T H E IONIZATION CONSTANT OF BENZOIC ACID Ah'D T H E ACTIVITI- COEFFICIENT OF T H E BENZOATE ION I N PRESENCE OF NEUTRAL SALTS ' BY I. M. KOLTHOFF AND WOCTER BOSCH'
The hydrogen ion activity was measured in dilute solutions of benzoic acid and sodium benzoate and from the results obtained the ionization constant of the acid was computed by application of the limiting Debye-Huckel expression. Measurement of the Hydrogen Ion Activity The activity of the hydrogen ions was measured with the hydrogen electrode. A simple cell was used as described in a previous paper,* the quinhydrone electrode in a mixture of 0.01N hydrochloric acid and 0.09 N potassium chloride served as standard half cell. The cell was refilled every day after cleaning the electrode. The connection between the two half cells was made by a saturated potassium chloride bridge in 3y0 agar, and no correction has been applied for the liquid junction potential. The measurements have been made in a thermostat at 2 5 ' * o.oj". The type of hydrogen electrode used in this work gives constant readings with ordinary buffer solutions within two to three minutes. Peculiar difficulties were encountered in the measurement of benzoic acid-benzoate solutions. There was a continuous drift in potential with time, the electrode becoming less and less noble. This irregular behavior could not be attributed to impurities in the hydrogen, as the latter was carefully purified and finally passed over red hot copper or nickel wire. Special experiments were made in order to see whether the effect could be attributed to a hydrogenation of benzoic acid, but no indication of such an action was found. Therefore, it seems that benzoic acid or benzoate exertsa polarizing effect upon the electrode. I t was found that the rate of change of the E. N. F. was proportional to the thickness of the layer of platinum black on the electrode, and for this reason the platinum spiral electrodes were covered with a very thin coat of platinum. A 1% solution of pure chloroplatinic acid3 was used for platinizing, with a current of 20 milliamperes during five minutes. After polarization in I N sulfuric acid, the electrode had a grayish appearance. Cleaning and recoating were often necessary, but with the type of electrode described, it was usually possible to obtain constant readings within ~j minutes, although, it should be mentioned, that the final reading was not made unless the potential had been constant for a few hours. In the presence of large concentrations of sodium benzoate ( 0 . 2 5 N or higher) no reliable results * Contribution from the School of Chemistry, University of Minnesota. Comp. Note I in the previous paper; J. Phys. Chem., 36, 1685 (1932). and Wouter Bosch: Rec. Trav. chim., 46, 434 (1927). E.Wichers: J. Am. Chem. SOC.,43, 1268 (1921).
* I. M. Kolthoff
1696
I. M. KOLTHOPF AND WOUTER BOSCH
could be obtained. Owing to the difficulties described, a t least three sets of independent measurements with each solution were made; the results are accurate to within 0.01 pH. I t may be mentioned that the sluggishness of the electrode is more pronounced in the absence of neutral salts; the latter exert a decidedly favorable effect. Since the quinhydrone electrode assumes a constant potential very readily, all measurements have also been made with such an electrode. It was found, however, that sodium benzoate changes the activity of the components of the quinhydrone in the solution causing an uncertainty in the calculation. At small benzoate concentrations (below 0.01 N), the effect is small, but a t higher benzoate concentrations the figures are no longer reliable. Neither E. Larsson4 nor M. Kilpatrick and E. F. Chase,5 who applied the quinhydrone electrode in their work, mention the specific effect of benzoate on the quinhydrone. The majority of measurements were made in solutions, containing only 0.01i Y benzoate in the presence of neutral salts. Quite generally the readings with the quinhydrone electrode gave slightly higher pH values than those with the hydrogen electrode. As a rule the differences were not larger than 0.02, but in the presence of larger amounts of nitrates they were much greater. The differences are partly accounted for by the salt error of the quinhydrone electrode in presence of large concentrations of neutral salts. A special study has been made of this error under the experimental conditions; the work is not completely finished and will be described later. In Table I1 the results are given of measurements with the hydrogen as well as the quinhydrone electrode; the figures obtained with the former are used in the calculation of the activity coefficient of the benzoate ion. The calculation of paH was based on the classical Sorensen equations. The relation between the Sorensen value and the negative logarithm of the hydrogen ion activity paH is given by: paH = pH 0.037
+
Ionization Constant of Benzoic Acid at 25" The hydrogen ion activity was measured in dilute mixtures of sodium benzoate and benzoic acid. After correction for the dissociated part of the acid
in which [H+]represents the Sorensen value of the hydrogen ion concentration, [cB-] the benzoate concentration (concentration sodium benzoate plus dissociated part of the acid), and [aHB] the activity of the undissociated acid, PIC' was calculated. From this value p&
=
- log IHf1
[aB-l was computed WBI
'E. Larsson: Z. physik. Chem., 148, 304 (1930). M. Kilpatrick and E. F. Chase: J. Am. Chem. Soc., 53, 1732 (1931)
6
IONIZATION CONSTANT O F BENZOIC ACID
'697
with the assumption that in the very dilute solution the simple Debye-Huckel expression holds : log fa- = - 0.5 4; log fg being the logarithm of the activity coefficient of the benzoate ion. Finally, pK represents the acid exponent after correction for the difference between the Sorensen exponent and paH: PK = pKo The data are given in Table I.
