Читать книгу Geochemistry - William M. White - Страница 126

Consider a chemical reaction such as:

carried out under isobaric and isothermal conditions. The Gibbs free energy change of this reaction can be expressed as:

(3.81)

At equilibrium, ΔG must be zero. A general expression then is:

(3.82)

where ν_i is the stoichiometric coefficient of species i. Equilibrium in such situations need not mean that all the reactants (i.e., those phases on the left side of the equation) are consumed to leave only products. Indeed, this is generally not so. Substituting eqn. 3.46 into 3.82 we obtain:

(3.83)

or:

(3.84)

The first term is simply the standard state Gibbs free energy change, ΔG°, for the reaction. There can be only one fixed value of ΔG° for a fixed standard state pressure and temperature, and therefore of the activity products. The activity products are therefore called the equilibrium constant K, familiar from elementary chemistry:

(3.85)

Substituting eqn. 3.85 into 3.84 and rearranging, we see that the equilibrium constant is related to the Gibbs free energy change of the reaction by the equation:

(3.86)

At this point, it is worth saying some more about standard states. We mentioned that one is free to choose a standard state, but there are pitfalls. In general, there are two kinds of standard states, fixed pressure–temperature standard states and variable P–T standard states. If you chose a fixed temperature standard state, then eqn. 3.86 is only valid at that standard-state temperature. If you chose a variable-temperature standard state, then eqn. 3.86 is valid for all temperatures, but ΔG° is then a function of temperature. The same goes for pressure. Whereas most thermodynamic quantities we have dealt with thus far are additive, equilibrium constants are multiplicative (see Example 3.6).