R, J, HIRKOAND R. H,BOYD
1990
This definition of deviations from ideality implies a statistical model in which cations are surrounded only by anions and vice versa. If formulated in terms of a lattice model, the ideal solution would correspond to random mixing of cations on a cation sublattice, without substitution of cations for anions (because of Coulombic energy considerations), However, the essential feature of this definition of ideality is the absence of cationcation and anion-anion contacts rather than a crystalline lattice. This treatment has been fruitful in the interpretation of the thermodynamic properties of molten mixtures of simple salts.32 One may attempt to apply this treatment to a system in which water is a minor component, although there is insufficient information on these systems to justify a reasonable model. The mole fraction
+
XH~O= n ~ z o / ( n H z o nd
(6)
would not distinguish among statistical models in which, in the limit of vanishing water content, water and cations mix randomly or water and anions mix randomly, or water and neutral salt molecules mix randomly. A model which has been applied successfully to the competing association and hydration equilibria in aqueous melts considers mixing of the water molecules and anions on sites adjacent to cations.12 This would correspond to preferential hydration of the cations rather than anions and would be consistent with a concentration scale defined by eq 6.
The linearity of the vapor pressure in the mole ratio of water up to quite high water concentrations leads one to speculate on whether any simple model would predict such behavior. One such model is that in which dissolved water occupies “sites” (or interstices) whose number is proportional to the number of moles of salt (or to the number of moles of cations or of anions). The ideal mixture, with this model, would be a random mixture of occupied and unoccupied “sites” in the salt, whether these “sites” were on cations, on anions, or in “interstices” in the molten salt. The nature of such sites is not clear and one would not expect random mixing of occupied and unoccupied sites to persist up to 50 mol % water, Density measurements in the system LiN03-KN03-H20 indicate that the molar volumes are nearly additive.14 This is difficult to reconcile with a site or interstitial model. Frame, Rhodes, and Ubbelohde2’proposed an interstitial model for the solubility of water (and other gases) in molten nitrates. Their conclusions, however, were based on results at very low water concentrations. It is unlikely that a molten salt contains enough “interstices” to accommodate water molecules a t concentrations up ’ without endothermic alteration of the structo 50 mol % ture. Until additional data in other systems over extended ranges of composition and temperature are available, the linearity of the plots of vapor pressure va. water mole ratio should be regarded as empirical rather than as justification for an oversimplified model.
The Activity Coefficients of Solutes in Acid Solutions. 111. The Relative Activity Coefficients of the Silver and Halide Ions in Aqueous Sulfuric and Perchloric Acid Solutions by R. J. Hirko and R. H. Boyd Department of Chemistry, Tl’tah State Cniversity, Logan, Utah
843.21
(Received October 2 8 , 1 9 6 8 )
Solubility determinations of silver chloride, bromide, and iodide in sulfuric and perchloric acid solutions were made by emf nieasurement,s. From solubility data for tetraethylammonium pentacyanopropenide and silver pentacyanopropenide measured here and previously, the activity coefficients of the silver and halide ions relative to the tetraethylammonium ion were computed. The point of rapid solubility increase for the silver halides was used to estimate the pk of hydrogen chloride as -6.5. The lack of such a point for silver bromide and iodide indicates pk’s of < - 10.
Introduction In order to understand the substantial effects of acid concentration on equilibria and reaction rates in concentrated acid media, it is necessary to have some knowledge of the variation of activity Coefficients of The Journal of Physical Chemistry
the solute species. For example, the behavior of acidity functions based on various indicator molecules can be rationalized1 in terms of measured activity (1) R. H . Boyd, J. Amer. Chem.
SOC.,
85, 1655 (1963).
ACTIVITYCOEFFICIENTB OF SOLUTES IN ACID SOLUTIONS coefficients of appropriate model compounds for the indicators. However, it is apparent that to understand such activity coefficient behavior, the interactions between solvent and solutes that are structurally more simple than indicator models must be delineated. Boyd and MTang2reported the behavior in sulfuric acid solutions of the activity coefficients of the silver and chloride ions relative to the tetraethylammonium (TEA+) ion from solubility measurements of silver chloride and silver pentacyanopropenide (Ag+PCP-) . Later, the effect of polarizability as a paramete? ih solute-solvent interaction was investigated by measuring the activity coefficient of the 1,1,2,6,7,7-hexacyanoheptatriene anion (HCHT-) relative to TEA+ in sulfuric acid solution^.^ The latter has an extremely high extinction coefficient ( E 150,000) indicating very high polarizability.5 The purpose of the present work is systematically to study the effects of solute ion size and polarizability by measuring the variation of the activity coefficients of the chloride, bromide, and iodide ions relative to TEA+ in both sulfuric and perchloric acids.