+ 0.037
TABLE I Ionization Constant of Benzoic Acid at Concentration Concentration sodium benzoate benzoic acid in moles p. 1 in moles p. I 0.05
0.025
0.025
0.025
0.025
0.0125
0.01
0.01
0.01
0.005
0.005
0.005
0.005 0.0025
0 . 0 0 2j 0.002j
o.oo2j
0.001zj
(0.001
0.001
pH
4.349 4.092 4.365 4.107 4.400 4.124 4.4'4 4.140 4.431 4.172
PK'
4.047 4.089 4.062 4.101 4.094 4.111 4.103 4.115 4.111 4.114
25'
PK.3
(4.172) (4.169) 4.141 4.151 4.144 4.146 4.138 4.140 4.136 4.130)
PK
4.178 4.188 4.181 4.183 4.175 4.177 4,'173
From these and other measurements an average value of pK equal to 4.17 j was found corresponding to an ionization constant of 6.7 X IO-^ at 25'. At the same temperature, Jones6 from conductivity data (not corrected for the difference between activity and concentration) derived a value of 7.0 x IO-^, whereas Kilpatrick and Chase5 in a note mention that according to the same method but corrected for activities a constant of 6.31X I O + is found. Activity Coefficient of the Benzoate Ions in the h e s e n c e of Neutral Salts Solutions of 0.01N sodium benzoate containing the indicated concentraThe paH of tions of neutral salt were saturated with benzoic acid at 25.00'. these solutions was measured at the same temperature with the hydrogen and quinhydrone electrode. In the further calculations only the hydrogen electrode values were used. The activity coefficient f B of the benzoate ions can be readily calculated from the relation, [aH+] [cB-]fB K = IaHB1 . . Jones: Am. Chem. J., 44,159 (1910); 46, 56 (1912).
1698
I. M. BOLTHOFF AXD WOUTER BOSCH
TABLE I1 Activity Coefficient fa of the Benzoate Ion in Salt Solutions Ionic strength PH -log f B of added salt H 1electr. quinEaiectr. pcB1.990 . I42 KCl 3.642 3.622 .09 .25 3.601 3.627 1.989 ,164 1.990 , I37 3.654 3.627 .SO I .oo l’ 1.990 . I12 3.698 3.652 1.989 ,164 .09 NaCl 3.601 , 3.625 I ,988 ,207 3 ’ 583 .2j ” 3.559 lJ 1.987 ’243 3 .j61 3‘ 524 .jo I ,988 ,220 3.567 ,09 LiC1 3,546 ,25 ” 3.502 3.532 1.987 .26j .$O ” 3.420 3.461 1.984 .350 1.990 .I20 .os KNOs 3.664 3.656 1.990 ,125 .09 ” 3.639 3.644 .2j ” 3.610 3.650 1.989 ‘155 1, ‘179 3.650 1.989 3 ’ 586 50 I .oo ” 3 .j68 3.689 I ,988 ,198 .os NaSOa 3.610 3.617 1.989 . I55 Jl ,167 3 ‘ 598 3.622 1.989 ‘09 J! 3 ’ 549 3 ’ 590 I ,988 ,217 .2j . jo 3.541 3.603 I ,988 . 2 2j ,OS LiN03 3.591 3.600 1.989 . I74 I ,988 . I91 3 ’ 590 .09 )’ 3.575 1.987 ,240 3.563 .25 3.527 I ,985 ,301 .SO ” 3.468 3.529 1.989 . I jo .09 KBr 3.650 3.61j .25 ” 3.622 3.649 1.989 . I43 I ,988 ,205 3.661 3.561 .SO )’ .09 K I 3.610 3.639 1,989 ‘I55 3.62j I ,988 ‘I39 .09 Ei2SOI 3.62j f2 . j0 3.657 3.617 1,990 . 107 3 593 1.989 ,187 .09 BaCll 3.578 .SO ” 3.427 3.427 1.984 ,343 3.574 I ,988 ,209 ,091 CaCL 3.557 ,506 ” 3.380 3.414 I ,982 ,392 ,091 SrC12 3.561 3.590 I ,988 . 2 0j ,508 ” 3.407 3.444 1.983 ,364 .09 Ba(N042 3.554 3 ’ 563 I .988 ,212 >, 3.497 3 ’ 508 I ,986 ,271 ,25 J , 3.478 3,507 I ,986 ,290 50 ,091 Ca(N03)2 3.495 3 ’ 503 I ,986 ‘273 ,253 ” 3.454 3.461 1.985 ,315 ” I .980 ,460 3.349 3,314 ,507 I ,988 ,190 3 563 .IZ Sr(NO8)Z 3.576 ,334 1r 3.466 3.476 1.985 ,303 ,668 ” 3.422 3.476 1.984 ,348 .09 Mg(N0s)z 3.563 3,541 I ,988 ,203 1.985 ,308 ,249 3.469 ” 3.461 11 3.451 1.984 ,350 3.420 .498 J ’
