Читать книгу Geochemistry - William M. White - Страница 134
Example 3.8 Calculating equilibrium constants and equilibrium concentrations
ОглавлениеThe hydration of olivine to form chrysotile (a serpentine mineral) may be represented in a pure Mg system as:
If this reaction controlled the concentration of Mg2+ of the metamorphic fluid, what would the activity of Mg2+ be in that fluid if it had a pH of 4.0 at 300° C?
Answer: Helgeson (1967) gives the thermodynamic data shown in the table below for the reactants at 300° C. From these data, we use Hess's law to calculate and as −231.38 kJ and −253.01 J/K respectively. The equilibrium constant for the reaction may be calculated as:
| Species | ΔH° kJ | S° J/K |
| Mg3Si2O5(OH)4 | −4272.87 | 434.84 |
| Mg2+ | −366.46 | 109.05 |
| H+ | 44.87 | 106.68 |
| Mg2SiO4 | −2132.75 | 186.02 |
| H2O | −232.19 | 211.50 |
The equilibrium constant for this reaction can be written as:
which reduces to if we take the activities of water, chrysotile, and forsterite as 1. Since pH = – log aH+, we may rearrange and obtain the activity of the magnesium ion as:
Taking the derivative with respect to temperature of both sides of eqn. 3.95 (while holding pressure constant), we have:
(3.96)
This equation is known as the van't Hoff equation.
