A RAMANSPECTRAL STUDYOF BISULFATE-SULFATE SYSTEMS
et (Table 11, third column, ref 46), approximate values, Kz’, of K z were calculated from eq 7. A plot of log Kz’ vs. m (Figure 11) is linear and extrapolates to Kz = 0.0101 mol/kg of HzO. The finite slope reveals the inadequacy of the assumption at the concentrations for which a has been meabured, although eq 7 is expected to be valid for I < 0.1. B . Use of Values of y+ for a Completely Ionized 1 :1 Eleclrolyte. An approximate value for K2 can also be obtained by using eq 6, if the value of y ~ t y H S 0 ~ is assumed to be very close to ST^ of some completely ionized 1: 1 electrolyte. We choose HC104, although the results would not be significantly different for HCl. The interpolated values of ST for HC10d4’ have been chosen for three different conditions: for the same ionic strength as the HzS04 solutions, for the same hydronium ion concentration, and for the same geometric mean ionic molality of 1 : l ions as that obtained using mHt and mHso4for a given HzSO4 solution.8 Plots of K2’, designated K I ~ ’ K,,t’ , and K,,’, vs. m are given in Figure 12. Extrapolation suggests values for Kz ranging from 0.010 to 0.011 mol/kg of HzO. It is interesting to note that the hydronium ion concentration is appar-
2681
ently the best basis for choice of y* a t these concentrations. For salt solutions of moderate to high concentrations we have frequently observed that mass law concentration quotients are independent of concentration and ionic strength.30 Such is not the case for acids, as illustrated here; the hydronium ion is responsible for the nonconstancy of the activity coefficient quotient in these systems.
Acknowledgments. This work was supported by the National Research Council of Canada. I n the final stages of the work the authors had the benefit of stimulating conversations with a number of workers: A. K. Covington, E. Grunwald, J. E. Prue, D. H. Whiffen, and P. A. H. Wyatt. Their criticisms and suggestions are greatly appreciated. The cooperation and contribution of the Computer Science Division, University of Waterloo, and especially IClr. A. Weerheim to the curve resolving routine is gratefully acknowledged. The assistance given by W. L. Elsdon and D. J. Lockwood is also appreciated. (46) A . K. Covington, J. V. Dobson, and W. F. Trans. Faraday Soc., 61, 2050 (1965).
K. Wynne-Jones,
(47) Reference 44, p 491.
A Raman Spectral Study of Bisulfate-Sulfate Systems. 111. Salt Effects by H. Chen and D. E. Irish* Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada
(Received April 6 , 1071)
Publication costs borne completely by The Journal of Physical Chemistry
The degree of formation of sulfate in 1.357 M NHdHS04 solutions containing various amounts of each of LiCl, and NHdBr has been measured by Raman spectrophotometry. The ionization XaC1, KCl, RbCl, CsCl, ”&I, is depressed by the salts in the order CsCl > RbCl KCl > KaCl NH4Br > SH&l LiCl, if sufficient salt is added. For addition of small quantities of LiCl and NR&l the ionization is enhanced. N
Introduction The equilibrium between an acid and its conjugate base is disturbed by addition of species foreign to the equilibrium. I n most studies of the salt effect on acid-base equilibria, data have been obtained for dilute solutions and the ionization quotients have been obtained for the acid a t infinite di1ution.l Thus self-interactions of the acid and possible complex formation between ions of the acid and ions of the salt have been excluded. The addition of small amounts of a neutral salt then increases the extent of ionization in accord with the Debye-Huckel theory.’Sz
N
N
Raman spectral data can only be obtained a t concentrations well above those for which the extended Debye-Hiickel theory is valid. Extrapolations to provide quantities which are directly comparable with those obtained from the dilute solution studies are not possible. The behavior at such concentrations is still of interest, however. I n conjunction with Raman studies of the ionization of b i ~ u l f a t e ~ ’ ~ (1) E. J. King, “Acid-Base Equilibria,” Pergamon Press Ltd., Oxford, 1965, p 269. (2) R . P. Bell, “Acid-Base Catalysis,” Clarendon Press, Oxford, 1941, p 14.
(3) D. E. Irish and H. Chen, J.Phgs. Chem., 74, 3796 (1970). (4) H. Chen and D . E. Irish, ibid., 75,2672 (1971).
T h e Journal of Physical Chemistry, Vol. 75,
17, 2971
H. CHENAND D. E. IRISH
2682 we have measured the apparent concentration quotient, sQe, for a fixed concentration of NH4HS04and various amounts of added salt. The alkali metal chlorides, ammonium &loride, and ammonium bromide were selected as these permit a comparison of univalent and no spectral manifestation of ion pairs was found.
