Aug., 1956
'
ACTIVITY COEFFICIENTS OF BENZOIC ACID IN SOME AQUEOUS SALT SOLUTIONS BY JAMES N. SARMOUSAKIS AND MANFRED J. D. Low W m . H . Nichols Chemical Laboratory, New York University, University Heights, New York 63,N . Y. Received February 6 , I966
NOTES
1139
tion of potassium (or sodium) salts of various univalent anions in aqueous solution would vary approximately as the molar activity coefficients of molecular benzoic acid in the solutions irrespective of the nature of the anion.
Results.-The values of the experimentally determined solubilities of benzoic acid in aqueous solutions of potassium thiocyanate, sodium thiocyanate and potassium liexafluorophosphate, all 0.01109 molar in sodium benzoate, are recorded in Table I as functions of the molar concentrations, C,, of the salts.
The considerable mass of data on the salting-out and salting-in of benzoic acid in aqueous solution' does not include any extensive contributions on the effects of thiocyanates2 or hexafluorophosphates on the solubility of benzoic acid in water. AccordTABLE I ingly, an investigation of the activity coefficients SOLUBILITY OF BENZOIC ACIDI N SALTSOLUTIONS AT 25.00' of benzoic acid in aqueous solutions of sodium thio(A11 solutions 0.01109 molar in sodium benzoate.) cyanate, potassium thiocyanate and potassium KPFs NalZNS KCNB hexafluorophosphate has been made, and its results Salt SoluSalt SoluSalt Soluconcn bility, concn., bility, concn bility, are now reported. mole/i: mole/l. mole/l. mole/l. mole/i: rnole/l. Experimental.-Solid benzoic acid was brought to e uilib rium with water or the various salt solutions in !Pyrex bottles turning over in a water thermostat a t 25 zk 0.01'. Samples of the resulting solutions were removed by means of wide-mouth pipets equipped with filter paper tips. Measured portions were then titrated with carbonate-free sodium hydroxide solution, employing phenolphthalein as indicator, while C02-free air was bubbled through the solution. Empirical corrections were applied for benzoic acid taken up by the filter paper tips. In most cases attainment of equilibrium was verified by titrating samples of a given solution after widely differing times of equilibration. Titration of aqueous solutions containing known amounts of benzoic acid with large concentrations of the various salts, after long standing, yielded analytical results agreeing with the stoichiometric amounts of acid within the experimental error of the analysis. Accordingly, indicator salt error and any effects due to chemical interaction of the salts with acid or water, leading to incorrect analytical results, were taken as negligible. The aaueous solutions were made UD by weiahina out the appropriate amounts of potassium hexafluorophosphate or concentrated thiocyanate solutions, standardized by the Volhard method, into calibrated volumetric flaskR, adding from a pipet the amount of carbonate-free sodium hydroxide solution necessary to render the final solution 0.01109 molar in that compound, and making up to volume with COIfree water. The benzoic acid was Baker U.S.P. grade. The values of the acid solubility in pure water obtained with this material did not differ significantly from those determined employing the following: Baker U.S.P. benzoic acid recrystallized up to four times from water, Baker U.S.P. benzoic acid precipitated from ethanol solution with water, Bureau of Standards benzoic acid, Bureau of Standards acid once recrvstallized from water, and Bureau of Standards acid precipitated from ethanol solution with water. Reagent grade sodium thiocyanate and potassium thiocyanate were recrystallized at least twice from water. Potassium hexafluor~phosphate~ was recrystallized at least once from water made alkaline with sodium hydroxide by the method of Woyski.4 The small corrections required to obtain the concentrations of molecular benzoic acid (molecular solubilities) from the stoichiometric solubilities were calculated from estimates of the clasAical dissociation constants of benzoic acid in the various salt solutions. These estimates were based on the data of IGlpatrick5 for the classical dissociation constants and molar activity coefficients of the molecules of benzoic acid in aqueous solutions of potassium chloride and sodium chloride a t 25". It wa8 assumed that the dissociation constants of benzoic acid a t a given concentra( 1 ) F. A. Long and W. F. R4cDerit. Chem. Reus., 61, 119 (1951). (2) H. Freundlich and A . N . Seal, KoZZokd 2.. 11, 257 (1912), report values of 0.02799, 0.02891 and 0.02950 M for the solubilities of benzoic acid in unbuffered 0.0, 0.5 and 1.0 M aqueous potassium thiocyanate
solutions, respectively. (3) The donation of a supply of this salt by the Ozark-Mahoning Company, Tulsa, Oklahoma, is gratefully acknowledged. (4) M. M . Woyski, "Inorganic Syntheses," Vol. 111, McGraw-Hill Book Co., Ino., New York, N . Y.,1953, p. 111. (5) M. Kilpatrick. J . Am. Chem. Sac., 7 6 , 585 (1953).
