,ti,, f a ) ' Cr) Ct7Z Cr) + * 1 C r) Compare this pressure P12 with the pressure P on (n^ng+n^) moles of organic and mercury confined in the same volume v at the same temperature T: P/&T* fa,+Kx+n9)/v + B (r, ^ ) / v z+ CCrfa)/?* + *"“ The difference between these two pressures must be caused by the presence of the mercury, so that (55) AP/er- (P u - P )/& T x -fa /i/ rA'a/tf** A ' c / V J 106 where in computing A^B and A c we ignore any interactions involving more than one mercury atoms (56) A'& - 2*,,*., &nCr) + &„(r) A C * CtxtCv) +$TLfTL$ C/iy (t ) Cy-1*. Ct ) Equations (55) and (56) may be rearranged slightly to gives AP - C-x* £ t / v][ / + Ad/v + A c / / * + J V * V ' / V • njo/Ar Volume N - 7Lf4 nz + 7l9 Aft * Z£X, fa Cr) + TCZ (r)l A c * 3 £zx,*zCIX 9(t) + X* C//3 (r) + 1} CZ2i&)'] Since the organic phase is an open system in contact with excess liquid mercury, the value of n^ along an isotherm depends on density and must be computed from the equilibrium relationship. We assume that the organic components are virtually insoluble in liquid mercury. For the standard state of pure mercury liquid at its vapor pressure (P^°) at T, the fugacity is given by where V^(L) is the molar volume of liquid mercury. Glasstone (5^) gives the gas phase fugacity in terms of the virial coefficients: (59) ~ ('V'fa&r) +ZA&/V + (*/?■) A C / y z + ...... Since liquid and vapor-phase fugacities are equal at eauilibrium, we have (60) Sto* (?$ V/%■$ fcl") ~t ft- J 1# Z-A&/y ■+ fa/l) Ac//Z Ml3 Equilibrium relation (60) along with pressure relation (57) may be used to correct observed pressure for the effect of mercury. A trial-and-error procedure is used to solve these 107 equations on the IBM 7090 computer. Values of A b and AC are estimated from Kihara and Lennard-Jones potential parameters for the pure components. The results are semi- quantitative, especially at higher densities where the three-constant virial equation is inadequate. Mainly, the results serve as an estimate of the experimental accuracy of the pressure at the higher densities,- as stated in Chapter V. Figure 20 shows the computed corrections for the critical vapor (193»91°C) and 230°C isotherms of Sample 22. The mercury vapor pressure corrected for the Poynting effect is also shown for these temperatures. The Poynting correction is easily derived from equations (60) and (57) by putting A b = A c = 0 (no mercury/organic interactions). The equilibrium relation ship becomes (6 1 ) * 3 £ T / v - f; exF [(P- f;) v, (l)/ £ r ] The pressure equation reduces to (62) AP= - X* R . t / v which is the usual form of the Poynting relationship. In this work, equation (62) was used to correct the pressure. The corrected mercury vapor pressure, calculated from equation (62), is given for each data point in Appendix VII. PRESSURE CORR EC T I0fl .p s i - 1.0 O Figure 20,. Estimated Correction for the Effect of Mercury on the Sample the on Mercury of Effect the for Correction Estimated 20,. Figure rsue — Pressure —o o— — o o 200 PRESSURE, 0 0 4 psia 193:91 y Poynting I Poynting 600 ° (critical) ° 5230 0 0 8 108 APPENDIX VII EXPERIMENTAL DATA 109 EXPERIMENTAL DATA . .. This appendix contains a tabulation of the pressure-volume-temperature points as calculated from the raw data by the procedure given in Appendix V. This tabulation of data is composed of pages from the computer print-out; the format and symbols are described below, followed by the tabulation. For the border curves, the column headed "TYPE" indicates dew, bubble, and critical ("CRTCAL") points, followed by columns of temperature (°G), pressure (psia), volume (liters/g-mole), density (g-moles/liter), and compressibility factor (Z = PV/RT). The last column, headed "PHGC", is the value of the vapor pressure of mercury corrected for the Poynting effect (in psi) which was actually used to compute the sample pressure. For an isotherm, the temperature (°C) appears at the top of the tabulation, below the sample number. Under "TYPE" of point, "CRT V ” and "CRT L" stand for critical vapor and critical liquid, respectively.- "FLUID11 implies an isotherm at a temperature above the critical; "VAPOR" is used below the critical temperature. The units and meanings of the other measurements are the same as for the border curve tabulation. 110 SAMPLE 21 BORDER CURVE TYPE Z = PHGC DEG C PSIA L/MOL MOL/L PV/RT PSI DEW 180.00 ,420.09, 0. 7321 I . 3660_ 562_8_ QjlL7_ DEW' 185.00 456.35 0.6411 1.5598 5295 0 21_ DEW 187. 53 474.92 0.5986 1.6705 51 18 0 22 DEF iso; 02 491 .94“ 0 . 5566' 1.7967' 4962" 0 24 DEW 192.63 513 ^19 0^5022' 1•9913 4588 27 DEW 195.00 531.68 0.4550 2. 1978 4285 29 DEW 196.30 '54O.93' "0.4367 2.2897 41 76 30 DEW 197.00 549.40 0.4133 2.4196 4005 31 DEW 198.00 558.60 0 •3872 2 . 5826 3807. 32 d e w ' 198.36 '561.38' 0'.'3797' 2 ."633"5 3749" 32 DEW 198.57 563.05 0.3741 2.6732 3 7 03 32_ DEW 199.00 567.57 0.3588 2.7872 3577 33 DEW 199.09 568.16 0.3539" 2.8253 3531 33_ DEW 199.20 569.55 0.3492 2.8641 3491 33 DEW 199.30 570.99 0.3398 2 . 9425 0 3406 0 33 JDEW_ 199.41 572.09 0. 3 372 2. 9 6 56 0 3335 0 33 DEW 199 • 52_ J572 .95 0.J3283 3.0463 0 3300 0 33 DEW 199.72 574.83 0.3120 3.2054 0 3145 0 34 DEW 199.83 575.54 0.3073 3.2546 3100 34 CRTCAL 199.83 576.43 0.2716 3.6817 2745 34 BUBBLE 199. 72 ^575.42 0.2408 _4.1532_ 2430 34 BUBBLE 199, 52 575.28" "6". 2329" 4". 29 4 0 2350 33 BUBBLE 199.40 574.47 0.2293 "4 .361 l" 2312 33 BUBBLE 199. 30 _573.45 0.2270 4.4058 O 2 285 33 BUBBLE 199. ,5 70 . 87~ 0*2223 4 :4980_ 2229, 33 'BUBBLE 199. 00 "570 .35 Q .2194 4j 5584 2198_ J3U8BLE 198.36 564.85 _0j21J5j 4.7291 .1.10 r BUBBLE" T98.00" "56 1^76 0.2067 4.8369' 2044 BUBBLE 197.33 556.14 ’6.2619' 4 .9537 1979 31 BUBBLE 197.00 5o3.52 0.1997 5.0065 1950 31 BUBBLE 196._00_ 5 4 4 .99 0.1954 5.1176 1882 0.30 BUBBLE 192.63 518.51 0 . 