STABILITY AND IONIZATION
CONSTANTS OF COMPLEXES
OF CATECHOL AND BORIC ACID
A THESIS PRESENTED IN PART REQUIREMENT FOR ADMISSION
TO THE DEGREE OF MASTER OF SCIENCE IN THE UNIVERSITY
OF NEW SOUTH WALES
BY
KWAT IE THE
SUBMITTED
JANUARY, 1962 TABLE OF CONTENTS
PAGE
ACKNOWLEDGEMENTS
ABSTRACT ii
CHAPTER INTRODUCTION
1.1 COMPLEX FORMATION OF BORIC ACID . .
1.2 STRUCTURE AND PROPERTIES OF BORIC ACID 2
1.3 COMPLEX COMPOUNDS OF BORIC ACID WITH Dl- OR POLY-HYDROXY COMPOUNDS 3
1.4 PREVIOUS QUANTITATIVE STUDIES OF BORIC AC I D-D IOL SYSTEM 6
1.5 SUMMARY 10
CHAPTER THEORETICAL CONSIDERATIONS
11.1 METHOD 12
1 I .2 TITRATION CURVE 12 I I .3 MATHEMATICAL FORMULATION OF EQUILIBRIA 16 I I .4 DERIVATION OF THE THEORETICAL EQUATIONS 18 I I .5 APPLICATION TO THE CASE WHERE MOLE RATIO OF CATECHOL: BOR I C ACID = I*. I 22
11.6 EVALUATION OF K, 28
CHAPTER 111 EXPERIMENT
I 1 1 .I MATER IALS 30
1 I I .2 APPARATUS 32
111.3 PROCEDURE 33
111.4 DISCUSSION OF THE METHOD 35
CHAPTER IV DISCUSSION OF THE RESULTS
IV.I CASE I; [ C] IS NEGLIGIBLE 38
IV.2 CASE 2; [ C] IS NOT NEGLIGIBLE 40
IV.3 THE APPROXIMATE VALUES OF K&t AND K_ TABLE OF CONTENTS. (CONTD)
PAGE
CHAPTER IV DISCUSSION OF THE RESULTS (contd)
IV. 4 CALCULATION OF K., K AND K. 42 a» 3 IV. 5 PROBABLE ACCURACY OF THE CONSTANTS .. 44
IV. 6 DISCUSSION OF THE VALUES OF [C] 45
IV. 7 CALCULATION OF THE CONCENTRATIONS OF THE VARIOUS SPECIES IN THE SOLUTION ., .. 45
IV. 8 DISCUSSION OF THE VALUES OF THE CONCENTRATIONS OF THE VARIOUS SPECIES 46
IV. 9 THE APPROXIMATE VALUE OF .. 59
IV.|0 JUSTIFICATION 0F THE ASSUMPTIONS 61
IV. I | EVALUATION OF K? FROM RIGOROUS TREATMENT 63
CHAPTER V CRITICAL EVALUATION OF PREVIOUS YORK ON CATECHOL-BORIC ACID COMPLEXES
V.I ANTIKAINEN'S EQUATION FOR THE DETERMINATION OF BORIC ACID-CATECHOL COMPLEX CONSTANTS 65
V. 2 CRITICISM OF ANTIKAINEN'S WORK 68
V. 3 THE WORK OF ROY, LAFERRIERE AND EDWARDS 70
V.4 CRITICISM OF THE WORK OF ROY AND CO-WORKERS 73
V.5 WORK OF SCHAFER 76 • • V.6 criticism of schafer’s work .. 77
CHAPTER VI. THERMODYNAMIC STUDIES
V INTRODUCTION 79
VI.2 EQUILIBRIUM CONSTANTS AND TEMPERATURE 80
V|.3 METHOD 82
V|. 4 RESULTS 82
VI.5 0 ISCUSSI ON OF RESULTS 87
SUMMARY 97
APPENDIX 1 101 I I IC7 I I I I 18 BIBLIOGRAPHY 13!
* Sj« !jf # ACKNOWLEDGEMENTS
THE AUTHOR IS GREATLY INDEBTED TO DR. A. BRYSON FOR HIS
ENCOURAGEMENT, HIS FRIENDLY SUPERVISION AND GUIDANCE
THROUGHOUT THIS WORK. HE ALSO WISHES TO THANK PROFESSOR
D.P. MELLOR FOR PERMITTING THE USE OF FACILITIES IN THE
SCHOOL OF CHEMISTRY, THE UNIVERSITY OF NEW SOUTH WALES,
MR. E. P. SERJEANT, COLLEAGUES AND STAFF OF THE DEPART
MENT OF ANALYTICAL CHEMISTRY FOR HELPFUL DISCUSSION ON
f NUMEROUS OCCASIONS, AND FINALLY, TO THE COMMONWEALTH OF
AUSTRALIA FOR THE COLOMBO PLAN SCHOLARSHIP
i ABSTRACT
Boric acid and catechol form a series of complexes similar to those formed with other diols,these being briefly specified by the formula HBC, HBC2 and HBC^,where the ratios of boric acid to catechol are respectively 1:1, 1:2 and 1:3*
From titration curves of solutions with mole ratio of 1:1 with 0H“, it was found that the calculated pKa values showed a steady drift during the course of the titration.This drift has been correlated with the progressive formation of the ion BC2“ as neutralisation proceeds and mathematical equa tions have been derived from which the constants K^, Kg, K^,
K and Ka2 for the following reactions:
HB + C v HBC K
HBC H+ + BC“
HBC + C HBC,
hbc2 v H+ + BC “
BC~ + C
ii have been evaluated. Of these constants,* K,1* , K at and K30 are able to be precisely defined, while and Kg are determined to a lower degree of accuracy.Further experiments with higher ratio of catechol to boric acid have enabled the values of Kg and Kg to be more accurately evaluated.
From these constants the concentrations of various species have been determined at different points of the
titration curve. Determination of the constants at five temperatures (10°C - 30°C) have enabled the thermodynamic quantities to be evaluated for the above reactions and these results have been used in assessing the factors responsible for establishing the various equilibria.
iii 1
CHAPTER ONE
INTRODUCTION
I.1 Complex Formation of Boric Acid Boron having a group valency of three, has one un occupied orbital and hence has a considerable tendency to form complex compounds by completion of its electron shell. This tendency is so great that on occasion is done by way of nback co-ordination” as in
Cl
B in Cl / Cl this being indicated by the smaller interatomic distances. Normally however, the octet is obtained by combination be tween the boric compound which behaves as a Lewis acid and a base which provides the required electrons, thus forming quadricovalent compounds, A typical example of these com pounds is probably tetrafluo-boric acid.
The tendency of boron to form complexes with diols was known as early as 1&42 when Biot reported that boric acid became acid to litmus upon addition of sugar. This obser vation has since been verified for many other organic 2
compounds having hydroxyl groups. In order to explain the unusual increase of acidity in solution of boric acid with increasing concentration of
( q } itself, Kohlenberg and Schreiner postulated the formation of polyboric acids. The presence of polyboric acids is in dicated by cryoscopic and ebullioscopic measurements and by measurements of partition and diffusion. Kolthoff^ postu lated that in concentrated solution of boric acid small quantities of tetraboric acid were formed.
By means of conductometric measurements Thygesen (5) has arrived at the same conclusion as Kolthoff concerning the existence of tetraboric acid but his investigations indicate in addition that other polyboric acids also exist. Both of them found that in solution of boric acid less than 0.1 M no appreciable autocomplex formation occurred. This is con- firmed by pH determination made by De Witt Stettenv with glass electrode and also by the works of Antikainen (7) and Dales!8*
I.2 Structure and Properties of Boric Acid Boric acid is a planar molecule, the OH groups being
120° apart. The acid is weak (pKa = 9*22)^ and a characteristic feature is the formation of a number of polyborates, the most important of which is the tetraborate 3
B^0?~. It is generally accepted that boric acid does not ionize by dissociation of its OH groups, but acts as a Lewis acidforming with OH” ions, initially the sym metrical B(OH)^” ion. The structure of the various poly borate ions subsequently produced is still a matter of dispute. A convincing picture of possible structures of these has been given in a recent paper by Dales. (8y) In order to achieve the tetrahedral configuration of the
B(OH)^“ ion the boric acid molecule must be changed from trigonal to tetrahedral configuration in order to allow union with the OH”. This confers an added stability on boric acid and is held to be responsible in part for its weak acidic nature.
1.3 Complex Compounds of Boric Acid with Pi- or Poly-Hydroxy Compounds The formation of a complex between boric acid and certain hydroxy compounds has been demonstrated by the increase in acidity, the increase in mutual solubility and the change in optical rotation. The first real measure ments of conductance in this field were made by Magnanni in 1890-93* Thomsonfound in 1893 that boric acid,which cannot be titrated in the usual manner, could be determined by titration in the presence of various polyhydroxy com pounds, using phenolphthalein as indicator. The present 4 method of determination of boric acid with the aid of manni<
tol is based on Thomson's observation.
Hermans has shown that Is 2 and Is 3 diols of cis- configuration generally form complexes which are acidic and which may be isolated. He assigns these complexes two
structures. One is a diester formed by splitting out two molecules of water between one hydrated borate ion and a
glycols o o / i
OH H0V -yOH ___^ /OH - + B ^---- [ ® \ + 2H20 1.1 OH H0/ X0H c - oy OH
The other is formed by splitting out four molecules of water between one hydrated borate ion and two molecules of a glycol:
\ / C - OH H0V - OH HO - C 'C - CL ,0 - C 1 + B I 1 1 C - OH ho' noh HO - C 'C - 0 0 - cx
+ tfl20 1.2
This nborospirantf structure has a centre of asymmetry and this would be expected to give rise to optical isomers. The (15) fact that some isomers have been resolved, support the proposed structure.
(i Kolthofi reported the existence of diborotartaric 5 acid of the type ^2^2° means of solubility determinations (17) and Darmois and Peryraux claimed to have obtained com
pounds of the type H2B2D from solutions which contained glucose, galactose and fructose in addition to borates.
Schafer' 'prepared salts of the complexes of boric acid and catechol isolating the lithium, potassium, sodium, magnesium, strontium of the monocatechol complex and the sodium, potassium of the dicatechol complex. He also succeeded in isolating a tricatechol complex in the form of its pyridinium salt. To these he gave the structures:
/°\ /°\ /\ M [CgH^ B - 0] xH,0 ; M [C^ B C6H ] V \ o / \ o/
OH (19) and C6H4' CcH,NH+ BN)- C6H4 5 7 °6H4 " 0H The salts are very largely hydrolysed in aqueous solution and Schafer calculated the equilibrium constant for the reaction:
BC“ + C 6
I.4 Previous Quantitative Studies of Boric Acid-Diol System Despite the large amount of qualitative work on diol
complexes of boric acid comparatively little work of a
satisfactory nature has been done on the thermodynamics of
complex formation and this section will describe the position
up to the present time.
Kolthoff^^ seems to have made the first quantitative
study of the diol-boric acid system. He treated the reaction
mechanism simply as:
H3B03 + alk. -—± H3B03 alk...... 1.3 where alk = polyvalent alcohol and the equilibrium constant
K complex being given by the expression:
[h3E03] [alk.] c " [H-jBOj alk.] ...... 1.4
He evaluated the constants for several polyols, including glycerol and mannitol. • • (lS) Boescken et al ^'found that the interger n in the reaction between fructose or mannitol and boric acid:
HB + nM HBM ...... 1.5 was equal to 2. Using this value of 2 for n, they reported a value of 1.7 x 10“^ for the equilibrium constant for the 7 reaction
HB + 2 M ' "T± BM2_ + H+ ...... 1.6 between boric acid and mannitol. An extensive series of experiments was carried out by Schaferv ’ using potentiometric method from which he confirmed Hermans1 postulates that boric acid can form com plex acids of the type - HBD, HBD2 with mannitol, fructose, galactose and catechol. As a result of these measurements Schafer further reported approximate values of the ioniza tion constants of the complex acids. The calculation of these values involved certain assumptions concerning the reaction mechanism and the potentiometric titration curves of the solution of boric acid containing diols, which we will later consider to be unjustified. (22} Mention can be made of the work of Thung and Chang who developed a graphical method to obtain the constant for the reaction:
B" + nM BMn” ...... 1.7 by assuming n to be equal to 2.
Deutsch and Osoling'( 2^} seem to have been the first to attempt the determination of the constants of the mono complexes. Working on the basis of Hermans’ postulates that 8
two complexes could be formed between boric acid and mannitol according to the reaction:
B” + M ,_—*• BM“ 1.8
B“ + 2M ^ • • • • • • - BM2" 1.9
they assumed that in excess of boric acid, only monocomplex
were formed, and developed an equation to determine the
equilibrium constants of the two reactions above.
(2 L) pH measurements were also used by Ross and Catotti' ^ in their study of the mannitol boric acid system in constant
ionic strength. Assuming that only the reaction (1.6):
HB + 2M H+ + BM2“
takes place in large excess of mannitol, the constant of the reaction is calculated on the basis of the following equations:
[H + ] [BMg*] [H + ] 2 n " [HB] [M]2 |[HBo]-[H + ]j|[M]- 2[H+'_}5'
...... I.10
(7) Antikainen based his investigation on a potentio- (25) metric method proposed by Kilpi. Briefly this method
depends on the measurement of the pH of a dilute solution 9
of a weak acid in water where the buffer capacity is at a minimum. Using certain assumptions he arrived at an equa tion relating the apparent ionisation constant of the mannitoboric acid in aqueous solution K , to the first dissociation constant of boric acid Kg, the first dis sociation constant of the mannitoboric acid K-jfT, the formation constant f for the reaction (1.5)s
HB + nM =± HBM x n and the concentration of mannitol C£ as:
K* = 1^" Kk C2n + Kb ...... 1.11
He used this equation extensively to determine the interger n. A modified form was then developed to accommodate the existence of the mono- as well as the di-complex in the , ... (26,27) solution. 9
The number of n in the reaction:
HB + nM Z=± BM ~ + H'r T n
(2B 29) has been extensively studied. Boescken v 1 y Thung among others obtained n = 2 with pH measurements in high ratio of mannitol:boric acid. Whereas Mehta and Kantak^^ reported the value of 2.26 as a result of similar measure ments. However, Krantz, Beck and Cans (31) obtained
(7) 1.3-1*4 for n and Antikainenw' found n to be 1.31. 10
I.5 Summary The following table is the summary of the values of the constant K obtained by the workers mentioned above for the n J reaction (1.6): HB + 2M 7—^ BM2 + H + between boric acid and mannitol. Some of them like that of
Deutsch and Osoling are not the result of direct calculations of the constant above. However, it can be easily converted into K with the aid of the known dissociation constant of n boric acid. TABLE 1
n found n assumed K Authors n
Boescken 2.0-2.1 1.7 x 10"4 Schafer 2.0 Thung and Chang 2.0 1.66 x 10-3* Deutsch and Osoling 0.31 x 10“4V Ross and Catotti 2.0 1.00 X lO'4** Krantz,Beck and Cans 1.3-1. 4 Mehta and Kantak 2.26 Antikainen 1.81 5.08 x 10~5+
10 Calculated, employing value of 6.O3 x 10“ for the dissociation constant of boric acid.
At 0.1 N KC1 solution.
