Читать книгу Geochemistry - William M. White - Страница 133

Since ΔG° = ΔH° – TΔS° and ΔG°_r = −RT ln K, it follows that in the standard state, the equilibrium constant is related to enthalpy and entropy change of reaction as:

(3.95)

Equation 3.95 allows us to calculate an equilibrium constant from fundamental thermodynamic data (see Example 3.8). Conversely, we can estimate values for ΔS° and ΔH° from the equilibrium constant, which is readily calculated if we know the activities of reactants and products. Equation 3.95 has the form:

where a and b are ΔH°/R and ΔS°/R, respectively. If we can assume that ΔH and ΔS are constant over some temperature range (this is likely to be the case provided the temperature interval is small), then a plot of ln K vs. 1/T will have a slope of ΔH°/R and an intercept of ΔS°/R. Thus, measurements of ln K made over a range of temperatures and plotted vs. 1/T provide estimates of ΔH° and ΔS°. Even if ΔH and ΔS are not constant, they can be estimated from the instantaneous slope and intercept of a curve of ln K plotted against 1/T. This is illustrated in Figure 3.17, which shows measurements of the solubility constant for barite (BaSO₄) plotted in this fashion (though in this case the log₁₀ rather than natural logarithm is used). From changes of ΔH and ΔS with changing temperature and knowing the heat capacity of barite, we can also estimate heat capacities of the Ba²⁺ and SO₄^2– ions, which would obviously be difficult to measure directly. We can, of course, also calculate ΔG directly from eqn. 3.86. Thus, a series of measurements of the equilibrium constant for simple systems allows us to deduce the fundamental thermodynamic data needed to predict equilibrium in more complex systems.

Figure 3.17 Log of the solubility constant of barite plotted against the inverse of temperature. The slope of a tangent to the curve is equal to −ΔH/R. The intercept of the tangent (which occurs at 1/T = 0 and is off the plot) is equal to ΔS/R. After Blount (1977).