T H E ACTIVITY COEFFICIENT OF BENZOIC ACID I N SOLUTIONS OF NEUTRAL SALTS AND OF SODIUM BENZOATE* BY I . M . KOLTHOFF AND WOUTER BOSCH'
In previous papers, the authors2have studied the influence of neutral salts on the activity coefficients of the anions of weak acids. The hydrogen ion activity of a very dilute buffer mixture of a weak acid and its salt, to which known amounts of neutral salts had been added, was measured and from these data the activity coefficients of the anion of the acid computed. In working with systems containing an undissociated acid and its monovalent anion, the difficulty was encountered that the change of the activity coefficient of the undissociated acid in the presence of neutral salts was not exactly known.* For this reason, it was decided to make a more extensive study of the system, benzoic acid-sodium benzoate, in which the activity coefficient of the undissociated acid could be kept constant or be determined in an experimental way. In the second paper the results of the measurements of the activity coefficient of the benzoate ion in the system benzoic acid (saturated solution in water), 0.01N sodium benzoate in the presence of various concentrations of neutral salts will be described. I n the third paper of this series the activity coefficient of the silver ions in a saturated solution of silver benzoate in the presence of various concentrations of the same neutral salts will be reported. From the silver ion activity and the solubility product of silver benzoate the activity coefficient of the benzoate ion could be computed and the figures compared with those found in the second paper in solutions of nearly the same ionic strength.
Materials used Water: Conductivity water was used throughout this work. Benzoic acid: A U.S.P. product (Eastman Kodak Company) was recrystallized a few times by pouring a concentrated solution in hot alcohol into a large volume of boiling water. After cooling, the crystals were collected by suction and dried over sulfuric acid to constant weight. Various tests (for details see thesis of W. Bosch) showed that the product was chemically pure. In addi*Contribution from the School of Chemistry, University of Minnesota. 1 The experimental part of this work waa carried out at the University of Minnesota in 1929 and 1930 and presented in the doctor's thesis of Wouter Bosch, submitted to the faculty of the Universit of Utrecht, in July 1931.After the work waa completed papers of E. Larason and E. F. Cxase and M. Kilpatrick Jr., partly covering the eame subject, were published. As in the latter's papers a complete discussion of the literature on the activity coefficient of benzoic acid is found, the authors for the sake of brevity omit such a discussion in the present paper. * Comp. I. M. Kolthoff and W. Bosch: Rec. Trav. chim., 46, 430 (1917);47, 558, 819, 826,861,873 (1928);48,37 (1929).
1686
I. M. KOLTHOFF AND WOUTER BOSCH
tion the normality of a solutioii of sodium hydroxide was determined according to standard methods with our product, one of the Bureau of Standards and one of Kahlbaum (fur kalorimetrische Bestimmungen) ; all data agreed within 0.02%. I n order to test the physical purity (possible presence of another modification) various amounts of solid body (between 0.8 and 6 g. with zoo cc. water) were used in solubility measurements; in all cases the data obtained agreed within 0.1%. If the saturated solution was poured off from the solid body and fresh water added, the same solubility was found. Moreover, Kahlbaum's product, before and after melting, gave exactly the same results as our own product. Sodium benzoate: A U.S.P. product (Merck) was twice recrystallized from water, washed with small amounts of cold water, finally with a small volume of absolute alcohol, and dried a t 150' to constant weight. By qualitative and quantitative tests its purity was established. Moreover, in many of the experiments, solutions of sodium benzoate were prepared from pure benzoic acid and standard base; exactly the same results were obtained as with solutions of the above salt of equivalent concentration. Seutral salts: C. P. salts were used, some of them recrystallized from water and their purity tested according to standard methods. Very sensitive tests were applied to establish the absence of acidic or basic impurities, (for complete description, comp. thesis of W. Bosch, p. 26-32) moreover, the water content of hydrates was determined in a quantitative way. It may be mentioned that the strontium nitrate was labelled as being a hydrate, whereas it did not contain more than o . z j y o water.