+ Thermodynamic, employing Debye-Hucke^s equation for correction. 11
It will be observed that considerable variations exist in the values of the constants evaluated for the best known diol-boric acid system shown above. The purpose of this thesis is to describe an experimental method, from which the various constants involved in the formation of boric acid - mono - and bis-diol complexes may be evaluated. The system of boric acid catechol has been chosen on two grounds
First, a considerable amount of work has previously been carried out on this system notably by Schafer' y and (27) Antikainen and secondly, the diol system is simpler than that of the polyols usually investigated. The method to be described should, however, be applicable to all boric acid- diol complexes. 12
CHAPTER TWO
THEORETICAL CONSIDERATIONS
11.1 Method The method developed consists in the titration of solutions of boric acid and catechol, first with sodium hydroxide to the stoichiometric equivalent point,and then by back titration with hydrochloric acid, the pH values being measured during the titration. The advantage of back titration consists in the establishment virtually of constant ionic strength since the borate ion being re placed by chloride ions. This necessitates titration with solutions of much greater normality than that of boric acid in order to obtain minimum volume changes, and the technique requires the use of micrometer-syringe.
11.2 Titration Curve • • ( 1 g \ In agreement with Schafer it was found that if an aqueous solution of boric acid catechol mixture is titrated with sodium hydroxide, a neutralisation curve similar to that of an acid-base titration curve is obtained.
The shape of the curve depends upon the mole ratio of boric acid to catechol in the solution. (See Figure 1.). 13
Potenti'ometric Titration* of Boric odd-
IQO — Catechol Solutions.
CURVE (catechol)
Mis of 219 N NaOH
FIGURE I 14
If the mole ratio of catechol to boric acid is small, i.e. there is an excess of boric acid in the solution, two jumps are observed in the neutralisation curve (curves 1 and 2 in Figure 1). This can be explained by the presence of two acids with different strengths, one being boric acid itself and the other the complex acid formed by catechol and boric acid. Schafer postulated that the first poten tial jump is due to the complex acid HBC alone and this jump is obtained after the addition of alkali equivalent to the amount of catechol present. In view of the shape of the curve and the slope present it is not easy to de termine exactly the position of the jump. The second potential jump follows when the added alkali corresponds to the total amount of boric acid present.
If the catechol is increased while the amount of boric acid is kept constant the first jump gradually dis appears, and at a one to one mole ratio of boric acid:cate chol, only one inflection point is observed at the equivalence point.
Further increase of the amount of catechol such that the mole ratio of catechol to boric acid becomes greater than one gives only one jump corresponding to the total amount of boric acid present. With increasing amount of catechol the titration curves become progressively lower 15
(curves 3,4,5,6 in Figure 1). This means that the solution
• • is becoming more acidic. Schafer concluded that this was due to the presence of di-catechol boric acid HBCg. The data of this project support this view. Reference to Figure 1, curves 1 and 2 will show the approximate pK values as measured by the pH at half neutralisation are all about the same value of about 6.8 until the ratio of boric acid to catechol is 1:1. Thereafter the pK values measured by the half neutralisation pH pro- cl gressively decrease. The inference is that a mono catechol boric acid is formed and is the main species during the titration when the catechol boric acid is less than or equal to 1:1, whereas with larger amounts of catechol an increasing amount of di-catechol boric acid is formed. When the pK& values were calculated for the acid present in the 1:1 mixture by the Henderson1s equation:
pH + acid a r base it was found that a steady drift towards higher value took place as the neutralisation proceeded. This feature was most noticeable in the 1:1 mixture and was also evident in all higher ratios of catechol:boric acid, but the drift became progressively less until at ratio of 7:1 the pK& values were almost, but not quite, constant (see Appendix
I, pages 101-106). 16
This behaviour means that at any point of the titration curves the pH values observed are higher than they should be, and a ready explanation for this lies in the reaction:
2 BC" + H+ HB + BC " whereby as neutralisation proceeds, the dicatechol borate ion is progressively formed and H+ ion is used up. At high catechol ratio not only BC2“ but may also be formed. This may explain the observations that even at these high ratios the calculated pKa values do not remain constant.
II.3 Mathematical Formulation of Equilibria As a result of the foregoing observations it has been found possible to establish the mathematical relations necessary to evaluate the constants for the various equi librium reactions involved in the titration. The following assumptions are made. In a 1:1 catechol boric acid mixture being titrated with sodium hydroxide the following species are present: HB, HBC, HBC^, BC“, BC2” and C, where HB represents boric acid and C represents catechol.
The water produced during the formation of the complex acids according to the equation:
h3bo3 + c6h (oh)2;zz± c6h4o2boh + 2H20 can be ignored. The reactions involved are as follows: 17
[HBC] HB + C HBC K- II.1 [HB] [C]
[BC] [H+] HBC ^ BC- + H+ K II.2 a t [HBC]
[hbc2] HBC+C HBC2 K2 II.3 [HBC] [C]
[bc2~] [H+] HBC, BC “ + H' II.4 [hbc2]
[bc2“] BC- + C II.5 [BC-] [C]
From equations II.2, II.4, II.3 and II. 5 it is readily-
shown that:
II.6
K, , K , K0, K 0 and K, are the equilibrium con- jl a * d j stants associated with the reactions concerned. These values apply to the reactions carried out at constant
ionic strength. The five reactions and their constants represent all
the possible reactions and constants between boric acid and catechol, assuming that no tricatechol borate complex is formed. From the results of investigations carried out so far this assumption will be shown to be adequately justi fied. However, at high catechol-boric acid ratio the presence of BC^" is likely and suitable adjustment must be made*
II•4 Derivation of the Theoretical Equations Let ,Tm" be the total concentration of boric acid at the initial of the titration. On addition of catechol, the total concentrations of boric acid in various forms should be equal to ,Tm,f, thus:
m = [HB] + [HBC] + [BC“] + [HBC2] + [BC2~] ...... II.7
The amount of B“ is so minute in the pH region of the ex periment, that the ionization of boric acid can be neglected and also that of catechol (pKa = 9.46). If r,a,T is the concentration of the catechol added, then the total concentrations of catechol in various forms
is equal to r,a".
/. a = [C] +[HBC] + [BC“] + 2[HBC2] + 2[BC2“] II.S 19
From the principle of electroneutrality, it follows that:
x + [H+] = [BC“] +[BC -] + [0H“] ...... II. 9 where x stands for [Na+] and is equal to the concentration of NaOH added, at any point of the titration. Since the amount of sodium hydroxide is of the order of 10 -3 , and the _7 concentration of hydrogen ion of the order of 10 , then
x » [H+]
x » [0H“] and hence it is reasonable to assume that:
x = [BC“] + [BC2-] ...... II.10
= [BC"3 (1 + K3[C]) II.11
Substituting for x = [BC“] + [BC^-] into equation II.7, it becomes:
[HBC] m = ------+ [HBC]' + x + [HBC] K„[C] KjCC] ^ m x = [HBC] + 1 + K2[C]|...... 11.12 20
The pK value of the acid HBC.i.e. for the reaction ^ o ’
HBC H+ + BC“ is calculated for points along the titration curve by the Henderson equation:
v u acid ^ o _ ^ + base
= pH + log ----- ...... 11.13
From equations II. 11 and 11.12 we have:
i —i— ♦ 1 + K„[C]i m - x [HBC] IK,[C] ^ J ----- = ------1...... 11.14 x [BC“] (1 + K [C])
Substituting the value of m ~ x in equation 11.13, we A obtain:
[HBC] i K,[C] + 1 + K2tC]J pK = pH + log —--- —...... 11.15 ° [BC“] (1 + K3[C] )
[HBC] K. [ C] + 1 + K2^C^ = pH + log ----- + log...... II. 16 [BC~] “ 1 + K,[C]
[HBC] Now pH + log ----- is the pK , value of the acid HBC,and [BC“] a' 21
hence:
K^[ C] + 1 + K2[C] 11.17 pKo = pKa'+ log 1 + K3[C] i. e.
K + 1 + K2[C] 11.18 K o 1 + K3[C]
Equation II.IS is a general equation giving the re lation between the value of the ionization constant Kq derived from the experimental values in terms of the ionization constant K . of the acid HBC, the concentration of the free catechol [C] in the solution, and of the con stants K-p K9 and . Being derived from the consideration of the total boric acid concentration it applies to all cases independently of the ratio of catechol to boric acid.
At high ratio of catechol:boric acid equation II.IS becomes:
1 + K [C] 11.19 1 + K3[C] and as [C]
K a t 11.20 K o 22
From equation II.6 we have:
a»
Hence:
a» a»
i.e. K = K 0 or o a 2
pK 11.21
i.e. the limiting value of the dissociation exponent is equal to pKa2. This, however, is true only if BC^“ or higher complexes are absent. This contention cannot be completely correct, since the values of pK0 are not con stant over the titration range, even in high concentra tions of catechol.
II.5 Application to the Case Where Mole Ratio of Catechol:Boric Acid = 1:1 Since the mole ratio of boric acid:catechol is equal to one, then m = a, and hence from equation II.& we find
a = m = [C] + [HBC] + [BC“] + 2[HBC] + 2[BC2“] 23
x = [C] + [HBC] + 2[HBC2] + [bc2-]
+ K^[C]1 = [C] + [HBC] -I 1 + 2K2[C] 11.22 [H+] j
Equating 11.12 and 11.22 we have:
[H3C] | K^JCI + 1 + K2[C] [C] + [HBC] 1 + 2K2[C] +
K K0[C] a' 3 11.23 [H + ]
(1). Our first attempt to evaluate the constants K , K-. ,
and from equations II.IS and 11.23 required the elimination of the quantity [C]. The simplest approach is to assume that in a 1:1 catechol-boric acid mixture, the bulk of the catechol is present as the mono- and di-catechol complexes, and that [C], therefore, is small. Under these conditions we have:
K ,K [C] 1 + 2 K„[C] + —±------11.24 iqTO + 1 + k2[ci 2 [H + ] from which K 1 K^ICl + k2[c] - 11.25 [H+]
It is reasonable to assume further that K^C] is small 24
compared to ^q-| and hence
[H + ] [C]' K,K K0 1 a' 3
11.26 [CJ VK1O3
From equation II.IS we have:
K1[C] + 1 + K2[C] a»
and assuming that K^C] and K^[C] are small compared to unity K a * 1 + ~ kxlcI 11.27 ro Substituting the value of [C] into equation 11.27
a r 1 + II.23 '1\niKa,K3
1 a t - 1 KX[H+] K fK0 aT 3 25
From which:
K - K a t o K^H*] K aTt K3q and hence:
K K K pH = 2 log 2 + log K "Lk 11.29 o a t 3
K -K Thus a plot of pH against log —^—— should give o a straight line with slope of 2 and intercept of log _JL__ K at K30. It will be shown(Chapter V.l) that the experimental results show a linear relation with a slope of 1.7. It appeared, therefore, that the assumption regarding [C] was in error.
II. A second approach is that the concentration of free catechol is not negligible compared to that of the other species. The assumptions previously made that K^CC] and
K^[C] are negligible compared to K^[C] no longer hold. It is, however, reasonable to assume that and that
K0[C] may be neglected compared to K~[C] or ——— . Thus 2 3 K^C] equation II.IS becomes
+ 1 "a' hF* 11.30 i + K3LC] 26
(This assumption is made, not because the free concentration of catechol is negligible, but because the product of and
[C] is small compared to —-— and K~[C]. The justification for this assumption is discussedKi[c] in Chapter IV.J
Equation 11.30 is a quadratic equation in [C],which
can be solved readily. Two solutions will be obtained, one
of which will be negative and therefore inadmissible.
Solving equation 11.30 for the positive solution for [C]
gives:
, „ 4K K K, -(K -K ) + \/ (K -K )2 + —°.. a-’-i a» o Vat o [C] 11.31 2 Ka. K3
This equation relates the concentration of free catechol with the experimentally measured K , and the constants K-^,
K t and K0. a t 3
Now equation 11.22 may also be written
K KJC] m - x - LC] = [HBC] < X + 2K [C] + ■ a-’-1— 11.32 2 [H+] and from 11.32 and 11.12: Ka.K^c] - X- fCl , 1 * 2K2[C] * m - x iqrc] + 1 + K2tc] 27
K K Lc] [C] 1 + 2 K2[C] + ■ ■■■ .’. 1 - 11.32 m - x iqrci + 1 + k2[g]
Assuming again that K^CC] is negligible compared with
1 ^a» and also with K~L C] since ---- is of the order of iqm 3 [H + ] unity, then:
K K0[C] 1 + a» 3 [C] r h+i 1 - m - x 11.33 1 KpLC] + 1
This equation is again a quadratic equation in [C] from which [C] may be solved to give tv/o solutions, one of which is negative and hence inadmissible. Solving [C] for the positive solution we have:
-1 + \l 1 + 4(m-x)K^-<
[C] 11.34 (m-x) K K 2K-X 1 +
From equations II.31 and 11.34 by successive approximations using the experimental values of (m - x), 28
[H+] and KQ, the values of [C], K^, and r may be de rived. Knowing these values together with equations II.7 and II.8, the concentrations of all components [C],[HBC],
[HBC^], [HB], [BC“] and [BC?“] may be calculated at all parts of the titration curve.
II.6 Evaluation of K^.
The term involving K^[C] has been assumed to be 1 negligible compared to K]ICl and K^[C] in the foregoing treatment. At high concentrations of catechol this term will be of greater significance since it may well be assumed that the component HBC^ will be present in appreciable amounts. It is possible to evaluate from considerations of these conditions.
