3796
D. E. IRISH AND H. CHEN
Young’s second r ~ l e ’ is ~ ~that ’ ~ the heat of mixing for two electrolytes having a common ion is independent of the common ion. The corresponding rule for free energy would imply that (4 - 1)”II is independent of the common ion. The rule should hold if only Bab(Ov1) (Brg(O,l)if common cation) and other coefficients with only a and b subscripts contribute to (4 - l)nlx,but not necessarily if other terms of higher power in concentration are important. Young’s third rule,la better known as the cross-square rule, states that for a group of electrolytes of the same valence type af, bf, ag, bg, the free energy of mixing 1 mol of af with 1 mol of bg plus that of mixing 1 mol of ag with 1 mol of bf is equal to that of mixing 1 mol of af with 1 mol of bf plus that of mixing 1 mol of ag with 1 mol of bg plus that of mixing 1 mol of bf with 1 mol of bg plus that of mixing 1 mol of ag with 1 mol of af. With our equations, it holds if BBbtg(2J) is zero. A recent paper20based on the treatment of Friedman gives terms which appear to be similar to the low-order
concentration terms in the ion-component treatment presented above. I n applying these equations2I the interaction parameters are determined separately for each ionic strength and vary with ionic strength. Some of the apparent complexities of our treatments arise from the fact that the equations for these treatments inalude both the variation with the fraction of each solute and with the overall solute concentration. Since the earlier treatment” of sea-water compositions as slightly perturbed NaC1 solutions was satisfactory at room temperature, the ion-component approach does not result in a great improvement. It is possible, however, that the ion-component treatment will be useful at higher temperatures, for which data now exist.22 (19) Y. C. Wu, M. B. Smith, and T. F. Young, J. Phys. Chem., 69, 1868 (1965). (20) P.J. Reilly and R. H. Wood, ibid., 73, 4292 (1969). (21) R. H.Wood, M. Ghamkhar, and J. D. Patton, ibid., 73, 4298 (1969). (22) H.F.Gibbard, Jr., personal communication.
Equilibria and Proton Transfer in the Bisulfate-Sulfate System by D. E. Irish and H. Chen Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada
(Received March 2, 1970)
Relative integrated Ramari intensitieshave been obtained from NH4HS04,KHS04,and (NH4)2SO4-HClaqueous solutions and KDS04-D20 solutions. The apparent concentrationquotient, Qv, and the degree of dissociation, CY, have been computed at each concentration. The broadening of the 981-cm-’ Raman line of sulfate is directly proportional to the hydronium ion concentration. This dependence is linked to the proton transfer occurring in these systems. An overall second-order rate constant of 5.5 X 10” M-l sec-l is implied. The spectra and the kinetics are rationalined in terms of the existence of ion pairs.
Introduction The explanation, in terms of constitution, of properties of sulfuric acid was one of the goals of Professor T. F. Young when, in collaboration with his students L. F. Maranville, H. F. Smith, and L. A. Blatz, he proceeded to design and construct one of the early photoelectric Raman spectrometers. The data obtained in those studies led to significant progress toward attainment of that At low concentrations the difficulty of obtaining meaningful Raman intensities precluded the possibility of getting an accurate value of K z , the second dissociation constant of H2SO4. K zhas been measured by a variety of other methods, and a value of 0.0102 mol kg-l a t 25’ has been obtained essentially independent of the method used.4~5 The Raman data were consistent with this valueP4 The Journal of Physical Chemistry, Vol. 74, No. $1, 1970
The quantitative interpretation of the Raman spectra are complicated by two features. The most intense 981-cm-l line of sulfate ion lies between the 1052- and the 892-cm-l lines of bisulfate ion. At most concentrations these lines overlap, especially in the wings, and some criterion of line shape is required to establish the intensities. The half-widths of Raman lines of acid molecules and their conjugate anions increase with con(1) T. F. Young and L. A. Blatz, Chem. Rev., 44, 93 (1949). (2) T.F.Young, Rec. Chem. Progr., 12, 81 (1951). (3) T.F. Young, L. F. Maranville, and H. M. Smith in “The Struoture of Electrolytic Solutions,” W. J. Hamer, Ed., Wiley, New York, N. Y., 1959,p 35. (4) T. F. Young and D. E. Irish, Ann. Rev. Phys. Chem., 13, 435 (1962). (5) R. E. Lindstrom and H. E. Wirth, J. Phys. Chem., 73, 218 (1969).
