Dissociation constant of bisulfate ion in aqueous sodium chloride

Oct 1, 1990 - Formation Quotients of Aluminum Sulfate Complexes in NaCF3SO3 Media at 10, 25, and 50 °C from Potentiometric Titrations Using a Mercury...
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J . Phys. Chem. 1990, 94, 7918-7985

7978

Dissociation Constant of Bisulfate Ion in Aqueous Sodium Chloride Solutions to 250 OC Andrew G. Dickson, Marine Physical Laboratory, S-002, Scripps Institute of Oceanography, La Jolla, California 92093-0902

David J . Wesolowski,* Donald A. Palmer,* and Robert E. Mesmer Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 -61 10 (Received: March 27, 1990)

The molal equilibrium quotients for the protolytic dissociation of bisulfate ion (HS04-) were measured potentiometrically in aqueous sodium chloride media by using a hydrogen-electrode concentration cell with liquid junction. The ionic strength was varied from 0.1 to 5.0 mol kg-l at temperatures ranging from 50 to 250 O C . Equilibrium quotients obtained from the measured potentials were combined with published values of the corresponding equilibrium constants, enthalpy, and heat capacity changes at infinite dilution and ambient temperatures, and fitted to an empirical equation containing the Pitzer form of the extended Debye-Hiickel term and nine adjustable parameters.

Introduction The second dissociation constant of sulfuric acid in aqueous solutions near room temperature has been the subject of intense investigation over the past 60 years because of the importance of sulfur chemistry in industry, oceanography, and geochemisHowever, measurements at elevated temperatures are sparse and considerable discrepancies exist among the available literature Several a ~ t h o r s ' ~ . ' have ~ , ~ ~discussed * * ~ the difficulties in computing precise and accurate values of the dissociation constant of HSO,-at low temperatures (less than 100 "C). These disparities arise because of the relatively large value of this constant at low temperature, resulting in computed dissociation constants which are highly dependent on the activity coefficient models used to reduce experimental results at finite solution concentrations. Pitzer et al.28have presented the most thorough analysis of the low-temperature cell data, applying the ion-interaction model in order to extract equilibrium constants consistent with measurements in a variety of aqueous electrolyte media. However, at higher temperatures, where the degree of dissociation is much less, the large differences among the available data sets cannot be solely attributed to activity coefficient models but must reflect substantial experimental errors or inadequate data reduction. This study provides an accurate and precise set of direct measurements of the molal equilibrium quotients of the reaction

in aqueous sodium chloride solutions (the most abundant electrolyte in natural waters) over a sufficiently wide range of temperatures (SO-250 "C) and ionic strengths (0.1-5.0 mol kg-I) to allow modeling of the chemistry of natural waters in geothermal and subseafloor environments, as well as to allow extrapolation of the equilibrium quotients to infinite dilution. The activity coefficient model used in the treatment of these results is similar to that adopted by Pitzer et aI.,**and their recommended values for the equilibrium constant ( K ) for reaction 1 at low temperature are incorporated into the fit, as are heat capacity data computed from the new results for bisulfate ion reported by Hovey and Hepler.I8 Experimental Section Materials and Equipment. Stock solutions were prepared from crystalline N a 2 S 0 4(Aldrich, gold label reagent) which had been dried a t 1 I O O C under vacuum; a standardized HCI (Alfa Products, ultrapure grade) solution stored under positive argon pressure; and a standardized NaCl solution (Fisher Scientific, ACS reagent grade) which had been previously purged of COz under acidic conditions, neutralized, and stored under argon. The water *Authors to whom correspondence should be addressed.

0022-~6S4/90/2094-1978$02.50/0

used throughout these experiments was distilled and then passed through a Barnsted triple-stage deionizing unit. The 99.999% H2 gas was obtained from Matheson Corp. The titrations were carried out in a Hastalloy C pressure vessel containing a Teflon liner and concentric inner cup which served as the titration and reference compartments, respectively. The liquid junction between the two solutions was achieved with a porous Teflon frit which had been pressed into a small hole in the bottom of the inner cup. The platinum-blacked tips of platinum-sheathed thermocouples extending into each cup served as hydrogen electrodes. The titrant was delivered to the outer (titration) compartment by using a Ruska hand-operated positive displacement pump (readability 0.002 cm3), the wetted parts of which were made from Zircalloy, and the titration lines were platinum capillary tubing. The entire vessel was submerged in an oil bath for those experiments above 75 OC and in a water bath at the lower temperatures. Temperature control and accuracy ( I ) Pitzer, K. S. J . Am. Chem. SOC.1937, 59, 2365. (2) Sherrill, M. S.; Noyes, A. A. J . Am. Chem. SOC.1926, 48, 1861. (3) Hamer, J. J . Am. Chem. SOC.1934, 56, 860. (4) Shrawder. Jr., J.; Cowperthwaite, I. A. J . Am. Chem. SOC.1934, 56, 2340. (5) Davies, C. W.; Jones, H. W.; Monk, C. B. Trans. Faraday SOC.1952, 48, 92 I . (6) Kerker, M. J . Am. Chem. SOC.1957, 79, 3664. (7) Nair. V . S. K.; Nancollas, G. H. J . Chem. Soc., London 1958,4144. ( 8 ) Hamer, W. J. The Structure of Electrolyte Solutions; Hamer, W. J., Ed.; Wiley: New York, 1959; pp 236-252. (9) Dunsmore, H. S.; Nancollas, G. H. J . Phys. Chem. 1964, 68, 1579. ( I O ) Covington. A. K.; Dobson, J. V.; Wynne-Jones, W. F. K. Trans. Faraday SOC.1965, 61, 2057. ( 1 1 ) Wallace, R. M. J . Phys. Chem. 1966, 70, 3922. (12) Davis, A. R.; Adams, W. A.; McGuire, M. J. J . Chem. Phys. 1974, 60, 1751. (13) Young, T. F.; Singleterry, C. R.; Klotz, 1. M. J . Phys. Chem. 1978, 82, 67 1. (14) Lo, C.-C.; Meites, L.; Matijevic, E. Anal. Chim. Acta 1982, 139, 197. (15) Larson, J. W.; Zeeb, K. G.;Hepler, L. G.Can. J . Chem. 1982, 60. 2141. (16) Kruus. P.; Hayes, A. C.; Adams, W. A. J . Solution Chem. 1985, 14, 117.

(17) Mussini, P. R.; Longhi, P.; Mussini, T.; Rondinini, S. J . Chem. Thermodyn. 1989, 625. ( I 8) Hovey, J. K.; Hepler, L. G. J . Chem. Soc., Faraday Trans. I , in press. (19) Lietzke, M. H.; Stoughton, R. W.; Young, T. F. J . Phys. Chem. 1961, 65. 2247. (20) Ryzhenko, B. N . Geochem. Int. 1964, 8 . (21) Quist, A. S.; Marshall, W. L.; J o k y , H. R. J . Phys. Chem. 1965, 69, 2726. (22) Quist, A. S.; Marshall, W. L. J . Phys. Chem. 1966, 70, 3714. (23) Marshall, W. L.; Jones, E. V. J . Phys. Chem. 1966, 70, 4028. (24) Dawson, B. S. W.; Irish, D. E.; Toogood, G. E.J . Phys. Chem. 1986, 90, 334. (25) Matsushima, Y.; Okuwaki, A. Bull. Chem. SOC.Jpn. 1988,61, 3344. (26) Oscarson, J. L.; Izatt, R. M.; Brown, P. R.; Pawlak, Z.; Gillespie, S. E.; Christensen, J. J. J . Solution Chem. 1988, 17, 841. (27) Baes, Jr.. C . F. J . Am. Chem. SOC.1957, 79, 561 1. (28) Pitzer, K. S.; Roy, R. N.; Silver, L. F. J . Am. Chem. SOC.1977, 99, 4930.