1801 5 . 5 529 1662 0.27 BUBBLE. J 90.00, 49 9 .78 P.'r 173.L 5 .7768 1549 0.24 . BUBBLE 187.53 _480.ai 0.1680, 5. 9 526 1454 0.22 b u b b l e 185. 00 461•69 0 .1629" _6_.„L395, 1361 0.21 B U B B L E 180 00 427.28 0.1562 _6 • 4038 1221 0. 17 END — 112- SAMPLE 21 T = 190.02 TYPEP. V. D. Z = CZ-1 )V PHGC PSIA L/MOLMOL/L PV/RTL/MOLPSI VAPOR 137.44 3.7655 0.2656 0.9266 -0.2765 0.24 VAPOR 163.02 3.1035 0.3222 0.9058 -0.2923 0.24 VAPOR 186.72 2.6502 0.3773 0.8860 -0.3022 0.24 VAPOR 212.48 2.2701 0.4405 0.8636 -0.3096 0.24 VAPOR 411 .22 0.8855 1.1292 0.6520 -0.3082 0.24 VAPOR 434.90 0.7912 1.2639 0.6161 -0.3038 0.24 VAPOR 454 • 64 0.7141 1.4004 0.5813 -0.2990 0.24 VAPOR 490.16 0.5664 1.7656 0.4970 -0.2849 0.24 s a m p l e 21 T = 195.02 TYPE P, V. D* Z = (Z-l )V PHGC PSIA L/MOLMOL/L PV/RTL/MOL PSI VAPOR 94.55 5.7410 0.1742 0.9615 -0.2212 0.28 VAPOR 113.90 4.7003 0.2128 0.9483 -0.2431 0.29 VAPOR 113.87 4.6991 0.2128 0.9478 -0.2453 0.29 o CM 3V VAPOR 138.30 3.8013 0.2631 0.9312 - 0 . 2616 . VAPOR 162.91 3.1612 0.3153 0.9122 -0.2775 0.29 VAPOR 212.34 2.3231 0.4305 0.8737 -0.2933 0*29 VAPOR 261.98 1.7923 0.5578 0.e319 -0.3013 0.29 VAPOR 425.03 0.8771 1 .1401 0.6603 -0.2979 0.29 VAPOR 460.59 0.7451 1.3421 0.6079 -0.2922 0.29 VAPOR 509.99 0.5672 1.7632 0.5123 - 0 . 2766 0. 29 VAPOR 529.69 0.4791 2.0872 0.4495 -0.2637 0*29 VAPOR 533.22 0.4582 2.1822 0.4328 -0 .2599 0. 29 END 113 SAMPLE 21 T = 199*83 TYPEP. V* D. Z = (Z-l)V PHGC PSIA L/MOL MOL/L PV/RT L/MOL PSI CRT V . 94 • 33 5.8301 0.1715 0.9642 -0.2087 0*33 CRT V 103.98 5.2543 0.1903 0.9579 -0.2213 0*33 CRT V 162.71 3.2143 0.3111 0.9170 -0.2669 0.33 CRT V 21 2 . 1 5 2.3626 0.4233 0.8788 -0.2864 0.33 CRT V 2 6 1 . 7 8 1.8293 0•5467 0.8396 -0.2934 0.33 CRT V 434.83 0.8767 I.1406 0.6684 -0.2907 0.34 CRT V 460.53 0.7871 1.2705 0.6355 -0.2869 0.34 CRT V 5 1 0 . 1 0 0.6262 1.5969 0.5601 -0.2755 0.34 CRT V 559.51 0.4511 2.2168 0.4425 -0.2515 0. 34 CRT V 5 7 5 . 1 6 0.3386 2.9534 0.3414 -0.2230 0.34 CRT V 5 7 6 . 0 0 0.3180 3.1446 0.3211 -0.2159 0.34 SAMPLE 2~f~~ T = 199*83 TYPE P. V. D. Z = (Z-l )V PHGC PSIA L/MOLMOL/L PV/RT ____L/MOL..___P.S..L______ CRT L 577.70 0.2509 3* 9856 0.2541 -0. 1-871 0.34 CRTL 579.61 0.2227 4.4896 0.2263 -0.1723 0.34 CRT L 5 8 8 . 5 4 0.2025 4.9376 0.2090 -0.1602 0*34 CRT L 608.46 0.1887 5.3005 0.2013 -0.1507 0*34 CRT L 6 4 8 . 3 9 0•1788 5.5924 0.2033 —0.1425 0.34 CRT L 7 0 8 . 3 2 0.1705 5 . 864.4 0.2118 -0.1344 0»34 CRT L 1007.97 0.1533 6.5226 0.2709 -0.1118 0.34 END SAMPLE 21 T = 205.04 TYPE P. V. D. Z = (Z-l )V PHGC PSIAL/MOL MOL/L PV/RTL/MOL PSI FLUID 94.56 5.8900 0.1698 0.9659 -0.2011 0.39 FLUID 104.20 5.3133 0.1882 0.9601 -0.2119 0. 39 FLUID 113.90 4.8320 0.2070 0.9544 -0.2202 0.39 FLU I D 138.33 3.9074 0.2559 0.9373 -0.2449 0*39 f l u i d 162.90 3.2598 0.3068 0.9209 -0.2580 0«39 FLUID 261.96 1.8630 0 *5368 0.8463 -0.2863 0.39 FLUID 444.97 0.8801 1.1362 0.6791 -0.2824 0.40 FLUID 460.80 0.8278 1 .2080 0.661b -0.2802 0.40 FLUID 510.29 0.6737 1.4843 0.5962 -0.2721 0.40 f l u i d 559.81 0.5341 1.8722 0.5165 -0.2572 0.40 FLUID 609.23 0.3596 2.7810 0.3799 -0.2230 0.40 FLUID 658.71 0.2024 4.9410 0.2312 -0.1556 0.40 f l u i d 808.46 0.1705 5.8653 0.2390 -0. 1297 0.40 FLUID 1008.23 0.1582 6.3201 0.2766 — 0.1145 0.40 SAMPLE 21 T = 215.00 TYPE P, - V. . D. Z = (Z-l )V PHGC PSIA L/MOL MOL/L PV/RTL/MOL PSI in o ■sf FLUID 113.92 4.9472 0.2021 0.9574 -0.2107 . FLUID 162.91 3.3475 0.2987 0.9264 -0.2463 0.54 FLUID 212.33 2.4803 0.4032 0.8947 -0.2613 0.54 FLUID 261.96 I.9373 0.5162 0.8621 -0.2671 0.54 • FLUID 464.90 0.8842 1*1310 0 0.6933 -0.2668 ;ui 1 FLUID 510.46 0.7525 1.3289 0.6525 -0.2615 0.54 m o FLUID 560.03 0.6275 1.5935 0.5970 -0.2529 - SAMPLE 21 T = 230.02 TYPE P. V* D* Z = (Z-l)V PHGC PSIAL/MOL MOL/L PV/HT L/MOL PSI f l u i d 113.65 5.1415 0. 1945 0.9630 ™-Q"J 90 1„.„„0 .• 8,4___ f l u i d 137.07 4.2127 0.2374 0.9517 -0.2037 0. 84 FLU ID 162.62 3.4953 C.2861 0.9368 -0.2210 0» 84 FLUID 212.03 2.6021 0.3843 0.9093 -0.2361 0. 84 FLUID 261.65 2.0402 0.4901 0.8798 -0.2453 0. 84 f l u i d 261.67 2.0425 0.4896 0.8808 -0.2434 0.84 f l u i d 510.38 0.8457 1•1825 0.7113 -0.2441 0 • 84 f l u i d 5 5 9 . 9 7 0.7267 1.3761 0.6706 -0.2393 0» 84 f l u i d 659.29 0.5342 1.8721 0.5804 -0.2241 0.85 f l u i d 758.72 0.3770 2.6528 0.4714 -0.1993 0 • 85 f l u i d 1007.94 0.2029 4.9284 0.3371 -0.1345 0*85 END \ 116 - S A M P L E 2 2 ____ BORDER CURVE TYPE T « P. Vi D. Z = PHGC D E G C PS I. A L/MOL MOL/L PV/RT PSI DEW 180.05 421.75 0.6666 1.5002 0.5144 0« 17 DEW 185.97 462.10 0.5531 1.8080 0.4617 0.21 DEW 191.58 505.23 0.4239 2.3589 0.3322 0.26 DEW 193.05 517.06 0.3763 2.6574 0.3461 0.27 DEW 193.7B 523.77 0.3284 3.0450 0.3055 0.28 DEW 193.89 524.37 0.3131 3.1935 0.2915 0.28 CRTCAL 193.91 524.75 0.3002 3.3314 0.2797 0. 28 BUBBLE 193.99 524.92 0.2725 3.6700 0.2540 0.28 b u b b l e 193.89 524.85 0.2721 3.6747 0.2536 0.28 b u b b l e 193.78 524.47 0.2624 3.8106 0.2444 0.28 • b u b b l e 193.59 523.60 0.2552 3.9177 0.2374 0.27 BUBBLE 193.06 518.73 0.2388 4.1874 0.2203 0. 27 BUBBLE 191.63 507.69 0.2205 4.5344 0.1998 0 • 26 BUBBLE 189.20 489.55 0.2041 4.8991 0.1792 0. 24 3 U B B L E 185.87 465.28 0.1926 5.1913 0.1619 0.21 b u b b l e 180.05 425.33 0.1803 5.5461 0.1403 0. 17 BUBBLE 170.01 363.37 0*1643 6.0872 0 . U 1 7 0.12 END ±1? SAMPLE 22 T = 180.05 TYPEP. V. D. Z= (Z-l>v PHGC PSIA L/MOL MOL/LPV/RT L/MOLPSI VAPOR 88.80 5.7667 0.1734 0.9370 -0.3633 0. 17 VAPOR 94.56 5.3850 0.1857 0.9317 -0.3676 0. 17 VAPOR 104.21 4.8447 0.2064 0.9238 -0.3691 0. 17 VAPOR 113.93 4 . 3 9 5 5 ~ 0.2275 0.9163 -0.3678 0. 17 VAPOR 133.46 3.6315 0.2716 0.8990 -0.3717 0. 17 VAPOR 163.02 2.9307 0.34 12 0.8742 -0.3686 0. 17 VAPOR 212.55 2.1268 0.4702 0.3272 -0.3676 0. 