Solubility of Benzoic Acid in Water and in Sodium Benzoate The solubility was determined in a thermostat at 2 jo + 0.01'. Weighed samples of benzoic acid with zoo cc. of water or salt solution were rotated in Pyrex glass bottles, closed with paraffined cork stoppers. After saturation had been reached, the bottles were allowed to stand in the thermostat until the supernatant liquid was clear and samples drawn out with the aid of suction with a carefully calibrated pipet at 2 jo. The tip of the pipet was connected with a piece of glass tubing, the latter being drawn out in the middle and filled with adsorbent cotton. The clear solution was titrated with standard carbonate-free sodium hydroxide, using phenolphthalein as an indicator. As a rule 1.5 g. benzoic acid was used in a volume of 2 0 0 cc.; the amount of acid, however, proved to be immaterial. I n agreement with M. Kilpatrick Jr. and E. F. Chase: it was found that after five hours' shaking the solution was saturated; as a rule, however, the bottles were rotated over night. All concentrations are expressed in moles per liter. As an average of thirty determinations with different amounts and products of benzoic acid a 0.00002 moles acid per liter at 2 5 ' was found, this solubility of 0.02775
*
3
M. Kilpatrick Jr. and E. F. Chase: J. Am. Chem. SOC.,53, 1732 (1931).
ACTIYITT COEFFICIENT OF BENZOIC ACID
1687
figure being in close agreement with the data reported in the literature (compare list given byKilpatrick and Chase3). The activity of the undissociated acid is smaller than the saturation value, since a small part of the acid is dissociated into its ions. [aH Benz] = 0 . 0 2 7 7 5 - cH+ in which cH' represents the hydrogen ion concentration (not the activity) of the saturated solution in water. iis will be shown later, the ionization constant' of benzoic acid at 2 jo is equal to 6.60 X 10-j. From this and the saturation figure, it is found that the hydrogen ion activity in the saturated solution is equal to 1.3I X IO-^. By applying the simple Debye-Huckel relation: -
log f
= 0.
jvqi
a hydrogen ion concentration of 1.36 X IO-^ is calculated and the activity of Undissociated benzoic acid in the saturated solution in water is found to be 0 . 0 2 i 7 5 - 0.00136 = 0.0264. Since this calculation involves the use of some slightly uncertain data, the activity of the undissociated acid was also derived in another way. The solubility of benzoic acid was determined in solutions of sodium benzoate of varying concentrations and the data after correction for the dissociated part plotted in a curve. By extrapolation to a sodium benzoate concentration equal t,o zero the activity of the acid is found. The correction for the dissociated part of benzoic acid in sodium benzoate is extremely small, as the common ion depresses the ionization of the acid. For example, in 0.01 N sodium benzoate, a solubility of benzoic acid of 0.02670 moles per liter was found, whereas the hydrogen ion activity as determined with the hydrogen electrode was found to be equal to 2.1 j X IO-^, or the hydrogen ion concentration approximately 2.4 X IO-^. Therefore, the concentration of undissociated acid in 0.01N sodium benzoate is 0.02670 - o.00024 = 0.02646. The correction for the dissociated part decreases with increasing benzoate concentration, which is rather fortunate, as the activity coefficient of the hydrogen ions is not knCwn and the accurate measurement of the hydrogen ion activity in such solutions is extremely hard. A summary of the results is given in Table 1. Sol. benz. acid denotes the experimental value of the solubility of benzoic acid in moles per liter, (cHB) the concentration of the undissociated acid, f, the activity coefficient of the undissociated acid in the benzoate solutions.
(cHB), is the extrapolated value of the concentration of the undissociated acid at a sodium benzoate concentration equal to zero, whereas ( c H B ) ~ , , ~ denotes the same in the benzoate solution of indicated strength.
1688
I. M. KOLTHOFF AND WOUTER BOSCH
TABLE I Solubility of Benzoic Acid in Sodium Benzoate and Inner Complex Constant a t 25' Sodium Sol. benz. acid benzoate moles per m. per 1. liter 1.00
0.75 0.5
0.25
0.04623 ,03933 ,03398 ,02934
0.1
,02757
0.05
,02704 .02682 .02672 ,02670
o .03 0.02 (0.01
IaH-I
I.22
x
[cHBl
IO-'
2.44 X IO-^ 4.57 X IO-' 7.31 X IO-$ 1.1 X IO-^ 2 . 1 5 X IO-^
0.00
0.04623 0.03933 ,03398 .02933 ,02754 .02699 ,02674 ,02660 ,02648 ,02635
f,
[cHBt-]
K
0.570 0.01988 1 . 3 ,671 ,0298 1.5 ,778 ,00763 I . j ,989 ,00299 2 . 2 ,958 .o0122 2.1 ,976 ,00069 1.9 ,985 ,00047 I .6 ,992 ,997) 1.000