0 1990 American Chemical Society

The Journal of Physical Chemistry, Vol. 94, No. 20, 1990 7979

Dissociation Constant of Bisulfate Ion were typically fO.l “C. Further details of this apparatus and the emf, pressure, and temperature monitoring instruments have been given in previous publication^.^^^^^ Potentiometric Measurements. In all experiments, known weights of solution were dispensed into the inner (reference) and outer (titration) compartments, the vessel was purged of air with H2,sealed, pressurized with several bars of HZ,and then the vessel was immersed in the oil or water bath. After the solutions in the vessel reached the bath temperature, several hours were required for the hydrogen atmosphere in the vessel to equilibrate with the magnetically stirred solutions and for excess oxygen to be consumed. Preliminary experiments in which a HCI NaCl solution was titrated into a N a 2 S 0 4 + N a O H NaCl solution with a reference solution containing HCI + NaCl gave reasonably stable, but irreproducible, potentials. No measurable reduction of the total sulfate in solution was detected to within f2%. Hence, it was concluded that long-term exposure of sulfate to the platinum black surface of the hydrogen electrode resulted in poisoning of the electrode and thus a mixed, irreproducible potential. Therefore, in order to minimize the time of exposure of sulfate to the hydrogen atmosphere, the cell was configured as follows (mi is the concentration of component i in mol kg-’) Hz,PtlHCl(m,),NaCl(m2)1 IHCl(ml),NaCl(m2)lPt,H2 (titration cup) (reference cup)

+

+

+

with m2 >> m,. The titrant, NaCl(m3) Na2S04(m4),with m3 approximately equal to m2 and m4 approximately equal to M I , was introduced to the titration compartment only after the cell had reached equilibrium with respect to temperature and hydrogen fugacity (a stable emf of 0 f 0.1 mV). The titrant solution compositions were predetermined so as to result in zero change in the ionic strength of the solution in the titration cell, except that due to hydrolysis. In this mode stable potentials were recorded up to 200 ‘C with slowly drifting readings at 225 and 250 “C, requiring that a drift correction be made. Measurements using this cell proved impossible at temperatures above 250 OC. Data Reduction. The potential difference between the titration and reference compartments can be expressed in terms of the following equation AE = - ( R T / F ) In (m(H+)/m(H+),) ( R T / F ) In MH+)/?W+)rl + E , j (2)

where m(H+) and m(H+), represent the molalities of hydrogen ion in the titration and reference compartments, respectively. Eli is the liquid junction potential and is computed31according to the Henderson equation from the molalities, charges, and limiting equivalent conductivities of the individual ions, the latter taken from Quist and Marshall.32 The magnitude of the liquid junction potential correction ranged from only +0.15 to -0.52 mV, which could be estimated from the Henderson equation to within ca. f The second term involving the stoichiometric activity coefficients (7’s) of hydrogen ion in each compartment is assumed to reduce to zero in the presence of a swamping electr~lyte.~’~’ The degree of proton association with the sulfate ion can be expressed conveniently in terms of ii ii = (m(HCI) - m(H+)

+ m(OH-)J/m(NazS04)

(3)

where m(HC1) and m(Na2S04) are the total computed stoichiometric molalities of acid and sulfate in the titration compartment assuming no hydrolysis, m(H+) is the actual measured concentration of hydrogen ion computed from eq 2, and m(0H-) is the molality of hydroxide ions (negligibly small in these experiments). Ideally, in the study of hydrolysis reactions with only one hydrolyzable species (in the present example the formation (29) Mesmer, R. E.: Baes. Jr., C. F.; Sweeton, F. H. J . Phys. Chem. 1970, 74, 1937.

( 3 0 ) Wesolowski, D. J.; Drummond, S. E.; Mesmer, R . E.; Ohmoto, H . Inorg. Chem. 1984, 23, 1120. (31) Baes, Jr., C . F.; Mesmer, R. E. The Hydrolysis of Cations; WileyInterscience: New York, 1976. (32) Quist, A. S.; Marshall, W. L. J . Phys. Chem. 1965, 69, 2984. (33) Henderson, P. Z . Phys. Chem. 1907, 59, 118; 1908, 63, 325.

l

,

l

I

4

-5

-4 A

Gf M -3

v

0

ri

-2

1 0

25°C

1

I(

2 3 4 molal)

5

Figure 1. Measured values of log Q for reaction 1 taken from the data in Tables I and 11 (A). The solid curves were computed from eq 6. The curves are drawn at 25-deg intervals from 25 to 250 O C , the temperatures at which the experimental data were taken (Table I). The log Q values plotted at 25 and 50 O C and zero ionic strength were computed from the equation given by Pitzer et a1.28

of H2SO4 can be ignored), a single ii value, preferably close to 0.5 for optimal sensitivity, would be sufficient to determine the hydrolysis constant. However, as bisulfate is a “moderately strong/weak acid”, especially at low temperatures, ii values are ) the cell (e.g., at 50 OC ii < limited by the initial acidity ( m lin 0.2 in most of these experiments). Consequently, the uncertainties in these values is greater and no attempt was made to obtain data below 50 “C.

Results The molal equilibrium quotient for reaction 1 is defined as Q = m(H+)m(S0,2-)/m(HS04-) = (1 - ii)m(H+)/(ii)

(4)

The compositions of the starting solutions in the titration and reference compartments and titrant pump, the amounts of titrant delivered, the measured emf s, the computed liquid junction potentials, etc. for each point in each titration are too numerous to present conveniently here but are available from the authors upon request. The computed final solution compositions in the titration compartment and the computed values of log (Q) for each titration point are listed in Table I. The values of u listed in Table 1 represent the estimated error in log (Q) computed from a statistical combination of probable errors in eqs 2 and 3 which arise from uncertainties in the starting solution compositions, volatilization of the cell solutions into the vapor space, thermal expansion of the PTFE, titrant density changes, the liquid junction potential calculation, temperature, and emf readings, etc., all of which are considered in the calculations. In this experiment the principal contributors to the total uncertainty were the inaccuracy of the emf reading (fO.l mV) and the liquid junction potential calculations (approximately f 10%). The measured emfs ranged from less than 5 to greater than 100 mV and the computed liquid junction potentials ranged from +0.15 to -0.52 mV. As shown in Table I, the largest uncertainties arise at the lowest temperatures, were ii values were approximately 0.2 or less, and at the lowest ionic strengths, where the hydrogen, sulfate, and bisulfate ions contribute significantly to the total ionic strength. Many u values less than 0.004 log units were computed at higher temperatures and ionic strengths. However, this value was chosen as a reasonable lower limit ( f l % of the value of Q) of the actual experimental uncertainty. The computed log (Q) values are plotted as a function of temperature and ionic strength in Figure 1. Because of the high

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The Journal of Physical Chemistry, Vol. 94, No. 20, I990

Dickson et al.

