ENTROPY A N D VOLUME CHANGES ON IONIZATION OF AQUEOUS ACIDS
species is cast by the fact that, on the basis of measurements in concentrated Pb(I1) solutions, Olin also postulates (Pb20H)3 + . In attempts at least-squares analysis, we were unable to obtain convergence with Olin's dilute Pb(I1) data6 if PbzOH3+was substituted for PbOH +, nor with hist concentrated Pb(I1) data' with PbOHf substituted for PbzOH3+. The tetramer, however, has received strong support from an X-ray diffraction studyIb of concentrated Pb(I1) solutions of
965
n ca. 1 . Beyond n
= 1, there is obviously a species of higher molecular weight ; O h ' s postulated Pb3(OH)42 + and PbS(OH)84+are consistent with our results.
Acknowledgment. The authors are indebted to Prof. S. Y. Tyree for inany helpful discussions. 0. E. Esval is appreciative of support received through an Oak Ridge Graduate Fellowship, administered by the Oak Ridge Institute of Nuclear Studies.
Entropy and Volume Changes on Ionization of Aqueous Acids
by Loren G . Hepler' Division of Physical Chemistry, Australian Commonwealth Scientific and Industrial Research Organization, Fishermen's Bend, Melbourne, Australia (Received October 6 , 1964)
A general linear relation has been observed for changes in entropy and volume (ASi"and APi") on ionization of aqueous acids. The slope, (dASi"/dAPi") = LO5 cal. deg.-' cn1.-3, has been explained in teriiis of a high pressure value of (bP/bT)v for water. The intercept, ASi" e -7 cal. deg.-' mole-' at A P i " = 0, has been explained in terms of the usual choice of standard states and the hydration of the proton in aqueous solution.
of aqueous acids have shown Several recent that consideration of entropies of ionization can yield useful information about the interactions of solute species with solvent and thence also about charge distribution and bonding in the solute species. The solute-solvent interactions that largely account for various acids having diff ererit entropies of ionization (AS,")should be expected to cause these acids to have different volume changes on ionization ( A 7,"). One reason for gathering the data summarized later in this paper was to test this expectation. Comparison of A PI" values for several acids (for instance, m-nitrophenol and p-nitrophenol) shows that for sonie acids one can at least confirm conclusions already reached from consideration of AS," values.a I n the process of making detailed comparisons of AS," and A 8 , " for various aqueous acids, the more general observations were made that constitute the subject of this paper. Entropies of ionization (AS,") of aqueous acids
have been calculated from the free energy of ionization and the teinperature derivative of the free energy and also froin coinbination of calorimetrically determined enthalpies with free energies. Volume changes (A Pi") have been calculated froin the effect of pressure on ionization constants and also froin results of density measurements. Data for 53 acids are summarized in Figure 1 in the form of a graph of ASi" VS. AVi". The ionization processes under consideration may be represented by t4hegeneral equation '
HA"(aq)
= ' H+(aq)
+ A"-'(aq)
(1)
(1) U. S. National Science Foundation Senior Postdoctoral Fellow, on leave from Carnegie Institute of Technology, Pittsburgh, Pa. (2) E. J. King, J . A m . Chem. Soc., 8 2 , 3575 (1960). (3) L. P. Fernandez and L. G. Hepler, ibid., 81, 1783 (1959). (4) F . J. Millero, J. C. Ahluwalia, and L. G. Hepler, J . Phys. Chem., 68, 3435 (19f.X).
Volume 69, WumbeT 3
March 1966
966
LORENG. HEPLER
H2NRCOOH(aq) = H+(aq)
+ HzNRCOO-(aq)
Although several systematic deviations (for instance, the methylamines) from the straight line in Figure 1 are obvious and worthy of detailed consideration, there is a remarkable general correlation of AS," with A P , " for a large number of quite diverse acids. The slope of the straight line in Figure 1 is 1.05 cal. deg.-l cm.-a and the intercept is AS," E -7 cal. deg.-l mole-' at A 7,"= 0. These quantities are interpreted as follows. The Maxwell relation
(bS/bV)T I
-28
-20
l
l
I
-4
-12
NT
I
I
+4
I
I
+I2
(cm3 mote")
Figure 1 . Graph of ASi" 2)s. A P i " for aqueous acids a t 25'. Numbered circles correspond to data for ionization of various acids as follows (note t.hat points for several acids fall within some circles): 1, HC03-; 2, third citric; 3, second malonic; 4, H,P04-; 5, H20 (1 m ) ; 6, HSOr-; 7, phenol; 8, trimethylacetic; 9, second oxalic; 10, second succinic; 11, butyric and isobut,yric; 12, propionic; 13, acetic; 14, second e-aminocraproic; 15, formic, benzoic, m-methoxybenzoic, p-methoxybenzoic, p-nitrophenol, first succinic, chloroacetic, bromoacetic, lactic, glycolic, and second citric; 16, first phosphoric; 17, m-nitrobenzoic and p-nitrobenxoic: 18, cyanoacetic; 19, (CH3)aNH+; 20, second hydroxyproline and second proline; 21, first salicylic and first citric; 22, (CH3)2NH2+; 23, second glycine and second alanine: 24, first glycine, first alanine, first hydroxyproline, and first proline; 25, diethylammonium ion 27, CHaNHa+ and and piperidinium ion; 26, HzN(CH~)ZNH~+; pyridinium ion; 28, ethylammonium ion, propylammonium ion, and first s-aminocaproic acid; 29, NH4+; 30, anilinium ion; 31, +H8N:CHz)2NH3+.Data are taken from the following: ( a ) S. D. Hamann, Chapter 7 in "High Pressure Physics and Chemistry," Vol. 2, R. S. Bradley, Ed., Academic Press, New York, N. Y., 1963; ( b ) W. Kauzmann, 84, 1777 A. Bodansky, and J. Rasper, J . Am. Chem. SOC., (1962); ( c ) A. Disteche, J . Electrochem. Soc., 109, 1084 (1962), and personal communication to S. D. Hamann; ( d ) H. S. Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions," 3rd Ed., Reinhold Publishing Corp., New York, N. Y., 1958; (e) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," Butterworth and Co., Lt,d., London, 1959; ( f ) L. P. Fernandez and,L. G. Hepler, J . Phys. Chem., 63, 110 (1959); ( g ) J. T. Edsall and J. Wyman, "Biophysical Chemistry," Vol. 1, Academic Press, New York, N. Y., 1958; ( h ) Z. L. Ernst, R . J. Irving, and J. Menashi, Trans. Faraday SOC., 60, 56 (1964); ( i ) R. G. Bates and H. B. Hetzer, J . Phys. Chem., 65, 671 (1961); ( j ) Ref. 2 and 3 of main text.