The extrapolated value of the activity of the undissociated acid a t an ionic strength of zero corresponds to a concentration of 0.02635,in close agreement with the value of 0.0264 calculated from the solubility of the acid in pure water and that of 0.0265 computed by Kilpatrick and Chasezat 25.15'. As may be seen from the figures in Table I, f, decreases with increasing sodium benzoate concentrations, a fact already found by E. L a r ~ s o n . As ~ a rule the activity coefficient of a non-electrolyte increases with increasing ionic strength (salting-out effect); from other measurements (vide infra), it is evident that sodium ions exert such a salting out effect; therefore, the decrease observed with sodium benzoate has to be attributed to a specific interaction between the benzoate ion and benzoic acid. L a r ~ s o nthinks ~ ~ it possible that we are dealing here with the formation of acid benzoate ions, as acid benzoates may clystallize from solutions, saturated with benzoic acid. " Jedoch musz man sehr vorsichtig sein aus der Rildung solcher Verbindungen auf ihre Existenz in Losung zu schliessen. Hierin konnen sie vollstandig dissoziiert sein." According to the authors' opinion, there seems to be little doubt that the benzoate forms a kind of inner complex with benzoic acid. It is known that benzoic acid in more concentrated solutions has a tendency to associate to give double molecules. This association is facilitated by the formation of the anion of the double molecule: HB B- e HBZthe case being somewhat similar to the inner complex formation of boric acid. If the above equation gives a true picture of what is happening, the following expression should hold : faB-I = K [aHB] [aHBa-l Since B- and HBg- both represent anions of a similar type, it can be approximately written: w3-1 = K [aHB] lcHB2-1 4 E.L-n: 2.physik. Chem., (a) 148, 148 (1930); (b) 153, 466 (1931).
+
1689
ACTIVITY COEFFICIENT OF BENZOIC ACID
The experimental test of this equation meets with some difficulties. [aHB] is equal to 0.02635 at 25' since all solutions were saturated with respect to benzoic acid. I t is harder to find the concentration of the associated anion HB2-. At first sight, it seems that [cHBz-] is equal to the total concentration of the undissociated acid in the benzoate solution ([cHB] in Table I) minus the activity of the benzoic acid (0.02635). This, however, is not true for two reasons: Part of the HB1- ions will combine with hydrogen ions to form associated molecules of benzoic acid (HB)2. Since the concentration of the later is negligibly small in a saturated solution of benzoic acid in water at 2 jo, it is assumed here that its concentration is equally negligible in the benzoate solutions which would mean that the associated benzoic acid behaves as a much stronger acid than the single molecules. A similar relation is found again with boric acid. The values of [cHB2-] in Table I have been calculated on the assumption that the associated acid is entirely present in the anion form. Even if this assumption holds rigorously an absolute constant value of K cannot be expected as the salting-out effect is neglected. I t is quite certain that sodium ions decrease the solubility of benzoic acid, whereas it may be expected that the benzoate ions also exert such a salting-out effect which in the present case is masked by the complex formation. Since the salting-out effect is not a linear function of the ionic strength ( - log f, is a straight line function of i.0 a deviation from constant values can be expected a t increasing sodium benzoate concentrations. Moreover, it should be added that if instead of sodium benzoate another alkali benzoate had been used, say potassium, a different value for K would have been found since the salting-out effect of potassium is less than that of sodium. The values of K in Table I have been calculated on the assumption that [cHBZ-] = [cHB] - 0.02635,and [cB-] = [cNa benzoate] - [cHBz-]. In a similar way the value of K has been calculated a t 18Ofrom data of E. L a r ~ s o n . ~ ~
TABLE I1 Solubility of Benzoic Acid in Sodium Benzoate and Inner Complex Constant a t 18' (Larsson) Sodium benzoate moles per liter 1.000
IcHBl
fo
[cHBz-I
K
0,0351
0.61
0.0135
2 .Oj
0.930
0.0341
2.22
0.02946
,628 ,724
0.012j
0.698
o ,00786
2.08
0.500
0.0268
,800
O.OOj2
2.06
0.46;
0.02638
,813
0.00478
I .90
0.2325 0.1032
o ,02383
,900
0.0226;
0.00223 0.0010j
I
0.000
0.02160
'947 I .oo
1.59 .58
Although no strict constant value for K is found, which theoretically is not to be expected, there seems to be little doubt that the increase of the solubility of benzoic acid in sodium benzoate must be attributed to the formation of
1690
I. M. KOLTHOFF AND WOUTER BOSCH
anions of the associated benzoic acid molecules. Comparing the values by Larsson a t 18" (Table 11) with those in Table I reveals that the complex ions become less stable a t higher temperatures, a behavior similar again to that of the inner complexes of boric acid.