TABLE I:

Computed Equilibrium Quotients for Reaction 1 and Molal Solution Composition of Titration Compartment Solutions at Each Titration Point in the Emf Experiments

Q

0

f, O C

-log m(Ht)

-1.796 -I ,804 -1.801 -2.134 -2.1 55 -2. I60 -2. I63 -2.518 -2.506 -2.497 -2.488 -2.844 -2.841 -2.842 -2.842 -2.839 -2.839 -3,187 -3.188 -3.185 -3.515 -3.505 -3.489 -3.802 -3.802 -4.135 -4.1 14 -4.462 -4.432

0.025 0.017 0.014 0.012 0.008 0.006 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.005 0.004 0.004 0.005 0.004 0.004 0.004 0.005 0.004

49.99 49.99 49.99 75.10 75.08 75.08 75.10 100.04 100.00 99.95 100.01 124.97 124.98 125.07 125.10 124.94 124.97 150.03 150.00 150.10 175.05 175.14 175.12 200.00 200.00 225.00 225.00 250.00 250.00

2.746 2.770 2.792 2.761 2.793 2.824 2.85 1 2.777 2.844 2.947 3.067 2.828 3.004 3.148 3.264 3.373 3.473 3.022 3.174 3.3 12 3.148 3.365 3.534 3.378 3.845 4.152 4.297 4.030 4.47 I

1O2m(S0:-) I = 0.1 m 0.0946 0. I400 0. I833 0.0750 0.1121 0. I490 0.1832 0.0474 0.0950 0.1787 0.2940 0.0420 0.1185 0.2010 0.2834 0.3749 0.4694 0.0619 0.1083 0.1648 0.0489 0.0978 0.1 575 0.0530 0.1710 0.1689 0.2402 0.0632 0.1807

-1.801 -2.135 -2. I33 -2. I36 -2.137 -2.441 -2.442 -2.442 -2.446 -2.447 -2.731 -2.731 -2.737 -2.739 -3.026 -3.023 -3.021 -3.022 -3.284 -3.288 -3.289 -3.521 -3.528 -3.531 -3.792

0.012 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.007 0.004 0.004 0.004 0.0 I O 0.004 0.004 0.004 0.004 0.004 0.004

75.07 100.05 100.10 100.04 99.95 125.03 125.05 125.10 125.08 125.02 150.03 150.15 150.07 150.05 175.10 175.10 175.07 175.02 200.08 200.08 200.14 225.02 225.06 225.06 250.12

2.493 2.381 2.457 2.526 2.588 2.408 2.516 2.6 I6 2.701 2.778 2.475 2.583 2.751 2.893 2.586 2.845 3.056 3.215 2.695 3.014 3.258 3.198 3.491 3.678 3.784

-1.389 -1.386 -1.381 -1.382 -1.376 -1.373 -1.676 - 1.677 -1.677 -1.675 -1.978 -1.977 -I ,976 - I ,974 -1.973 -1.974 -1.975

0.017 0.012 0.010 0.016 0.013 0.013 0.007 0.006 0.007 0.008 0.004 0.004 0.004 0.004 0.004 0.004 0.004

50.02 50.02 50.02 50.03 50.03 50.03 74.98 74.98 74.99 74.99 100.00 100.00 100.00 100.00 100.00 100.00 100.00

2.09 I 2.131 2.166 2.044 2.086 2. I24 2.074 2.142 2.203 2.260 2.117 2.223 2.316 2.405 2. I22 2.234 2.331

1%

I02m(HS04-)

m(Nat)

m(CI-)

0.0106 0.0151 0.0187 0.0177 0.0258 0.0323 0.0375 0.026 1 0.0436 0.0634 0.0775 0.0437 0.08 I5 0.0994 0.1071 0.1096 0.1089 0.0905 0.1 1 I8 0.1232 0.1139 0.1348 0.1419 0.1407 0.1548 0.1623 0.1575 0.1711 0.1654

0.097 1 0.0966 0.0962 0.0972 0.0968 0.0964 0.0960 0.0974 0.0968 0.0959 0.0947 0.0974 0.0963 0.0954 0.0946 0.0937 0.0928 0.0968 0.0962 0.0956 0.0969 0.0963 0.0956 0.0970 0.0957 0.0960 0.0954 0.0975 0.0963

0.0969 0.0954 0.0939 0.0972 0.0959 0.0946 0.0934 0.0978 0.0959 0.0928 0.0889 0.0976 0.0941 0.091 1 0.0884 0.0855 0.0827 0.0956 0.0936 0.09 I 5 0.0955 0.0934 0.09 14 0.0949 0.0908 0.09 1 1 0.0890 0.0947 0.091 1

I = 0.5 m 0.5543 0.1176 0.2432 0.3694 0.4962 0.0854 0.1909 0.3098 0.4237 0.5449 0.0802 0.1458 0.2781 0.4277 0.0779 0.205 1 0.3718 0.5477 0.0693 0.1879 0.3499 0.1833 0.3644 0.5476 0.401 2

0.1 126 0.0668 0.1155 0.1506 0.1755 0.0922 0.161 1 0.2074 0.2359 0.2542 0. I443 0.2050 0.2692 0.3004 0.2145 0.3087 0.3432 0.35 16 0.2687 0.3530 0.3758 0.3858 0.3972 0.3904 0.4086

0.4895 0.4940 0.4924 0.4909 0.4896 0.4943 0.4927 0.49 1 1 0.4898 0.4885 0.4943 0.493 1 0.49 12 0.4895 0.4952 0.4930 0.4910 0.4892 0.4959 0.4938 0.4919 0.4957 0.4935 0.4915 0.4935

0.4805 0.495 I 0.4898 0.4849 0.4805 0.4956 0.4903 0.4853 0.4810 0.4767 0.4946 0.4908 0.4847 0.4792 0.494 1 0.4873 0.48 I O 0.4753 0.4939 0.4875 0.48 17 0.4888 0.4826 0.4768 0.481 5

I = 1.0m 0.5965 0.8723 1.1341 0.2843 0.5710 0.8404 0.29 18 0.5838 0.8745 1.1659 0.2641 0.5552 0.8584 1.1937 0.2789 0 5916 0.9 137

0.1184 0.1569 0.1859 0.0619 0.1 114 0.1492 0.1166 0.2001 0.2601 0.3032 0.1916 0.3149 0.3920 0.4428 0.1978 0.3253 0.4025

0.9835 0.9807 0.9781 0.9849 0.9820 0.9793 0.9845 0.98 I2 0.9781 0.9752 0.9861 0.9824 0.9790 0.9755 0.9860 0.9820 0.9784

0.9785 0.9691 0.9604 0.9877 0.9776 0.9685 0.9860 0.9748 0.9643 0.9543 0.9866 0.9741 0.9627 0.951 1 0.9860 0.9728 0.9608