Let n = total catechol = [C] + [HBC] + 2[HBC2]
+ 2[BC2~] + [BC“]
/ *. n - x -[C] = [HBC] 1 1 + 2K2[C] + K^K& f [C] 1,--- 11.35 [ H+]
k,k re] 1 + 2K0[C] + --- n - x - [C] ______Z______[H+] m - x 11.36 + 1 + K„[C] K.[C] 29
Let n - x = a, and m - x = b
K,K [C] 1 + 2K [C] + —— a - rci 2 [H+] + 1 + K2[C] K^C] from which the following cubic equation is obtained
, fbK, K K [cf + ^ ---l 3 + K, - K.K (a - 2b) [C] K1K3 \ [H+] 112 J
{l - K1(a - b)}[C] - a = 0 ...... 11.37
Also equation 11.18 may be stated in the quadratic form:
J pK-^K^ - KXK, | [C]2 + /pK-, - K1} [C] - 1 = 0 ...... 11.38
where p a»
From the values of t , K-^ and previously evaluated, it is possible to evaluate from equations
11.37 and II.38. 30
CHAPTER THREE
EXPERIMENT
III.l Materials Distilled water was redistilled twice in the pre sence of alkaline permanganate. The product of the second distillation was collected under nitrogen which had been passed through 5 N H9S0^, 5 N KOH solutions and distilled water. (See figure below). This gave water with pH of
6.6 to 6.8. 31
The stock solution of boric acid (A.R. ) of o 2 x 10 molar strength was prepared in this CO^ free water and kept in a paraffin wax treated flash protected by guard tube containing Ascarite from CO^ and delivered from a 50 mis automatic filling burette. Sodium hydroxide: The titrating solution of sodium hydroxide (2.010 N) was prepared by diluting a saturated solution of MerkTs proanalar grade material which had been filtered through a sintered porous crucible. The solution was kept in 1000 ml flask pro tected against C0^ by means of a guard tube containing
Ascarite. The normality was determined by the potassium hydrogen phthalate method and by comparison with a solu tion of HC1 of known normality. It was checked from time to time. Hydrochloric acid: The solution of 3.97 N HC1 was prepared in C0o free water and kept in a polythene container. Its normality was determined with borax using methyl orange as indicator, the titration being carried out with a micrometer syringe.
Catechol: Catechol was recrystallised several times from benzene to give m.p. of 104.5 - 105°C. (Lit. 105°C). The catechol was dried in an oven at about
60° - 70°C for about an hour and then in a vacuum 32
desiccator for four days before use.
III.2 Apparatus The titration vessel was a 250 ml tall beaker
sealed into a water jacket through which water from a
thermostatically controlled bath was calculated, thus maintaining the solution at the temperature required
io.5°C. The electrodes were held by means of a rubber
bung which also had holes for the introduction of a micro meter syringe, a nitrogen inlet and thermometer calibrated
in 0.1°C divisions.
Volumetric apparatus: A 2 ml semimicro burette
subdivided into 0.01 ml interval was used for the addition of the sodium hydroxide solution. A 0.5 ml micrometer
syringe subdivided into 0.0005 ml was used to deliver the hydrochloric acid solution.
The pH was measured with a Cambridge portable pH meter, a Cambridge saturated calomel electrode fitted with sintered glass and an Electronic Instruments Ltd glass electrode.
The linearity of the pH meter plus the glass electrode was checked as follows: The glass electrode was calibrated at the required temperature in a 0.05 M borax solution and the pH of a 0.05 M potassium hydrogen phthalate solution was then determined. Values are shown 33 in Table 2.
TABLE 2
Temperature in C. pH of KH.phthalate Borax (0.05 M) (0.05 M) o o rr\ 4.04 (4.01) 9.14
25° 4.03 (4.01) 9.18 o ro o 4.01 (4.00) 9.23 15° 4.00 (4.00) 9.27 O i o —
1 4.00 (4.00) 9.31
( ) values are taken from Bates, R.G.: "Electrometric pH Determinations” (John Wiley & Sons Inc., 1954). The pH meter was found to give a reproducibility of -0.02 pH unit.
III.3 Procedure All the measurements were carried out in the -2 following manner: 100 mis of a 2 x 10 molar solution of boric acid, delivered from a 50 ml automatic filling burette, was placed in the titration vessel and the re quired amount of catechol added. A magnetic stirrer was employed to stir the solution. After the temperature had been established at the required value, the solution 34
'//CXOfi/fTT*. SY//VC£-
£/£cr/eoi>£s - \/r?eo6£» ///ter
THE TITRATION VESSEL EMPLOYED TO EXCLUDE C09 FROM THE SYSTEM 35 was neutralised with the stoichiometric amount of 2.010 N sodium hydroxide (1 ml.) and back titrated with 3*97 N hydrochloric acid. The pH was read after each addition of 0.010 ml of hydrochloric acid solution delivered from a micrometer syringe. The procedure took about three hours to complete the titration.
In the case of the first series of solutions, con taining boric acid:catechol mixture with less than 1:1 mole ratio (Figure 1), a forward titration with 2.19 N sodium hydroxide was employed. No attempt was made to back titrate in these cases, since the result was used for qualitative studies and to obtain an approximate value of the pKa| of the acid HBC.
III.4 Discussion of the Method In this method back titration is employed, and this requires the addition of sodium hydroxide as well as hydro chloric acid solutions. This addition changes the total volume gradually. It is known that a considerable change in volume introduces error. To avoid this error relatively strong sodium hydroxide and hydrochloric acid solutions were used. The increase of volume due to these additions was minimised. It accounted for only 2% of the total volume and this may be considered as negligible. 36
Back titration was preferred because by this method
the pK^ values were determined in a solution of reasonably constant ionic strength, the process being essentially the
replacement of BC”, BC^"* anc* Possi^^y BC3” by chloride ion
The pH method is satisfactory for substances whose
pK values lie between 4 and 10, and if those substances are reasonably soluble in water. However, it has some weaknesses: (a) It is always desirable if the experiments can be
carried out in very dilute solution as to approach the limiting value of the activity coefficients. But then the buffer effect produced by very small concen trations of acids and bases is negligible and the pH measurements are therefore much more influenced by extraneous conditions than in more concentrated solution. (b) pH reading gives only an approximate value of the
hydrogen ion concentration, since it actually gives
the activity of the hydrogen ion. It is, of course, true that an approximation can be made to obtain the true concentration of the hydrogen ion. However,
since the concentration of the hydrogen ion is re
latively small compared with that of the other ions, 37
the error involved by assuming that the pH reading
gives the concentration of the hydrogen ion is not
serious •
(c) The Cambridge pH meter employed gives only -0.02
pH units accuracy. CHAPTER FOUR
DISCUSSION OF THE RESULTS
IV.1 Case 1: [C] is Negligible
Two equations have been obtained, one derived from an assumption that [C] is negligible compared to that of the other components in the system, the other being derived from a viewpoint that [C] is not negligible compared to the other components. If [C] is negligible then equation 11.29 applies:
K - K K, pH = 2 log -----2 + i0g x K at K,3 which should give a graphical solution by plotting pH K f - K against log ——g-----. This involves an approximation of o the value of KaT which may be made readily from the titration curves (see also ChapterXV.3 page 41) K f - K The plot of pH against log —------is shown in o Figure 2, page 39. As can be seen from the graph the K t - K relationship of pH and log —“ -*-3 not perfectly o linear, but assuming that the data for the end part of the line can be ignored, the remaining data can be considered 39 2
FIGURE 40 to give a straight line. The slope of this line, however, does not give a value of 2, but 1.7, the intercept at zero
K T - K value of log —--- — is equal to 7.20. Hence: o
% l0s TTTTaT 3 = 7>2 from which:
'1 = 3 • 0
It will be shown by the more rigorous treatment that
K1 it— = 1.92. It is clear that the assumption that [C] the 3 amount of free catechol is negligible is incorrect.
IV.2 Case 2: [C] Is Not Negligible
If the concentration of the free catechol [C] is not negligible compared to that of the other components in solution, then two equations for solving [C] were obtained:
(m-x)K K0 -1 + / 1 + 4(m-x)K1-< 1 + _____ at 3 [H+] [C] _(m-x)K____ at K30 2K± ^ 1 + [H + ] 41
and
4K K ,K0 + o at 3
[C] 11.31 K at.K 30
This means that if the correct values of K-^, and
K , the experimental values of (m-x), [H+] and the experi mental calculated values of K , are substituted in equations II.31 and 11.34, both equations should give the same value of [C] for a given point along the titration curve.
IV.3 The Approximate Values of pK&T and K~
The approximate value of pK is easily obtained a' from the titration curve of the solutions containing less than 1:1 ratio of catechol:boric acid. The approximate value of pK is half way of the first potential jump of that curve which lies between 6.£-6.9. As mentioned earlier the exact position of the first jump is very difficult to obtain from the graph.
To obtain the approximate value of K^, the equations relating to the case where the mole ratios of catechol: boric acid are greater than one can be used. 42
Equation II.IS
—-— + 1 + K,[C] !ai = K1[C] K0 1 + K3[C] applies in all cases irrespective of the total catechol
concentration. At high values of the catechol-boric acid 1 ratio,[C] is large and K-^[C] and K^LC] can be considered small compared with K^[C]. (This assumption is adequate for
the present purpose). Equation II.IS thus becomes:
K = K + K KJC] ...... IV.1 o at aT 3
A plot of Kq against [C] should give a straight line with a slope of from which the approximate value of
can easily be obtained (see Figure 3). It should be noted
that [C] is the concentration of free catechol which is not known. For the present approximation, however, it is reasonable to assume that the concentration of free catechol
[C] is equal to:
[C] = initial concentration of catechol - 2 concen
tration of boric acid.
IV. 4 Calculation of K-^, K& f and K~
Having obtained an estimate of the values of K ^ and K^, we then can proceed to solve equations 11.31 and
11.34 by successive approximation, i.e. by varying the x IO PLOT
OF
K, CATHECQL AGAINST 43 FIGURE (c)
x
i
o
: AT 3 CONC.
IQ
C. OF
FREE 44 values of K^, ^ and until equations II.31 and 11.34 give the same value of [C] for any point along the titra tion curve. The results of [C] calculated are tabulated in Appendix II,pages 107-17. The values of the equilibrium constants were found to be as follows:
TABLE 3
Temperature pjq pK k3 pic3 K1 Ka. * a t o o o OJ 154 -2.19 1.340 x 10“7 6.87 80.0 -1.90 25° 150 -2.18 1.500 x 10“7 6.82 78.0 -1.89 O o ro 145 -2.16 1.580 x 10“7 6.80 76-0 -1.88 O i ir\ —
1 140 -2.15 1.738 x 10“7 6.76 74.0 -1.87 1 o — O 1 135 -2.13 1.900 x 10“7 6.72 70.5 -1.85
IV.5 Probable Accuracy of the Constants Pending a complete analyses of the experimental data by means of the University Computor,it is perhaps advisable to make an estimate of the accuracy of the constants in Table 3 derived by the method described. It has been found that the value most sensitive to adjustment is r, the values of which may be provisionally given as within limits of -3fo. The values of and are subject to somewhat greater uncertainty which may be estimated at -5%. 45
IV.6 Discussion of the Values of [C]
In general the agreement of the values of [C] calcu lated from the two equations II.31 and 11.34 are quite close, the differences being in the order of 5% or less. This is well within the range of the accuracy of the ex periment. However, we are not able to get a close agree ment at the beginning as well as at the end of the titration curve. There is a "drift" observed in these regions which are about 15% each at both ends of the titration curve. This is due to the fact that at those regions the solutions are unbuffered and a minute amount of error in the addition of 4 N HC1 will cause a considerable amount of error in the concentration of the hydrogen ion, and since both of the equations are direct or indirectly dependent on pH, these regions are therefore not suitable for solving the equations above. One may confidently say that the equations apply to 70°/o of the titration curve.
IV.7 Calculation of the Concentrations of the Various Species in the Solution From the obtained values of [C] at any point of the titration curve, the constants K-, , K . and K~ and the ’ 1J a t 3 equations:
m = [HB] + [HBC] + [HBC?] + [BC“] + [BC2“]
[C] + [HBC] + 2[HBCp] +[BC~] + 2[BC2~] 46 we have five equations with five unknowns, i.e. [HB],[HBC],
[HBC^], [BC“] and [BC^”] and hence the equations can be solved. Thus the concentrations of the various species in the solutions at any point of the titration curve can be estimated. The values of the concentrations of these species are shown in Appendix III, pages 113-130 and Figures 4,5,6,7 and 3.
IV.3 Discussions of the Values of the Concentrations of the Various Species It is obvious from the values obtained for the con centrations of various species in solutions that apart from
[HBC9], none of the concentrations of the other species can be considered negligible. Therefore, assumptions to the contrary will lead to incorrect conclusions. Hence the graphical method obtained from an equation derived from the assumption that [C] is negligible compared to that of the others (Chapter IV page 33) failed to give satisfactory results, since the concentration of the free catechol is considerable (about 50f%o of its initial concentration at the beginning, progressively dropping to about zero at the end of the titration).
There is also a considerable amount of free boric acid in the solution. However, it is slightly larger than that of the free catechol and the difference increases as CONCENTRATION XlO Plot mis,
of
of conoof
HC1 ■mis.
FIGURE in
various of
back 47 3.97
4
N titration species
HCI
against
gt m CONCENTRATION X 10' Plot mis,
of
of
cone HCI
of mis. in
25 various
FIGURE
back
48 of C
3.97
titration
5 speceis
N
HCI
at against w concentration XIo Plot mis,
of
of
cone,
HCI mis
of
ir> FIGURE
20 of various
back
3.97 49
C. 6
N titration speciesr
HCI ------
against at 50
Plot of cone, of various species against mis.
of HCI in back titration at 15 C.
mis. of 3.97 HCI------FIGURE 7 201 concentration x io —
1 m o le s:( /|te r ' cone,
of of
H varfous CI
Plot at in
mis.
back
spg IO°C. Of
FIGURE of eje
5!
•
ti 26 s 3.97 tration
oqainstmls 8
N
H Cl *14
-
•02 52
the neutralisation proceeds. The decrease of the concentra tion of the free boric acid [HB] with increase of pH, is quite different to that of [HBC]. Figures 4-$ show that
[HBC] drops relatively faster than [HB] with increase of pH.
This is partly due to the fact that boric acid is a weaker acid than HBC, and partly also due to the regeneration of
HB though the reaction:
2BC“ + H+ HB + BC " where HB is released indirectly from HBC complex. If the above reaction did not take place, then the decrease of the concentration of HB with pH should be similar to that of
HBC, because according to the reactions:
HB + C HBC ...... (I)
HBC ^=± BC~ + H+...... (II)
H+ + OH' ^ H20 ...... (Ill) addition of 0H~ to the solution would push reaction (III) to the right and this automatically resulted in pushing reaction (I) and (II) to the right as well, thus the de crease of the concentration of HBC should be proportional to that of HB. This is not the case.
In agreement with Hermans, Schafer and others the mono complex acid was found to be a weak acid and therefore 53
its concentration at low pH was the largest. The plot of
[HBC] against pH gives a similar curve to that of a weak acid-base titration curve. The [HBC] drops rapidly with pH due to the following reaction:
HBC ^=± BC“ + H+
H+ + 0H~ H^O
The graphs of concentrations of various species vs. pH of the solutions (Figures 9,10,11,12,13),show that at the intersection of the curves of [HBC] and [BC“], where
[HBC] = [BC“], the pH of the solution is equal to the pK cl ' of the acid HBC. The values so found are in excellent agreement with the calculated results.
The results also indicate the simultaneous forma tion of the two complexes. It is evident that even at a pH value as low as 6.00, a considerable amount of BC^" was formed. The formation of BC2“ takes place through the reaction
BC~ + C ^=± BC2~ which has an equilibrium constant of 7S at 25°C.
But the reaction:
2BC" + H+ ~—HB + BC2' certainly contributes to the formation of BCp~ as well.