The Activity of Benzoic Acid in Neutral Salt Solutions The solubility of benzoic acid was determined in 0.01N sodium benzoate as a solvent in the presence of various amounts of neutral salts. As before concentrations are expressed in moles per liter. The results are given in Table 111. f, has been calculated by dividing the solubility of the acid in 0.01N sodium benzoate by that found in the presence of neutral salts. A correction for the dissociated part of the acid does not have to be considered, as it is about the same in all solutions and very small as the ionization of the acid is suppressed by the excess of benzoate.
TABLE I11 Activity Coefficient f, of Benzoic Acid in Salt Solutions in the Presence of Molar Sodium Benzoate at 25' Salt added
t o 0.01 molar
Na benzoate
-
Ionic strength salt 0.01
KCl
.09 .2 5 ' 50
,, 11
,, KaC1
,,
I
,,
,, ,, t,
,, NaN03
,>
,, ,, ,,
,0142
. 2 j
,02408
1.111
,02 I70
I , 232
.09
. 0 2j j 8
1.045
,0192
. 2 j
,02394 ,02160 .026j8 ,02640 ,02610
I .1 2 7
.o@o
.Oj .09 '25 ' 50
.02
558
I .oo
,02432
.os
,02648 ,02634 .026j8
.09 '25
1)
,000
1.033 I ,089 I . I80 I ,380
,1398 ,0179 ,0457 ,0906
>I
LiNO3
t log f,
.09
.oo
1,
KNOB
fo
1.000
,02456 ,02266 ,01938 . 0 2 568
11
LiCl
Normality benzoic acid o ,02676 . 0 2 588
0.01
1.042
,0370 ,0718
I , 238
,0928
,006 ,013
,0027
1.022
,0093 ,0192
I I
1.045 1.097
.0058
,0402
1.010
,0042
1.025
,0066 ,0176
I
,041
,091
'
, 0 2 4 jz
I
1.012
.09
,02642 ,02618
1.022
,0378 ,0053 ,0094
.25
,02552
I
,048
,0204
,02470
I
,083
,0345
50 .oj
1691
ACTIVITY COEFFICIENT O F BENZOIC ACID
TABLE I11 (Continued) Activity Coefficient f, of Benzoic acid in Salt Solutions in the Presence of Molar Sodium Benzoate a t 2 j a Ionic etrength salt
Normality ealt
,09
to9
'25
'25
KI
.09
.09
KnSOa
.09
Salt added to 0.01 molar Na benzoate
KBr 19 3,
.50
,>
40
,,
Jl
J,
BaClz IJ
CaC12
,
SrCL
'25
'25
'50
. j0
.09 50 ,091 ,506 ,0914
,060
50
,508
J j
Ba(N0dz 1,
1J
Ca(N03)~
,,
.09 . 2 j '50
,0912 253
J )
'507
Sr(NOdz
.I20
f, 1,
Mg(N03)Z
,, Jl
50
.09
'
NaC104
'
,060 ,333 ,09
,334 ,668 ,0896 '249 ,498
,333 .06I '337 ,061 ,339 .06 ,168 ,333 ,0608 ,169 ,338 ,080 ,223 ,445 ,0597 ,166 ,333
Normality benzoic acid
,02608 , 0 2562 ,02364 ,02642
fo
0.01
+ log f,
I . 0 2j
,0108
I ,068
, 0 2 8j
I .
132
1.012
,0537 ,0053 ,0244
,02528
1.058
,02620
1.021
,02412
I ,
119
,0450
,02630 .oz590 ,02554 ,02614 ,02376
I ,027
,0072
1,033 I ,060 I ,023 I . 126
,0141
,02608
1.025
,0108
,02348
I39 I ,026 I .140 I ,009
,0564 ,0113 ,0568 ,0040
,02604
,02346 ,02650 ,02608 ,02564 ,02646 ,02624 .02j82
,02640 .02580
,02506 ,02646 ,02594 ,02534
I
'
,0090
,0253 ,0098 ,0516
I,025
.OIIO
1.043
,0182
1.010
,0045
,019 I ,036 I ,013 1,037 I ,067
,0084
I
1.010
,031 1.055
I
,0154 .oo j 8 ,0157
,0283 ,0045 ,0131 ,0234
I n Figs. I and 2 , log f, is plotted against the ionic strength p of the salt added. In all cases (except with magnesium nitrate and barium nitrate) a straight line is found as may be expected from the relation: log f, = k p In practically all cases a close agreement was found with the data of E. Larsson6 with the exception of potassium bromide, for which salt Larsson gives a E. Larsson: Z. phyeik. Chem., 153, 299, 466 (1931).