17 VAPOR 252.09 1.7034 0.5371 0.7857 -0.3650 0. 17 VAPOR 305. 19 0.8541 1.1708 0.6020 -0.3399 0.17 VAPOR 395.02 0.8052 1 .2419 0.5820 -0.3366 0. 17 VAPOR 404.85 0.7575 1.3201 0.5612 -0.3324 0. 17 VAPOR 414.67 0.70.59 1.4166 0.5356 -0.3278 0. 17 VAPOR 420.55 0.6744 1.4829 0.5190 -0.3244 0.17 s a m p l e 22 T = 190.02 TYPEP. V* D. Z = (Z-l>v PHGC PSIA « L/MOL MOL/L PV/RTL/MOL PSI VAPOR 94.49 5.5414 0.1805 0.9375 -0.3466 0.24 VAPOR 113.84 4.5257 0.2210 0.9224 -0.3511 0. 24 VAPOR 133.38 3.7984 0.2633 0.9071 -0.3530 0.24 VAPOR 212.32 2.2129 0.4519 0.8412 -0.3514 0.24 VAPOR 261.95 1.6966 0.5894 0.7957 -0.3466 0.24 VAPOR 411.01 0.8405 1.1893 0.6185 -0.3207 0.24 VAPOR 430.74 0.7599 1.3160 0.5860 -0.3146 0.24 VAPOR 450.47 0.6801 1 .4704 0 • 5485 -0.3071 0.24 VAPOR 470.19 0.5970 1.6751 0.5025 -0.2970 0.24 VAPOR 489.85 0.4913 2.0352 0.4309 -0.2796 ! • p ! II END -118- SAMPLE 22 T =_____193.91 TYPEP. V. 0* Z = CRT V 94 .63 5.5911 0.1789 0.9394 -0.3389 0.27 CRT V 113.98 4.5754 0.2186 0.9259 -0.3389 0.27 CRT V 133.51 3.8442 0.2601 0.9113 -0.3411 0.27 CRT V 153.16 3.2999 0.3030 0.8973 -0.3388 0.27 CRT V 192.64 2.5267 0.3958 0.8642 -0.3431 0«27 CRT V 232.28 2.0173 0.4957 0.8319 -0.3390 0.27 CRT V 416.10 0.8552 1 .1693 0.6318 -0.3149 0.28 CRT V 430.90 0.7969 1.2549 0.6097 -0.3111 0.28 CRT V 4 5 0 . 6 6 0.7227 1.3838 0.5782 -0.3048 0.28 CRT V 470.40 0.6499 1.5386 0.5428 -0.2971 0.28 CRT V 489 . 9 2 G .5728 1.7458 0.4983 -0.2874 0.28 CRT V 509.61 0.4827 2.0716 0.4368 -0.2719 0.28 CRT V 519.41 0.4157 2.4057 0.3833 -0.2563 0.28 CRT V 523.15 0.3677 2.7199 0.3415 -0.2421 0.28 ...... ' CRT V 5 24. 0 9 O'. 3433 2.9130 0.3194 -0.2336 0.28 no o CVJ CRT V 524.59 0.3162 3*1624 0.2945 -0.2231 . SAMPLE 22 T = 193.91 TYPE P. V. D. Z = (Z-l>v PHGC PSIA L/MOLMOL/LPV/RT L/MOL PS I . CRT L 5 2 5 . 1 3 0.2631 3.8007 0.2453 -0.1986 0.28 CRT L 527. 0 5 0.2363 4.2317 0.2211 -0.1841 0.28 CRT L 529.02 0.2303 4.34 1 5 0.2163 -0.1805 0. 28 CRT L 532.98 0.2221 4.5024 0.2102 -0.1754 0.28 CRT L 538.95 0.2151 4.6498 0.2058 -0.1708 0.28 CRT L 548. 9 2 0.2076 4.8181 0.2023 -0.1656 0.28 CRT L 5 6 8 . 8 7 0•1988 5.0307 0.2008 -0.1589 0.28 CRT L 608.79 0.1906 5.2457 0.2061 -0.1514 0.28 CRT L 6 8 8 . 6 8 0.1805 5.5401 0.2207 -0.1407 0.28 CRT L 788.56 J . 1735 5.7651 0.2429 -0.1313 0.28 CRT L 9 08 . 4 2 0.1674 5.9750 0.2699 -0.1222 0.28 CRT L 1008.31 0.1639 6.1001 0.2935 -0.1158 0.28 . END — 1 1 9 SAMPLE 22 T =_____205*04 TYPE p. V. D. Z = (Z-l)V PHGC PSIA L/MOLMOL/LPV/RT L/MOL PSI f l u i d 89.83 6.0783 0.1645 0.9469 -0.3229 0.39 f l u i d 94*62 5.7495 0.1739 O'. 9434 -0.3253 0. 39 FLUID 104.27 5.1880 0.1928 0.9381 -0.3211 0.39 FLUID 113*97 4.7161 0.2120 0.9321 -0.3202 0.39 f l u i d 123.70 4.3125 0.2319 0.9251 -0.3230 0.39 FLUID 13 3.47 3.9693 0.2519 0.9187 -0.3226 Oi39 f l u i d 153.10 3.4085 0.2934 0.9050 -0.3240 0. 39 f l u i d 182.69 2.7922 0.3581 0.8846 -0.3222 0.39 f l u i d 212.38 2.3413 0.4271 0.8623 -0.3224 0.39 FLUID 242. 12 1.9974 0.5007 0.8387 -0.3223 0.39 FLUID 271.92 1.7285 0.5785 0.8151 -0.3196 0.39 f l u i d 438.98 0.8608 1•1617 0.6553 -0.2967 0.40 . ■t* o f l u i d 440.95 0.8538 1.1713 0.6529 -0.2964 o f l u i d 450.85 0.8206 1 .2186 0.6416 -0.2941 0.40 f l u i d 460.74 0.7872 1 .2703 0.6290 -0.2921 0.40 . o f l u i d 470.63 0 . 755.3 1 .3240 0.6164 -0.2897 o FLUID 490.41 0.6945 1 .44 00 0.5906 -0.2843 0.40 FLUID 510.20 0.6351 1 .5746 0.5619 -0.2782 0.40 f l u i d 534.05 0.5634 1 .7749 0.5218 -0.2694 0.40 FLUID 559.73 0.4880 2.0493 0.4737 -0.2568 0 • 4 FLUID 583.52 0.4099 2.4394 0.4148 -0.2399 1.40 f l u i d 609.16 0.3150 3.1743 0.3328 -0.2102 0.40 f l u i d 633 . 00 0.2533 3.9472 0.2781 -0.1829 0.40 f l u i d 658.83 0.2275 4.3952 0.2599 -0.1684 0.40 f l u i d 682.82 0.2154 4.6423 0.2551 -0.1605 0.40 f l u i d 708.71 0.2066 4.8402 0.2539 -0.154 1 0.40 f l u i d 758.68 0.1970 5.0772 0.2591 -0.1459 0.40 END SAMPLE 22 T = 215. 0 0 TYPE P. V* D. Z = CZ-1)V PHGC PSIA L/MOL MOL/L PV/KTL/MOL PS I FLUID. 94 • 54 5.9033 0.1694 0.9481 -0.3065 0.54 f l u i d 104.17 5.3333 0.1875 0.9438 -0.2997 0.54 f l u i d . 113.87 4 .8501 C •2062 0.9382 -0.2997 0.54 f l u i d 123.61 4.4432 0.2251 0.9330 -0.2976 0.54 f l u i d 133.36 4.0838 0.2449 0.9252 -0.3055 0. 54 f l u i d 152.99 3.5146 .0.2845 0.9134 -0.3042 0.54 f l u i d 172.70 3.0737 0.3253 0.9018 -0.3019 0* 54 f l u i d 212.26 2.4227 0.4128 0.8736 -0.3062 0.54 f l u I D 251.94 1.9771 '0.5058 0.8462 -0.3041 0.54 j o in <■ FLUID 271.81 1.8031 0.5546 0.8326 -0.3019 • FLU I D 460 . 8 3 0.8587 1•1645 0.6723 -0.2814 0 . 54 f l u i d 490.54 -j .7709 1.2973 0.6424 -0.2757 0 • 54 FLUID 520 . 2 5 0.6895 1.4503 0.6094 -0.2693 0.54 FLUID 559.90 0.5906 1.6931 ,0.5618 -0.2588 0. 54 f l u i d 609.49 0.4749 2.1057 0.4917 -0.2414 0.54 f l u i d 6 59. 0 9 0.3644 2.7442 0.4080 -0.2157 0.54 f l u I D 708.78 0.2786 3.5900 0.3354 -0.1851 0* 55 f l u I D 758.60 0.2361 4.2349 0.3043 -0.1643 0. 55 FLUID 808.49 0.2171 4.6058 0.2982 -0.1524 0.55 FL U I D 908.32 0•1980 5.0509 0.3055 -0.1375 0 • 55 F l u I D 1008.20 0.1879 5.3216 0.3218 -0.1274 0.55 END 121'~.. SAMPLE 22 T = 230.02 TYPE p . V. D. Z= (Z-l)V PHGC PSIA L/MOL MOL/L PV/RT L/MOL PS I f l u i d 1 13.71 5.0297 0.1988 0.9426 -0.2888 0 . 84 f l u i d 137.lb 4. 1 157 0•2430 0.9303 -0.2870 0* 84 f l u i d 162.68 3.4182 0.2925 0.9165 -0.2856 0 . 84 [oo 1 O f l u i d 186.38 2.9380 0.3404 0.9025 -0.2865 • f l u i d 212.08 2*5400 0.3937 0.8878 -0.2850 0 * 84 f l u i d 261.70 1.9917 0.5021 0.8590 -0.2808 0. 84 f l u i b 500.48 0.8368 1•1951 0.6902 -0.2592 0. 84 F l u ID 510.40 0.8106 1.2336 0.6819 -0.2579 0* 84 f l u i d 559.99 0.6941 1.4407 0.6406 -0.2495 0.84 f l u i d 609.62 0.5925 1.6879 0.5952 -0.2398 0.85 f l u i d 659.29 0.5038 1.9847 0.5475 -0.2280 0.85 f l u i d 708.99 0.4260 2.3477 0.4977 -0.2140 0.85 f l u i d 758.73 0.3591 2.7850 0 .4490 -0.1978 0.85 END ± 2 2 S A M P LE 23______BORDER CURVE TYPE______T.