The graph of [BC2~] vs. pH has a very unusual curve. It Cone, of different species against 54 O jOI
*
UOI
J)U93U03
FIGURE cone, of various species against pH at 2 5 C. < ----- _0|X 55
J2)J(
/S2|01U
Ul
UOUDJJU30UOD
—
FIGURE 10 55
O CO
in K I
I
FIGURE
O r*
a.
in v6
O <------Oix j»;i \js2>\oiu ui uoaDJiuaouo^ m3 cone, of vorious species oqaiost pH ot 15 C. 57 ------s Ol x
Ul
UOjJDJiUMUOO
FIGURE 12 pH a t IO C. 58 pf
X
I
/s»|OUJ
UJ
UOI.IDJ
JU»0UO3
FIGURE 13 59
reaches a maximum corresponding to 12% of the total concen
tration and drops gradually to zero (extrapolated). This is
because of the reaction
HB + BC “ + OH- : ** 2BC“ + Ho0 2 * 2
This also accounts for the concave nature of the [BC”]
curve.
No [HBCp] is found. The amount of -0.05 x 10“^
molar for the concentration of HBCp obtained from cal
culation is less than the experimental error. The virtual
absence of HBCp means that the constant K9 is small. Hence
from equation
k3 X a r K2 x Ka2
the acid HBCp must be considerably stronger than HBC.
IV.9 The Approximate Value of Kp
Hitherto nothing has been said about the evaluation of Kp. This constant is small and cannot be determined from
the amounts of HBCp, HBC and C in the solution. However,the approximate value of Kp can be reaily obtained from the equations relating to the case where the mole ratios of
catechol:boric acids are greater than one. As before equation II.IB K^rcl1 + 1 + Kp[C] K o 1 + K3[C] 60
applied* At larger excess of catechol, [C] is of the order of lO-1 mole/litre and hence:
1 1 K^C] 102 X 10_1 and can be assumed to be negligible compared to unity. So equation II.IS becomes:
Ka, 1 + K2[C]
Kq 1 + K [C]
1 + k2[C] 1 - 1 - a.» 1 + K3[C]
1 + KJC]
K -K k3[c] - K2[C] o a t
IV.2 (k3-k2)[C]
Hence a plot of ~ against -t-q*;— should give a ko a» L J
straight line, the intercept of which is -—y~ * *3 2
The difficulty again lies in the fact that the concentration of free catechol is not known. As before an approximate for the value of [C] is given by the equation:
[C] = total initial concentration of catechol - 2x concen
tration of boric acid. 61
As it can be seen from Graph 14 page 62 the intercept of Ko 1 o the plot of ——^--- vs. v cv" at 10°C is equal to o“a* L J
1.025, i.e. -y'K- = 1.025 K3"K2
Since = 70.5 K2 = 1.8
Further the slope of the line is equal to —^^— and is 3 2 found from the graph to be --gg- . This compares very well
with the calculated value of —g-g y" •
It is evident that since is small, its precise
evaluation is a matter of difficulty.
IV.10 Justification of the Assumptions In the derivation to obtain the final equation for solving [0], as assumption was made that Kp[C] was negli gible compared to gj and Kg[C]. This assumption was based on the evidence that the dicatechol-boric acid was a stronger acid than the monocatechol-boric acid presented in the titration curves. (Figure l,page 13) .
The approximate value of K9 was found to be 1.&,
K2[C] = 2 X 10 X 10“3 = 2 x 10-2
-2 68 x 10 K [C] 150x10 x 10-3 ,.7 0- PLOT AGAINST AT IO C. 62
FIGURE 14 63
K3[C] = 75 x 10 x 1CT3 = 75 x 10“2 taking the average value of [C] to be 10 x 10“ 3 The value 1 of K^LC] is about jfo of the values of K^[C] and K^Tcl- This is well within the experimental error and hence the assumption made is well justified.
IV.11 Evaluation of from Rigorous Treatment
Substituting known values of K^, K&? and and selective values of in equation 11.38 we obtain the values of [C] which substituted in cubic equation 11.37 gives the values of K^. By successive approximation two values of were made to coincide. However it was found that two disturbing trends became evident:
With the 1:7 mole ratio of boric acid:catechol at
10°C, the values of show a drift from 1.5 at the be ginning to 2.5 towards the end. Whereas in 1:4.5 boric acid:catechol at 10°C values of range from 3.5 to 5.5 along the titration curve. This drift may be due to in accurate value of and the possible presence of BC^".
Investigations of this problem are being undertaken by the use of the Uticom Computer but the results at the moment are not available. It seems quite evident however that is much smaller than K~ and its numerical evaluations are 64 therefore sensitive to other constants and an accurate estimate for the present data will not be possible. 65
CHAPTER FIVE
CRITICAL EVALUATION OF PREVIOUS WORK OI\f CATECHOL-BORIC ACID COMPLEXES
V.1 AntikainenTs Equation for the Determination of Boric Acid-Catechol Complex Constants^ '7»^6,2 7)
As described in Chapter I page 3, Antikainen has made an extensive study of the boric acid diol system. He used Kilpi's method of minimum buffer capacity which
essentially determines the pH of a solution of boric acid
in the presence of known amount of catechol. Since the values of the constants K-^1 and I(9'L (AntikainenTs nomen
clature) for the reactions:
B” + C V=± BC~ ...... V.l
B" + 2 C BC2‘ ...... V.2 between catechol and boric acid differ considerably from the values obtained in this project (see page 75) a re examination of his equation is necessary.
Firstly he considered only the reaction
HB + n HBC € n V.3 66
whose formation constant is K, CHBCn k CHB,Ccn
X1 CH+-CBC“ and its dissociation constant is K-. = —x------=— nBCn
From the principle of the conservation of mass and the electroneutrality he obtained:
V Kl11-Kk1-CHB C2n + K1CHB - cH+ V.4 CH+ and
C1 CH+ C V.5 HB ’ CH+ (1 + V ^ + C2n + KB where and C0 are the stochiometric concentrations of boric acid and catechol respectively, Cg+ is concentration of the added alkali, and Kg is the dissociation constant of boric acid. Now the essential assumption of AntikainenTs develop- 1 n ment is that the quantity 1 + 1 and this was based on his belief that in a solution of boric acid con taining excess catechol the ratio 67
is very small hence equation V.5 becomes:
C1 V V. 5a 'HB cH+ . ♦ k/1 k/ c2n + kb
from which:
K1U KkX C1 C2n + K1 C1 V.6 “ CH+ V CH+ + Kx • Kk C2 + Kg
In order to obtain the relation between pH and the remaining quantities in V.6 for the acid solution,
Antikainen uses Kilpi’s method in which the second de rivative of V.6 is equated to zero to give the position of minimum buffer capacity. This leads to the relation
* 11 In K = K1X-L. C2 + Kb ...... V. 7 or
p(K* - Kg) = p(K111 Kk1) - n log C2 ...... V.8
It should be noticed that the differentiation procedure requires that (the concentration of free catechol) should remain constant. This was assumed to be equal to the total concentration of catechol.
Graphical treatment of the experimental data was found to satisfy equation V.8 from which the values of n and were found.
In a later paper Antikainen replaced his assumption
of a complex whose composition corresponds to a mean ligand
number of n, by the view that only the boric acid-mono-
and cis-diol complexes were present. He derived an
empirical modification of equation V.7 stated thus:
* K LB V.9
from which he derived the composite constants
log 3.972 and log 4.263 at 25°C.
V.2 Criticism of Antikainenfs Method The chief assumptions of AntikainenTs method are:
(a) In a boric acid-catechol solution with excess
catechol the ratio of HBC^HB is negligible.
(b) The concentration of free catechol = total
concentration of catechol and this is in
dependent of pH.
These assumptions are not independent since assumption
(a) leads to (b). Thus if HBCn is small, most of the catechol in the acid solution thus being uncomplexed.
It has been shown in Chapter IV page 46 that the ratio HBC:HB is by no means negligible. It may be 69 calculated that at pH 6 the value is about 1.10:1. On the other hand the ratio HBC^ : HB is certainly negligible.
It follows that Antikainenfs assumption (a) and (b) are inadmissible.
AntikainenTs equation V.9 can readily be derived from equation II. IS of this project:
Ka' I 1 + K3[C]}
1 + K1LC] + K2^C^ as follows:
Sinee is assumed to be small by Antikainen then:
EHBCJ_ small and hence is large. iVl - [HB][C]
It follows that equation II.IS becomes:
Kat {i * iqcc]} K o qlcll
= K^CC] + K1 KaT K3 [C]2 V.10
11 11 1 n2 ■c + K, (AntikainenTs terms) neglecting which is negligible. Hence it is obvious that AntikainenTs constants and K^^K. are 70
based on erroneous assumptions and will not be equal to
the values derived by the present method. Before com
paring the values of Antikainen with that of the present
method, it is advisable to discuss the work of Roy et al.
(^2) V.3 The Work of Roy, Laferriere and Edwardsv? Roy and co-workers who used a borax solution to
which various amounts of catechol were added assumed that
the equilibrium of the complex of boric acid and catechol
is governed by the expression:
1 K LSJfn! V.ll [B-][C] where BCn“ is the total amount of the complex anion.
This expression can be transformed under their experi
mental conditions and assumptions into:
K1 = iq1 + K,1 [C] ...... V.X2 when and are the formation constants of the reactions:
rsc~i B“ + C ----v BC“ V.13 [B-][C]
EBC2~3 B" + 2 C V. 14 [B“][C]2 71
The following assumptions were made:
[B]0 = [HB]0 = [HB] ...... V.15
[B] 0 = [ET] + [BC~] + [BC2-]...... V.16
[C] = [C]Q - {[BC-] + [BC,,-]}...... V.17
where [B] = initial borate ion, [HB ]Q = initial boric acid, and [C] = initial catechol.concentrations.
From equations V.13 and V.14 we have:
[BCT] 1 K [C] 1 [ B~]
[bc2~] Kg1 [C]2 [B“] the sum of which:
[BC-] [BC2“] K-j1 [C] + K23- [C]2 V. 18 [B‘] + [B-]
Dividing equation V.16 by [B-], we have:
[B]q [B-] + [BC-] + [BC2-] ^ [BC-] + [BC2-]
[B~] " [B“] + LB"]
...... V. 19
From V.lS and V.19 it follows that
1 + [C] + K2X [C]2 V. 20 [B-] 72
Hence:
CB]0 2. 12 ---2 - 1 = K,1 [C] + K, [C]2 ...... V.21 [B“] 1 2
Since the assumption is made that [B]q = [HB] (borax
being used) [HB] 9 -----1 = K-. [C] + K0 CC3 ___ ...... V. 22 [B“] 1 ^
Since Kg [3"] £H+1 [HB]
' [H + ] 1 K11 + K21 [C] ...... V.23 [C] / where Kg is the ionization constant of boric acid. Now from equation V.ll we have
1 [£bc2-] K [B‘][C] and since [BC“] + [BC2“] = [B]q - [B“] (from equ. V.16)
= [HB]q - [B“
x [BC~] + [BC2“] K = ------[B“] [C] 73
V. 24
Hence from equations V.23 and V.24:
K1 = K11 + K?1 [C]
which is equation V.12
V.4 Criticism of the Work of Roy and Co-workers. Assumptions expressed in equations V.15 and V.16 infer that [HBC] is negligible under their experimental condition, i.e, at half neutralisation. This assumption has already proved invalid. (Chapter V page 68 ).
Furthermore the expression:
[C] = [C]Q - ([BC-] + [BC2“]) as given in equation V.17 is not a valid simplification of the accurate expression: 74
[C] = [C]0 - ([HBC] + [BC“] + 2[BC2"]) since our data show, apart from [HBC] being not negligible, the amount of BC^" at half neutralisation is about 12% of the total concentration and is therefore substantial pro portion of the total catechol present. The final equation V.12 developed by Roy and co workers can readily be equated with our equation as follows: 1 KB If we multiply K with — where K-, is in our termin- K1 1 ology we have:
[s BCn'] [B"][C]
[BC~] + [BCp~] [B-][H+] [HB][C] ------y ------y------[B~] [C] [HB] [HB C]
= Kat + Ka^ [C] ... (our constants)
This equation is our equation IV.1, page 42 which we used to obtain the approximate value of K^.
Hence it is obvious that the constants K-^ and obtained by Roy and co-workers are based on erroneous assumptions and will not be equal to the values derived by the present work. 75
The following table illustrates the respective results (N.B: Antikainen’s constants are given in the
K 11 K 1 K 11 K, _2____ k2_ form of log ------tt------and log and must ‘B LB be equated to the expressions of Roy and co-workers
K1 Ka. log K-^ and log and our expressions log and KB
log KlKa,K3) kb K
KiUKki i k,k log log Kp = log — kb B
Roy et al. 3.59
Antikainen 3.97
Present work 4.57
K,K1 a»# K-3 log —??------= log Kp = log K r,B * B
Roy et al. 4.15
Antikainen 4.26
Present work 6.47 76
It is not very surprising that the values of Antikainen and Roy et al. are of the same order and smaller than those derived by the present method, since both use essentially the same assumption which implies small values of K^.
V.5 Work of SchSfer(18) Schafer assumed that dicomplex formation between boric acid and catechol is slow and does not take place immediately at 0°. The assumption was made from the observation that if one immediately titrates a solution of NaBC^to which excess catechol has been added with alkali at 0°C the equivalent amount of alkali required to neutralise the excess of catechol is larger than that if one titrates at 25°C. Schafer claimed that this difference was due to the formation of BC^” alone. Hence if a solution mixture which has been left standing at 25°C to acquire equilibrium is cooled rapidly to
0°C and titrated for the excess of the catechol, one obtains the concentration of the free catechol associated with the reaction;
BC“ + C 7^ BC2“ assuming that BCp" does not decompose into BC“ and C at 0°C and the pH region involved. Using the equation;
[BC2-] = [C]o - [B-]o - [C]
[BC_] = [B"]o - [BC2-] 77 where index o indicates initial concentrations. Schafer estimated the equilibrium constants:
[EC']
3 [BC] [C] to be 2.3 at 25°C.
V.6 Criticism of SchaferTs Work
The data obtained from this project show firstly that
BC~ and BC^" are formed simultaneously at 1:1 mole ratio of boric acid:catechol, and secondly, that increases with temperature, i.e. the concentration of free catechol de creases with increase of temperature. Assuming that the change of with temperature to be linear, would be about 66 at 0°. Hence there is still quite a large amount of BC2~ being formed at 0°C at equilibrium. While no kinetic study has been undertaken to disprove directly
SchaferTs assumption that no BC^” being formed at 0°C during the first half hour, our data indicate that the difference of alkali required to neutralise the excess catechol immediately at 0°C and that at 25°C observed by
Schafer, is due to the increase of with temperature, and not due to the formation of BC^”" alone from none at 0°C to a considerable amount at 25°C. Furthermore the presence of large excess of catechol will favour the simultaneous 78 formation of BC“ and BC^"".