Experimental Section With the knowledge of the solubility in pure water (So) and the solubility in a solvent mixture (X), the mean activity coefficient for the solute salt can be computed froma f&= (SO/S)fO (1) where the standard state in this work has been chosen as the solubility in pure water; Le., fo = 1. Electromotive force measurements were employed in the measurement of the silver halide solubilities. The solubility may be computed from the Eo of the reaction Ag+
+ x- * AgX
cell 2
+ + 2Ag+ + 2e --+ 2Ag QHz Q + 2H+ + 2e ---f
(3c) (34
--+
where Q is quinone and QHz is hydroquinone. Adding eq 3a through 3d results in eq 2. Using eq 3a and 3b and formulating the Nernst equation gives for cell 1 Q . QHz-AgX cell,
E* where k
=
=
EO*- (k/2) log(
a Q H 2UAgX2
analogous equation for cell 2 (eq 3c and 3d) is Q.QHz-Ag cell, E**
)
ax-2aA2aH+2aQ (4)
0.059158 absolute volt8 a t 25O.’
The
=
EO**- (k/2) log
(aAgkQaH+2) ~ A , + ’ ~ Q H2
(5) Making the substitution a = fC, where f and C are the activity coefficient and molarity, respectively, and rearranging eq 4 and 5 gives
E’ E”
=
E* - k log Cx-
=
Eo* - ( k / 2 ) log bangx2
=
E**
=
EO** f (k/2) log p
+ k logfx-
(6)
- k IOg CAg’
+ k 10gfAg’
(7)
where p = aQH2/aA:aQaH+’ and C is the concentration in moles per liter. The right-hand sides of eq 6 and 7 a t low Cx- and Cap+, in a given acid solvent, should become constant with respect to variation of X- or Ag+. At zero concentration of X- and Ag+, they can be considered as Eo’ and EO”of reactions 3b and 3c, with the acid solvent of a given acid concentration considered as a pure solvent. It was found empirically that when E’ and E” are plotted against 2/c, a modest straight-line extrapolation to C = 0 gives Eo’and Eo”. (See Table I for typical results. Complete tabulation may be found in the thesis of R. Hirko, Utah State University.) With the stipulation that the quinhydrone electrodes are identical in eq 6 and 7, which is the case in a saturated electrode system, addition of eq 6 and 7 gives at equilibrium (E* E** = 0)
+
+
EO’ Eo”
=
- k log (CX-CAg’)
(8)
or
(2)
The quinhydrone electrode was used as a standard electrode us. both silver and silver halide electrodes such that Q+2H++2e+HzQ (34 cell 1 2X2Ag 2e 2AgX (3b)
I 1
1991
log
Eo“ x = - Eo’ + 2k
(9)
The reference quinhydrone electrode was constructed from a fiber-tipped casing which contained a 5% HzSOrquinhydrone saturated solution.8 A pure platinum wire dipping into the solution completed the electrode. The inner solution was made fresh daily, and the electrode was stored in acid when not in use. (2) R. H. Boyd and 0. Wang. J. Phys. Chem., 69, 3906 (1965). (3) E. Grunwald and E. Price, J. Amer. Chem. Soc., 86, 4517 (1964). (4) R. Hirko and R. H. Boyd, unpublished results reported in the chapter “Acidity Functions,” by R. H. Boyd in “Solvent Interactions.” J. F. Coetzee and 0.D. Ritchie, Ed., Marcel Dekker Inc., New York, N. Y., in press. (5) W. Kauzmann, “Quantum Chemistry,” Academic Press Inc., New York, PI;. Y., 1957,p 579. (6) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” 3rd ed, Reinhold Publishing Corp., New York, N. Y., 1958, p 586. (7) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” 2nd ed, Butterworth and Co. Ltd., London, 1959, p 469. (8) D. G. Ives and G. J. Janz, “Reference Electrodes,” Academic Press, New York, N. Y., 1961, p 311. Volume YS, Number 6 June 1968
R. J. HIRKOAND R, H.BOYD
1992 Table I: Typical Extrapolation to Obtain Eous. Quinhydrone of Silver and Silver Halide Electrodes (48.18% Sulfuric Acid) 7-
lO'(Ag+), equiv
2.4931 4.0780 8.0919 10.206 13.096 17.644 22.053
SilveE. V
-0.20387 -0.19158 -0.17443 -0.16872 -0.16250 -0.15520 -0.14981 &"(Ag+) = 0.01023 V
-
E
- k log (Ag+) 0.00930 0.00894 0,00848 0 00823 0.00804 0.00769 0.00735 I