______P i______V*______D*____Z=______PHGC DEG C PSIA L/MOL ~ MOL/L PV/RT PS I DEW ______17 0 . 0 1____ 366• _7l _ 0 ^ 3 7 19_ 1 .1469 ' 0 . 5 983 0« 12 DEW ______174.98 __398.*25_ ,_Jo • 7676_ l\ 30 2 8 __ _0.5657_ 0. 14_ DE W ~~ 180".06"~ ~'4 32~~9 9 ~ q7663 8 1 .5066 "~~0 V5 2 5 9 " q¥ 77~ DEW 185.04 467.55 0.5736 1 .7434 0.4854 0*21 DEW’ 190.03 505.47 ' 0.4755 2.1029 0.4304’ 0.24" D E W ___ 1 92.01 _5\lVq 1_ 0.4325 _^ 2.3~'l22 0 .4017 Q. 26 DEW ' . 193.89 ’ 536.53^ 0•3823 _2~.6158 0.3642 Q.28~ DEW______L ___ 545. 39^ ’__0j._34 05 ’ 279 3 6 8__ 0. 3290 jO. 29 DEW __ 195V l 4 " ~~546.~~87_0.331 7 ~ 3 . 0 144 0 . 32 1 3 0~. 2 9 DEW______195.24 547.85 “ 0. 3~266 3.0621 0.3168__0.29 DEW 195.39 549.14" 0.3065 3.2630 0.2979 0.29 DEW 195.40 ' 549.37 0.2969' 3.3679 0.2887 0.29 DEW 195.43 549.58 0.2869 3.4859 0.2790 0«29_ CRT CAL 195.50 549.97 0.2785 3.5903 0.2711 0.29' ~ BUBBLE 195.40“' • 5 4 9 7 4 7 " 0.2612 " 3 .”8 2 8 9 ” 0 .254*0 ” 0.29 “BUBBLE"' " 195.40 549 • 39 0.2558 3.9096 07*2487 0."29 "Bubble" ’ "195.26 “548737 0.’2460~ 4 T 0 6 5 2 ’ 0 .“2 3 8 8 0 • 2 9 BUBBLE" 195.14 547.29 "572396 477731 0.2322 0_.29' BUBBLE 1 9 4751 542. 25" 6 7 2 254___‘~4’.4358____ 0 * 2 1 6 8 '67 26 J3UB3LE _____ 1 93.90 5 37 • 0~2 " 0. 21 74 J 4 . 60 0 6 ___ 0.2073 _ 0. 28 "BUBBLE’ 192*01 521".92 0 . 2 0 2 6 479352 ’ 0. 1885" 6726 BUBBLE " ” 190703 506Vl 3 677936 5 7 7 6 4 7 ” 0. 1755 6.24 BUBBLE 185.03 469.05 0.1788 575934 0 •1513 ’0»21 BUBBLE 17 4 .97 400.82 O'.TdS19 6«1~760 ’"577201 5777 3UBBLE 170.01 370.04 07l544 6.4777 0.1069 0*12 END SAMPLE 23 T = 130,02 TYPE P, V, D* Z= “ (Z-l)V PHGC PSIA L/MOL MOL/L PV/RT L/MOL PS i' VAPOR " 75,26 6,0095 0.1664 0,9303 -0,4191 0,02' VAPOR J34*80 5_*2622__^_0• 1909178 •_43 2 4 __Pjj02_ VAPOR' '9 4 '.43 "“ "4,6628' ~ 0 • 2145 ~~ 0,9056" 0^44*00 0*02 VAPOR' 104,11 4.1660 0,240Q 078921 -0.4496 0«02 VAPOR_____ 1 1 3 .86_ 3 . 7 5 1 4 0 . 2 6 6 6 __ 0.8786 -0.4556 Q.Q2 VAPOR 123. 54 3.4033 ___0 .2938_ 0 .8655 -0.4578 0.02 VAPOR 133.44 3.0986 , 0.3227 0.8505 -0.4634_0 .02 VAPOR_____ 1 43 . 2 7 ___ 2.8349 0.3528 __ 0.8354 -0.4667_0.0 2_ V APOR ..153.13" 2.6034' 0.3841 6". 820 0 -0.4687 oVo2 VAPOR 172.86 2.2120 0^4521_ 0.7865 -0.4722_Q. Q 2 SAMPLE 23 T =_____ 17 0 .01______■______ TYPE P. V7 pY~ Z= 1Z-H7 PHGC PSIA L/MOL. MO L / L " PV/RT L/MOL PSI VAPOR 8 4 .88 5.96 9 7 0.1675 0.9482 -0.3094 0.12 VAPOR 89, 67 5.6240 0.1778 0.9437 -C.3168 0. 12 VAPOR _94j 47 5.3146 0.1882 0.9395 -0.3216 0. 12 VAPOR 99. 31 5.0317 0.1987 0.9351 -0.3268 0. 12 VAPOR 104, 15 4.7753 0.2094 0.9307 -0.3311 0. 12 V a p o r 1 13, 87 4.3271 0.2311 0.9220 -0.3375 0. 12 V a p o r ‘123, 64 3.9467 0.2534 0.9131 -0.3430 0. 12 v a p o r l33] 44 3.6200 0.2762 0 .9039 -0.3479 0. 12 V a p o r 14 3, 26 3.3365 0.2997 0.8944 -0.3523 0 . 1 2 VAPOR 153. 1 1 3.0900' 0 . 3236___ 0.8853 -0.3544 __Q. 12 VAPOR____ 162^.9 7____2.8707 0.3483 ___ 0. 87 5 4 - 0 . 3 5 76 0.12 V APOR 1,72 .84___2.6751____ 0.373 8 ___0.8652 -0.3607 0 *1.2_ VAPOR _____ 192.63 2.3460 ___ 0.4263_•_0 . 8 4 5 6 __ -0.3621 0 . 12___ VAPOR 212.46 2.0738 ~ 0.4822___0.8245 -0.3640 0 . 12__ VAPOR 222.37 1.9553 0.5114 0.8136 __ -0.3645 0._12.__ V A P O R ___ 232 .3 1___1. 84 4 4 ____0 .5 4 2 2 ___ 0 . 80 1 8 _ _-p .3656 0 .12__ VAPOR _ 242.24 "" I.7442 0.5733 "6^7906 ~-0.3652 CU12__ VAPOR ___366.34 0.8745 1.1436 ' 0.5994 * -0.3503 0 . 1 2 ~ VA“p 6 fT 366.53 0*8730 T.T455”' ‘ "oV5983 '“’-073503 Q. 1 2 END SAMPLE 23 T = 190,02 TYPE V » D. Z = (Z-l)V PHGC PSIA L/MOL MOL/L PV/PT L/MOL PSI VAPOR 99.38 5.3251 0.1878 0.9475 -0.2796 0.24 VAPOR j.04,21 J5 • 0558" O'. 1978 079433' ■0 . 2867 0 * 24 VAPOR ‘ 1 T3*93” 4T5905’ "0.2778’ ______0.9364 •5.2927' 'oT2 SAMPLE 23 T = 195,50 -• TYPEP, V* D, Z = ( Z - l )V PHGC PSIAL/MOLMOL/L PV/RT L/MOL PSI CRT V 94,7b 5.6799 0. 1761 0.9526 -0.2693 0*29 CRT V 114,16 4.6480 0.2151 0.9389 -0.2839 0.29 CRT V 133.68 . 3.9074 0*2559 0.9243 -0.2959 0.29 CRT V 163,18 3.1242 0.3201 0.9021 —0.3059 0.29 CRT V 192.81 2.5749 0.3864 0.8785 -0.3129 0. 29 CRT V 222.54 2.1712 0. 4606 0.6549 -0.3149 0. 29 CRT V 252.32 1.6583 0.5381 0.6297 — 0 *3165 0*29 CRT V 421.30 0.8825 1.1331 0.6579 -0.3019 0.29 CRTV 431.16 0.8456 1.1826 0.6451 -0.3001 0*29 CRT V 460.83 0.7398 1.3517 0.6033 -0.2935 0.29 CRT V 490.47 0.6378 1 .5678 0.5536 -0.284a 0.29 CRT V 520. 14 0.5308 1.8836 0.4886 -0.2715 0.29 CRTV 549.56 0.3533 2.8302 0.3436 -0.2319 0.29 SAMPLE 23 T =_____200 .03 TYPE p. V. D. Z = (Z-l )V PHGC PSIA L/MOLMOL/L PV/RT L/MOL PSI FLUID 90.84 6.0164 0.1662 0.9578 -0.2539 0.34 f l u i d 94.68 5.7598 0.1736 0.9557 -0.2550 0.34 f l u i d 98.54 5.5153 0.1813 0.9525 -0.2622 0.34 f l u i d 104.33 5.1888 0.19H7 0.9487 -0.2660 0.34 1 F L U I D 2_1 •°-5- _ 53.__0 • 2121 '679425 -0.‘2 713 0. 34 FLUID f 14.07 “ 4~. 7101 '0.2123 0.94'l6 "-6Y275T 0.34 FLUID 123.80 4.3128 0.2319 0 9357 -0.2773 0.34 f l u i d 133.58 3.9640 0.2523 0 9280 -0.2854 0. 34 f l u i d 143.42 3.6622 0.2731 0 9205 -0.2912 0. 34 FLUID 153.24 3.4046 0.2937 0 9143 -0.2916 0. 34 f l u i d 153.25 3.4015 0.2940 0 9136 -0.2940 0.34 f l u i d 163.10 3.1737 0.3151 0 9071 -0.2947 0.34 FLU ID 172.97 2.9693 0.3368 0 9001 -0.2966 0.34 FLUID 182.84 2.7820 0.3594 0 8915 -0.3020 0. 34 f l u i d 192.70 2.6208 0.3816 0 8851 -0.3012 0.34 f l u i d 212.51 2.3384 0.4276 0 8709 -0.3019 0.34 f l u i d 212.57 2.3359 0.4281 0 8702 -0.3032 0.34 f l u ID 232.35 2.1000 0.4762 0 8551 -0.3042 0.34 f l u i d 252•05 1.8974 0.5270 0 8381 -0.3072 0. 34 f l u i d 252.27 1.8961 0.5274 0 8383 -0.3066 0. 34 FLU I D 261.99 1.8081 0.5531 0 8302 -0.3071 0. 