J
J
)’
J ’
’
’
IONIZATION CONSTANT O F BENZOlC ACID
I699
in which [aHB] is a constant (0.02637 at 2 jo,see previous paper') since the solution is saturated with benzoic acid and [cB-] the benzoate concentration (sodium benzoate dissociated part of the acid) - log f B = - log K - log [aHB] - paH - pcB- = 4.17j - 1.579 -paH - pcBpcB- denotes the negative logarithm of the concentration of the benzoate ions. The results are given in Table 11.
+
Discussion The change of the activity coefficient of the benzoate ion with the ionic strength of the solution can no longer be represented by the simple DebyeHuckel expression, -log f = o . j l / i , because the electrolyte content of the solutions is too high. Only in the case of lithium chloride does the influence of the ionic size seem to be negligibly small (in 0.25 N LiCl: -log fs found 0.265; calculated 0.25 j; in 0.5 N LiCl: -log f B found 0.350; calculated 0,357). I n most other cases the change of the activity coefficient with the ionic strength can be represented by the more complicated expression: -log f n
0.56
=
I
+A
6
in which A is a constant for each salt. In Table 3 examples are given of the application of this equation to solutions in potassium and sodium nitrate respectively. I n KNO,, A = 1.266; in NaN03, A = 0.340.
TABLE I11 Calculated and Experimental Figures of -log f a in K N 0 3 and NaN03 Total
KNOI
p
-log fB exp.
-log fB calc. 0.094
Total p
NaNOt -log fB exp. -log fB talc
0.0602
0,155
0.113
0.1003 0.2603
0.167
0,155
0.113 0.155
0.217
0.147 0.217
0.5103
0 .I 7 9
0.188
0.5103
0.225
0.287
0.010
0.198
0.221
0.0602
0.120
0.1002 0.2602
0.125
I n most other cases the values of A have not been calculated, since the number of measurements and the concentration range were too small. A weak point in the measurement of individual ion activities is that uncertainties are introduced on account of the liquid junction potential. E. A. Guggenheim' even states that the electric potential difference between two points in different media never can be measured and has not yet been defined in terms of physical realities. It is gratifying, therefore, that in one instance at least, it is possible to check the reliability of our results with those in which no uncertainty is involved. Kilpatrick and Chases derived the mean activity 7
E. A. Guggenheim: J. Phys. Chem., 33, 842 (1929).
I. M. KOLTHOFF AND WOUTER BOSCH
I 700
a,
coefficient of the ions of benzoic acid, from potentiometric and kinetic measurements in solutions of potassium chloride in presence of some sodium benzoate; no uncertainty caused by the liquid junction potential occurs here. In our work, fg was experimentally determined, whereas f H could be calculated in potassium chloride solutions by application of the empirical equation of N. Bjerrum and A. Unmack.s
- log f H
=
0.178 +F-
0.1j4c
- 0.003 ( 2 5 ' ;
KCl a t c =
0.001-
1.5)
From the experimental value of f g and the calculated value of f H the mean was calculated. The data are given in Table IV activity coefficient and compared with those Kilpatrick and Chase. A better agreement can hardly be expected, considering the experimental difficulties in our work.