1692
I. M. KOLTHOFF AND WOUTER BOSCH ./4
.IO
.02
.o/ 0
.I
.z
-5
FIG.I Salting-out Effect upon Benzoic Acid
value of k equal to 0.07, whereas in the present investigation a value of 0 . 1 1 was derived. For salts of divalent cations, Larsson gives the expression: log f, = kc, where c represents the salt normality. If his figures are recalculated on the basis of ionic strength, the following values of k are found: La.rsson K. and B.
BsCL
SrClz
CaCI2
MgClz
0.IO
0.11
0.11
0.11
0.10
0.11
0.11
.04
.02
* o0
.2
.4
.6
FIG.2 Sslting-out Effect upon Benzoic Acid
ACTIVITY COEFFICIENT O F BENZOIC ACID
7693
A comparison of our figures with others reported in the literature is omitted here (compare, however, thesis of W. Bosch), since E. F. Chase and M. Kilpatrick, Jr.6 have recently given a complete review of the published data. Our values are in agreement with the results of other reliable investigations. In the present investigation, it is found that the salting-out effect of the cations decreases in the order: Li
> Na > K > Ca > Sr > N g > Ba
A simple relation between ionic size and salting-out effect as suggested by E. F. Chase and M. Kilpatrick, Jr.6does not exist. For the anions, the following order is found: C1- > Br- > SOa- > J- > NOa- > C104The interpretation of the salting-out effect of cations seems to be fairly well in agreement with the theory of P. Debye and McAulay ;’greater difficulties, however, are encountered in the interpretation of the anion effect. In the present study it is found that the nitrate and perchlorate ion have an increasing influence on the solubility of benzoic acid. More striking examples of a negative salting-out effect are found in studies of K. Linderstrom-Lan2 and especially of H. R. Kruyt and C. R o b i n ~ o n . ~Kruyt and Robinson8 attribute the tendency of electrolytes to increase the solubility of non-electrolytes or undissociated organic molecules entirely to a definite orientation of the dipoles of the water molecules around the ions, by which the solvent effect should be increased. The polar organic molecules of the solute, however, also exert an orienting effect on the water molecules, therefore, a most favorable orientation can be expected in a solution of the substance in pure water as a solvent. Any change of the orientation will result in a decrease in the solubility (salting-out effect) and it is hard to see how Kruyt’s and Robinson’s explanation accounts for the opposite effect observed. I n the presence of electrolytes (and especially of cations), the latter will compete with the organic molecules with regard IO orientation of the water, resulting in a less favorable orientation of the water molecules around the organic substance or in an increase of the latter’s activity. This is the true salting-out effect which decreases in the order Li > Na > K > R b > Cs. Moreover, it seems necessary to assume a direct interaction between the ions in the solution and the dipoles of the solute; resulting in a mutual polarization and deformation. I n extreme cases this may lead to a definite complex formation as is the case with benzoate and benzoic acid and otherwise to a decrease of the activity of the solute or increase in solubility. From the studies of Kruyt and Robinson, it seems that the salting-out effect is more likely to be determined by the kind of cations, whereas the deforming effect is governed by the kind of anions present. ~~
E. F. Chase and M. Kilpatrick: J. Am. Chem. SOC., 53,2589(1931); see also Haessler: Thesis, Columbia University, 1929. Debye and McAulay: Physik. Z.,24, 185 (1923). * K . Linderstrom-Lang: Compt. rend. trav. lab. Carlsberg, 15, 4 (1924);17, No. 13 a
’
(1 929).
H. R. Kruyt and C. Robinson: Proc. Acad. Amsterdam, 29, 1244 (1926).
I . M. KOLTHOFF AND WOUTER BOSCH
1694
More extensive studies with different types of organic substances, in which the change of the activities of the ions in the presence of the organic solute are also measured, are necessary before a good understanding of the influence of neutral salts on the activity of undissociated molecules can be obtained.
I. 0.02775
Summary The solubility of benzoic acid in water at 25' was found to equal to =t0.00002 mols per liter, whereas the activity of the acid to be 0.02635
to 0.0264. 2. The solubility of benzoic acid in sodium benzoate solutions has been determined. The increase in solubility with increasing salt content is attributed to the formation of anions of double molecules of benzoic acid. The stability constant of this complex ion has been approximated. 3. The influence of various neutral salts on the activity of benzoic acid has been determined. In the interpretation of the experimental data it is assumed that electrolytes exert two effects: (a) a true salting-out effect, mainly governed by the type of cations and resulting in an increase of the activity of the solute. (b) a mutual deforming effect, mainly governed by the type of anions and resulting in a decrease of the activity of the solute. Minneapolzs, Mznn.