34 f l u i d 432.98 0.8755 1.1422 0 6643 -0.2939 0.34 FLUID 440.89 0.8473 1 .1803 0 6547 -0.2926 0.34 FLUID 450.78 0.8130 1 .2301 0 6422 -0.2908 0.34 FLUID 460.68 0.7793 1 .2832 0 6292 -0.2890 0.34 FLUID 470.56 0.7464 1.3398 0 6155 -0.2870 0.34 FLUID 490.35 0.6839 1.4621 0 5877 -0.2820 0.34 FLUID 510.14 0.6219 1.6079 0 5560 -0.2761 0.34 f l u i d 529.93 0.5593 1 .7879 0 5194 -0.2688 0. 34 f l u i d 549.71 0.4933 2.0270 0 4753 -0.2589 0. 34 FLUID 569.45 0.4144 2.4134 0 4135 -0.2430 0.34 FLUID 579.28 0.3597 2.7804 0 3651 -0.2283 0.34 f l u i d 589.03 3.2812 3.5560 0 2903 -0.1996 0.34 f l u i d 598.88 0.2338 4.2776 0 2454 -0.1764 0.34 f l u i d 608.83 0.2185 4.5773 0 2331 -0.1675 0.34 f l u i.d 628 . 7 6 0.2043 4.8948 0 2251 -0.1583 0.34 f l u i d 648.72 0.1964 5.0904 0 2233 -0.1526 0.34 END 12?" SAMPLE 23 T = 2 1 5 . 0 0 TYPE p. V* D. Z = (Z-l )V PHGC PSIA L/MOL MOL/L PV/RT L/MOLPSI i 1 io i. j i i j f l u i d 8 6 . 7 6 6.5532 0.1526 0.9659 -0.2238 ini FLUID 8 8 . 6 7 6.4050 0.1561 0.9648 -0.2255 0.54 FLU ID 9 2 . 5 0 6.1279 0.1632 0.9629 -0.2272 0. 54 FLU ID 98.27 5.7500 0.1739 0.9599 -0.2306 0. 54 FLUID 104.06 5.4114 0.1848 0.9566 -0.2349 0.54 FLU I D 113.74 4.9173 0.2034 0.9501 - 0 . 2453 0* 54 in ° • FLU ID 4.9167 113.76 j j 0.2034 0.9502 -0.2450 ! f l u i d 123.50 4.5014 0.2222 0.9444 -0.2503 0.54 F L U 1D. 133.28 4.1442 0.2413 0.9383 -0.2557 0.54 FLUID 147.01 3.7199 0.2688 0.9290 -0.2641 0 • 54 f l u i d 152.91 3.5653 0.2805 0.9261 -0.2634 0.54 f l u i d 162.76 3.3236 0.3009 0.9190 -0.2693 0.54 f l u i d 182.50 2.9236 0.3420 0.9064 -0.2736 0 • 54 f l u i d 192.37 2.7542 0.3631 0.9001 -0.2753 0. 54 f l u i d 192.47 2.7512 0.3635 0.8995 -0.2764 0* 54 f l u i d 2 0 2 . 2 8 2.5984 0.3849 0.8929 -0.2784 1 0.54 in 0 f t ■ f l u i d 202. 3 6 2.5964 0.3852 0.8925 -0.2790 • f l u i d 2 1 2 . 2 7 2.4572 0.4070 0.8861 - 0 . 2799 0.54 f l u I D 212.51 2.4554 0.4073 0.8864 -0.2789 0*54 f l u i d 2 3 1 . 9 8 2.2178 0.4509 0.8740 -0.2795 0.54 f l u i d 232 . 3 2 2.2147 0.4515 0.8740 -0.2790 0. 54 f l u i d 251.96 2.0092 0.4977 0.8600 -0.2813 0*54 f l u i o 252.17 2.0097 0.4976 0.8609 -0 . 2 7 9 5 0* 54 f l u i d 271.73 1.8349 0.5450 0.8470 -0 . 2 8 0 7 0 • 54 f l u i d 271 . 8 3 1.8311 0.5461 0.8456 -0.2828 0* 54 f l u i d 4 6 1 . 0 5 0.8860 1.1287 0.6939 -0.2712 0.54 f l u 10 4 6 1 • 1 3 0.8861 .1.1286 0.6941 -0.2710 0. 54 f l u i d 4 7 0 . 9 4 0.8552 1•1693 0•6842 -0.2701 0.54 f l u i d 4 9 0 . 6 9 0.7978 1.2535 0.6650 -0.2672 0*54 f l u i d 5 1 0 . 5 5 0.7437 1.3447 0.6450 - 0 . 2640 0* 54 END ■128 SAMPLE 23 T = 230•03 _ TYPE______P. ______V. D»______Z =______(Z- 1JV P HGC ^ ______PSIA____ L_/M0L____ MOL/L __PV/RT___ L/MOL PSI FLUID. 104.19 5.5973 '0.1736 0.9612 -0.2172 0.84 “ FLUID “ 113.39 5.0996' 0.1961 0.9572 -0.2184" 0*84 "FLUID 123.61" 4 .'6727 0.'2140 0.9519 '-0.2248'.oT84 fluid' 1 3 3 . 3 7 4 . 3 0 3 4 o'.2 3 2 4 ' o'.'9459 - 0 . 2 3 2 9 o.*84' FLU'ID 152.99 ' 3.7096 0.2696"' 0.9353"' -0.2399' 0.84 FLUID 182.58 "3.0538 " 0.3275 “0.9189" -0 •2477" 0*84 FLUID ’ 212.25 2.5789 0.3878 0.9021 -0.2525 0.84“ F L U I D ______• 01 2 .21 71~~__ 0 .451 0__ 0_. 8843'"_"-0 • 25 6 5 0 • 84_ FLU ID 27lT82 1 .9345 0.51~69 " 0 .8666' "-5“. 2 5 8 1 " o ■ 84 ” FLU ID 4 94 . 77 0 .8773 ~ 1~. 13 9 8 __ 0.7154 ~-0~.249~7_0. 84_ F L U I D 5 1 0 . 6 2 0.8360 1 *1962" 0V7035 -0.2479 J.S4 f l u i d 5 3 0 . 4 4 __ o . 7870 ~ 1. 2 7 0 6 0 . 6 8 8 0 - 0 . 2 4 5 5 0 . 8 4 FLU. ID_____ 560.21 0.7195 1.3899 0.6642 -0.2416 0.84 FLU I D,_____ 589. 9 8__ 0.6573 1.5215 0.6391 __-0 .2372 __ C._8_4_ FLUl D~ "'619.86 0".5995 176681 0.6124" -c". 2324 0^85 FLUID 649.69__ 0.5467 1.8293 0.5853~ -0.2267 0.85~ FLUID 689.45 0.4813 2.0777 0.5469 -0.2181 0.85 FLUID" 729.24 0.42~16 __2.3717" " 0.5067 -Q.2080___ 0«"85 FLUID 769.04 0.3674" 2.7216" 0.4657 -0.1963 0.85 END SAMPLE 24 BORDER CURVE TYPE T. P. V.» D. Z = PHGC DE G C P S I A L/MOL MOL/LPV/RTPSI DEW 130,02 178.92 2 . 1 1 7 5 0.4723 0.7793 0.02 DEW 170.00 366.58 0 * 8816 1'. 1 342 0.6048 0. 12 DEW 180.05 431• 17 0•6847 1.4606 0.540 2 0. 17 DEW 185.03 466.01 0*5953 1.6798 0.5021 0.21 DEW 190.03 504 . 6 3 0.4974 2.0106 0.4494 0.24 DEW 192.52 524.61 0.4459 2.2426 0.4166 0.27 DEW 195.02 54 5 . 5 9 0. 3 8 2 8 2.6121 0.3700 0.29 DEW 195.95 553.69 0*3517 2.8433 0.3442 0.30 DEW 196.65 5 6 0 . 3 9 0.-2950 3.3894 0.2918 0.30 DEW 196.66 5 6 0 . 5 3 0*28 8 9 3.4611 0.2859 0*30 CRT CAL 196.65 5 6 0 . 6 5 0.2730 3.6629 0.2702 0.30 BUBBLE 195.96 5 5 5 . 4 2 0.22 6 7 4.4109 u.2226 0.30 BUBBLE 195.02 547.81 0.2138 4.6783 0.2074 0.29 BUBBLE 1 92 • 53 527.80 0.1962 5.0975 0.1844 0.27 BUBBLE 190.01 508.24 0.1862 5.3713 0.1694 0.24 b u b b l e 185.03 471. 18 0.1733 5.7696 0.1478 0.21 BUBBLE 180.05 4 3 6 . 3 6 0.1646 6.0744 0.1314 0. 17 BUBBLE 170.00 372 . 8 5 0.1527 6.5481 0. 1066 0. 12 BUBBLE 130.02 185.24 0.1282 7.7987 0.0489 0.02 END SAMPLE 24 T = 130.02 TYPE P. V« 0* Z = (Z-l)V PHGC PSIA L/MOLMOL/L PV/RT L/MOL PSI VAPOR 78 . 6 3 5.7332 0.1744 0.9272 -0.4172 0.02 VAPOR 84.37 5.3000 0.1887 0.9197 -0.4254 0.02 VAPOR 94. 02 4.6901 0.2132 0.9070 — 0 * 4362 0.02 VAPOR 103.72 4.1897 0.2387 0.8938 -0.4449 0.02 VAPOR 1 13.46 3.7736 0.2650 0.8806 -0.4504 0.02 VAPOR 123.25 3.4206 0.2923 0.8671 -0.4545 0.02 VAPOR 133.06 3.1162 0.3209 0.8528 -0.4586 0.02 VAPOR 142.88 2.8514 0.3507 0.8380 -0.4620 0.02 VAPOR 152.75 2.6164 0.3822 0.8220 -0.4656 0.02 VAPOR 162.62 2.4107 0.4148 0.8063 -0.4669 0.02 VAPOR 172.49 2.2270 0.4490 0.7901 -0.4674 0.02 o o CVI VAPOR 177.44 2.1400 0.4673 0.7810 -0.4686 • VAPOR 178.42 2.1242 0.4708 0.7795 -0.4683 0.02 SAMPLE 24 T” 170700 TYPE P. V. D. Z = (Z-l )V PHGC PSIA L/MOL MOL/L PV/RTL/MOL PSI VAPOR 86.60 5.8475 0.1710 0.9476 -0.3064 0.12 VAPOR 94.30 5.3329 0.1875 0.9411 -0.3144 0.12 VAPOR 103.96 4.7932 0.2086 0.9325 -0.3237 0*12 VAPOR 113.68 4.3439 0.2302 0.9241 -0.3298 0. 12 1 OJ a • VAPOR 123.45 3.9594 0.2526 0.9147 -0.3379 1 OJ O! • VAPOR 133.25 3.6317 0•2753 0.9056 -0.3429 i VAPOR 152.82 3.1016 0.3224 0.8870 -0.3506 0. 