Читать книгу Geochemistry - William M. White - Страница 130

It is often difficult to determine activities for phase components or species, and therefore it is more convenient to work with concentrations. We can define a new “constant,” the distribution coefficient, K_D, as:

(3.88)

K_D is related to the equilibrium constant K as:

(3.89)

where K_λ is simply the ratio of activity coefficients:

(3.90)

Distribution coefficients are functions of temperature and pressure, as are the equilibrium constants, though the dependence of the two may differ. The difference is that K_D values are also functions of composition.

An alternative to the distribution coefficient is the apparent equilibrium constant, which we define as:

(3.91)

(3.92)

with K_γ defined analogously to K_λ. The difference between the apparent equilibrium constant and the distribution coefficient is that we have defined the former in terms of molality and the latter in terms of mole fraction. Igneous geochemists tend to use the distribution coefficient, aqueous geochemists the apparent equilibrium constant.

Another special form of the equilibrium constant is the solubility product. Consider the dissolution of NaCl in water. The equilibrium constant is:

where aq denotes the dissolved ion and s denotes solid. Because the activity of NaCl in pure sodium chloride solid is 1, this reduces to:

(3.93)

where K_sp is called the solubility product. You should note that it is generally the case in dissolution reactions such as this that we take the denominator (i.e., the activity of the solid) to be 1 (see Example 3.7).