The Journal of Physical Chemistry, Vol. 94, No. 20, 1990 7981

Dissociation Constant of Bisulfate Ion TABLE I (Continued) log Q -1.975 -1.974 -1.977 -1.977 -1.976 -2.264 -2.266 -2.264 -2.264 -2.531 -2.534 -2.533 -2.541 -2.540 -2.535 -2.780 -2.789 -2.785 -2.794 -3.030 -3.038 -3.035 -3.241 -3.439

U

I , OC

-log m(Ht)

102m(S042-)

0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004

100.00 100.00 100.00 100.00 100.00 124.96 124.95 124.95 124.92 149.93 149.86 149.89 150.09 150.00 150.03 175.00 174.90 174.90 174.90 200.00 200.00 200.00 225.00 250.00

2.416 2.133 2.222 2.318 2.401 2.142 2.276 2.395 2.501 2.51 1 2.707 2.831 2.472 2.666 2.809 2.606 2.669 2.904 3.048 3.253 3.016 3.219 3.445 3.290

1.2348 0.2550 0.5526 0.8636 1.1754 0.1791 0.4005 0.6544 0.9287 0.5556 0.9599 1.3081 0.4786 0.8520 1.2358 0.4342 0.5090 0.9399 1.2825 1.2520 0.7260 1.1538 1.2361 0.5828

- I .228 -1.225 -1.506 -1.505 -1.503 -1.500 -1.768 -1.767 - I ,765 - I ,763 -2.027 -2.024 -2.024 -2.022 -2.253 -2.248 -2.245 -2.45 1 -2.442 -2.253 -2.248 -2.245 -2.451 -2.442 -2.43 1 -2.630 -2.627 -2.624 -2.793 -2.793

0.022 0.021 0.012 0.007 0.005 0.004 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004

49.97 49.91 75.12 75.13 75.12 75.08 99.95 99.97 99.90 99.94 125.05 125.05 125.04 125.10 150.02 150.07 150.09 174.89 174.97 150.02 150.07 150.09 174.89 174.97 174.97 200.05 199.98 200.05 224.93 224.94

2.112 2.143 2.055 2.105 2.150 2.193 2.074 2.142 2.204 2.260 2.101 2.193 2.277 2.352 2.119 2.337 2.438 2.436 2.591 2.1 19 2.337 2.438 2.436 2.591 2.71 1 2.637 2.789 2.909 2.795 2.956

-1.258 -1.263 -1.263 -1.262 -1.258 -1.253 - I ,247 -1.491 -1.492 -1.492 -I ,487 -1.486 -1.742 -1.741 -1.742 -1.739 -1.739 -I .949 -1.944

0.038 0.020 0.013 0.010 0.009 0.007 0.007 0.009 0.005 0.005 0.004 0.004 0.005 0.004 0.004 0.004 0.004 0.004 0.004

50.01 50.00 50.01 50.01 50.00 50.01 50.01 75.00 75.00 75.00 75.00 75.00 100.10 100.10 100.17 99.75 100.07 125.07 124.89

2.023 2.048 2.072 2.095 2.1 I7 2.138 2.158 2.076 2.149 2.149 2.208 2.266 2.088 2.173 2.246 2.316 2.381 2.215 2.305

102m(HSOL) 0.4480 0.1851 0.3140 0.3937 0.4417 0.2372 0.3914 0.4838 0.5380 0.5807 0.6452 0.6579 0.5612 0.6372 0.6574 0.648 1 0.6716 0.7137 0.7143 0.7495 0.7621 0.7553 0.771 8 0.8216

m(Na+) 0.975 1 0.9863 0.9825 0.9789 0.9757 0.9850 0.98 17 0.9786 0.9756 0.9822 0.9777 0.9743 0.9828 0.9786 0.9748 0.9825 0.98 17 0.9772 0.9739 0.9760 0.9821 0.9778 0.9788 0.9889

m(CI-) 0.9497 0.9871 0.9743 0.9625 0.95 17 0.9863 0.9750 0.9647 0.9548 0.9683 0.9540 0.943 1 0.97 IO 0.9574 0.945 1 0.9698 0.9670 0.9525 0.9420 0.9440 0.9609 0.9478 0.9467 0.9695

I = 3.0 m 0.9242 1.1998 0.2861 0.5670 0.8393 1.1045 0.2425 0.4950 0.7484 1.0002 0.2023 0.4246 0.6598 0.9022 0. I497 0.5426 0.7894 0.5123 0.8460 0.1497 0.5426 0.7894 0.5123 0.8460 1.1899 0.6551 0.9833 1.3149 0.7093 1.0476

0.1207 0.1449 0.0808 0.1424 0.1889 0.2242 0.1198 0.2084 0.2722 0.3183 0.1703 0.2875 0.3684 0.4222 0.2041 0.4418 0.5061 0.5308 0.6003 0.2041 0.4418 0.5061 0.5308 0.6003 0.6252 0.6447 0.6764 0.68 15 0.7066 0.7205

2.9807 2.9780 2.9873 2.9841 2.9812 2.9784 2.9881 2.9849 2.9819 2.9792 2.9896 2.9863 2.9832 2.9803 2.991 7 2.9853 2.9821 2.9902 2.9856 2.9917 2.9853 2.9821 2.9902 2.9856 2.9815 2.9977 2.9929 2.9885 3.0070 3.0016

2.9687 2.9597 2.9896 2.9792 2.9696 2.9605 2.9905 2.9801 2.9705 2.9615 2.9917 2.9813 2.9716 2.9625 2.9943 2.9746 2.9649 2.9783 2.9653 2.9943 2.9746 2.9649 2.9783 2.9653 2.9534 2.9804 2.968 1 2.9567 2.9874 2.9745

I = 5.0 m 0.1892 0.3787 0.5703 0.7544 0.9365 1.1158 1.2940 0.41 83 0.8467 0.8467 1.2280 1.6130 0.3109 0.6514 0.9705 1.3164 1.6586 0.5633 0.8737

0.0325 0.0622 0.0885 0.1 108 0.1294 0.1455 0.1589 0.1088 0.1866 0.1866 0.2334 0.2679 0.1403 0.2408 0.3043 0.3491 0.3780 0.3052 0.3802

4.9888 4.9869 4.9849 4.9830 4.98 12 4.9794 4.9777 4.9875 4.9828 4.9828 4.9789 4.9750 4.9884 4.9843 4.9807 4.9781 4.9736 4.9887 4.9848

4.9942 4.9876 4.981 1 4.9748 4.9688 4.9629 4.9572 4.9864 4.971 1 4.97 1 1 4.9582 4.9455 4.9889 4.9755 4.9639 4.953 1 4.9408 4.9805 4.9685

7982

The Journal of Physical Chemistry, Vol. 94, No. 20, 1990

Dickson et al.