Experimental Section Solutions were prepared from NH4HS04, NH4C1, LiC1, CsCl (Fisher Certified Reagent), KaC1 (B &A ACS Reagent), KC1 (B.D.H. Laboratory Reagent), RbCl (Fisher Purified Reagent), and NH4Br (Matheson Coleman and Bell). Solutions of 1.357 M NH4HS04 with inert electrolytes added were obtained by dissolution of a weighed amount of dried halide in 50.0 ml of 2.715 M NH4HS04 followed by dilution to 100.0 ml; 1.357 M NH4HSOb is an optimum lorn concentration for which intensities are still accurately measurable and spectral contours can be resolved. All solutions were treated with activated charcoal for at least 30 min and filtered through a 100-mp Millipore filter before being transferred into the Raman cell. This eliminates any fluorescence and optical attenuation. On addition of the salts, some of the colorless, clear NH4HS04solutions became very pale yellow. The color is believed to result from a trace of FeCL-, formed from impurity iron in the chlorides. The color causes absorption at 340.0 nm with a tail of the absorption band at the wavelength of the Raman exciting line and the Raman lines. The position of the absorption maximum agrees with that of dilute solutions of FeCL in aqueous HCl.685 The suppliers indicated iron impurity in the range 0.0001 to 0.002%. The faint color of some solutions had no effect on the data, as discussed below. Spectra of samples at 25" and computer analyses were obtained as previously d e ~ c r i b e d . ~
Results The degree of formation of S042-, CY, can be related t o the intensity ratio 1981/11060 (the ratio of the intensities of the strong lines of S042- and HSOh-, respectively). For those solutions which were colored, this ratio is independent of color if the two lines are affected to the same extent by the low absorbance. Because of the closeness of the two lines, 455.3 and 456.7 nm, the difference in absorbance is not significant and no color correction has been applied. The expression for CY is derived as follows
[S042-][1
1
+ 1.87 11050
1981
T h e Jownal of Physical Chemistry, Vol. 7 5 , X o . 17, 1971
CY =
[S042-I = [NHIHSOI]
[
+
1,87'-]0& I981
where Ji is the molar intensity of line Pi and these values have been The quantity I981/Il060 is more sensitive to the uncertainty of curve resolving than measurement of 1981 alone and thus CY obtained from the above relation is less accurate than QI measured d i r e ~ t l y . ~More attempts were made to resolve a single spectrum and a mean value of the intensity ratio was taken. Data are presented in Table I. The sulfate ion concentration varies from 0.35 to 0.5 M in these solutions. Over this range the change of half-width resulting from proton transfer4 is not significant. Thus the ratio of apparent peak heights serves as a check and confirmed the trends found from the ratio of integrated intensities. I n the absence of salt, Qe for 1.357 M KH4HS04 is 0.252. The fractional change in Qc is defined as (sQC - QJ/ Qc = (sQo - 0.252)/(0.252). A positive value indicates enhanced sulfate formation in the presence of the salt and vice versa. The plot of this function us. salt concentration clearly shows how the different salts affect the degree of formation of sulfate (Figure 1). For the addition of sufficient salt, all salts depress the formation of sulfate in the order CsCl > RbCl KC1 > NaCl SH4Br > LiCl n"4Cl. In dilute salt solutions there is indication of enhancement of the concentration of sulfate.
-
-
-
Discussion The equilibrium, in the presence of foreign salts, is described by the equation K = sQCsQy where K is the thermodynamic equilibrium constant and sQy is the activity coefficient quotient. Values of sQY are given in Table I; the value 0.010 is used for K at 25". Log s Q Y is plotted against the square root of ionic strength in Figure 2. The broken curves represent approximately the trend of the salt effect for infinitely dilute weak acid solutions found in the 1iterature.l)' The salt effect observed in this work is qualitatively in accord with those described in the literature. I n the same figure, the data for the stoichiometric NH4HS04 solutions are also shown for comparison (zero salt). For NH4C1 and LiCl the first addition of salt increases the acid dissociation (decreases s Q y ) . On further addition the degree of formation of sulfate passes through a maximum and decreases; eventually dissociation is depressed from that observed for the acid in pure water. The initial increase was not observed for the other salts at the concentrations used, although a small enhancement may occur, judging from Figure 1. Both theory ( 5 ) D. E. Metzler and R. J. Myers, J . A m e r . Chem. SOC., 72, 3776 (1950). (6) H . L. Friedman, ibid., 74, 5 (1952). (7) H . S.Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions," 3rd ed, Reinhold, New York, N . Y . , 1958, p 675.