Our data also suggest that at high pH values the BC^ breaks down into BC“ and C. This decomposition was assumed by Sch’afer not to take place at 0°C. This assumption is very doubtful since no justification is offered. I 79
CHAPTER SIX
THERMODYNAMIC STUDIES
VI.1 Introduction In a reaction involving the dissociation of an acid:
BH + H,0 ;=± B" + H30+ ...... VI.1
the dissociation constant K a is related to the free energy changes A G° for the reaction by the expression:
AG° = - RT In Ka...... VI.2
^ G° is dependent only on the free energies of the factors and products and these concern the molecules in their ground state . It is, of course, true that K = l/v , where K, a ^2 1 and are the rate constants for the forwards and reverse reactions respectively. But as all protonation reactions are exceedingly fast with little energy of activation, this consideration is of no significance. Substitution pK for - log K we have a a
AG° = 2.303 RT pK ...... VI.2a a The pK value of the acid is therefore proportional to the a free energy requirements for dissociation. VI.2 Equilibrium Constants and Temperature The effect of temperature in the dissociation constant K is governed by the equation ct
d In K& a H° VI.3 d T RT2 where aH° is the heat of ionisation. Since A H° in most cases is a function of temperature, a number of empirical equations have been employed for representing the ionisation constants as a function of temperature directly and for com puting the thermochemical function. In view of the lack of an exact theoretical equation and also the fact that ioni sation constants are known accurately over comparatively short temperature range, (0° - 60°) it is difficult to know which of the possible empirical equations to use. The normal o method has been to assume that 4H can be expressed as a power series in T.
A-H° = AH + a T + b T2 + ...... VI.4
4C ° = AC +aT + 2bT2 + VI.5 P po
The difficulty lies in the fact that the behaviour of A with temperature is unpredictable and difficult to know.
One simplification is to assume that A is independent SI
of temperature. This kind of treatment is very satisfac (33 ) torily employed by Wynne-Jones and Everett, ' whose
equations may be written as:
A G° = A H o -T.iSop - AC T. In T...... VI.6
A H° = A H + T. A C ...... VI. 7 o p
T.4S 0 = T.4S + T (1 till) A C ...... VI. 8 o p
Quite a number of workers have since tried to verify these. o . equations. However for the purpose of this project A H is
taken to be constant over the experimental range of
temperature. This enables us to integrate equation VI.3,
which gives:
A H° + constant lnKa R T VI.9
or A 4.57S7 log K = - + constant...... VI.9a
This expression shows that a plot of 4.57$7 log against
1/T, i*e. the reciprocal of the absolute temperature, should yield a straight line; the slope of this line will be -AH°. 82
VI.3 Method The thermodynamic evaluations in this project were
carried out according to the above principle, equation VI.9a. Knowing the values of the constants f, and
at five different temperatures, a plot of 4.5787 log 1•/ - against 'T was carried out.
VI.4 Result The fact that straight lines are obtained from the i/ plot of 4.5787 log K against 'T shows that the values of A H° associated with the constants K , and K0 can be a t I 3 considered as constants over the experimental range of temperature. The departure from linearity of a few points is most likely due to experimental error, since all of them are considered to be within a range of - jfo.
The values of the thermodynamic quantities A H°, A G° and AS° at experimental condition of 0.02 molar ionic strength are shown in Tables 4 and 5.
TABLE 4
Constant K , aT Ki K3
A H° -2.98 kcal/mole 1.12 kcal/mole 0.94 kcal/mole S3
TABLE 5
1 K a» K3 O CO AG° 1 < TEMP A S° AG° aG° A S° cal cal/deg.mole cal cal/deg.mole cal cal/deg.mole
10°C 8710 -40.9 -2760 13.7 -2390 12.8
15 8910 -41.3 -2830 13.7 -2460 12.8
20 9120 -41.3 -2900 13.7 -2520 12.8 25 9310 -41.2 -2970 13.7 -2580 12.8
30 9540 -41.3 -3030 13.7 -2640 12.8
The values of A H° were obtained from the slopes of the graphs. The values of AG° were calculated from the equation:
A G° = 2.303 R T pK
The values of AS° were obtained from the equation:
AG° = A H° - T. AS0 o1 4 *5 7 8pK 7 0( against / j vertical lin e s represent -2% 84
FIGURE 15 85
in in n O
O in in O
UJ >- 2: o
-J cc
-J o < o o < in 2 o* 16
FIGURE o m O*
S 8 VERTICAL LINES ACCURACY 86
0-33 5 0 34 0 0-3 4 5 0 3 5 0 VI.5 Discussion of Results The ionization constants of a number of weak acids exhibit maxima between 0° and 60°C. Harned and Smbrie^^ suggested that this is a property of all weak electro lytes. They also showed that as first approximation the equation:
log K - log Kq = - p (t - 0)2 represents closely the results provided that is applied in the neighbourhood of temperature 0, at which the ionization constant is maximum or Kq. Thus the ionization constant is given a parabola form in terms of two empirical constants
0 and Kq and a universal constant p, which was found to be 5 x 10 for most substances. On the other hand the ionization constants for cationic acid (NH^+ etc.) usually increase with temperature indicating a positive value of A H° with correspondingly low entropy change AS°. The behaviour of monocatechol boric acid indicates that the acid behaves in the temperature region above that corresponding to the maximum degree of ionization. That is the ionization constant decreases with temperature. The evidence available does not indicate that a maximum value occurs at some temperature lower than 10°C, for the 88
graph of pK or K v. temperature (Figures 18,19) is almost a straight line.
By contrast the formation constants K-^ and pro
gressively increase with temperatures indicating a positive heat of reaction. The values of the entropies of formation are both positive and of the same order, and this is doubtless an indication of relative numbers of / molecules on each side of the equations.
Ki \ B(OH)3 + C6H4 (OH)2^=r C6H4 8OH + 2 H?0
/°\ C6V /B-(0H>2 + C6H4 (0H)2: ^WzBOzW 0 + 2 H20.
It is obvious that the increase in entropy of formation is due to the increase in the number of molecules, from two of the reactants to three of the products, because of the liberation of two molecules of water.
There are two different kinds of dissociation of acids depending upon the nature of the acids. If the acid is in the form of BH+, the dissociation reaction is as follows:
BH+ + H20 ; ■-> B + H30+ 89
FIGURE 18
PLOT OF KQi v. TEMPERATURE .
Temp, in *C - a___ i____I------l
PLOT OF pKa v. TEMPERATURE
670
FIGURE 19 90
there is no change in th£ number of charges. Hence the
entropy change is small and most of the energy of ioniza
tion comes from enthalpy change.
On the other hand acids of the type BH dissociates
thus:
BH + HO B- + H30+
Since the number of ions increases by two, a larger entropy
loss, is to be expected due to orientation of water mole
cules around the ions. It has been pointed out by (35 ) Pitzer that the magnitude of the entropies of ioniza
tion of neutral acids are usually about - 22 cal/deg.mole.
However they are exceptions: citric, malic0 and
tartaricv ’ acids have entropy values of about
-12 cal/mole degrees. On the other hand boric acid^’^^
phenyl boronic acid (39) have entropies of ionization of
- 31-Ocal/mole degree and - 34.0cal/mole degree respectively.
Value of - 41.2 cal/mole degree continues the trend evident
in the change from B(0H)^—> RBlOH)^—* R-^R^SOH. It is
noteworthy that the figure of - 41.2 entropy units for
monocatechol boric acid is the most negative value we have
been able to locate in the literature.That this estimate
is highly probable stems from the fact that A H° is o negative and a G is positive and the signs of these
quantities are almost certainly not in dispute. 91
The interpretation of the changes of entropy associated with dissociation of weak acids is not simple.
The proton shift, the structural features of the acids and the orientation of the solvent molecules should certainly be taken into consideration. It is likely that orientation of solvent molecules in electrostatic field adjacent to the ions plays an important role in deter mining the sign and magnitude of the change in entropy when an acid dissociates. When the dissociation produces an increase of charge, as it does with uncharged acids and acid anions, it leads to increase solvent orientation and attendant immobilization of solvent molecules, and this should bring about a decrease in entropy.
It is hard to say how much contribution each of these factors makes in determining the magnitude of the entropy effect. At the present time even qualitative predictions are often of little value.
It is nevertheless worthwhile to compare the observed values of this thermodynamic quantity for acids of like structure, to note the similarities and to attempt to explain the differences.
With acids of like structure, such as fatty acids, the conventional contribution due to translation,rotation, vibration and free volume of the molecules, could reasonably be assumed to produce no larger fluctuation of 92
A S° in computing the entropy of ionization.Almost all the
difference of entropy of ionization must arise from the
interaction between solute and solvent molecules.
TABLE 6
Acids A S° cal/mole degree
Formic - 17.3
Acetic - 22.1
Propionic - 23.0
Butyric - 24.4
Valeric - 24.5
Data from: D.H.Everett, D.A.Landsman and 3.R.W. Pinset: Proc.Roy.Soc. , 215A, 4OB (1952).
When orientation of water molecules about simple ion takes place, a compressed primary hydration sheath of water with low entropy, and disordered or depolymerised region of abnormal high entropy outside this primary sheath, develop. Only at larger distances from the ion the normal loose-packed semicrystalline structure of water is re established.
Much less is known about the arrangement of water molecules about the ion, but it certainly produces a strong 93
ordering of neighbouring water molecules. In the case
with formate ion, it may be assumed that water molecules from the primary hydration shell are such arranged that the ,Tback?T of the anion is outside the tightly bound primary layer. Introduction of a group would not give rise to displacement of water in this primary layer, but v,ell in the outlying disordered region. Thus the methyl
group in the acetate ion would protrude into the dis ordered region rather than in the primary hydration shell. This will make the entropy of the acetate ion more negative than that of the formate ion because the methyl group displaces water from the disordered region and reduces the positive contribution to the entropy and by its virtue of the structure the methyl group causes an ordering of water molecules in the disordered region with a decrease of entropy. With propionate ion the ethyl group protrudes much further into the disordered region and gives rise to a still more negative entropy of ionization. Since the range of influence of carboxylate o U2) group is about 5 A it is logical to expect that further increase of chain length beyond this sphere of influence will cause a little or no change in entropy. That the effect of introduction of group depends upon the nature of the group, is well illustrated by the 94 regular increase of AS0 from succinic acid to tartaric acid. This suggests that progressive substitution of the two carbon atoms lying between the carbonyl groups with polar -OH group, is accompanied by an increase of solution of the acid molecules. Hence the difference of solvent orientation about the acid molecules fromthat about the anions is reduced.
TABLE 7
Acids A S° cal/mole degree
COOHCH2CH2COOH^3' -16.8 (37) COOHCHOHCHpCOOH -13.4 (38) COOHCHOHCHOHCOOH -11.4
The data of entropy of ionization of boron con taining acids suggest a similar case with that of fatty acids. Thus the entropy of ionization of phenyl boronic acid is more negative than that of boric acid, because the•introduction of a non-polar phenyl group would protrude in the disordered region and causes a decrease in entropy just as the case of the introduction of methyl group in acetate ion. Since C^H^O^ - group is a larger group, it is to be expected to give rise to a still more negative entropy of ionization. 95
TABLE a
Acids A S° cal/mole degree
(ho)2b(oh) - 31.0
C6H5v
^B(OH) - 34.0 hct
/°\ C,H. B - (OH) - 41.2 6 0
The observation that the entropies of ionization of boron containing acids are more negative than that of the usual value of - 22 cal/mol degree is explained by Edwards (39) and Sederstrom " on the basis that the co-ordination number changes from three in the acids to four in the anions. This necessarily requires that one more water molecule be lost in the ionization process than for a normal acid. Hence the entropy change for the process:
RB(OH) + 2H20 ..[RB(OH)2]“ + H-0+ should be more negative than the process:
RB(OH) + H?0 ~' [RBO]- + H 0+ 96
The change of configuration, however, takes place most likely in the formation reaction, the planar structure of boric acid being replaced by a tetrahedral structure of catechol-boric acid. This results from the change in magnitude of the angle of
0 - B - 0 from 120° in boric acid to about 109° in tetrahedral catechol-boric acid with an unoccupied orbital in the fourth position. Consequently the introduction of an OH-group becomes easier and this explains why catechol-boric acid is a stronger acid than boric acid itself. 97
SUMMARY
A study has been made of the equilibrium and ionization constants involved in the reactions between boric acid and catechol. The equilibria are: h HB + C ~ ^ HBC
K a t HBC ^...... H+ + BC“
K3 BC~ + C ^=± BC2“
K2 hbc + c ::z± hbc2
HBC2~ H+ + BC2“
where HB = boric acid
C = catechol 9^
From the conditions of electroneutrality and the
stoichiometry involved during the titration with sodium hydroxide of mixtures of boric acid and catechol in
various proportions, it has been possible to develop mathematical expressions from which all the constants have been evaluated. For three of these, K-, , K , and K~
the data are sufficiently accurately known at five temperatures to enable evaluation of the thermodynamic data A S] A G° for each reaction. Furthermore the
concentrations of the species C, HB, HBC, BC”, BC^" and
HBC^ at any point along the titration curves have been estimated. Mathematical justifications for the assump tions made during the derivation of the equations are given. , a i Temp. — pK3 Ki 1 Ka- PKa. K3
10° c 135 -2.13 1.90 x 10“ 7 6.72 70.5 -1.85 15° 140 -2.15 1.73&C 10“ 7 6.76 74.0 -1.87 o c ro 145 -2.16 1.58 x 10“7 6.80 76.0 -1.88 25° 150 -2.18 1.50 x 10“7 6.82 78.0 -1.89 o o r~\ 154 -2.19 1.34 x 10“7 6.87 80.0 -1.90
are found to be about 2-5. 99
Constants K a t h K3 •* AH -2.96 kcal/mole. 1.12 kcal/mole 0.94 kcal/mole ------1
k3 Ka. TEMP o>;< c* A G°* AS A G°* AS AG°* AS cal cal/deg.mole cal cal/deg.mole cal cal/deg.mole
10°C 8710 -40.9 -2760 13.7 -2390 12.8
15° 8910 -41.3 -2830 13.7 -2460 12.8
20° 9120 -41.3 -2900 13.7 -2520 12.8
25° 9310 -41.2 -2970 13.7 -2580 12.8 o o c<~\ 9540 -41.3 -3030 13.7 -2640 12.8
in 0.02 molar ionic strength.
The values of log ^l^aT and log ^l*va *IV3 differ kb kb considerably with that determined by Antikainen and Roy and co-workers.
loe KlKa. log KlKa. kb kb
This research 4.57 6,47
Antikainen 3.97 4.26
Roy et al. 3.89 4.15 100
These differences have been shown to be due to unjustified assumptions made by the authors. An interpretation of the thermodynamic quantities in terms of structure has been given. 101
APPENDIX I.