TABLE I (Continued) log Q -1.947 - I ,945 -2.145 -2.141 -2. I39 -2. I38 -2.1 37 -2.3 I O -2.305 -2.305 -2.305 -2.304 -2.438 -2.434 -2.554 -2.565 -2.557 -2.553

U

1, o c

0.005 0.006 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004

124.88 124.99 150.12 149.94 150.05 149.98 150.01 174.98 175.02 175.10 175.08 175.08 200. I O 200.00 225.00 225. I O 225.10 225.10

-log m(H+) 2.384 2.468 2. I39 2.267 2.380 2.475 2.568 2.1 17 2.276 2.417 2.536 2.648 2.231 2.425 2.528 2.492 2.666 2.801

1O2m(S0:-)

1.1670 1.5312 0.2292 0.5008 0.7974 1.0985 1.4375 0.1341 0.3716 0.6523 0.9525 1.2972 0.2261 0.5165 0.5640 0.493 1 0.8302 1.1797

102m(HSOL)

m(Na+)

m(CI-)

0.4270 0.4592 0.2323 0.3744 0.4586 0.5054 0.5321 0.2088 0.3976 0.5045 0.5597 0.5877 0.3637 0.5275 0.5991 0.5824 0.6462 0.6656

4.98 14 4.9774 4.9980 4.9935 4.9893 4.9855 4.98 15 5.0089 5.0036 4.9987 4.9942 4.9895 5.0284 5.0212 5.0400 5.0398 5.03 18 5.0244

4.9579 4.9456 4.9984 4.9851 4.9730 4.96 I8 4.9501 5.01 17 4.9975 4.9845 4.9725 4.9599 5.0261 5.0093 5.0257 5.0273 5.0109 4.9957

TABLE 11: Thermodynamic Properties of Reaction 1 Taken from the Literature, and Determined from Eq 6 of This Study (Shown in Braces)

so

"C

log K

kJ mol-'

J K-I mol-'

ACP0, J K-I mol-I

25 iS

(-I ,964 f 0.021 1 -1.836 f O.OIOb (-1.834 f 0.025)" -1.979 f O.OIOb -2.112 f 0.010b 1-2.101 f 0.015)" -2.297 f O.OIOb (-2.316 f 0.0121" - I ,987

1-22.8 f 0.8)

1-1 14 f 2)

1-275 f 17)

-23.5

-1 I 7

AHO,

1,

25 35 50 25 25 25 25 25 25 25 25 25 IO

- I .99 f 0.02 -1.98 f 0.02

3

ref this study' 28

28 28 28 19

-22.6 f 1.0*.' -21.71

- I I4

-300

-1 1 1

15

13 17

-2 1.8 f 1 ,Ob.' -23.8' -23.4' -20.5'

1

-280 f 5b -335 f 25' 1-305 f 23)" -262 f 5b -234 f 15' 1-250 f 13)" -224 f 15' (-231 f 11)"

25 40 55

37 38 39 18d 36 36 36 36

'Errors represent 30. "These quantities were used in the fit of eq 6. CTheseenthalpy and heat capacity changes were measured directly by calorimetry. dRecalculationof the earlier result reported by Larson et aI.,l5 as discussed by Hovey and Helper.I8 precision of these results, there is extensive overlap among the plotted points at any individual temperature and ionic strength combination, as is readily apparent from a comparison of Figure 1 and Table 1.

Discussion The ultimate goal of this research is to apply the Pitzer ion interaction model to a variety of emf, isopiestic, and calorimetric experiments recently r e p ~ r t e d , ~ or ~ . in ~ ~progress , ) ~ in our laboratories and elsewhere, in order to describe quantitatively the thermodynamic properties of solutions in the system Na+-H+HS04--S042--CI- over a wide range of temperatures and ionic strengths. The equilibrium constant of reaction 1 at infinite dilution over the temperature range of interest must be known precisely in order to carry out this modeling effort, as pure electrolyte parameters for bisulfate ion cannot be obtained directly because of appreciable dissociation of this ion. Pitzer et aL2*have reviewed the available potentiometric results at low temperature which give a quantitative measure of the formation constants of reaction 1. Because the intent is to generate a model consistent with these low-temperature cell data, the current results have been (34) Holmes, H. F , Mesmer, R E. J . Chem Thermodyn 1986, 18, 263 ( 3 5 ) Rard J A J Chem Thermodyn 1989, 21. 539

fitted to a temperature and ionic strength function which incorporates ionic strength terms similar to those used in the earlier treatment.28 Values for the dissociation constant of reaction 1 at infinite dilution computed from an equation given in the earlier study28were incorporated into the fit, as were heats of reaction at 25 "C reported by Pitzer' and Larson et aI.I5 Also included in the fit were heat capacity changes for reaction 1 in the 10-55 OC range at infinite dilution computed by H ~ v e from y ~ ~the results of his measurements of the heat capacity of bisulfate ion, together with other pertinent data referenced in Hovey and Hepler.'* A revised value for the standard-state heat capacity change for reaction 1 of Larson et al.I5 referred to by Hovey and HeplerI8 was also included. These additional quantities incorporated into the least-squares analysis, together with their assigned uncertainties, are listed in Table 11. The molal equilibrium quotient for reaction 1 is expressed as log Q = log K

-

log Ir(H+) T(SO~~-)/T(HSO~-)I(5)

(36) Hovey, J. K. Private communication, 1990. (37) Austin, J. M.; Mair, A. D. J . Phys. Chem. 1962, 66, 519. (38) Christensen, J. J.; Izatt, R. M.; Hansen, L. D.; Partridge, J. A. J . Phys. Chem. 1966, 70, 2003. (39) Izatt. R. M.; Eatough, E. W.; Christensen, J. J.; Bartholomew, C. H. J . Chem. SOC.( A ) 1969. 45.

The Journal of Physical Chemistry, Vol. 94, No. 20, 1990 7983

Dissociation Constant of Bisulfate Ion TABLE 111: Coefficients of the Smoothing Function of log Q,Eq 6 PI = 562.7097 P2 -13273.75 P3 = -102.5154 P5 = -1.117033 X IO-" Ps = -57.07583 P4 = 0.2477538 P7 = -1.144759 X IO-' Ps = 46.72816 Pg = 2.499849

where K is the equilibrium activity ratio and the 7 ' s are stoichiometric molal activity coefficients (which approach unity at the limit of infinite dilution). A variety of functions were tested by using the ORGLS general least-squares fitting programsa The following equation provided a fit to the data in Tables I and I1 which is generally within the assigned error log Q = pI

+ p 2 / T + p 3 In T + p 4 T + p 5 p- 4f4/ln

10

V

3

ri

m

a.

A

-0.02

w

1

-0.04'

'

'

50

'

'

'

100

'

'

'

150

200

'

250

T("C)

+

0.04,

p6(1/ r ) + F(I)@7T + pS/ r ) + pS(p/ r ) (6)

,

,

,

,

I

I

b.