The silver electrode was a billet type and a similar one was used in making the halide electrodes. In making the AgX electrodes, the silver was chemically cleaned for about 12 hr with a KCN solution. This produced a velvet white coating on the silver. The electrode was then washed under running water for a few minutes and finally soaked for 12 hr in distilled water. After soaking, the silver was electrolyzed in a 0.1 M acidified halide solution for 15-20 min using B standard 1.5-V dry-cell battery. After electrolysis, the electrode was aged in acid (-1 M HzS04) for at least 3 days prior t o use. Intercomparison of similar electrodes was generally better than 0.3 mV. The cell in which measurements were made was thermostatically controlled a t 25.00 f 0.03" and was stirred by a magnetic stirrer. A Rubicon potentiometer with a Leeds and Northrup (Model 9834) d.c. null detector was used to measure the cells. The total system was grounded and shielded. The silver ion was introduced as silver nitrate (Goldsmith, 99.9+%) and a t higher acid concentrations as silver sulfate (Fisher Scientific, 99.95%) owing to insolubility of the nitrate. The halides were introduced as potassium salts (Baker Analyzed, 99.9%) except at higher perchloric acid concentrations where tetraalkylammonium salts (Eastman Organic Chemicals) were used. The solid samples were weighed to 1 pg in a Teflon cup which was also put into the solution. Weights were used to give about a 5X M solution initially and cover about an order of magnitude concentration range using four to eight samples. A 100- or 200-ml volume, known to 0.05%, was used as the volume of solution. Owing to the high electrical resistance, stable values were not obtained in pure aqueous solutions. The solubilities determined by Owen and Brinkley,O who used a supporting electrolyte and extrapolated to zero concentration, were used. The stabilities of the emf readings were generally constant to better than 0.1 mV for periods of 15-30 min except for the AgI system. There was slight discoloration of the cell solution when runs were made past 50% acid using I-. The potential would slowly go The Jouriinl of Physical Chemistry
, lOd(Br-), equlv
1.2653 3.6714 9.1449 13.853
Silver bromidc E, V
E
0.58025 0.60747 0 63095 0.64155 E{(AgBr) = 0.81090 V I
- k log
7
(Br-)
0.81084 0.81069 0.81072 0.81065
through a maximum. The maximum reading was the value recorded. The solubilities of the PCP- salts were measured spectroscopically via the PCP- anion as in earlier The solvent compositions were determined by deneity measurements1° and titration of weighed samples for sulfuric and perchloric acids, respectively. The agreement for the solubility of AgCl in H2SO4with the results of Boyd and Wang2 was reasonably good up to the highest point measured in this work (48.18%). Above this acid concentration, a slow drift in emf was observed, but it did not seem characteristic of the onset of protonation of C1- in this acid. The solubility of AgPCP in H 8 0 4 solutions does not agree well, and the previous results appear to be erroneous. We have no explanation for the discrepancy, but we have paid particular attention to the purity of the AgPCP in this work. The log f * curves for Ag+ and Cl- of that paper which depended on the AgPCP data should be superseded by those of the present work. In particular, a hump in the logfcl-* curve is no longer present. The chloride cell became very unstable in 59,72y0 HC104 acid which we believe indicates that the chloride ion is protonated in this acid. The Eo values for the Ag+ and halide electrodes us. our quinhydrone electrode alocg with the derived solubilities and activity coefficients relative to pure water are reported in Tables I1 and 111. The solubility data for Ag+PCP- and TEA+PCP- are reported in Table IV. The definitions used in earlier papers1V2for the comparison of the mean activity coefficient to a standard ion have also been used in this work, i.e.
f+* E f+/fTEA+
(10)
f-*
(11)
f-fTEA+
The relative activity coefficients, f+* and f-*, were computed from the measured activity data through the (9) B. B . Owen and 8. R . Brinkley, J. Amer. Chem. Soc., 6 0 , 2233 (1938). (10) "International Critical Tables," Vol. 111, 1st ed, McGraw-Hill Book Co., Inc., New York, N. Y., 1928,p 56.