2683
A RAMAN SPECTRAL STUDYOF BISULFATE-SULFATE SYSTEMS Table I : Data for 1.357 M NHaHS04 in Salt Solutions Salt
Msalt
I~8i/Iiaso~
0.00 0,937 2.000 3.084 4.107 1.992 3.007 4.000 1,191 1.914 2.780 4.087 1.988 2.990 4.044 1.411 2.051 2.426 3.022 1.651 0.990 1.862
None NHaCl
NHaBy
LiCl
NaCl
KC1
RbCl CsCl
0.348 0.368 0.355 0.327 0.304 0.332 0.304 0.272 0.379 0.361 0.339 0.314 0.327 0.310 0.278 0,327 0.299 0.289 0.255 0.314 0.323 0,297
1.00 1.09 1.03 0.91 0.82 0.93 0.82 0.70 1.14 1.06 0.96 0.86 0.91 0.84 0.72 0.91 0.80 0.76 0.64 0.86 0.89 0.79
8&Yb
0,252 0,291 0.265 0.216 0.180 0,224 0.180 0.138 0.314 0.277 0.236 0.195 0.216 0.189 0.143 0.216 0.173 0.159 0.118 0 195 0.209 0.170
0,0397 0,0344 0.0377 0.0463 0.0555 0.0444 0.0555 0.0725 0.0318 0.0361 0.0424 0.0513 0,0463 0,0529 0.0694 0.0463 0.0568 0.0629 0,0847 0.0513 0.0478 0.0588
I
a Average of four to eight curve resolvings wit'h uncertainty of 0.02-0.04. 2[SOP-].
0.2
i-
\
1.0
BQY
- 1.400
- 1.463 -1.423 -1.334 -1.255 -1.352 -1.255 -1.139 - 1.498 -1.442 -1.372 -1.290 -1.334 -1.276 -1.158 - 1.334 - 1.245 -1.201 -1.072 -1.290 -1.320 -1.230 =
E&,
O.OlO/s&,.
'I,
[SO,~-Id
IO
0,472 0.499 0.482 0.444 0.412 0.450 0.412 0.369 0,514 0.490 0.460 0.426 0.444 0.421 0.376 0.444 0.406 0 392 0.346 0.426 0.438 0.403
2.30 3.29 4.32 5.33 6.29 4.25 5.19 6.09 3.58 4.25 5.03 6.30 4.23 5.19 6.15 3.66 4.22 4.57 5.07 3.86 3.22 4.02
dKC 1.52 1.81 2.08 2.31 2.51 2.06 2.28 2.47 1.89 2.06 2.24 2.51 2.06 2.28 2.48 1.91 2.05 2.14 2.25 1.96 1.79 2.00
= '/zZMiZia = Msalt 4- 1.357
4-
I
0
I_----
,/*-
log
SQC
P
3.0
2.0
4.0
C
Figure 1. Effect of salt on the concentration quotient of the bisulfate-sulfate equilibrium, shown by: (sQC- Qo)/Qo us. the molarity of salt: a, NH&1; 0, LiC1; C , NH4Br; 8 , KaC1; 9, KCl; A, RbC1; V, CsCl.
and experiment confirm an enhancement in dilute solutions in accord with the decrease of activity coefficients on increase of ionic strength. la2 The same trend was reported by Harned and Robinsonag They reported that for n'aC1-acetic acid solutions, the maximum in a was apparent for acid concentrations less than 5.4 M but not detected for 10.2 M . Working at much lower acid concentrations (0.2 M) than used in this study they found the increased dissociation to be in the order BaC12 > LiCl > NaCl > KCI. A rule,8 valid for many studies, is
I 0
I
Jr,
2
Figure 2. Log E&, us. dFofor a 1.357 M NHdHSOd solution with added foreign salts. Symbols defined in Figure 1: A, for stoichiometric solutions of NH4HS04.
that a t a given ionic strength and acid concentration, s&, of a weak acid is greater in the solution of an alkali metal halide which in the pure solvent water possesses (8) H. S. Harned and R. A. Robinson, J . Amer. Chem. Soc., 50, 3157
(1928).