12 VAPOR 172.58 2.6875 0.3721 0.8679 -0.3550- 0. 12 VAPOR 182.47 2.5102 0.3984 0.8571 -0.3587 0. 12 VAPOR 192.37 2.3553 0.4246 0.8478 -0.3584 0.12 VAPOR 202.29 2.2138 0.4517 0.8380 -0.3586 0. 12 VAPOR 222.12 1.9650 0.5089 0.8168 -0.3601 0. 12 j i o cvj! ^•4 i • : i VAPOR 359.21 0.9232 1.0832 0.6206 -0.3503 ! i o ! — j VAPOR ! 363.14 0.9012 1.1097 0.6124 -0.3493 END SAMPLE 24 T = 196.65 TYPE ______P ^ ______V.______p*______Z-______(Z-l )V PHGC PSIA L/MOL MOL/L PV/RT L/MOL PSI CRT _V______94.35 5.7377 __ Q. 1 743 ___ 0 .9556__- 0 . 2 550 0. 3 0 C R j ’j/ 103.98 5.1717__ 0.1934___0 .9492 _-^0.^2627__ 0. 30 CRT V 1 13 .72 *4.6949 *' ~ 0.2 130 "6 .'9424*" -0 .2704 0 « 30~ CRT V 133.25 3.9446__ C.2 5 3 5 ____ 0.9278 -0^2849_0. 30 CRT V_____ 152.91^ 3.3851 *0.29*54 ' 0. 9**137 - 0 . 2 9 2 3 Q.~30 CRT V* 172.65 2.9517 0.3388' *0.899*5 -0.2966 0.30 CRT V 192.43 ' 2.6037 0.3841 0.8844 -0.3010* 0.30* CRT V 2j2/24_ 2.3208* ' 0*.~4309 0.8694 '*-0.3030 U~.3*0 CRT V *23*2.06 2.0858**..**0.4794.. "”5.8544 *"-0.~3038 67 3 o" CRT__V ___4*1*4ji92*__ 0^922 7_~___ U 0 8 3 7 ___ C • 6*758 * -0.2992 0.30* CRT V 430.7*5 0.8631 1.*1*586 0~.6562 -0.2967 0.30 CRT V__ 45 0.53 ___0.7925 ___1 .261*8____ 0jl6 3 0 | L _ “P *2 9 30__0j.*30 C RT V 470.33____ 0.7251 1.37*90 0.6020 - 0 . 2 8 8 *6_0^_3C CRT V _ _ i 1 _ j0.6589_ Jj>5J 77_ _ l q ._5700 _ r 0*.283*3__ 0 . 30 C RT*'V ~~ * 5 0 9 .88 ~ " 0.5926 **1.6875' 0*. 53:33 -o'.2765 ' 0.*30 CRT V 529.70 0.5283 1.89*28 *0.*494*0* -0.2673 0.30 C R T V "'* 549.*39 0 . 4 3 38 __ 2*.3*054 *0.4 2 0 6 -0*.251 3 0 .30* CRT___V___ 5 5 4.29__" 0 . 4 0 2 2 __ 2.4*86*6 0.393*5" -0.2439 0.3 0 CRT V 559.14 0.3525 ___2.8365 *0.3479 -0.2299 5.30 END 132 SAMPLE 24 T = 230.02 TYPE p. V» D« Z = (Z-l)V PHGC PSIA L/MOLMOL/L PV/RT L/MOLPSI f l u i d 103.77 5.6454 0.1771 0.9655 -0.1949 0 • c34 f l u i d 113.45 5.1360 0.194 7 0.9603 -0.2039 0. 84 f l u i d 133.01 4.3332 0.2308 0.9499 -0.2172 0.84 f l u i d 152.64 3.7312 0.2680 0•9386 -0.2290 0. 84 f l u i d 182.23 3•0700 0.3257 0.9220 -0.2394 0. 84 FLUID 211.92 2.5913 0.3859 0.9050 -0.2461 0 • 84 f l u i d 271.49 1.9453 0.5140 0.8704 -0.2521 0 . 84 f l u i d 480.44 0.9234 1.0829 0.7312 -0.2482 0.84 FLUID 490.37 0.8953 1.1169 0.7235 -0.2475 0. 84 FLUID 520.10 0.8178 1.2228 0.70 1 C -0.2445 0. 84 . FLUID 549.89 0.7473 1.3381 0.6773 -0.2412 o ! C D ! \f> CO f l u i d 579.66 0.6829 1.4644 0.6524 -0.2374 i ° f l u i d 609.47 0.6243 1.6019 0.6270 -0.2328 0. 85 f l u i d 639.30 0.5698 1.7551 0.6003 -0.2277 0.85 f l u i d 669.13 0.5186 1 .9284 0.5719 -0.2220 0.85 f l u i d 698.95 0.4708 2.1242 0.5423 -0.2155 0.85 O C o in f l u i d 728.78 0.4261 2.3470 0.5118 -0.2080 . FLUID 758.60 0.3844 2.6014 0 . 4806 -0. 1997 0.85 END SAMPLE 25 BORDER CURVE TYPE T, P. V. D. Z = PHGC D E G C PSIA L/MOL MOL/L PV/RT PSI DEW 129.98 181.31 2.0708 0.4829 0.7723 0.02 DEW 170.04 367.51 0.8620 1.1600 0.5928 0. 12 DEW 174.58 392.27 0.7856 1.2725 0.5709 0. 14 DEW 178.01 413.14 0.7040 1 .4204 0.5346 0.16 CVJ o o DEW 184.02 448.38 0.6440 1.5529 0.5237 . DEW 188.07 473.27 0.5932 1.6358 0.5048 0.23 DEW 191.15 493.01 0.5571 1.7950 0.4905 0.25 DEW 193.08 50 4.99 0.5391 1.8550 0.4842 0.27 DEW 193.81 523.80 0.4618 2.1653 0.4296 0. 28 DEW 194.26 535.39 0.3917 2.5529 0.3721 0.28 DEW 194.26 535.37 0.3919 2.5514 0.3723 0. 28 DEW 194.29 538.84 0.3024 3.3071 0.2891 0 • 28 CRTCAL 194.26 538.71 0.2926 3.4173 0.2797 0. 28 BUBBLE 193.10 529.85 0.2289 4.3679 0.2158 0.27 BUBBLE 191.13 514.27 0.2106 4.7493 0.1934 0. 25 BUBBLE 138.08 491.17 C.1964 5.0922 0.1734 0.23 BUBBLE 184.03 461.61 0.1843 5.4255 0.1543 0.20 BUBBLE 170.04 370.77 0.1623 6.1630 0.112613 0. 12 BUBBLE 170.04 370.82 0.1624 6.1560 0.1127 CVJ END SAMPLE 25 T = 129.98 TYPEP. V. D. Z = (Z-l )V PHGC PSIA L/MOLMOL/L PV/RT L/MOLPSI VAPOR. 84 • 37 5.3072 0. 1884 0.9211 -0.4189 0*02 VAPOR 9 4 . 0 0 4.6967 0.2129 0.9082 -0.4313 0«02 VAPOR 103.67 4.1978 0.2382 0.8952 - 0 .4399 0.02 VAPOR I 13.38 3.7786 0.2646 0.8813 -0.4486 0.02 VAPOR 123.16 3.4224 0.2922 0.8671 -0.4550 u. 02 VAPOR 137.39 2.9808 0.3355 0.8455 —0.4606 0.02 VAPOR 152.65 2.6158 0.3823 0.8214 -0.4672 0.02 VAPOR 167.47 2.3138 0.4322 0.7971 —0.4695 0.02 S A M P L E 25 T =~ 170.04 TYPE P. V. D. Z = (Z-l>V PHGC PSIA L/MOLMOL/L PV/RT L/MOLPSI VAPOR 94.29 5.3374 0.1874 0.9417 -0.3113 ° i 0. 1 1 12j I | 1 1 ! VAPOR 103.96 4.7959 OJ 0.2085 ! 0.9329 -0.3218 1 j o OJ VAPOR 113.68 4.3433 0.2302 0.9239 - 0 . 3307 •' VAPOR 123.45 3.9603 0.2525 0.9148 -0.3374 0. 12 VAPOR 133.25 3.6345 0.2751 0.9062 -0.3410 0. 12 VAPOR 152.91 3.0990 0.3227 0.8867 -0.3512 0.12 VAPOR 172.64 2.6839 0.3726 0.8670 -0.3571 0. 12 VAPOR 192.43 2.3517 0.4252 ' 0.8468 -0.3604 0. 12 VAPOR 2 12 . 2 2 2.0749 . 0.4819 0.8239 -0.3653 0. 12 VAPOR 232. 10 1.8475 0.5413 0.8023 -0.3652 0. 12 VAPOR 361.13 0.8989 1.1125 0.60 74 -0.3529 0.12 END 135--- ~ SAMPLE 25 T = 194.26 TYPEP, V. D. Z = (Z-l>v PHGC PSIA L/MOLMOL/L PV/RT L/MOL PSI CRT V 113.81 4.6615 0.2145 0.9412 -0.2739 0.28 CRT V 113.35 4.6609 0.2146 0.9414 -0.2730 0.28 CRT V 133.38 3.9148 0.2554 0.9264 -0.2882 0.28 CRT V 153.04 3.3567 0.2979 0.9114 -0.2974 0.28 CRT V 172.75 2.9219 0.3422 0.8955 -0.3053 0.28 CRT V 192.60 2.5778 0.3879 0.8808 -0.3072 0.28 CRT V 212.41 2.2940 0.4359 0.8645 -0.3109 0.28 CRT V 232.24 2.0561 0.4364 0.8472 -0.3142 0.28 CRT V 260.03 1.7850 0.5602 0.8235 -0.3151 0.28 CRT V 421.01 0.8701 1•1492 0.6499 -0.3046 0.28 CRT V 4 40 . 7 7 0.7950 1.2579 0.6217 -0.3C08 0.28 CRT V 460.56 0.7227 1.3838 0.5905 -0.2959 0.28 CRT V 490.17 0.6159 1•6235 0.5356 -0.2860 0.28 CRT V 509.95 0.5390 1.8552 0.4877 -0.2762 0. 28 CRT V 529.63 0.4404 2.2709 0.4138 -0.2531 0.28 CRT V 535.35 0.3917 2.5531 0.3720 -0.2460 0.28 END SAMPLE 25 T = 230.01 TYPE P. V. D» Z = (Z-l>v PHGC PSIA L/MOL- — • MOL/L PV/RT L/MOLPSI FLUID 113.50 5. 