The following tables contain the values of pKQ calculated
from the Henderson equation:
PKo = PH +
(0.5070 ml of HC1 was used to back-titrate the neutralised catechol-boric acid solutions.) 102
[BORIC ACID]: [CATECHOL] = 1:1.0
10c>C. 25c*0. pH pH pH PKo pH PKo PKo PKo
6.29 6.863 7.13 7.084 6.38 6.953 7.21 7.163 6.35 6.872 7.18 7.099 6.44 6.963 7.26 7.179
6.41 6.886 7.24 7.124 6.50 6.976 7.31 7.190
6.47 6.901 7.28 7.129 6.55 6.981 7.37 7.219
6.52 6.909 7.33 7.144 6.61 6.999 7.42 7.234 6.57 6.918 7.3S 7.158 6.66 7.008 7.48 7.258 6.62 6.929 7.44 7.180 6.705 7.014 7.53 7.270
6.67 6.941 7.51 7.212 6.76 7.031 7.60 7.302 6.70 6.953 7.57 7.234 6.81 7.043 7.66 7.324 6.77 6.966 7.64 7.263 6.86 7.056 7.72 7.343 6.82 6.981 7.71 7.291 6.90 7.061 7.79 7.371
6.92 7.011 7.85 7.341 7.01 7.101 7.93 7.421
6.97 7.026 - - 7.06 7.116 8.01 7.462 7.03 7.052 8.02 7.410 7.11 7.132 8.10 7.490 7.08 7.068 8.12 7.456 7.16 7.148 8.18 7.516 103
[BORIC ACID]: [CATECHOL] = 1:2.0
10c*C 25c*C pH pH pH pH PKo PKo PKo PKo
5.96 6.533 6.66 6.613 6.06 6.633 6.76 6.713 6.01 6.533 6.71 6.629 6.11 6.633 6.80 6.719 6.06 6.536 6.75 6.634 6.16 6.636 6.845 6.729 6.11 6.541 6.785 6.634 6.21 6.641 6.89 6.739 6.16 6.549 6.825 6.639 6.26 6.649 6.93 6.744 6.21 6.558 6.865 6.643 6.31 6.658 6.97 6.748 6.25 6.559 6.91 6.650 6.35 6.659 7.02 6.760 6.29 6.561 6.96 6.662 6.40 6.671 7.06 6.762 6.335 6.56$ 7.00 6.664 6.44 6.673 7.10 6.764 6.3^ 6.576 7.05 6.673 6.485 6.681 7.15 6.773 6.42 6.581 7.10 6.681 6.525 6.686 7.20 6.781 6.4-6 6.585 7.15 6.688 6.565 6.690 7.25 6.788 6.50 6.591 7.20 6.691 6.605 6.696 7.30 6.791 6.54 6.596 7.25 6.702 6.645 6.701 7.35 6.802 6.58 6.600 7.31 6.700 6.68 6.702 7.41 6.800 6.625 6.613 7.38 6.716 6.72 6.708 7.47 6.806 104
[BORIC ACID]: [CATECHOL] =1:3.0
10°C 25°c pH pK pH pK pH pK pH pK r 0 r 0
5.72 6.293 6.41 6.363 5.85 6.423 6.535 6.488
5.77 6.293 6.445 6.364 5.90 6.423 6.57 6.489
5.82 6.296 6.48 6.364 5.95 6.426 6.61 6.494
5.87 6.301 6.52 6.369 6.00 6.431 6.65 6.499 5.915 6.304 6.56 6.374 6.05 6.439 6.69 6.504
5.960 6.308 6.60 6.378 6.10 6.448 6.73 6.508 6.00 6.309 6.64 6.330 6.14 6.449 6.77 6.510
6.045 6.316 6.69 6.392 6.18 6.451 6.81 6.512 6.09 6.323 6.73 6.394 6.22 6.453 6.85 6.514 6.13 6.326 6.77 6.393 6.26 6.456 6.90 6.523 6.17 6.331 6.815 6.396 6.30 6.461 6.945 6.526 6.21 6.335 6.86 6.398 6.34 6.465 6.99 6.528 6.25 6.341 6.91 6.401 6.38 6.471 7.04 6.531 6.29 6.346 6.96 6.412 6.42 6.476 7.085 6.537 6.33 1 6.352 7.02 6.410 6.46 6.482 7.14 6.530 6.37 6.358 . 7.08 6.416 6.50 6.488 7.20 6.536
______1 105
[BORIC ACID]: [CATECHOL] = 1:4.5
10c5C 25c C pH pH pH pH PKo PKo PK0 PKo
5.51 6.083 6.175 6.128 5.645 6.213 6.3O 6.253
5.565 6.088 6.21 6.129 5.70 6.223 6.34 6.259
5.61 6.086 6.25 6.134 5.75 6.226 6.38 6.264 5.66 6.091 6.29 6.139 5.80 6.231 6.42 6.269
5.705 6.094 6.33 6.144 5.84 6.229 6.45 6.264 5.75 6.098 6.37 6.148 5.885 6.233 6.49 6.268
5.79 6.099 6.41 6.150 5.93 6.239 6.53 6.270 5.83 6.101 6.45 6.152 5.97 6.241 6.57 6.272
5.87 6.103 6.49 6.154 6.01 6.243 - -
5.91 6.106 6.53 6.153 - - 6.65 6.273 5.95 6.111 6.575 6.156 6.085 6.246 6.695 6.276 5.98 6.105 6.62 6.158 6.12 6.245 6.74 6.278 6.02 6.111 6.67 6.161 6.16 6.251 6.79 6.281 6,06 6.116 6.72 6.172 6.19 6.246 6.83 6.282
6.10 6.122 - 6.23 6.252 6.88 6.270
6.14 6.128 6.82 6.152 6.265 6.253 6.94 6.276
.--i . - , j 106
[BORIC ACID]: [CATECHOL] = 1:7.0
10°c 25°c
pH pK pH pK pH pK pH pK ^ 0 - 0
5.29 5.863 5.935 5.888 - - 6.04 5.994
5.34 5-863 5.975 5.884 5.44 5.963 6.08 5.999
- - 6.01 5.894 5.49 5.966 - -
5.43 5.861 6.045 5.894 - - 6.15 5.999
5.475 5.864 - - 5.58 5.969 6.185 5.999
5.52 5.868 6.12 5.898 5.62 5.968 - -
5-56 5.869 6.16 5.900 - - 6.26 6.000
5.60 5.871 6.20 5.902 5.70 5.971 6.30 6.002
- - 6.245 5.909 5.74 5.973 - -
5.68 5.876 - - -- 6.3S 6.OO3
5.72 5.881 6.335 5.916 5.82 5.981 6.425 6.006
- - 6.3S 5.918 5.85 5.975 - -
5.79 5.881 - - - 6.52 6.011
5.83 5.886 6.48 5.932 5.92 5.976 6.56 6.012
5.865 5.887 6.54 5.930 5.96 5.982 - -
5.90 5.888 - 6.00 5.988 6.66 5.994
— 107
APPENDIX II
This contains the concentrations of free catechol,
[C], along the titration curve, calculated from the
equations:
(m - x) K K_ a 1 3 -1 + / 1 + 4 (m - x) Kx 1 + [H+ [C] .. A I i 1 l [H+] J
and
2 4K K K- -(K K ) +,/ (K - K ) + 0 a t o \/ a» o B [C] 2 Ka. K3
by ?tsuccessive approximation ...n
Column [CHa contains the [C] calculated from equation A and Column [C]3 contains that calculated for equation B. 108
30 °C
K&t = 1.34 x 10“7; Kx = 154; K = 80-0
HC1 [m-x] [H+] K [C] 0 [C4 L JB pH pK mis 10 3 107 108 103 10 3
.45 17.89 6.84 9.120 6.937 11.561 7.45 7.55 .44 17.49 6.13 7.413 6.948 11.272 7.30 7.32 .43 17.09 6.22 6.026 6.968 10.765 7.09 6.93 .42 16.69 6.29 5.129 6.973 10.641 6.90 6.84 .41 16.29 6.36 4.074 6.986 10.327 6.71 6.60 .40 15.89 6.42 3.802 6.993 10.163 6.51 6.48 .39 15.49 6.48 3.311 7.003 9.931 6.33 6.30 • 3$ 15.10 6.54 2.884 7.016 9.638 6.14 6.08 .37 14.70 6.60 2.512 7.031 9.311 5.85 5.83 .36 14.30 6.65 2.239 7.039 9.141 5.76 5.71 .35 13.90 6.70 1.995 7.048 8.954 5.57 5.57 .34 13.50 6.75 1.778 7.059 8.730 5.42 5.42 .33 I3.ll 6.80 1.585 7.071 8.492 5.29 5.23 .32 12.71 6.85 1.413 7.O83 8.260 5.06 5.07 .31 12.31 6.90 1.259 7.096 8.017 4.88 4.89 .30 11.91 6.95 1,122 7.111 7.745 4.71 4.70 .29 11.52 7.00 1.000 7.125 7.499 4.52 4.53 .28 11.12 7.05 0.891 7.141 7.228 4.35 4.33 109
30°C Kai = 1.34 x 10“7; Kx = 154; K- = 80-0 r HC1 [m-x] [H+] K [c]A [c]B pH 0 PKo mis 103 107 108 103 103
.27 10.72 7.10 0.794 7.156 6.982 4.18 4.17
.26 10.33 7.15 0.708 7.172 6.730 4.02 3.99 .25 9.94 7.20 O.63I 7.188 6.486 3.84 3.83 .24 9.54 7.25 0.562 7.203 6.266 3.68 3.67
.23 9.14 7.30 0.501 7.219 6.039 3.53 3.52 .22 8.74 7.35 0.447 7.234 5.834 3.37 3.38 .21 8.34 7.405 0.284 7.254 5.572 3-24 3.21 .20 7.95 7.46 O.346 7.274 5.321 3.04 3.04
.19 7.55 7.52 0.302 7.298 5.035 2.88 2.86 .18 7.15 7.58 0.263 7.320 4.786 2.72 2.70 .17 6.75 7.64 0.229 7.342 4.550 2.56 2.56 .16 6.36 7.70 0.200 7.364 4.325 2.42 2.40
.15 5.96 7.76 0.174 7.383 4 * 140 2.28 2.29 .14 5.56 7.83 0.148 7.411 3.882 2.12 2.13
.13 5.16 7.90 0.126 7.438 3.648 1.97 1.95 .12 4.77 7.97 0.107 7.461 3.459 1.83 1.88 .11 4.37 8.05 0.089 7.502 3.148 1.69 1.70
.10 3.97 8.125 0.075 7.515 3.055 1.55 1 • 64 .09 3.58 8.21 0.062 7.546 2.844 1.41 1.52
.08 3.18 8.30 0.050 7.573 2.673 1.27 1.41 110
25°C
Ka) = 1.50 x 10"7; Kx = 150; - 78.0
I 1 1 1 3 X — HC1 _ [H+]
1 K 1 pH 0 £c3b PKo
J
j V O mis £ 107 108 103 103
•45 17.89 5.995 10.116 6.892 12.823 7.60 7.66 • 44 17-49 6.08 8.318 6.898 12.648 7.39 7.54 • 43 17-09 6.16 6.918 6.908 12.360 7.17 7.30 .42 16.69 6.24 5.754 6.923 11.940 7.00 7.03 .41 16.29 6.31 4.898 6.936 11.588 6.80 6.82 .40 15.89 6.38 4.169 6.953 11.146 6.58 6.58 • 39 15-49 6.44 3.631 6.963 10.890 6.37 6.32 • 36 15.10 6.50 3.162 6.976 10.568 6.18 6.05 • 37 14.70 6.55 2.818 6.981 10.448 6.02 6.02 .36 14.30 6.61 2.456 6.999 10.023 5.81 5.73 • 35 13.90 6.66 2.188 7.008 9.817 5.65 5.58 • 34 13.50 6.705 1.972 7.014 9.683 5.46 5.46 • 33 13.11 6.76 1.738 7.031 9.3H 5.30 5.24 • 32 12.71 6.81 1.549 7.043 9.057 5.10 5.07 • 31 12.31 6.86 I.38O 7.056 8.790 4.92 4.90 .30 11.91 6.90 1.259 7.061 8.690 4.78 4.84 .29 11.52 6.95 1.122 7.075 8.414 4.60 4.64 .28 11.12 7.01 0.977 7.101 7.925 4 * 40 4*34 .27 10.72 7.06 0.871 7.116 7.656 4.23 4.17 .26 10.33 7.11 0.776 7.132 7.379 4.04 4.00 •25 9.94 7.16 0.692 7.148 7.H2 3.89 3.83 — Ill
25°C
Kai = 1.50 x 10"7; K1 = 150; Kj = 78.0
HC1 [m-x] [H+] K pH pK 0 £c4
mis 103 107 108 103 10 3
.24 9.54 7.21 0.617 7.163 6.871 3.72 3.67 .23 9.14 7.26 0.550 7.179 6.622 3.55 3.52 .22 8.74 7.31 0.490 7.190 6.457 3.41 3 *44 .21 8.34 7.37 0.427 7.219 6.039 3.22 3.17 .20 7.95 7.42 O.38O 7.234 5.834 3.07 3.05 .19 7.55 7.48 O.33I 7.258 5.521 2.90 2.87 .13 7.15 7.53 0.295 7.270 5.370 2.77 2.79 .17 6.75 7.60 0.251 7.302 4-989 2.59 2.56 .16 6.36 7.66 0.219 7.324 4.742 2.44 2.42 .15 5.96 7.72 0.191 7.343 4.539 2.30 2.30 .14 5.56 7.79 0.162 7.371 4.256 2.14 2.14 .13 5.16 7.86 0.138 7.398 3.999 1.99 2.00 .12 4.77 7.93 0.118 7.421 3-793 1.85 1.88 | .11 4.37 8.01 0.098 7.462 3.451 1.70 1.68 1 .10 3.97 8.10 0.079 7.490 3.236 1.54 1.57 .09 3.57 8.18 0.066 7.516 3.048 1.41 1.49 .08 3.18 8.28 0.053 7.553 2.799 1.26 1.30 .07 2.78 8.36 0.044 7.564 2.729 1.14 1.31 112
20°C
Ka> = 1.58 x 10-7; K1 = 145; K3 = 76.0
HC1 [m-x] LH+] K pH 0 tc3B PKo mis 10 3 107 10s 103 103
.42 16.69 6.21 6.166 6.893 12.794 7.10 7.40 .41 16.29 6.28 5.248 6.906 12.417 6.90 7.15 .40 15.89 6.35 4.467 6.923 11.940 6.70 6.70 .39 15.49 6.41 3.890 6.933 11.668 6.50 6.65