where n is zero or an integer indicating the charge on the acid. In the case of amino acids, the first ionization refers to +H&RCOOH(aq)
=
H+(aq)
and the second ionization to The Journal of Physical Chemistry
=
(bP/bT)v
)
+ H2NRCOOH(aq)
suggests that the slope (bAS,"/bA 7 , ' ) is ~ related to an appropriately chosen (bP/bT)v. Except for a factor related to standard states that is discussed below, entropies of ionization are chiefly determined by effects of the various solute species on the orderliness of arrangement of nearby water molecules, and A P , " values are similarly determined by the related space occupied by the water molecules near the various solute species. Since a variety of evidence indicates that the effective pressure near ions or polar solute molecules in water is quite high (of the order of 10' atm.), we might expect the slope of the line in Figure 1 to be approximately equal to ( d P / b T ) v for H 2 0 at a suitable high pressure. Some values of (bP/dT)v of water, taken from Dorsey's compilation,6 are shown in Figure 2. A value of (bP/dT)v appropriate to the high effective pressures near solute species is apparently about 40-45 atm. deg.-'. Exact agreement between (bAS,"/dA P,O)T and (bP/bT)vmay be obtained by taking the effective (bP/dT)v = 43 atm. deg.-' = 1.05 cal. deg.-' ~ m - ~ . Now consider the intercept, AS," -7 cal. deg.-' mole-' a t AP," = 0. Instead of comparing HA"(aq) with water as in reaction 1, we might choose another reference system and consider HA"(aq)
+ C03-2(aq) = A"-' ( w ) + HCO3-(aq)
(2)
or some other reaction series. The best straight line through the resulting 53 - 1 = 52 points has the same slope as the line in Figure 1 and passes through the origin where AS," = 0 = AP,". Since both AS," and AT," for symmetrical reactions like (2) are determined almost entirely by solute-solvent interactions, it is expected that the graph of AS," vs. AP," should go through the origin, as it does. Reaction 1 might be rewritten as HA"(aq)
+ H20 = H30+(aq) + A"-'(aq)
(3)
( 5 ) N. E. Dorsey, "Water-substance," Reinhold Publishing Corp., New York, N. Y . , 1940.
ENTROPY AND VOLUME CHANGES ON IONIZATION OF AQUEOUS ACIDS
I
I 4
5
t PX
7 6 IO-', otm.
9
t o l l
I2
Figure 2. Graph of ( dP/d2')~ for liquid water us. pressure.
in Figure 1 is seen to arise from the conventional choice of the pure liquid as solvent standard state. It is also of interest to consider the intercept in relation to the state of the proton in aqueous solution. The above simple interpretation of the intercept in terms of H30+(aq) may be taken as evidence that protons in aqueous solution are best described as hydrated HSO+ ions, with the implication that the hydrations of a H30+ ion and a water molecule in liquid water are about the same. This latter implication is supported by the accumulation of evidence that absolute values of the standard partial niolal entropy and also molal volume of H+(aq) are both only slightly negative. We might also consider the proton as being hydrated by x water molecules, as represented by H(HzO),+(aq). Then, taking the principal species in liquid water to be z-mers, we could write (3) as HA"(aq)
to make it more explicitly symmetrical. Standard states for the species in (3) are ordinarly taken to be the hypothetical 1 m solution for H30+(aq),A"-l(aq), and HA"(aq) and the pure liquid for H20. If we should take the standard state of H2O to be 1 m, then all conventional Asia values (such as those in Figure 1) must be increased by R In 55.5 = 8.0 cal. deg. -l mole-'. Z -7 at APio = 0 Thus the intercept value of
As,"
967
+ (HzO), = H(HzO)z+(aq)+ A"-'(aq)
(4)
On this basis, the effect on AS," of changing the standard state of water from the pure liquid to a 1 m solution of (HzO), is R In (1000/18x), from which we calculate shifts of 8.0, 6.7, and 5.2 cal. deg.-' mole-1 when x = 1, 2, and 4,respectively.
Acknowledgments. The author thanks Dr. S. D. Hamann and Dr. J. A. Barker for their hospitality and many helpful discussions.
Volume 69,Number 3
March 1965