3

I

where T i s the absolute temperature, I is the stoichiometric molal ionic strength ( I = { 1/2)zj[mizi2], i = H+, Na+, HS04-, S042-, Cl-), and

f4 = -A&x/(l + 1 . 2 ~ +) (2/1.2) F(r) = 1 - e - y 1

In (1

+ 1.2~))

+ 2x)

determined from least-squares minimization, are listed in Table 111. The first five terms in eq 6 represent log K , while the remaining terms reflect the functional form of the Pitzer ion-interaction model for eq 5.28 The 4fl term is the extended Debye-HUckel limiting slope for reaction l used in the Pitzer treatment.28 Values of A,, the Debye-Hiickel osmotic coefficient parameter, were computed from a least-squares polynomial fit of A, values along the liquid-vapor saturation curve for pure water (0-300 "C) computed from the model of Haar, Gallagher, and Ke1I4'

+ + +

+

3.75692 X 104t 2.55932 x 10-6t29.96273 X 10-11t3 5.98066 X 10-3e((r-270)/10) 1.39987 X 10-2/(t 20) 18.4374/(315 - t ) - 554.596/(315 - t)' + 7684.77/(315 - t ) 3 - 54091/(315 - t ) 4 154381/(315 - t)' (9) where t is the temperature in degrees Celsius ("C). This equation was provided to us by Howard F. Holmes of Oak Ridge National Laboratory. The solid curves in Figure 1 were generated from eq 6. Figure 2 is a deviation plot of the difference between the observed (Table I) and calculated (eq 6) values of log Q. Obviously, the maximum deviations occur at the lowest temperatures and ionic strengths. However, as discussed above, this is where the largest estimated errors in the observed quantities occur. The computed values (eq 6) for the quantities in Table I1 used in the fit, together with their uncertainties, are listed in Table 11. The agreement factor (AF) for this fit is 1.75, as computed from the following equation

+

- - - - -

+

(10)

where W is the squared reciprocal of the estimated error in any one observed quantity ( Yob = log Q,AH, or AC ), N is the number of data points (1 68) and N, is the number of independent variables (9). If all errors were random and were estimated accurately, AF would approach unity. The standard error of the fit represented by eq 6 is 0.009 in log Q. Values of log K computed from eq 6 at infinite dilution ( I = 0) are compared with various literature values at temperatures to 60 O C in Figure 3. They agree within experimental error with the spectrophotometric data of Young et aLi3 in the 5-55 OC range, as well as the emf data of Davies et al.5 from 0 to 60 OC. The agreement with the conductivity results summarized by Kerker6 is also within experimental error at temperatures below (40) Busing, W . R.; Levy, H. A . A General Forrran Leasl Squares Program: Oak Ridge National Laboratory, Report ORNL-TM-271. Aug 1962. (41) Haar, L.: Gallagher, J. S.: Kell, G.S.Proceedings of the 8th Symposium on Thermophysical Properties, Vol. 11, Sengers, J. V . , Ed.; American Society of Mechanical Engineers: New York, 1981: p 298.

-

A

i-

v

M

-004l

'

'

0

'

'

1 ,

'

2

3

5

4

I

I(mola1)

Figure 2. Deviation plot of the differences between log Q values for reaction 1 determined in this study [log QOh, Table I}and those computed from eq 6 (log Q,,] as a function of (a) temperature, and (b) ionic

strength.

2.51

I

1

1

1

1

1

1

1

I

1

I

1

I t

2.3

+

AF = [IzWLYobs - YcaJi21/(N - Nv)11'2

i

: A

In eqs 7 and 8, x = I l l 2 . The values of the parameters in eq 6,

A, = 0.322863

:

GV 0.02 -

(7) (8)

'

n

?c: 2 . 1 -

.d

v

1

M 0

d

I

1.9-

0

20

60

Figure 3. Comparison of -log K values ( I = 0) for reaction 1 computed from eq 6 (solid curve) with the corresponding values computed from the equation given by Pitzer et a1.28(dashed curve). These curves are compared with the reported -log Kvalues of Young et aLI3 (A);Kerker6 (a), and Davies et aL5 (V).

50 OC. The difference between values computed from eq 6 and those computed from the equation given by Pitzer et becomes unacceptably large at temperatures near 0 and 60 OC as seen in Figure 3. However, the magnitude of ACpo for the dissociation reaction (Table 11) makes a simple linear log K versus 1 / T relationship28inadequate at the extremes of this temperature range. In general, eq 6 appears to represent most reported literature values of log K within 0.02-0.03 log units at low temperature. As discussed above, the strong dissociation of bisulfate makes log K inherently uncertain at low temperatures. Covington et reviewed the 25 OC emf data on reaction 1 available at that time. All of the studies they referred to employed a simple extended Debye-Huckel equation

7984 The Journal of Physical Chemistry, Vol. 94, No. 20, 1990

Dickson et al.

-0

190 08

10

12

14

1.6

18

b Figure 4. Values of -log K at 25 "C and I = 0, computed by Covington

et a1.I0using several values of the Debye-Huckel ion size parameter ( b ) from the data of Hamer' ( 0 ) ;Davies et (B); Nair and Nancollas' (A);and their own measurements'o (V).Also shown are two alternative values for -log K given by Pitzer et aI2*( 0 ) ,and the value computed from eq 6 of this study (0)

0

100 200 300

400

T("C) to extrapolate potentiometric measurements at low ionic strengths to infinite dilution. Covington et al.IOdemonstrated that simply varying the value of b in eq 1 I , referred to as the "ion size parameter", resulted in a variation in the computed values of log K of up to 0.04 log units. This problem is illustrated in Figure 4, which is a plot based on their calculations. Aside from this model-dependent variation in log K, Figure 4 also illustrates the rather large absolute variation in log K from one study to the next, also on the order of approximately 0.04 log units. Pitzer et a1.28 attempted to reduce these discrepancies by treating all of the available high-quality cell data using the ion-interaction model with an internally consistent set of interaction parameters in order to minimize specific ion interactions in computing log K values from cells involving different electrolytes. The 25 "C value of log K favored by Pitzer et aLZ8is plotted in Figure 4 at a b value of I . 2 (the value used in eq 7). Also plotted is the log K value computed from eq 6, which is within 0.016 log units of Pitzer's value. Pitzer et a1.28 presented an alternate set of log K and interaction parameters which also provided a good fit to much of the available cell and isopiestic data. However, the alternate value of log K at 25 "C of -1.92 (also plotted in Figure 4), while agreeing with some cell data as discussed by Pitzer et a1.,28does not appear to agree with most other data sets, including the results of this study. The discussion presented here is intended simply to demonstrate the extreme difficulty of assigning a highly accurate value for log K at low temperature, despite the fact that an extensive body of very precise measurements exists. At elevated temperatures the results of this study and those of Matsushima and OkuwakiZ5are the only direct measurements of reaction 1 using a potentiometric technique. The latter study was done in 1.0 m KCI solutions in a concentration cell with hydrogen electrodes, similar to the equipment used in this study. However, the authors did not describe in sufficient detail their extrapolation to infinite dilution or provide sufficient documentation in order to make a reasonable comparison with the results of this study. Thus, their results will not be discussed further in this article. Values of log K computed from eq 6 are compared in Figure 5 with results from a variety of high-temperature experiments, including the solubility of silver sulfate19 and calcium sulfate,23conductivity of dilute H 2 S 0 4solutions,20and heats of mixing of H2SO4 with Na2S04.26The latter authors had to select a value of log K at 150 "C (-3.56) and choose an activity coefficient model (they used y,(NaCI) as a substitute for all molal activity coefficients) in order to extract log K values from their mixing enthalpy measurements. Despite the rather severe limitations of this model, their results agree very well with the values computed from eq 6, even in the extrapolation of our results beyond 250 "C. The results of this study agree within experimental error