• 3# 15.10 ------.37 14.70 6.53 2.951 6.961 10.940 6.14 6.17 .36 14.30 6.58 2.630 6.969 10.740 5.93 6.03 .35 13.90 6.64 2.291 6.988 10.280 5.75 5.76 .34 13.50 6.69 2.042 6.999 10.023 5.56 5.55 .33 13.11 6.735 1.841 7.006 9.863 5.39 5.43 .32 12.71 6.79 1.622 7.023 9.4&4 5.19 5.20 .31 12.31 6.84 1.445 7.036 9.204 5.02 5.02 .30 11.91 6.89 1.288 7.051 8.892 4 * 64 4.83 .29 11.52 6.94 1.148 7.065 8.610 4.66 4.65 .28 11.12 6.99 1.023 7.081 8.299 4.47 4.46 .27 10.72 7.04 0.912 7.096 8.017 4.30 4.28 . 26 10.33 7.09 0.813 7.112 7.727 4.12 4.10 .25 9.94 7.14 0.724 7.128 7.447 3.96 3.94 113
20°C
Ka) = 1.58 x 10-7; Kx = 145; K3 = 76.0
HC1 [m-x] [H+] K [C]A [C]B pH 0 PKo mis 103 107 108 103 103
.24 9.54 7.19 0.646 7.143 7.194 3.79 3.77 .23 9.14 7.24 0.575 7.159 6.934 3.62 3.62 .22 8.74 7.30 0.501 7.184 6.546 3 *44 3.39 .21 8.34 7.36 0.437 7.209 6.180 3.27 3.17 .20 7.95 7.41 O.389 7.224 5.970 3.12 3.06 .19 7.55 7.46 0.347 7.238 5.781 2.96 2.94 .18 7.13 7.52 0.302 7.260 5.495 2.79 2.78 .17 6.75 7.59 0.257 7.292 5.105 2.63 2.56 .16 6.36 7.65 0.224 7.314 4.853 2.47 2.41 .15 5.96 7.72 0.191 7.343 4.539 2.31 2.24 .14 5.56 7.78 0.166 7.361 4.355 2.16 2.15 .13 5.16 7.86 0.138 7.398 3.999 1.94 1.95 .12 4.77 7.94 0.115 7.431 3.707 1.84 1.80 .11 4.37 8.02 .0955 7.472 3.373 1.69 1.62 .10 3.97 8.10 .0794 7.490 3.236 1.55 1.55 .09 3.57 8.19 .0646 7.526 2.979 1.40 1.42 .08 3.18 8.28 .0525 7.553 2.799 1.27 1.32 .07 2.78 8.39 .0407 7.594 2.547 1.12 1.20 114
15°C
Ka) = 1.738 x 1CT7; Kx = HO; K = 74.0
HC1 [m-x] [H + ] K pH pK 0 [°3a mis 10 3 107 10s 103 10 3
.42 16.69 6.1S 6.607 6.863 13.710 7.20 7.40 .41 16.39 6.25 5.623 6.876 13.305 6.98 7.17 .40 15.89 6.32 4.786 6.893 12.794 6.78 6.S3 .39 15.49 6.38 4.169 6.903 12.503 6.57 6.65 .32 15.10 6. 44 3.631 6.916 12.134 6.40 6.37 .37 14.70 6.50 3.162 6.931 11.722 6.20 6.16 .36 14.30 6.56 2.754 6.949 11.246 5.98 5.88 .35 13.90 6.61 2.455 6.958 11.015 5.81 5.74 .34 13.50 6.66 2.188 6.969 10.740 5.61 5.58 .33 I3.ll 6.71 1.950 6.981 10.445 5.43 5.30 .32 12.71 6.76 1.738 6.993 10.163 5.18 5.21 .31 12.31 6.81 1.549 7.006 9.863 5.00 5.03 .30 11.91 6.86 1.3S0 7.021 9.528 4.90 4.88 .29 11.52 6.91 1.230 7.035 9.226 4.71 4.67 .28 11.12 6.96 1.096 7.051 8.8 92 4.53 4 • 46 .27 10.72 7.01 0.977 7.066 8.590 4.35 4.33 .26 10.33 7.06 0.871 7.082 8.279 4.18 4.11 .25 9.94 7.11 0.776 7.098 7.980 4.02 3.94 115
15°C
K&t = 1.738 x 10'7; Kx = 140; = 74.0
HC1 [m-x] [H + ] K pH pK 0 mis 10 3 107 106 103 103
.24 9.54 7.16 0.692 7.113 7.709 3.85 3.80 .23 9.14 7.21 0.617 7.131 7.400 3.67 3.62 .22 8.74 7.27 0.537 7.154 7.015 3.48 3.42 .21 8.34 7.32 0.479 7.169 6.780 3.32 3.28 .20 7.95 7.37 0.427 7.184 6.550 3.18 3.16 .19 7.55 7.435 0.367 7.213 6.124 2.98 2.93 .IS 7.15 7.49 0.324 7.230 5.888 2.S3 2.78 .17 6.75 7.55 0.282 7.252 5.598 2.67 2.65 .16 6.36 7.61 0.245 7.274 5.321 2.52 2.50 .15 5.96 7.68 0.209 7.303 4.977 2.36 2.32 .14 5.56 7.75 0.178 7.331 4.667 2.20 2.16 .13 5.16 7.82 0.151 7.358 4.385 2.02 2.01 .12 4.77 7.90 0.126 7.391 4.064 1.88 1.85 .11 4.37 7.98 0.105 7.432 3.698 1.73 1.67 .10 3.97 8.07 0.085 7.460 3.467 1.56 1.57 .09 3.57 8.16 0.069 7.496 3.192 1.42 1.41. .08 3.18 8.25 O.O56 7.523 2.999 1.28 1.33 .07 2.78 S.36 0.044 7.564 2.729 1.13 1.21 116
10°C
Ka) = 1.90 x 10“7; K1 = 135; ~ 7°'5
HC1 [m-x] [H + ] K pH 0 PK0 mis 10 3 107 108 103 103
.45 17.89 5.91 12.303 6.807 15.596 7.91 8.10 • 44 17.49 6.00 10.000 6.818 15.206 7.71 7.83 .43 17.09 6.08 8.318 6.828 14.860 7.53 7.65 .42 16.69 6.16 6.918 6.843 14.355 7.28 7.35 .41 16.29 6.23 5.888 6.$56 13.932 7.08 7.08 .40 15.89 6.29 5.129 6.363 13.709 6.90 6.95 .39 15.49 6.35 4.467 6.872 13.433 6.70 6.76 • 3$ 15.10 6.41 3.890 6.886 13.002 6.50 6.52 .37 14.70 6.47 3.388 6.901 12.560 6.31 6.26 .36 14.30 6.52 3.020 6.909 12.331 6.12 6.14 .35 13.90 6.57 2.692 6.918 12.080 5.95 5.98 .34 13.50 6.62 2.399 6.929 11.776 5.75 5.81 .33 13.11 6.67 2.138 6.941 11.452 5.56 5.62 .32 12.71 6.70 1.995 6.953 11.143 5.38 5.44 .31 12.31 6.77 1.698 6.966 10.811 5.18 5.24 .30 11.91 6.82 1.514 6.981 10.446 5.02 5.08 .29 11.52 6.87 1.349 6.995 10.120 4.82 4.87 .28 11.12 6.92 1.200 7.011 9.750 4 * 64 4.65 .27 10.72 6.97 1.072 7.026 9.419 4.46 4 • 43 .26 10.33 7.03 0.933 7.052 8.8 72 4.27 4.20 .25 9.94 7.08 0.832 7.068 8.551 4.10 4.01 117
10°C
Kat = 1.90 x 10-7; Kx = 135; K3 = 70.5 i +
HC1 — [m-x] i [C]B pH O tc4 PKo
J 0 0 — o O mis 103 f 103 103
.24 9.54 7.13 0.740 7.084 8.241 3.92 3.84 .23 9.14 7.18 0.661 7.099 7.962 3.74 3.69 .22 8.74 7.24 0.575 7.124 7.516 3.56 3.46 .21 8.34 7.28 0.525 7.129 7.430 3.42 3.41 .20 7.95 7.33 0.468 7.144 7.178 3.26 3.28 .19 7.55 7.38 0.417 7.158 6.950 3.11 3.16 to i — • 1 7.15 7.44 0.363 7.180 6.607 2.94 2.98 .17 6.75 7.51 0.309 7.212 6.138 2.74 2.74 .16 6.36 7.57 0.269 7.234 5.834 2.60 2.59 .15 5.96 7.64 0.229 7.263 5.458 2.42 2.41 .14 5.56 7.71 0.195 7.291 5.H7 2.26 2.25 .13 5.16 7.78 0.161 7.318 4.808 2.08 2.10 .12 4.77 7.85 0.141 7.341 4.560 1.95 1.95 .11 4.37 ------.10 3.97 8.02 0.096 7.410 3.890 1.63 1.66 .09 3.57 8.12 0.076 7.456 3.499 1.47 1.48 .08 3.18 8.22 0.060 7.493 3.214 1.31 1.34 .07 2.78 8.325 0.047 7.529 2.958 1.17 1.24 118
APPENDIX III.
The calculation of the concentrations of various species in solution was carried out as follows:
From the equilibrium constants we have:
[HBC] [HBC] -----= K [C] ...... I 1 [HB] [C] [HB] 1
[3C-][H+] [HBC] [H+] II [HBC] [BC~] K a i
EBC2~3 [BC2-] = k3[c] III 3 [BC'][C] [BC-]
Let [BC“] be equal to x, then equation I. equation II and equation III can be rearranged as:
[BC2~] = K3[C] X ...... Ilia
[HBC] = L x ...... I la ua'
rhbi = CHBG] = [H+] x K1[C] KlKa-[C] 119
Substituting these values in the equations derived from the principle of conservation of mass and assuming
[HBCp] = y, we have: m = [HBC] + [BC~] + [HBC2] + [BC2“] + [HB]
[H+] [H+] x = — x + x + y + K„[C]x + 77-r?—ryr-r ...... IV
where m = the total concentration of acid.
[H+] ) y = m 1 + k3[c] X IVa KlEa.[Cf’
Since the mole ratio of catechol:boric acid is equal to one, it follows : m = [HBC] + [BC“] + 2[HBC2] + 2 [BC./"] + [C]
[H+] = yr--- x + x + 2y + 2 K3[C]x + [C] ...... V
Multiplying equation IV with 2, and substract equation V from it:
[H + ] [H+] x 2 m = 2 --- x + 2x + 2y + 2 K~[C]x + K, K # a r ^ 1 a» rcj 120
H + m = —— x + x + 2y + 2 K^[C] x + [C]
m = |— x+x+0 + 0 + 2 - [C] a» 1 a'L J
TH + 1 x + ■x + P r h+1 x = m + [C]
m + [C] x = VI 1 + + - 2 [H x K rK' nKT" f[C] a» 1 a rL
Since the values of m, [C], [H+], K-, , K and K~, are -L at j known, equation VI can be solved to obtain x. The concentrations of [HB“], [HBC], [BC9“] and [HBGp] can then be readily determined from equations la, Ila, Ilia and IVa respectively. 121 l 30°C
Kx = 154; Kar = 1.34 x 1CT7; = 50-0
Total Concentration of Acid = 20.05 x 10“7 Molar
i r 1 0 m _
i [HBC] [ ] [HBC2] HC1 pH [H+] [C] [bc2-] HB ^ o mis 10? 103 rH 103 103 103 103
.45 6.04 9.120 7.50 1.40 0.84 9.57 8.28 -0.04
, 44 6.13 7.413 7.31 1.67 0.94 9.23 8.20 -0.03 .43 6.33 6.026 7.01 1.95 1.10 8.78 8.15 +0.05 .42 6.29 5.129 6.87 2.23 1.23 8.55 8.10 -0.06 .41 6.36 4.074 6.66 2.67 1.42 8.11 7.89 -0.04 .40 6.42 3.802 6.50 2.79 1.45 7.94 7.84 + 0.03
.39 6.48 3.311 6.31 3.08 1.56 7.60 7.82 -0.01
• 3# 6.54 2.884 6.11 3.38 1.65 7.37 7.73 + 0.02 .37 6.60 2.512 5.84 3.69 1.72 6.92 7.68 +0.04 .36 6.65 2.239 5.70 3.98 1.82 6.63 7.57 +0.05 .35 6.70 1.995 5.57 4.28 1.91 6.38 7.44 +0.04 .34 6.75 1.778 5.42 4.62 2.00 6.12 7.33 -0.02
.33 6.80 1.585 5.26 4.95 2.08 5.85 7.21 -0.04
.32 6.85 1.413 5.06 5.26 2.13 5.55 7.11 -0.00
.31 6.90 1.259 4.89 5.61 2.19 5.27 7.00 -0.02 .30 6.95 1.122 4.70 5.95 2.24 4.98 6.59 -0.01
.29 7.00 1.000 4.52 6.31 2.28 4.71 6.75 0.00
.28 7.05 ' 0.891 4.34 6.67 2.31 4.43! 6.62 +0.02 1 122
30°
K, = 154; K = 1.34 x 10~7; K, = 80-0 j- a t j
Total Concentration of Acid = 20.05 x 10"^ Molar
HC1 pH [H+] [C] [BC~] [BC2~] [HBC] [HB] [hbc2]
mis 107 103 103 103 103 103 103
.27 7.10 0.794 4.17 7.03 2.35 4.16 6.48 +0.03 26 7.15 0.708 4.00 7.40 2.37 3.91 6.35 +0.02
.25 7.20 0.631 3.84 7.77 2.38 3.66 6.19 +0.05 .24 7.25 0.562 3.67 8.22 2.42 3.44 6.08 -0.05
.23 7.30 0.501 3.52 8.54 2.41 3.19 5.89 0.00 .22 7.35 0.447 3.38 8.93 2.41 2.98 5.72 +0.01 .21 7.405 0.394 3.22 9.36 2.40 2.75 5.54 0.00 .20 7.46 0.346 3.04 9.76 2.38 2.52 5.38 +0.01
J.9 7.52 0.302 2.87 10.19 2.34 2.29 5.20 +0.02 to 1 — • 1 7.58 0.263 2.71 10.64 2.31 2.09 5.00 +0.01 .17 7.64 0.229 2.56 11.08 2.27 1.89 4.80 +0.01 j.6 7.70 0.200 2.41 11.55 2.23 1.71 4.58 -0.02
J.5 7.76 0.174 2.29 12.00 2.19 1.56 4.37 -0.07 .14 7.83 0.148 2.13 12.40 2.12 1.37 4.17 -0.01 i — • 1 7.90 0.126 1.96 12.81 2.01 1.21 3.98 + 0.04