0.0739 0.02669 .1293 ,02679 .2683 ,02719 ,3236 .02726 .4012 .02739 .4809 ,02757 ,4943 ,02761 .6807 ,02777 .7077 .02786 .989 .02824 1.361 .02847 1.463 .02851 1.571 ,02847 1.935 .02829 2.892 ,02739 3.237 ,02641
0,1495 0.02647 ,1573 ,02648 02645 .3247 ,3547 02645 ,5511 ,02635 ,6429 ,02621 ,02616 ,7429 ,02582 1.150 ,02578 1.153 ,02450 1.995 ,02351 2.324
0.0540 0.02651 ,1092 ,02645 ,1096 ,02641 1635 ,02640 ,2181 ,02628 ,2187 ,02642 ,2719 ,02629 ,3256 ,02630 ,3813 ,02616 ,4425 ,02609
An estimate, - 1.5794, of the logarithm of the molecular solubility, So, of benzoic acid in 0.01109 molar sodium benzoate solution was obtained by graphical extrapolation to zero concentration of added salt in plots of the logarithms of the molecular solubilities, S , of the acid in the thiocyanate solutions, or by the method of least squares for the hexafluorophosphate solutions assuming a linear relation of log S to the salt concentration. The logarithms of the molar activity coefficients, f, of the molecular benzoic acid given by the relation f = SQ/S,as function of the concentrations, C,, of t,he added salt in the solutions are represented in Fig. 1 together with the least square line for the hexafluorophosphate solutions and the visually estimated best smooth curves through the points for the thiocyanate solutions. In dilute solution the activity coefficient of the non-electrolyte, benzoic acid, is given by the relation' logf = ~ B SksCs, where k , is the salting-out parameter and k g is the "self-interaction" parameter for the benzoic acid. The limiting slopes of the curves in Fig. 1 at zero concentration of salt serve as estimates of k,, namely, 0.004, -0.037 and 0.017 for sodium thiocyanate, potassium thiocyanate and potassium hexafluorophosphate, respectively. In the case of the thiocyanates the expected additive property of the salting-out parameter6 is exhibited since the value of IC, for sodium thiocyanate minus that for potassium thiocyanate is 0.041, to be compared with the corresponding values, 0.041 and
+
(6) E. Larsson, 2. physik. Cham., 163, 299 (1931).
1140
NOTES
0.05 0.04
0
/
- NQCNS
0.03 0.02 *:
g 0.01
3
0 -0.01
-0.02
-0.03
2
1
3
C., mole/l. Fig. 1.