1341 0.1948 0.9604 -0.2034 0.84 FLU I D 133.03 4.3339 0.2307 0.9502 -0.2158 0.84 FLU I D 152.65 3.7319 0.2680 0.9389 -0.2281 0. 84 f l u i d 172.34 3.2666 0.3061 0.9278 -0.2358 0 . 84 f l u i d 192• 1 0 2.8942 0.3455 0.9163 -0.2422 0 . 84 FLUID 21 1 .90 2.5904 0.3860 0.9047 -0.2470 0. 84 FLUID 231.74 2.3388 0.4276 0.8933 -0.2496 0. 84 FLUID 291.37 1.784 0 0.5605 0.8567 -0.2556 0. 84 f l u i d 490.42 0.8896 1.1241 0 .7190, -0.2500 0.84 f l u i d 520.15 0.8114 1.2324 0.6956 -0.2470 0.84 f l u i d 549.92 0.7404 1.3507 0.6710 -0.2436 0 • 84 f l u i d 589.60 0.6556 1.5254 0.6370 -0.2379 0 . 84 FLUID 629.32 0.5794 1.7260 0 .6009 -0.2312 0.8 5— f l u i d 669.08 0.5106 1.9584 0.5631 -0.2231 0 . 85 FLU IdT~ 71 8jQ2_ " 0 ^ 4 3 2 7 ^ . T l T z 0 ^ 5 1 2 6 ..-0~.21~09 * oVs5 Fluid 768 .“5 7 ’ 0 • 3653“ *2T 7374 674627 7o7i963 o.ss f l u i d 808.39 0.3211 3.1146 0.4278 -0.1837 0.85 FLUID 818.36 0.3111 3.2144 0.4196 -0.1806 0.85 . f l u i d 848.24 0.2863 3.4934 0.4002 -0.1717 0.85 f l u i d 878.18 0.2666 3.7510 0.3859 -0.1637 0.85 END 137. SAMPLE 26 BORDER CURVE TYPE T . P. V. D. Z = PHGC D E G C PSIA L/MOL MOL/L PV/RT PSI DEW 130,00 160.40 2.4740 0.4042 0.8163 0.02 DEW 170,00 359.71 0.9273 1.0784 0.6242 0 * 12 DEW 175,03 392.20 0.8157 1.2259 0.5920 0. 14 DEW 178.86 417.97 0.7380 1.3549 0.5659 0. 16 DEW 184.00 451.81 0.6517 1.5345 0.5341 0.20 DEW 188.00 479.79 0.5365 1.7049 0.5061 0. 23 DEW 192.00 510.79 0.5153 1.9406 0.4692 0.26 DEW 196.00 548.11 0.4076 2.4532 0.3949 0.30 DEW 197.46 561.93 0.3517 2.8435 0.3482 0*31 __ — DEW 198. 15 568.48 0.3110 3.2150 0.3111 0. 32 DEW 198.17 568.72 0.3058 3.2700 0.3060 0.32 DEW 198.17 569.31 0.2755 3.6301 0.2759 0.32 CRT CAL 198.15 569.19 0.2720 3.6758 0.2725 0. 32 b u b b l e 197.46 564.24 0.2265 4.4146 0.2252 0.31 BUBBLE 196.00 552.16 0.2030 4.8081 0.2030 0.30 BUBBLE 192.00 520. 0 5 0.1367 5.3557 0. 1731 0.26 BUBBLE 188.00 489.58 0.1755 5.6983. 0.1545 0.23 BUBBLE 184.00 460.65 0.1676 5.9662 0. 1401 / 0.20 BUBBLE 178.86 425.50 0.1602 6.2405 0.1251 } 0*16 BUBBLE 175.04 400.94 0.1553 6.4400 0. 1152/ 0. 14 BUBBLE 170.00 370.03 0.1503 6.6552 0. 1 040 0. 12 END — -— “ ^38 SAMPLE 26 T = 130.00 TYPE P. V. D » Z = (Z-l)V PHGC PSIA L/MOL MOL/L PV/RT L/MOL PS I VAPOR 60.90 7.6433 0.1308 0.9575 -0.3252 0.02 _ VAPOR _64*68 ___7 • 164 i 0.1396 _ 0.9531 -0.3358 0* 02 'VAPOR 74 • 2 0 “ '“' 6 7 1 6 5 3 "~0*T6 2 2 ... 0^9411 -0 .3634 0• 0 Z V APOR 83.83 5.3827 0.1858 0.9282 -0.3867 0.02 VAPOR 93 . 55 4.7574 0.2102 0.9155 -0.4022 OJ VAPOR 103.30 4.2450 0.2356 0.9020 -0.4160 0.0 2 VAPOR 113.09 3.8195 0.2615 0.8885 -0.4259 0.02 VAPOR 127.85 3.2975 0.3033 0.8672 -0 .4380 0.0 2 VAPOR 142.65 2.8806 0.3472 0.8452 -0.4458 0.02 VAPOR 157.49 2.5382 0*3940 0.S222 -0.4512 0.02 SAMPLE 26 T = 170.00 TYPE P. V. D. Z = (Z-l)V PHGC PSIA L/MOLMOL/L PV/RT L/MOL PSI VAPOR 68.69 7.5600 0.1323 0.9717 -0.2136 0. 12 VAPOR 74.40 6.9467 0.1440 0.9671 -0.2282 0.12 W V APOR 84.00 6.1015 0.1639 0.9591 -0.2496 0. 12 V APOR 93.69 5.4208 0.1845 0.9504 -0.2690 0. 12 VAPOR 103.42 4.8632 0.2056 0.9412 -0.2861 0. 12 VAPOR 113.22 4•40 1 4 0.2272 0..9325 -0.2971 0. 12 VAPOR 127.95 3.8374 0.2606 0.9188 -0.3116 0. 12 VAPOR 142.73 3.3884 0.2951 0.9050 -0.3219 0. 12 VAPOR 157.54 3.0241 0.3307 0.8915 -0.3281 0. 12 VAPOR 172.41 2.7169 0.3681 0.8765 -0 .3354 0. 12 VAPOR 192.24 2.3806 0.4201 0 . 8 5 6 4 -0.3419 0.12 END SAMPLE 26 T = 198• 1 5 TYPE______P(______Dj____ Z=______(Z-l )V P HGC PSIA L/MOL MOL/L PV/RT L/MOL PSI CRT V 83.81 __6 . 5 9 2 6 ~" 0 . 1 5 1 7 0.9722 -0.1834 0 .32 _ C RT V 9 3 . 4 8 _ 5.871 __ 0. 1 703 0 . 9 6 5 7 ~__-o72016 0. 32 CRT~V 103.18 ~~5'^2856 "07 1892" 0.9596 " - 0 ,2 136'~ 6 T 3 2 _ C RT V__ 1 12. 9 6 4 . 7 9 4 2 0.2086.___ JO • 9529 -Q.2259 0.32_ CRT V 132.61 4.0193 0.2488 0.9379 -0*2495 0*32 CRT V 132.84 4.6130 0.2492 0.9380 -0.2490 0.32 CR T V ___ 1 52 . 58 3 7 4 4 2 8 ... 0.2905 0.9243 -0.2607___ Q. 32 _ CR T V____1 7 2 . 3 8 ___ 3 . 0 0 1 2 __ 0.3332___ 0 . 9 103____-0.2693_ 0.32 _ C R T V " ~ 1 9 2 . 2 1 ~2~»6 4 6 1" "'673779 " 0^8949 '"-0.2781 ""'0~^3 2 ’ CRT V 212.05 2.3563 ~0. ~ 4 2 4 4 __ 0.8791 - 0 . 2 6 4 8 0.32 CRT V 361.15 1.1744 0.6515 "o. 7463 -0.’2980 0. 32 CRT V "380.91 ' 1 .0826 0. 9 2 3 6 " ' 0 . 7 2 5 7 ’ -6.2970 0. 32 CRT V "410.56 0.9592 1.0425__ ~0.693 0 __ -0.2945 0.32 J CRT__ V ____ 440.33 0.8482 ' l7l 790___ 0.6572___- 0 . 2 908__0 . 3 2 CRT V 470*66 0.7455 ~ 1.3413 ' ”0^6166 "-0.2858 0.32 C RT V ’ 4 9 9 . 8 3 0 ."64"78 " 1.5436 0.5697 " -5.2787 0.32 " CRT V 529• 57 0.5477 1.8258 *0".51~04 -0.2682" 0.32* CRT V ' 559.23 "674204 27 3784""" "6.4"'l37 -0.2465 0.32 CRT V 565.13 ' 0.3755" 2.6632 "" 0.3734 -0.2353 0.32 END -I^O- sample 26 T = 230.00 TYPE P. Vi D< Z = (Z-l )V PHGC PSIA L/MOL MOL/L PV/RTL/MOL PS I fluid 83.82 7.1238 0. 1404 0.9841 -0.1131 0.83 FLU ID 93.45 6.3612 0.1572 0.9797 -0.1288 0.83 FLUID 103.17 5.7329 0.1744 0.9748 -0.1444 0 * 83 fluid I 12.95 5.2090 0.1920 0.9697 -0.1578 0.84 FLUID 132.56 4.3905 0.2278 0.9592 -0.1790 0. 84 FLUID 152.28 3.7760 0.2648 0.9477 -0.1975 0*84 i O O C - f s ■ FLUID 172.01 3.3026 0.3028 0.9363 -0.2104 • FLUID 191 .86 2.9275 0.3416 0.9257 -0.2175 0.84 FLUID 211.69 2.6183 0.38 19 0.9135 -0.2265 0.84 FLUID 2 3 1 .sa 2.3669 0.4225 0.9034 -0.2287 0. 84 FLUID 410.57 1.1637 0.8593 0.7875 -0.2473 0.84 fluid 430 .38 1.0909 0.9167 0.7738 -0.2468 C . 84 FLUID 460.11 0.9923 1.0078 0.7525 -0.2456 0 . 84 fluid 489.88 0.9042 1•1060 0.7300 -0.2441 0.84 FLUID 519.69 0.8254 1.2115 0.7070 -0.2419 0.84 i D C 0 - } s ■ fluid 549.52 . 0.7540 1.3263 0.6829 -0.2391 i FLUID 5 8 9 . 2 6 0.6688 1.4952 0 .6496 -0.2344 0. 84 FLUID 629.02 0.5924 1.6881 0.6141 -0.2286 0.85 fluid 678.75 0.5047 1.9812 0 . 