ACTIVITY COEFFICIENTS OF SOLUTES IN ACIDSOLUTIONS
s"
1993
I I
Volume Y8, Number 6 June 1969
R. J. HIRKOAND R. H. BOYD
3994
e,
The Jozirnal
OJ'
Physical Chemistru
1995
IN ACIDSOLUTIONS ACTIVITYCOEFFICIEKTS OF SOLUTES
relations1v2 fAg**
E fAg+/fTEA’
=
and
(13) The resulting values of log f* are tabulated in Table V.
Discussion The deviations of the anions in sulfuric acid relative to TEA+ as represented by the logf-* curves (Figure 1) show the competing effects of charge-influenced interactions as well as nonelectrolyte interactions. The anion curves all fall below the zero axis corresponding to salting in, i.e., an increasingly attractive interaction (compared t o the large hydrocarbon ion TEA+) between the salt and the solvent as the sulfuric acid concentration increases. The curves are also negative to a variety of neutral molecules. This behavior indicates that the hydronium ion is more effective than water in solvating the anions-a situation that is enhanced by charge attraction. The order of the halide curves (increasingly negative, 1: + GI-) is a consequence of the smaller ion’s undergoing stronger chargeinfluenced interaction with the hydronium ion. In the absence of other effects, a very large anion would be expected to approach zero deviation if it were compared to a very large cation as standard (which the TEA+ ion was chosen to represent). However, the effects of noncharge interaction are apparent also as shown by the
5t
Figure 1. Activity coefficientvariations (referred to tetraethylammonium ion as a standard) in aqueous sulfuric acid solutions.
W t V o HClQ
Figure 2. Activity coefficient variations (referred t o tetraethylammonium ion as a standard) in aqueous perchloric acid solutions.
PCP- and HCHT- curves (Figure 1). These ions are large and have delocalized charge distributions which would lead to weak solvation through the charge effect. However, they are highly polarizable as evidenced by their high molar extinction coefficients (23,000 and respectively). The high polarizability 150,000 at A, leads to a relatively strong attractive interaction with the solvent which in turn leads to the relatively large negative deviation in log f-*. The cations plotted in Figure 1 are relatively small or have exposed charges. Their deviations (compared t o TEA+) are all positive as a result of the inability through charge repulsion of the hydronium ion to solvate the cations and because the bisulfate ion is less effective than water in solvation. The approach of cation curves to nearly zero deviation relative to TEA+ as the size and shielding of the ion increases has been previously shown.’ The Ag+ curve lies considerably above that of K+, and the difference would not seem attributable to size difference since the crystal radii are similar” (1.33 A, Ag+; 1.26 hi, K+). However, specific coordination effects may be important in determining Ag+ behavior. It would be helpful in assessing size m. nonelectrolyte interaction effects for cations if data were available for the other alkali metals. From Figure 2, it is apparent that perchloric acid behaves similarly t o sulfuric acid. As acidity function behavior is similar also, this is not surprising, and indicates that the important effects on the solutes are solvation by the hydronium ion and water and poor (11) L. Pauling. “The Nature of the Chemical Bond,” University Press, Ithaca, N. Y., 1948.
Cornell
Volume 75, Number 6 June 1960
1996
U. S. MEHROTRA, M. C. AGRAWAL, AND S. P. MUSHRAN
Table VI: Estimate of pk Values of Halogen Acids from Protonation in Sulfuric and Perchloric Acids
Acid solvent
HzSOi
Acid solvent concn a t Halogen half-protonation acid of halogen acid, %
HzS04
HCl HBr
H2S04
HI
HCIOd HClOi HClOi
HC1
-75
>80 >70
HBr
-57 >80
HI
>80
H- a t halfprotonation
-6.8