3797
SYMPOSIUM ON STRUCTURES OF WATERAND AQUEOUS SOLUTIONS
I
RAMAN
Figure 1. Raman spectra of 50 mol
SOMOLE% NyHSQ
lOf0
A-''i"
93%
I\
% NH4HS04a t 93".
centration. This enhances the overlap, compounding the problem. The line broadening has been attributed to rapid proton transfer between acid molecule and ani0n6-9 and is thus of interest in its own right. The present vibrational spectral study was initiated with the intent of using the bisulfate-sulfate equilibrium as a probe to determine the effects of background electrolyte on the concentration quotient. The complications necessitated a thorough reexamination of the spectra of bisulfate salts in water, including DSO4- in D2O.
Experimental Section Materials. Solutions were prepared from NH4HSOl and KHS04 (Fisher Certified reagent), NaHS04 (fused BDH Analar reagent), Hi304 (95.5% C-I-L CP reagent), and doubly distilled deionized water. Crystalline KDSO4was prepared by adding 59.6 g of DzS04 (99% isotopic purity, Bio Rad Laboratories) to 20 g of KzS04 dissolved in 120 ml of DzO. This preparation was carried out in a nitrogen atmosphere. Spectra. Raman spectra excited by the 4358-8 line of mercury were recorded on a Cary 81 Raman spectrophotometer. A saturated n'aNOz solution or a Kodak 2A Wratten filter was used as optical filter. Filtered solutions were contained in cells equipped with water jackets for temperature control. A Haake constant temperature circulator was used to maintain the temperature at the desired value-usually 25 i= 0.02". Integrated intensities, corrected for cell and instrument ,settings, were obtained relative to the intensity of the 458-cm-' line of carbon tetrachloride used as an external standard. Line areas were measured with a polar planimeter. Infrared spectra were recorded on a Beckman IR-9 spectrophotometer. Liquid films were contained between AgCl or AgBr plates separated by a 0.0125-mm Teflon spacer. Curve Analysis. A hybrid analog-digital computer routine was used to resolve band envelopes. Frequency-intensity data are read from spectral charts and punched onto IBM cards. These generate the experi-
mental curve which is displayed on the screen of a storage oscilloscope. A synthetic curve, a sum of invoked component bands each described by a Lorentz-Gaussian product function, is generated. The mean, variance, and area of each component are adjusted until the sum curve and experimental curve superimpose. The difference curve is a measure of the goodness of fit. Differences are minimized.
