Experimental procedures used in this study are the same as those developed by Sakai and Dickson (1978). 0.005 M Na(2)S(2)O(3) solutions were heated to 400℃ under 1000 bar water pressure in a gold bag of Dickson gold-bag equipment (Fig. 1). At an elevated temperature Na(2)S(2)O(3) quickly and completely decomposed into 1:1 mixture of SO(4)(2-) and H(2)S (eq. (1)) and subsequent isotope exchange (eq. (2)) was monitored by consecutively withdrawing aliquots of solution for chemical and isotopic analyses at desired time intervals. For the preparation of SO(2) for isotope analyses, 2 to 5 mg BaSO(4) was thoroughly mixed with silica glass powder of 10 times the BaSO(4) in weight and heated to 1400℃ or so in sealed, evacuated silica glass tubings (see Fig. 2 and equation (4)). The technique is a modification of Holt and Engelkemeir (1971). The (18)O/(16)O ratios of SO(2) thus formed stayed constant by exchange with silica glass powder (Fig. 3). Numerical data of the three runs performed in this study are summarized in Tables 1 to 3. In runs 2 and 3, a small aliquot of (34)S- enriched H(2)SO(4) was added into the starting solution and thus equilibrium was approached from above the quilibrium value (see Fig. 4). When isotope exchange occurs between two molecules, X and Y, the reaction rate, r, is related to the extent of exchange, F, at given time, t, by equation (17), where X and Y indicate concentrations of given species, α(e), α(o) and α denote the fractionation factor at equilibrium, at time t=0 and at an arbitrary time t, and F = (α - α(o))/(α(e) - α(0)) or the extent of isotope exchange. Assuming the exchange rate is of the first order with respect to both X and Y and to the β'th power of hydrogen ion activity, a(H)(+), eq. (17) reduces to eq. (19), where k(1) denotes the rate constant. If X, Y and pH of solution stayed constant during the run, the half-time, t(1/2), of the exchange reaction can be obtained graphically as shown in Fig. 5. The t(1/2) for runs 1, 2, and 3 are determined to be 5.8, 5.5 and 6.1 hrs,
respectively. Introducing F=0.5 and t=t(1/2) into eq. (19), we obtain eq. (20) which is graphically shown in Fig. 6 using the data by the present work and those by Sakai and Dickson(1978). The numerical values of log k(1) + 0.16 may be obtained by extrapolating the lines to pH=0 and, from these values, the rate constant, k(1) , may be calculated for temperatures of 300° and 400℃. From these two values of k(1) and from the Arrhenius plot, the activation energy of the exchange reaction was calculated to be 22 kcal/mole, a much smaller value than 55 kcal/mole obtained by Igumnov (1977). The value of β is found to be 0.29 at 300℃ and 0.075 at 400℃, although the physico-chemical nature of β is not clear to the present authors. Using these values, eq. (24), where C is a constant, is derived which would enable us to calculate the t(1/2) of any system of known ΣS and pH. However, as we do not know yet how β varies with different systems, eq. (24) is applicable only to limited systems in which temperature, total sulfur contents and pH are similar to those of the present study. Fig. 7 illustrates how t(1/2) varies with pH and total sulfur content at 300° and 400℃ and predicts t(1/2) for some solutions obtainable by hydrothermal reactions of seawater with various igneous rocks. The average equilibrium fractionation factor at 400℃ obtained by this study is 1.0153, in good accord with 1.0151 given by Igumnov et al. (1977). Theoretical fractionation factors between SO(4)(2-) and H(2)S have been calculated by Sakai (1968) , who gives too high values compared to the experimental data obtained by this and other researchers (Fig. 9). In the present study, the reduced partition function ratio (R.P.F.R.) of SO(4)(2-) was recalculated using two sets of the vibrational frequencies of SO(4)(2-) (shown in Table 5) and the valence force fields of Heath and Linnett (1947), which reproduces the observed frequencies of SO(4)(2-) better than Urey-Bradley force field used by Sakai (1968). The results of new calculation are shown in Table 6. This table also includes the R.P.F.R. of H(2)S which was calculated by Thode et al. (1971). Using these new R.P.F.R. of SO(4)(2-) and H(2)S, the fractionation factors between SO(4)(2-) and H(2)S were calculated and are listed in the last column of Table 6 and plotted in Fig. 9. Fig. 9 indicates that the new calculation gives values more shifted from the experimental values than before. The major sulfate ions in our solution at 300° and 400℃ exist as NaSO(4)(-) (Sakai and Dickson, 1978; see also Table 4 of this paper) and, therefore, the measured fractionation factors are those between NaSO(4)(-) and H(2)S. The discrepancy between the theory and experiments may, at least, be partially explained by this fact, although other more important reasons, which are not known to us at the moment, may also exist.