J.2 7.97 0.107 1.83 13.30 1.94 1.06 3.76 -0.02 J.1 8.05 0.089 1.70 13.78 1.87 0.91 3.50 -0.01
J.0 8.125 0.075 1.60 13.25 1.84 0.80 3.26 -0.07 1 123
25°C
K,l = 150;7 K a t = 1.50 x 10_7; K, = 78-0
Total Concentration of the Acid = 20.05 x 10 J Molar
HC1 pH [H+] [C] [ESC-] [3C2-] [HBC] [HB] [hbc2] mis 107 103 103 103 103 103 103
.45 5.995 10.120 7.63 1.41 0.84 9.48 8.31 +0.01 • 44 6.08 8.318 7.41 1.66 0.96 9.20 8.29 -0.05 .43 6.16 6.918 7.23 1.92 1.08 8.90 8.20 -0.05 .42 6.24 5.754 7.02 2.21 1.21 8.49 8.20 -0.05
.41 6.31 4.898 6.80 2.46 1.30 8.21 8.05 -0.02 .40 6.38 4.169 6.58 2.76 1.41 7.87 7.96 +0.02 .39 6 • 44 3.631 6.35 3.10 1.54 7.51 7.88 +0.02
.33 6.50 3.162 6.12 3.39 1.62 7.15 7.80 -0.01 .37 6.55 2.818 6.02 3.70 1.73 6.94 7.68 0.00 .36 6.61 2.455 5.77 4.00 1.80 6.55 7.65 +0.05 .35 6.66 2.188 5.61 4.32 1.89 6.30 7.50 +0.04 .34 6.705 1.972 5.46 4.62 1.97 6.05 7.40 +0.01
.33 6.76 1.738 5.27 4.96 2.04 5.75 7.28 + 0.02 .32 6 • Si 1.549 5.08 5.29 2.10 5.47 7.17 0.00
.31 6. S6 1.380 4.91 5.63 2.16 5.18 7.05 +0.04 .30 6.90 1.259 4.80 5.95 2.22 5.00 6.93 -0.04
.29 6.95 1.122 4.60 6.30 2.26 4.70 6.80 -0.01
.28 7.01 0.977 4.34 6.70 2.26 4.35 6.70 +0.04
.27 7.06 0.871 4.20 7.07 2.32 4.10 6.51 + 0.05 124
25°C
K, = 150: K . = 1.50 x 10"?; K0 = 78-0 1 7 a» 7 3 Total Concentration of Acid = 20.05 x 10”^ Molar ------1 1 0 —
l bc [HBC2] HC1 pH [H+] [BC“] [ 2-] [HBC] [HB] 1
mis 107 --- 103 103 103 103 103 - . 26 7.11 0.776 4.02 7.45 2.34 3.85 6.40 + 0.01 .25 7.16 0.692 3.86 7.82 2.36 3.60 6.23 +0.04 .24 7.21 0.617 3.70 8.20 2.37 3.37 6.07 +0.04 .23 7.26 0.550 3.53 8.56 2.37 3.15 5.93 +0.04 .22 7.31 0.490 3.42 9.00 2.80 2.94 5.73 -0.01 .21 7.37 0.427 3.19 9.42 2.35 2.68 5.59 -0.00 .20 7.42 0.380 3.07 9.82 2.36 2.47 5.40 0.00 .19 7.48 0.331 2.88 10.24 2.29 2.25 5.21 -0.01 .IS 7.53 0.295 2.78 10.62 2.30 2.09 5.01 +0.02 .17 7.60 0.251 2.57 11.12 2.23 1.86 4.81 + 0.02 .16 7.66 0.219 2.43 11.60 2.18 1.6a 4.62 -0.03 .15 7.72 0.191 2.30 11.95 2.14 1.52 4.41 +0.03 .14 7.79 0.162 2.14 12.48 2.08 1.33 4.16 -0.01 .13 7.86 0.138 2.00 12.90 2.01 1.17 3.96 + 0.01 .12 7.93 0.118 1.86 13.30 1.93 1.05 3.75 +0.02 .11 8.01 0.098 1.69 13.82 1.82 0.90 3.54 -0.03 .10 8.10 0.074 1.55 14.32 1.73 0.76 3.25 -0.01 .09 8.18 0.066 1.43 14.74 1.64 0.66 3.02 0.00 .08 8.28 0.053 1.28 15.20 1.52 0.53 2.77 +0.03 125 20°C Kx = 145; Kat = 1.58 x 10~7; K3 = 76.0 Total Concentration of Acid = 20.05 x 10-7 Molar 1 1 1 1 1 + _ w 0 to — — _ 1 1 1 HC1 pH 1 [C] [BC-] [HBC] [HB] [HBC2] mis 107 103 103 103 103 103 103 .41 6.28 5.248 6.90 2.46 1.29 8.16 8.16 -0.02 .40 6.35 4.467 6.70 2.77 1.41 7.83 8.06 -0.02 .39 6.41 3.890 6.50 3.06 1.52 7.5 2 7.98 -0.03 .3^ ------ .37 6.53 2.950 6.15 3.70 1.73 6.90 7.75 -0.03 .36 6.58 2.630 5.98 3.98 1.80 6.63 7.65 -0.01 .35 6.64 2.291 5.75 4.34 1.89 6.29 7.54 -0.01 .34 6.69 2.042 5.55 4.65 1.96 6.00 7.45 -0.01 .33 6.735 1.841 5.40 4.94 2.03 5.76 7.35 -0.03 .32 6.79 1.622 5.20 5.31 2.10 5.44 7.22 -0.02 .31 6.84 1.445 5.02 5.63 2.15 5.17 7.11 +0.01 .30 6.89 1.288 4.84 5.98 2.20 4.88 6.98 +0.01 .29 6.94 1.148 4.66 6.36 2.25 4.63 6.84 -0.03 .28 6.99 1.023 4.46 6.74 2.28 4.36 6.72 -0.05 .27 7.04 0.912 4.29 7.09 2.31 4.09 6.57 -0.01 .26 7.09 0.813 4.11 7.45 2.32 3.83 6.43 +0.02 .25 7.14 0.724 3.95 . 7.85 2.36 3.60 6.26 -0.02 j 1 126 20°C Kx = 145; Kar_= 1.58 X 10-7; K3 = 76-0 Total Concentration of Acid = 20.05 x 10-3 Molar HC1 pH [H+] [C] [BC-] [3C2-] [H3C] [HB] [HBC2] mis 107 103 103 103 103 103 103 .24 7.19 0.646 3.78 8.20 2.36 3.35 6.11 +0.03 .23 7.24 0.575 3.62 8.60 2.36 3.13 5.95 +0.01 .22 7.30 0.501 3.41 9.04 2.34 2.86 5.78 +0.03 .21 7.36 0.437 3.24 9.49 2.33 2.63 5.60 +0.03 .20 7.41 0.389 3.10 9.88 2.33 2.43 5.41 0.00 .19 7.46 0.347 2.95 10.22 2.29 2.25 5.25 +0.04 .IS 7.52 0.302 2.78 10.68 2.26 2.04 5.05 + 0.02 .17 7.59 0.257 2.60 11.20 2.21 1.83 4.81 0.00 . 16 7.65 0.224 2.45 11.60 2.16 1.65 4.64 0.00 .15 7.72 0.191 2.29 12.09 2.10 1.46 4.40 0.00 .14 7.78 0.166 2.15 12.50 2.05 1.31 4.20 -0.01 .13 7.86 0.138 1.95 12.97 1.92 1.13 4.00 +0.03 .12 7.94 0.115 1.82 13.50 1.86 0.98 3.72 -0.01 .11 8.02 0.096 1.66 13.92 1.76 0.84 3.51 +0.03 .10 8.10 0.079 1.55 14.40 1.69 0.72 3.22 + 0.02 .09 8.19 0.065 1.41 14.88 1.59 0.61 2.98 -0.01 .08 8,28 0.053 1.29 15.33 1.50 0.51 2.73 -0.02 .07 8.39 0.041 1.16 15.92 1.40 0.41 2.41 -0.06 127 15°C K-, = 140; K , = 1.738 x 10“7; K, = 74-0 Total Concentration of Acid = 20.OB x 10”^ Molar HC1 pH [H+] [C] [BCT] [bc2-] [H3C] [HB] [hbc2] mis 107 103 103 103 103 103 103 .40 6.32 4.786 6.80 2.81 1.41 7.73 8.12 +0.01 .39 6.3B 4.169 6.59 3.09 1.50 7.32 8.04 +0.08 -CO 6.44 3.631 6.38 3.42 1.61 7.15 8.00 -0.10 .37 6.50 3.162 6.18 3.73 1.71 6. BO 7.84 0.00 .36 6.56 2.754 5.93 4.08 1.80 6.47 7.74 -0.06 .35 6.61 2.455 5.77 4.40 1 • BB 6.22 7.63 -0.05 .34 6.66 2.188 5.60 4.69 1.95 5.91 7.53 0.00 .33 6.71 1.950 5.40 5.01 2.00 5.63 7.45 -0.01 .32 6.76 1.738 5.20 5.32 2.05 5.32 7.32 +0.07 .31 6. Bl 1.549 5.01 5.69 2.11 5.07 7.22 -0.01 .30 6. B6 1.380 4.87 6.05 2.18 4.80 7.05 0.00 .29 6.91 1.230 4.69 6.41 2.22 4.54 6.91 0.00 .28 6.96 1.096 4*49 6.76 2.24 4.27 6.76 +0.04 .27 7.01 0.977 4.34 7.14 2.29 4.00 6.61 +0.04 .26 7.06 0.871 4.15 7.53 2.31 3.77 6.49 -0.02 .25 7.11 0.776 4.00 7.88 2.34 3.52 6.29 +0.05 128 15°C Kx = 140; Ka( = 1.738 x 10“ 7; K, = 74-0 Total Concentration of Acid = 20.08 x 10”p Molar i J + — — [HBC2] l [HBC] HC1 pH « [C] [BC“] [BC2~] [HB] -0 mis O 103 103 103 103 103 103 .24 7.16 0.692 3.83 8.28 2.34 3.29 6.13 + 0.04 .23 7.21 0.617 3.64 $.63 2.32 3.07 6.02 +0.02 .22 7.27 0.537 3.46 9.10 2.33 2.81 5.82 +0.02 .21 7.32 0.479 3.30 9.47 2.31 2.61 5.65 +0.04 .20 7.37 0.427 3.18 9.90 2.32 2.43 5.47 -0.04 .19 7.435 0.367 2.96 10.37 2.28 2.19 5.27 -0.03 . IS 7.49 0.324 2.80 10.75 2.23 2.00 5.10 0.00 .17 7.55 0.282 2.66 11.20 2.20 1.81 4.87 0.00 .16 7.61 0.246 2.51 11.60 2.16 1.65 4.67 0.00 .15 7.68 0.209 2.34 12.10 2.09 1.45 4.44 0.00 .14 7.75 0.178 2.18 12.53 2.02 1.29 4.23 +0.01 .13 7.82 0.151 2.02 13.00 1.95 1.13 3.98 +0.02 .12 7.90 0.126 1.87 13.50 1.86 0.98 3.72 +0.02 .11 7.98 0.105 1.70 13.94 1.76 0.84 3.54 0.00 .10 8.07 0.085 1.57 14.45 1.66 0.71 3.22 +0.04 .09 8.16 0.069 1.42 14.91 1.57 0.60 2.98 +0.02 .08 8.25 0.056 1.30 15.40 1.48 0.50 2.72 -0.02 129 10°C K, = 135; K , = 1.90 x 10"7; K, = 70.5 1 7 a» 1 j> Total Concentration of Acid = 20.03 x 10“^ Molar 1 ' • i l o — — [HB] [hbc2] l bo HC1 pH [H+] i [BC~] [ 2-] [HBC] J j i V — o mis 107 i 103 103 103 103 103 ------ .45 5.91 12.300 7.95 1.42 0.78 9.20 8.62 0.00 . 44 6.00 10.000 7.71 1.68 0.91 8.85 8.58 + 0.01 .43 6.08 8.318 7.65 1.98 1.07 8.69 8.45 -0.06 .42 6.16 6.918 7.28 2.26 1.16 8.23 8.38 0.00 .41 6.23 5.888 7.08 2.56 1.27 7.93 8.30 -0.04 .40 6.29 5.129 6.92 2.82 1.37 7.61 8.18 +0.05 .39 6.35 4.467 6.73 3.12 1.48 7.40 8.08 -0.05 6.41 3.890 6.51 3.42 1.57 7.00 7.97 +0.07 .37 6.47 3.388 6.28 3.76 1.66 6.72 7.91 -0.02 .36 6.52 3.020 6.13 4.06 1.75 6.36 7.83 +0.03 .35 6.57 2.692 5.96 4.37 1.83 6.18 7.69 -0.06 .34 6.62 2.399 5.78 4.68 1.90 5.90 7.57 -0.02 .33 6.67 2.138 5.58 5.00 1.96 5.63 7.45 0.00 .32 6.70 1.995 5.40 5.32 2.03 5.32 7.35 +0.01 .31 6.77 1.698 5.21 5.67 2.08 5.07 7.21 0.00 .30 6.82 1.514 5.05 6.02 2.14 4.81 7.05 0.00 .29 6.87 1.349 4. $4 6.36 2.17 4.53 6.95 +0.02 .28 6.92 1.202 4.64 6.73 2.21 4.24 6.77 +0.03 .27 6.97 1.072 4.47 7.12 2.24 4.00 6.65 +0.03 130 10° c K]_ = 135; Ka, = 1.90 x 10“7; = 70.5 Total Concentration of Acid = 20.03 x 10“3 Molar HC1 PH [H+] [C] [BO'] [bc2-] [H3C] [HB] [HBC2] mis 107 103 103 103 103 103 103 .26 7.03 0.933 4.23 7.55 2.25 3.70 6.50 +0.03 .25 7.08 0.832 4.06 7.92 2.26 3.47 6.36 +0.02 .24 7.13 0.740 3.88 8.30 2.27 3.24 6.19 + 0.05 .23 7.18 0.661 3.71 3.66 2.27 3.01 6.02 + 0.05 .22 7.24 0.575 3.51 9.14 2.26 2.76 5.84 + 0.05 .21 7.28 0.525 3.42 9.48 2.28 2.62 5.67 0.00 .20 7.33 0.468 3.27 9.87 2.27 2.42 5.51 -0.02 .19 7.38 0.417 3.12 10.20 2.24 2.24 5.32 + 0.05 .13 7.44 0.363 2.96 10.66 2.22 2.04 5.12 +0.02 .17 7.51 0.309 2.74 11.14 2.15 1.82 4.89 +0.05 .16 7.57 0.269 2.60 11.58 2.12 1.65 4.68 +0.03 .15 7.64 0.229 2.42 12.09 2.07 1.46 4.46 +0.05 .14 7.71 0.195 2.26 12.57 2.00 1.29 4.22 -0.03 .13 7.78 0.164 2.09 13.05 1.92 1.11 3.92 +0.05 .12 7.85 0.141 1.95 13.38 1.84 0.99 3.77 +0.05 .11 ------ .10 8.02 0.096 1.65 14.42 1.67 0.72 3.25 -0.03 .09 8.12 0.076 1.48 14.92 1.55 0.60 2.99 -0.03 .08 8.22 0.060 1.32 15.30 1.42 0.50 2.75 131 BIBLIOGRAPHY (1) LEVY, H.A., and BRACKWAY, L.O., J.A.C.S., 22,2085 (1937) . 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