Читать книгу Geochemistry - William M. White - Страница 104

Let's consider the behavior of a real solution in view of the two solution models we have already introduced: Raoult's law and Henry's law. Figure 3.8 illustrates the variation of chemical potential as a function of composition in a hypothetical real solution. We can identify three regions where the behavior of the chemical potential is distinct:

1 The first is where the mole fraction of component Xi is close to 1 and Raoult's law holds. In this case, the amount of solute dissolved in i is trivially small, so molecular interactions involving solute molecules do not significantly affect the thermodynamic properties of the solution, and the behavior of μi is close to that in an ideal solution:(3.26)

2 At the opposite end is the case where Xi is very small. Here interactions between component i molecules are extremely rare, and the behavior of μi is essentially controlled by interactions between i and those of the solvent. While the behavior of μi is not ideal, it is nonetheless a linear function of ln Xi. This is the region where Henry's law holds. Let's define the constant η (eta) such that for conditions where Henry's law holds:Figure 3.8 Schematic plot of the chemical potential of component i in solution as a function of ln Xi. Here μ° is the chemical potential of pure i at the pressure and temperature of the diagram. After Nordstrom and Munoz (1986).(3.38) Comparing this equation with eqn. 3.10, we see that η is merely another form of the Henry's law constant; whereas h has units of pressure, η is dimensionless. The compositional dependence of the chemical potential in the Henry's law region can be expressed as:(3.39) This equation can be rewritten as:(3.40) By definition, η is independent of composition at constant T and P and can be regarded as adding or subtracting a fixed amount to the standard state chemical potential (a fixed amount to the intercept in Figure 3.8). By independent of composition, we mean it is independent of Xi, the mole fraction of the component of interest. η will depend on the nature of the solution. For example, if Na is our component of interest, ηNa will not be the same for an electrolyte solution as for a silicate melt. We can define a new term, μ*, as:(3.41) Substituting eqn. 3.40 into 3.39 we obtain:(3.42) When plotted against ln Xi, the chemical potential of i in the range of very dilute solutions is given by a straight line with slope RT and intercept μ* (the intercept is at Xi = 1 and hence ln Xi = 0 and μi = μ*). Thus, μ* can be obtained by extrapolating the Henry's law slope to X = 1. We can think of μ* as the chemical potential in the hypothetical standard state of Henry's law behavior at X = 1.

3 The third region of the plot is that region of real solution behavior where neither Henry's law nor Raoult's law apply. In this region, μ is not a linear function of ln X. We will introduce a new parameter, activity, to deal with this region.