The Journal of Physical Chemistry, Vol. 76,N o . 17,1971
2684
NOTES
the smaller mean activity coefficient. This rule cannot be extended to include ammonium salts, however. The mean activity coefficients of the salts in water decrease in the order LiCl > NaCl > NH4Br > KCl > NH4C1 > RbCl > CsCl. It is clear that NH&1 should be more comparable to KCl if the “rule” had wider significance. Although the trends are consistent with the initial decrease and subsequent increase of activity coefficients as ionic strength increases the order and the magnitudes find no simple explanation. The order is not in keeping with a lowered dielectric constant of aqueous electrolyte solutions as proposed by Hasted, et aL;9 the order for depressing the dissociation would have to be LiCl > NaCl > KC1 RbC1. Rationalization in terms of structure-making and structurebreaking ions is possible but this approach lacks in predictive capabilities.lo One correlation which deserves further exploration concerns hydration of the
-
ions. The less the “free” water (all water not bound to ions) the lower the degree of formation of sulfate. The free water concentration, FC)”, is given by TC, hCs - Cw’. T C is~ the total water concentration, h is a total hydration number for salt of concentration CS, and C,’ is the water bound by the proton, sulfate, bisulfate, and ammonium ions. For the ternary systems of this study T C is~ not known. The values for binary salt-water solutions, however, do permit estimation of FC, values which lead to a correct sequence if spectroscopic estimates of h are used, i.e., h of 4 for LiC1, 3 for SHdC1, and 5 or larger for the other halides of larger ionic radii.
Acknowledgments. This work was supported by the National Research Council of Canada. (9) H . B. Hasted, D. Nl. Ritson, and C. H . Collie, J . Chem. P h y s . , 16, l(1948). (10) H . Chen, Ph.D. Thesis, University of Waterloo, Waterloo Ontario, Canada, 1971, p 103.
NOTES Viscosity Independence of the Half-Width of the vl(A1) Raman Line of Sulfate Ion by D. E. Irish” and R . C. Meatherall Department of Chemistry, The University of Waterloo, Waterloo, Ontario, Canada (Receiued A p r i l 6 , 1971) Publication costs borne completely by The Journal of Physical Chemistry
The liquid state is characterized by random molecular motions. Transitions from one equilibrium position to another, hindered partial rotations, and collisions are occurring with a high frequency. The mean lifetime of a molecule betn-een random reorientations has been linked to changes in the half-widths of Raman lines and infrared lines of liquids. Studies of pure organic liquids at different temperatures and of organic mixtures reveal a relationship between half-width and the reciprocal of v i s c ~ s i t y . ~ - Few ~ width studies have been performed on aqueous electrolyte solutions. Concentration narrowing has been reported for alkali metal nitrite solutions and the inferred encounter rate constant increases with the solubility of these highly soluble salts.* Both specific and nonspecific dependences have been observed for the width of vibrational lines of alkali metal nitrate^.^ T h e Journal of Physical Chemistry, Vol. 76, KO.1 7 , 1971
The changes in width resulting from collisions and hindered motions generally do not exceed 10 cm-l. These processes account for most of the width of vibrational lines of molecules in the liquid phase providing chemical processes are absent.6 The latter include ultrafast proton transfer between hydronium ion and a base. Broadenings of more than 30 cm-’ result if the mean lifetime of the species is of the order of sec.’ I n recent work on the bisulfate-sulfate equilibrium a proportionality has been found between the broadening of the 981-cm-l symmetric stretching vibration of sulfate ion and the total hydronium ion concentration p r e ~ e n t . ~The , ~ data have provided strong support for an interpretation in terms of ultrafast proton transfer and insight into the mechanism of the transfer process. It is important, in view of the literature cited above, to ensure that this interpretation is not in error (1) A. V. Rakov, T r . F i z . l n s t . A k a d . S a u k S S S R , 27, 111 (1964). (2) I. I. Kondilenko, V. E. Pogorelov, and K . Khue, O p t . Spectrosc., 28, 367 (1970). (3) S. Higuchi, S. Tanaka, and H . Kamada, S i m o n Kagalcu Zasshi, 89, 849 (1968), Chem. Abstr., 70, 7706 (1969). (4) D. E. Irish and M . H. Brooker, Trans. Faraday Sac., 67, 1916 (1971). ( 5 ) D . E. Irish and A. R. Davis, Can. J . Chem., 46, 943 (1968). (6) K . S. Seshadri and R . N . Jones, Spectrochim. Acta, 19, 1013 (1963). (7) E. Grunwald, Progr. P h y s . Org. Chem., 3 , 317 (1965). (8) D. E. Irish and H . Chen, J . P h y s . Chem., 74,3796 (1970). (9) H . Chen and D. E. Irish, ibid., 75,2672, 2681 (1971).