Figure 5. Comparison of -log K values ( I = 0) for reaction 1 computed from eq 6 (solid curve, dashed where extrapolated beyond 250 "C) with the data of Marshall and Jones2)( 0 ) ;Lietzke et aI.l9 (v);Oscarson et a1.26(B); and Ryzhenko20 (e).

with the conductivity data of RyzhenkoZoand the Ag2S04solubility data of Lietzke et aI.I9 At elevated temperatures, the log K values computed from eq 6 deviate substantially and systematically from the corresponding values reported by Marshall and Jones,23which were computed from an analysis of their measurements of the solubility of CaS04 in H2S04(aq). However, these authors did not consider ion-pair formation between the doubly charged Ca2+ and S042-ions in their experimental solutions. If such an interaction occurred to any significant extent in their experiments, an erroneously large computed value of log K would have resulted. The divergence between the log K values of this study and those of Marshall and JonesZo increases with increasing temperature, which is also consistent with the formation of CaS040(aq) in their solubility studies. Smoothed values of log Q computed from eq 6 and the thermodynamic parameters calculated from differentiation of this equation are given as a function of temperature and ionic strength in Table IV. In order to perform the necessary differentiations at constant pressure, the AVof reaction 1 was assumed equal to that of the dissociation of H 2 0 as given by Busey and M e ~ m e r . ~ ~ The AVvalue for water dissociation (-23 f 2 cm3 mol-') at 25 "C and infinite dilution reported by these authors is very similar to values for reaction 1 at the same conditions reported by Larson et aI.l5 (-21 cm3 mol-'), Hovey and HeplerI8 (-22.5 em3 mol-'), and Rohwer et aL4) (-20 f 1 cm3 mol-'), providing partial justification for this assumption. This is equivalent to assuming that the volume change is zero for the reaction HS04-

+ OH-

;t

SO,2- + H 2 0

a reasonable assumption, considering that only negative ions are involved in reaction 12, and the charge change is small (Azz = 2), thus minimizing electrostriction effects. In any case, even if this assumption were very poor, the resulting errors in the computed values of AH and AC, would be negligibly small in the pressure range of this study (the liquid-vapor saturation curve of the solutions studied). The thermodynamic properties of reaction 1 at 25 "C and infinite dilution are compared with a number of literature values (42) Busey, R. H.; Mesmer, R. E. J . Chem. Eng. Dora 1978, 23, 175. (43) Rohwer, F. C. H.; Brink, J . A.; Cruywagen, J. J. J . South Africon Chem. Inst. 1975, 28, I .

The Journal of Physical Chemistry, Vol. 94, No. 20, I990 7985

Dissociation Constant of Bisulfate Ion TABLE I V Calculated Thermodynamic Quantities for Reaction 1 in Aqueous NaCl Media along tbe Lquid-Vapor Saturation Curve Computed from Eq 6 (All Errors Represent f3u)

0.009 0.008 0.007 0.007 0.007 f 0.008 f 0.009 f 0.012

AH, a, kJ mol-' J K-'mol-' I = 0.0 m -87.6 f 3.7 -15.2 f 1.1 -22.7 f 0.8 -113.9 f 2.3 -29.1 f 0.6 -134.5 f 1.6 -34.7 f 0.4 -151.2 f 1.1 -40.0 f 0.3 -165.9 f 0.8 -45.4 f 0.3 -179.9 f 0.9 -51.3 f 0.4 -194.2 f 1.0 -58.2 f 0.4 -209.8 f 1.0 -66.4 f 0.4 -227.7 f 1.0 -76.6 f 0.9 -248.7 f 1.8 -89.6 f 1.9 -273.7 f 3.7

-1.198 -1.487 -1.817 -2.161 -2.504 -2.840 -3.167 -3.488 -3.804 -4.118 -4.432

f 0.030

I = 0.1 m -14.5 f 1.1 -76.1 f 3.7

-0.900 -1.178 -1.493 -1.817 -2.135 -2.442 -2.735 -3.015 -3.282 -3.537 -3.778

f 0.030 f 0.017

-0,788 -1.055 -1.358 -1.669 -1.972 -2.261 -2.533 -2.788 -3.027 -3.248 -3.447

f 0.031 f 0.018 f 0.010

-0.737 -0.971 -1.238 -1.511 -1.775 -2.020 -2.244 -2.446 -2.624 -2.775 -2.892

f f f f f

-0.806 -1.010 -1.250 -1.495 -1.730 -1.946 -2.140 -2.309 -2.450 -2.560 -2.629

1, O C

0

25 50 75 100 125 150 175 200 225 250 0 25 50 75 100

125 150 175 200 225 250 0

25 50 75 100 125 150

175 200 225 250 0

25 50 75

IO0 125 150 175 200 225 250 0 25 50 75 100

125 150

175 200 225 250 0 25 50

75 100

125 I50 175 200 225 250

1%

-1.659 -1.964 -2.316 -2.686 -3.061 -3.436 -3.809 -4.182 -4.561 -4.951 -5.355

Q f 0.030

f 0.018 f 0.012

f f f f f

f 0.017 f 0.010

f 0.007 f 0.006 f 0.005 f 0.005 f 0.006 f 0.006 f 0.007 f 0.010

f 0.009

f 0.005 f 0.004

f 0.003 f 0.003 f 0.004 f 0.004

f 0.005 f 0.009

-21.5 -27.2 -32.0 -36.3 -40.3 -44.6 -49.2 -54.6 -60.9 -68.0 -14.0 -20.6 -25.8 -30.0 -33.4 -36.5 -39.4 -42.3 -45.4 -48.3 -50.7