a
TABLE IV
dfxin KCl Solutions a t 25' Concentration KC1
0.09
K. and B. 0.79
0.25
0.764
0.5 I .oo
0.80 0.90
m
Kilpatrick and Chaae Potent. Kin.
0.81 0.80 0.805 0.90
0.805 0.78 0.79 0.93
Considering the figures in Table 11, it is evident that the activity coefficient of the benzoate ion passes through a minimum in about 0.25 N potassium chloride. From there on it increases with the ionic strength and seems to become even larger than that of the hydrogen ions. E. Guntelberg and E. SchiodtQin their excellent paper, found f H equal to 1.50 and f B to 1.93 in 3 N potassium chloride, on the other hand, in the more dilute electrolyte solutions, we find fg smaller than f E . In the dilute sodium chloride solutions f g is smaller than in potassium chloride solutions of corresponding strength. By application of the empirical Bjerrum-Unmack8 relation in sodium chloride : -log
fH
= 0.161i / c
a
- 0.178 c - 0.003 ( 2 5 ' )
the following values of are calculated in sodium chloride solutions: 0.78 jn 0.09 N NaCl; 0.74 in 0.25 N NaCl; 0.725 in 0.5 N NaCl. In 3 N NaCl, Guntelberg and Schiodt found a mean activity coefficient of 1.89. From the above, it is evident that the minimum in the activity coefficient of the benzoate ion lies a t a higher concentration of sodium chloride than of potassium chloride. Guntelberg and Schiodtlo conclude that apparently the benzoate ion can be used for activity studies in which an ion with an extremely high activity coefficient is required. This is true a t high salt concentrations; from our 8 9
N. Bjerrum and A. Unmack: Kgl. Danske Videnskab Selskab, 9, I (1929). E. Guntelberg and E. Schiodt: Z. physik. Chem., 135, 393 (1926). Ref. 9, p. 442.
IONIZATION CONSTANT O F BENZOIC ACID
1701
study it appears that at relatively small ionic strengths the activity coefficient of the benzoate ion is comparable with that of many other monovalent anions. It seems that in relatively dilute solutions the Debye-Huckel expression accounts for the decrease in activity of the benzoate ion; the effect increases with decreasing ionic size: Li> N a > K. In more concentrated solutions, the Debye-Huckel effect is compensated by the salting-out action, which also decreases in the order, Li> Na> K. Therefore, it is quite possible that a t very high salt concentrations, the activity coefficient of the benzoate ions is the largest in lithium, smaller in sodium, and the smallest in potassium solutions, or the reverse of that in dilute solutions. The influence of divalent cations on the activity coefficient of the benzoate ion in relatively dilute solutions is of the same order as that of the lithium ions; the effect seems to decrease in the order, Ca> Sr> Mg> Ba, but the differences are relatively small. I n agreement with results of former studies,ll it is found that the anion effect in relatively dilute solutions is very small S-arY
The quinhydrone electrode no longer gives reliable results in solutions of sodium benzoate. The hydrogen electrode is useful, if the noble metal is covered with a very thin coat of platinum. 2. The ionization constant of benzoic acid is equal to 6.7 X IO+ at 2 5 ' . 3 . The activity coefficient of the benzoate ion in the presence of various electrolytes has been determined. It passes through a minimum a t about 0.25 N potassium chloride, at a higher concentration of sodium chloride and still higher concentration of lithium chloride. The cation effect may reverse a t high ionic strengths. There is a pronounced cation effect, but a slight anion effect. I.
Minneapolzs,Minnesota.
I. M. Kolthoff and W. Bosch: Rec. Trav. chim., 47, 558, 819, 826, 861, 873 (1928); 48, 37 (1929).