Results and Discussion Spectra. The degree of dissociation of bisulfate ion in a 50 mol yoammonium bisulfate solution is small a t 93". Raman spectra recorded with both polarized and unpolarized mercury excitation are shown in Figure 1. The Sod2- 981-cm-I ulAl line appears only as a weak shoulder for 50 mol % NH4HS04 (-10 dB at 93"). Other lines of S02- (451,613, and 1110 cm-') are not detectable. Therefore all the Raman lines observed except 981 cm-' are due to HS04- ion. The prominent lines, half-widths, and features of HSOd- are, respectively, 424 cm-l, 39 cm-', dp, asymmetric; 592 cm-', 36 cm-', dp, asymmetric; 872 cm-I, 59 cm-', p; 1040 cm-I, 43 cm-', p; and 1204 cm-l, 115 cm-l, dp. The frequencies depend on concentration. I n particular the intense line at 1040 cm-I is found in the region 10521055 cm-' in more dilute solutions (-2 M ) . The bisulfate ion is largely surrounded by ammonium cations in the concentrated solution; these are replaced by water molecules on dilution and line frequencies reflect this change in environment. Raman spectra of 2.00 M solutions of NHdHS04, NaHS04, KHS04, and H2S04run under identical operating conditions at 25.0" are illustrated in Figure 2. The frequencies are essentially independent of cation. Line overlap is apparent, and the (6) M.M.Kreevoy and C. A. Mead, J . Amer. Chem. SOC.,84, 4596 (1962). (7) M.M. Kreevoy and C . A. Mead, Discussions Faraday Soc., 39, 166 (1965). (8) A. K. Covington, M. J. Tait, and W. F. K. Wynne-Jones, ibid., 39, 1 (1965). (9) W. J. Albery, Progr. React. Kinet., 4, 353 (1967). The Journal of Phgsical Chemistry, Vol. 76, No. $1, 1970
3798
D. E. IRISH AND H. CHEN
I100
lo00
CM"
000
a00
40 0
Figure 2. Raman spectra of 2.00 M H2SO6, KHSO,, NaHSO,, and NH4HSOd solutions.
solid line. Between0.117 and 1.0 M (NH4)zS04 15 values of the integrated intensity were obtained in triplicate; between 1 and 3.83 M 9 values were obtained in duplicate. Relative integrated intensity is directly proportional to sulfate concentration with very little scatter. Intensities relative to the 458-cm-I line of CC14are
Is81 = 0.281[S042-] Ill10 = 0.111[504~-]
Figure 3. Computer analysis of 0.455 M ( N H I ) ~ S O I I h m a n spectrum.
breadths of lines of Hz804are noteworthy. The intensity ratio of the 981-cm-1 line of sulfate and the 1050-cm-l line of HS04- is a qualitative measure of the extent of dissociation. Assuming that molar intensities of both lines are independent of cation, the spectra indicate that the extent of dissociation of HS04- ion is approximately in the order of cations NH4+ > Na+ > K+. Intensity Study. The spectral region 900-1200 cm-' of SOk2- can be fitted accurately by computer analysis using a Lorentz-Gaussian product function for line shape. I n the plotter portrayal of the computer analysis (Figure 3) the points read from original spectra are designated by X and the sum of two Lorentz-Gaussian functions positioned at 981 and 1110 cm-' is given by the The Journal of Physical Chemistry, Vol. 7 4 , hro. 21, 1070
obtained with sensitivity 2 for CC14 and 10 for sulfate. The total width a t half-peak height (called the halfwidth in this paper) of the 981-cm-1 line was found to be 18.0 cm-' independent of concentration at a slit width setting of 15.0 cm-I. The computer analysis of the spectral region 8001400 em-' of a 0.225 M NH4HS04solution is illustrated in Figure 4. Analysis of many spectra of many concentrations with line shapes described as Lorentz, Gaussian, and Lorente-Gaussian indicated that the best fit was obtainable with Lorentz-Gaussian functions. Even so a good fit was not obtainable in the -1020- and 940cm-' regions unless two additional lines were invoked, vix. a weak line a t 948 4 cm-l and another ~ e a line k at 1024 AZ 4 cm-l. These lines have not hitherto been reported in Raman spectra of bisulfate solutions. Thus we were concerned lest these be results of the method of curve analysis and not real. The lines were found in solutions of different cation-bisulfate salts-NHb+, H30+,Ka+, and K+. The asymmetry of the 890- and 1 0 5 0 - ~ m -lines ~ is apparent on original traces. I n the infrared spectrum where the 981-cm-l line of Sod2- is