0.009

-13.5 -19.9 -24.8 -28.7 -31.7 -34.1 -36.3 -38.2 -40.0 -41.1 -40.8

0.032 0.019 0.011 0.007 0.006 f 0.005 f 0.005 f 0.005 f 0.005 f 0.006 f 0.01 I

-11.6 -17.5 -21.9 -25.1 -27.2 -28.6 -29.3 -29.5 -28.7 -26.3 -20.8

f 0.032 f 0.019 0.01 1

-9.9 -15.5 -19.7 -22.5 -24.2 -25.0 -25.0 -24.1 -22.0 -17.7 -9.5

f 0.005 f 0.004 f 0.003

f 0.003 f 0.004 f 0.004 f 0.005 f

* f

0.006

f 0.005 f 0.005 f 0.004 f 0.005 f 0.005 f 0.006

f 0.012

f 0.8 f

0.6

f 0.4 f 0.3

0.3 f 0.4 f 0.4 f 0.4 f 0.9 f 1.9 f

I = 0.5 f 1.1 f 0.8 f 0.6 f 0.4 f 0.3 f 0.2 f 0.3 f 0.3 f 0.4 f 0.9 f 1.9

f 0.6 f 0.4 f 0.3 f

0.2

f 0.3 f 0.3

0.4 0.9 f 1.9 f f

28.3 f 17.3

f 28.3

-288.0 -234.5 f 1.6 -185.6 f 1.1 -149.8 f 0.7 -127.6 f 0.6 -117.1 f 0.7 -116.2 f 0.7 -121.3 f 0.8 -125.5 f 1.8 -118.7 f 3.8 -84.5

f 28.3 f 17.3 f 11.1

f 11.1 f 10.0 f

9.5

f 8.0 f 5.6 f

9.0

f 19.2 f 33.4 f

51.1

f 17.3 f 11.1

f 9.7 f 9.5 f

7.9

f 5.6 f 9.1

f 19.2 f 33.4 f 51.4

m -68.5 -91.6 -108.5 -120.9 -130.5 -138.4 -145.4 -152.1 -158.7 -164.8 -169.3

f 3.7 f 2.3

-86.9 -102.8 -114.3 -122.6 -129.0 -134.2 -138.7 -142.4 -144.7 -143.9

2.3 f 1.7 f 1.1 f 0.6 f 0.5 f 0.6 f 0.6 f 0.8 f 1.9 f 3.8 f

I = 5.0 m f 1.2 f 0.8 f 0.6 f 0.4 f 0.3 f 0.2 f 0.3 f 0.3 f 0.4

f 9.6 f 9.4 f 7.9

f 5.6 f

9.1

f 19.3 f 33.5

f 51.2

-278.4 f 28.3 -225.0 f 17.2 -173.5 f 11.0 -134.1 f 16.2 -107.4 f 9.4 -91.1 f 7.8 -82.4 f 10.1 -76.1 f 9.2 -63.0 f 19.4 -28.5 f 33.6 53.0 f 51.3 -259.8 -206.8 -150.1 -104.1 -68.9 -41.8 -18.3 9.4

f 28.4 f

17.2

f 11.0 f

9.5

f 9.3 f 7.8

f 5.6 f 9.3

5 5 . 5 f 19.5 142.9 f 33.7 316.5 f 51.4

-51.5 f 3.7 -71.4 f 2.4 -84.8 f 1.7 -93.2 f 1.1 -97.9 f 0.7 -99.9 f 0.6 -99.9 f 0.7

-249.6 f 28.4 -196.6 f 17.2 -137.2 f 11.0 -87.8 f 9.5 -48.1 f 9.3 -15.4 f 7.8 16.0 f 5.6 -98.0 f 0.7 5 5 . 1 f 9.3 -93.4 f 1.0 118.7 f 19.5 -84.7 f 2.0 234.7 f 33.7 -68.6 f 4.0 459.0 f 51.4

in Table 11. As can be seen, the results of the present study agree extremely well with the available literature data. A particularly severe test of eq 6 is a comparison of the computed values of ACPo

-200

t

I ?c

.+

-305.5 -252.0 -207.8 -178.2 -164.0 -163.7 -176.7 -201.6 -235.8 -276.6 -323.2

I = 3.0 m f 1.2 -56.4 f 3.7 f 0.8 -77.2 f 2.4 f 0.6 -91.5 f 1.7 f 0.4 -100.9 f 1.2 f 0.3 -106.9 f 0.7 f 0.2 -110.5 f 0.5 f 0.3 -112.3 f 0.6 f 0.3 -1 12.6 f 0.7 f 0.4 -1 10.9 f 0.9 f 1.0 -106.0 f 2.0 f 2.2 -95.2 f 3.9

f 1.0 f 2.0

ACp,

J K-'mol-' f

I = 1.0m f 1.1 -64.6 f 3.7 f 0.8

i

-328.8 -274.9 -237.0 -215.2 -210.1 -222.7 -252.3 -300.8 -370.4 -466.7 -606.3

-100.6 f 2.3 -119.Of 1.6 -133.3 f 1 . 1 -145.1 f 0.8 -155.7 f 0.8 -165.9 f 0.9 -176.7 f 0.9 -188.3 f 0.9 -201.1 f 1.8 -214.9 f 3.7

ol-

-300

I

4

0

E

-400

z . t uCL -500

o

U

-600

0

50

100

150

200

250

T("C) Figure 6. Comparison of ACpo for reaction I a t infinite dilution computed from eq 6 ( * ) with the equivalent quantities for the dissociation of water42 (dashed curve) and H2P04-4s (heavy solid curve).

for reaction 1 at infinite dilution with other acid dissociation equilibria, as is shown in Figure 6. Mesmer et al.44have demonstrated that the heat capacity changes for most reactions of this type are remarkably similar and the excellent agreement between the current results and the ACis for H 2 0 and H2P04-dissociation42.45offers further support that eq 6 is a good representation of the dissociation constant of bisulfate in aqueous solutions over the temperature range investigated.

Conclusions The equilibrium constants for the dissociation of bisulfate in aqueous solution obtained in this study are shown to be in quantitative agreement with the extensive literature data available for this reaction at ambient temperatures and pressures. Our results tend to confirm the less extensive high-temperature values obtained from measurements of the conductivity of dilute H2S04(aq),20the solubility of Ag2S04in H2SO4(aq),I9and enthalpies of mixing of Na2S04(aq)with H2S04(aq).z6Furthermore, the log K values computed from eq 6 at elevated temperatures are in excellent agreement with corresponding values calculated by Hovey and Hepler'* from their volume and heat capacity results at temperatures at or below 55 OC, using the Helgeson-Kirkham-Flowers The results of this study provide an accurate model for the dissociation of bisulfate ion both at infinite dilution and in aqueous sodium chloride solutions to 5.0 mol kg-' at temperatures to 250 OC, encompassing the range of temperatures and salinities of natural waters in most shallow crustal conditions. These results can now be coupled with isopiestic, calorimetric, and solubility studies in order to develop a reliable and internally consistent model for the speciation and activity/ composition relationships in the system Na+ + H+ HS04+ CI- in aqueous solutions over a wide range of temperatures and salinities.

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Acknowledgment. We thank Howard F. Holmes for many helpful discussions during the analysis of our experimental results. Jamey K. Hovey was very helpful in sharing with us his heat capacity and volume measurements of bisulfate solutions, as well as heat capacities of dissociation of bisulfate ion, prior to their publication. Financial support for this research was provided by the U.S. Department of Energy, Geothermal Technology Division, Office of Renewable Energy, and the Division of Mathematical and Geosciences, Office of Basic Energy Sciences, under contract DE-AC05-840R21400 with Martin Marietta Energy Systems, Inc. (44) Mesmer, R. E.; Marshall, W. L.; Palmer, D. A.; Simonson, J. M.; Holmes, H . F. J . Solulion Chem. 1988, 17, 699. (45) Mesmer, R. E.; Baes, Jr., C. F. J . Solution Chem. 1974, 3, 307. (46) Helgeson, H. C.; Kirkham, D. H.; Flowers, G. C. Am. J . Sci. 1981, 281, 1249.