0.039, for chlorides and nitrates' and 0.042 for bromides.8 The ionic salting-out constants for the thiocyanate and hexafluorophosphate ions, based on a value, 0.070,6Jfor that of potassium ion, are -0.107 and -0.053, respectively. These numbers, when compared with corresponding data for other ions, follow reasonably well the generally recognized increasing trend of the ionic salting-out parameters with decreasing ion size.' Ionic salting-out parameters for the anions C1-, Br-, I-, NOy-, C1Od-, PFs- and CNS-, are 0.70,' 0.038,8 -0.016,8 -0.034,' -0.052,' -0.053 and -0.107, respectively. Corresponding anion crystal radii (in A.) are 1.81,9 1.95,9 2.16,92.6,'O 22.9," 2.912 and 3.1,13 respectively. The radius given for the linear thiocyanate ion is an estimate of half the length of that ion and is to be looked upon as a maximum value. (7) I. M. Kolthoff and W. Bosch, THISJOURNAL, 36, 1685 (1932). The values of ks for chlorides and nitrates were computed by applying least squares to the data of these authors. (8) G. M. Goeller and A. Oaol, J . A m . Chem. Soc., 69, 2132 (1937). (9) L. Pauling, "The Nature of the Chemical Bond," Cornell University Press, Ithacrt, N. Y.,Second Edition, 1940, p. 346, (IO) An estimate obtained by adding to the N-0 bond distance, 1.21 A., in sodium nitrate (M. Elliott, J . A m . Chem. Soc., 69, 1380 (1937)) the van der Waals radius for oxygen, 1.40 A. (ref. 9, p. 189). (11) An estimate obtained by adding to the C1-0 bond distance, 1.50 A,, the van der Waals radius for oxygen. The C1-0 bond distance used here is an average of values obtained by C. Gottfried and C. Schusterius (2. Krist., 84, 65 (1933)) for potassium and ammonium perchlorates, and a value of W. H. Zachariasen, (Z.Krist., 1 8 , 141 (1930)) for sodium perchlorate. (12) An estimate obtained by adding to the P-F bond distance, 1.58 A., in potassium hexafluorophosphate (H. Bode and H. Clausen, 2. anorg. alleem. Chem., 266, 229 (1951)) the van der Waals radius of fluorine, 1.35 I. (ref., 9, p. 189). (13) This value is obtained by adding to the N-C and C-S bond distances in potassium thiocyanate, 1.24 and 1.58 A., respectively (A. P. Klug, 2. Krist.. 86, 214 (1933)) the van der Waals radii of nitrogen and sulfur, 1.5 and 1.85 A., respectively (ref. 9, p. 189).
Vol. 60
It is seen that the orders of salting-out parameters and anion radii have the expected correspondence. Features worthy of note in Fig. 1 are the nonlinearity of the curves for thiocyanates and the minimum in log f for potassium thiocyanate a t about 1.5 M salt concentration. Usually the relation of log f to the molar concentration of a given salt is linear.' No ready explanation is a t hand for the two effects mentioned. Any specific interactions of the thiocyanate ion with the non-electrolyte acid molecules might be expected t o be monotonically increasing with the concentration of the salt. Further, with respect to interaction of the salt ions with water, the ratio of the total internal pressure in aqueous uni-univalent salt solutions to the square of the molar concentration of the water, has been shown by Gibson14 in the case of potassium thiocyanate to be the same function of molal concentration of salt as in the case of the chlorides, bromides and iodides of sodium and potassium, of potassium nitrate, and cesium chloride. This last correlation leads to the presumption that the answer ta the problem of explaining the form of the curves for thiocyanates does not lie in an unusual specific interaction of the thiocyanate involving the variables dealt with by Gibson. The authors wish to express their thanks to Dr. Martin Kilpatrick of the Illinois Institute of Technology for having suggested the study of the thiocyanates. (14) R. E. Gibson, Sci. Monthly, 46,103 (1938).
THE ORDER-DISORDER PROBLEM FOR ICE BYKENNETH S. PITZER AND JANPOLISSAR Department of Chemistry and Chemical Engineering, Uniuersity of California, Berkeley, California Received February IO, 196%
I n 1935 Pauling' proposed a structure for ice which provided for hydrogen bonds throughout the crystal but involved a disordered pattern of proton locations. The proton was assumed to be unsymmetrically located in each hydrogen bond and about each oxygen atom two protons were assumed to be nearby, comprising a water molecule, and two farther away. This disorder involves an entropy of R In 3/22 = 0.81 cal./degree mole, which is in excellent agreement with the residual entropy at O'K., found by Giauque and Stout2 t o be 0.82 f 0.05 for HzO and by Long and Kemps to be 0.77 f 0.1 for D2O. Although the agreement in entropy of disorder is excellent and the neutron diffraction results of Wollan, Davidson and Shul14are consistent with the Pauling structure, it is also desirable t o estimate the interaction energies which would tend to remove the disorder. BjerrumKinitiated this sort of study and obtained approximate results, which in(1) L. Pauling, J . A m . Chem. Soc., 67, 2880 (1935). (2) W.F. Giauque and J. W. Stout, ibid., 68, 1144 (1936). (3) E. A. Long and J. D. Kemp, ibid., 68, 1829 (1936). (4) E. A. Wollan, W. L. Davidson and C. G. Shull, Phva. Rev., 76, 1348 (1949). (5) N . Bjerrum, Kgl. Danaks Videnskab. SeIskab. Alnth-fus. A f s d J . , 37, 1 (1951); Science, 116, 385 (1052).