*
3799
SYMPOSIUM ON STRUCTURES OF WATERAND AQUEOUS SOLUTIONS Table I : Data for Aqueous Ammonium Bisulfate Solutions [HzO I
LNH4HSO41
42.6 44.0 45.3 47.0 48.7 50.5 52.6 52.9 53.0 53.2 53.6 53.7 54.2 54.2 54.7
8.013 6.571 5.257 3.942 2.957 2.007 1.045 0.963 0.911 0.828 0.682 0.641 0.470 0.427 0.225
[Sole-la
1.67 1.60 1.47 1.30 0.991 0.731 0.377 0,336 0.311 0.277 0.247 0.202 0.176 0.155 0.108
[so42- l b
[HSOI-]'
ad
QYB
1.68 1.60 1.47 1.28 1.02 0.705 0.365 0.337 0.319 0,290 0,240 0.226 0.168 0.153 0.082
6.33 4.97 3.79 2.67 1.94 1.30 0.680 0.626 0.592 0.538 0.442 0.415 0.302 0.274 0.143
0.210 0.243 0.280 0.324 0.345 0.351 0.349 0.350 0.350 0.350 0.352 0.362 0.357 0.358 0.365
0.447 0.512 0.572 0.612 0.537 0.381 0.195 0.181 0.172 0.156 0.130 0.122 0.093 0.085 0.047
Ivf
11.4 9.76 8.20 6.50 5,oo 3.41 1.77 1.64 1.55 1.41 l.lG 1.09 0.81 0.73 0.39
(w
- WOY
14 i 3 10 f 2 8 . 3 f0.7 7.3 4.5 4.6 2.6 2.2 2.1 1.5 2.2 1.4 1.6 1.0 0.5
C - [S042-]b. Least-squares fit based on 38 individual measurements. Mean values of 1 9 s l / J ~= s l1981/0.281in moles liter-'. f I , = ionic strength = C(1 2a). g Half-width of 981-cm-l line (tu) - half-width in (NH4)t8 &, = [&//(1 - .)IC. SO4 solution (wo), a
d
+
[S042-] /C.
Figure 4. Computer analysis of 0.225 M NH4HS04 Raman specbrum.
very weak (it is forbidden by selection rules but shows up weakly in the solution phase) a distinct shoulder is observable on the low-frequency side of the 1050-cm-' line of HSOd-. For these reasons we consider these lines real and discuss provisional assignments later. The relative integrated intensities of the 981-cm-' lines of Sod2- in the bisulfate solutions were obtained excluding contributions from these two weak components. Division by the molar intensity of S042- (Jesl = 0.281) provides the sulfate ion concentrations. The difference between these and the stoichiometric concentrations of bisulfate salt gives the apparent bisulfate ion concentrations. The apparent concentration quotient and degree of dissociation were obtained in accordance with the definition Qv
=
[S042-] [H,O+] - -cx2Ca [HS04-] 1-a
These quantities are given in Table I. As one self-consistency test of the data, the intensity of the 1050-cm-' line of HSOI- WBS plotted us. [HSOr-] obtained by difference, and a straight line was obtained. The extrapolation of &,-concentration data to obtain K z cannot be made with high precision because Raman data cannot be obtained a t sufficiently low concentrations. A simple extrapolation of a Qv us. C plot indicates that K z is 0.01 in general agreement with values obtained from methods which provide data in much more dilute solution^.^ The extent of dissociation obtained in this work is much less than that reported earlier.a This is attributed to the difference in the way in which the Raman spectra were resolved. Less intensity has been attributed to the sulfate ion in this work because the 948- and 1024-cm-' lines are recognized as arising from undissociated species. Similar but fewer data were obtained for I.(HSO4 in HzO, KDSO4 in DzO and (NH~)zS04-HC1mixtures. These are presented in Table 11. The degree of dissociation of the deuterated form is less than that of the protonated form as expected. Proton-Exchange Study. The broadening of the 981cm-l line of S042-, (w- too), is directly proportional to the concentration of hydronium ion (Figure 5). All three sets of data-NH4HS04, 1