5 6 4 6 -0.2197 0.85 FLUID 728.54 0.4264 2.3450 0.5120 -0.2081 0.85 fluid 808.24 0.3207 3.1179 0.4272 - 0 . 1837 0 . 8 5 fluid 907.94 0.2412 4.1459 0.3609 -0.1541 0* 85 END BIBLIOGRAPHY 1. Dalton, J. Mem. Manchester Phil. Soo., 5*585 (1802). 2. Lecat, M. L ’azeotropism, donnees experimentales, bibllographie, Burxelles (191&). 3. Lecat, M. Tables Azeotroplques 1 , Bruxelles (19*+9). SwTetoslawski, W. Rozniki Chem. 32, 929 (1958). . 5. Swietoslawski,. * iiskuasmntim}K»<. .... Aoad»...... ■ Polon. ■ ■ in . Soi...... iet. III Lettres i n ■ n I ■■■A ■■■ ,9 19 (1950). \ 6 . Swietoslawski, W. Bull. Aoa%L. Polon. Soi. et. Lettres A , 87 (1951). | f 7. Horsley, L. H. "Azeotropic j&ata," American Chemical Society, Washington, 1952; Supplement, American Chemical Society, 1962. 8. Kay, W. B. J. Phys. Chem. 68, 827 (196*0. 9. Jordan, L. W., and Kay, W. B. Chem. Eng. Prog. Series 59» *+6 (1963). 10. Skaates, J. M . , and Kay, W. B. Chem. Eng. Sci. 19, *1-31 (196*+). 11. Kreglewski, A. Bull. Acad. Polon. Sci., C. Ill, 323 (1957). • 12. Ibid., p. 329. 13. Ibid., p. 431. l*+. Hildebrand, J. H. , and Scott, R. L. ,!The Solubility of Non-Electrolytes," Reinhold Publishing Corporation, New York, 1950. 15. Rowlinson, J. S. "Liquids and Liquid Mixtures," Academic Press, Inc., New York, 1959 j PP. 333—^5- 16. Westwater, W., Frantz, H. W., and Hildebrand, J. H. Phys. Rev. 31, 135 (1928). 17. Hildebrand, J. H. Phys. Rev. 3*4-» 6*+9, 98*+ (1929). 18. Hildebrand, J. H., and Carter, J. M. J. Am. Chem. Soc. 5*+» 3592 (1932). 19. Hildebrand, J. H., and Wood, S. E. J. Chem. Phys. 1 , 817 (1933). 1*+1 142 20. Brown, C. H. M. Sc. thesis, The Ohio State University, 1959. 21. Pennington, R. E., and Kobe, K. A. J. Am. Chem. Soo. 79. 300 (1957). 22. Bottomley, G. A., and Spurling, T. H. Mature 195, 900 (1962). 23. Browni I., and Smith, F. Australian J. Chem. 13, 37 (I960). 24. Lambert, J. D., Roberts, C. A. H., Rowlinson, J. S., and Wilkinson, V. J. Proo. Roy. Soo. (London) A196, 113 (1949). 25* Leverett, G. F. Ph. D. dissertation, The Ohio State University, 1959. 26. Young, S. J. Chem. Soo. (London) £1, ^ 6 (1897)• 27. Rose-Innes, J., and Young, S. Phil. Mag. 5 47, 353 (1899). 28. Young, S. Soi. Pro. Roy. Dublin Soo. 12, 374 (1910). 29. Beattie, J. A., Levine, S. W., and Douslin, D. R. J. Am. Chem. Soc. 74, 4478 (1952). 30. McGlashan, M. L., and Potter, D. J. B. Proo. Roy. Soc. A267, 478 (1962). 31. Garner, M. D. G., and MoGoubrey, J. C. Trans. Faraday Soo. 1524 (1959). 32. Jepson, W. B., Richardson, M. J., and Rowlinson, J. S. Trans. Faraday Soo. 53, 1586 (1957). 33. -Tepson, W. B., and Rowlinson, J. S. J. Chem. Phys. 23, 1599, (1955). 34. Rowlinson, J. S., Sumner, F. H., and Sutton, J. R. Trans. Faraday Soo. 50, 1 (1954). 35* Kay, W. B., and Rambosek, G. M. Ind. Eng. Chem. 45, 221 (1953). 36. Kay, W. B., and Donham, W. E. Chem/ Eng. Soi. 5 , 1 (1955). 37. Timmermans, J. ’'Physico-Chemical Constants of Pure Organic Compounds," Elsevier, New York, 1950. 1^3 38. Hirschfelder, J. 0., Curtiss, C. F., and Bird, R. B. "Molecular Theory of Gases and Liquids," John Wiley and Sons, Inc., New York, 195^. 39. McAdams, W., M. Sc. thesis, The Ohio State University, 1958. ^0. Kobe, K. A., and Lynn, R. E. Chem. Rev. 52, 117 (1953)* *H. Beattie, J. A., Levine, S. W., and Douslin, D. R. J. Am. Chem. Soc. 73. *(431 (1951). ^2. Othmer, D. F., and Ten Eyke, E. H. Ind. Eng. Chem. ifl, 2897 (19^9). ^3« Rowlinson, J. S."Liquids and Liquid Mixtures," Academic Press, Inc., New York, 1959j pp. 211-13. ^4. Skaates, J. M. Ph. D. dissertation, The Ohio State University, 1961. ^5. Hodgman, C. D. "Handbook of Chemistry and Physics," Edition 31> Chemical Rubber Publishing Co., Cleveland, 19^9, P. 1722. 4-6. Comings, E. W. "High-Pressure Technology," McGraw Hill, New York, 1956, pp. 161-5 . ^7. Shand, E. B. "Glass Engineering Handbook," Corning Glass Works, Corning, New York, 1955* ^8 . Johnson, D. P., Cross, J. L., Hill, J. D., and Bowman, H. A. Ind. Eng. Chem. ^9» 20^6 (1957). ^9» Cross, J. L. "Reduction of Data for Piston Gage Pressure Measurements," National Bureau of Standards Monograph 65» U. S. Government Printing Office, Washington, D. C., June 17, 1963. 50. Adamson, A. W. "Physical Chemistry of Surfaces," Interscience Publishers, New York, i960, p. 6 . 51. Guggenheim, E. A. J. Chem. Phys. 13» 253 (19^5). 52. Forsythe, W. E . , Ed. "Smithsonian Physical Tables," 9th Ed. Rev., Smithsonian Institute, Washington, D. C., 195^» p. 606. 53. Douglass, T. B., etal. J. Res. National Bureau Standards ^6 , 33^ (1951)« 144 54-. Taylor, H. S., and Glasstone, S. (Editors) "A Treatise on Physical Chemistry,” 3rd ed., Vol. II, D. van Nostrand Co., Inc., New York, 1951> P» 228. AUTOBIOGRAPHY I, Robert Homer Cherry, Jr., was born in Philadelphia, Pennsylvania, on March 1931* I attended public schools in Glenside and Abingdon, Pennsylvania. I received my undergraduate training at Pennsylvania State University, which granted me the Bachelor of Science degree in Chemical Engineering in 1953- After three years of industrial experience with the Ethyl Corporation in Baton Rouge, Louisiana, I entered the University of Michigan, which granted me the degree Master of Science in Chemical Engineering in 1958. In October, 1958, I was appointed Linde Postgraduate Fellow in Chemical Engineering at the Ohio State University. This appointment was renewed in October i960. For the academic year 1959-1960, I was the DuPont Postgraduate Teaching Assistant for the Department of Chemical Engineering. During the summer of i960, I was appointed National Science Foundation Summer Teaching Fellow. From 1962 until March 196^, I served as a Research Assistant to Professor Webster B. Kay in this department. Since March 196^, I have been a Senior Chemical Engineer at Battelle Memorial Institute.