Page 42 - Soil and water contamination, 2nd edition

Basic environmental chemistry 29

G 0 G 0 f products G 0 f reactants (2.32)

0
where ΔG = the free energy of formation, tabulated for standard conditions (25 °C and 1
f
atmosphere pressure) in many standard chemical, geochemical, or hydrochemical textbooks
(e.g. Stumm and Morgan, 1996; Drever, 2000; Morel, 1983).

The reaction quotient Q is:
[ C [] c D] d
Q a b (2.33)
[ A [] B]
where [A], [B], [C], and [D] refer to the activities of the chemicals A, B, C, and D. Note that
the square brackets refer to activities. As remarked before, the effect of ionic strength may
be neglected for dilute fresh waters, so that for approximate calculations, activities may be
-1
approximated by concentrations. Activities for dissolved species are expressed in mol l ; pure
solids and the solvent (H O) have activities equal to 1; gases (whether in the gaseous phase
2
or dissolved) are expressed in units of partial pressure . The reaction quotient is also referred
to as the ion activity product. If ΔG is positive, the reaction (Equation 2.30) proceeds to
the left until ΔG becomes zero. Conversely, if ΔG is negative, the reaction proceeds to the
right until ΔG becomes zero. If ΔG is zero, the system is at equilibrium and the forward and
reverse reactions in Equation (2.30) occur at the same rate, so the chemical composition of
the system does not change. Thus at equilibrium, the following is valid:
G 0 RT lnQ 0 (2.34)

Hence,

G 0 RT ln Q (2.35)

At equilibrium , the reaction quotient Q equals the equilibrium constant K:

[ C [] c D] d 0
K e G / RT (2.36)
[ A] a [ B] b

This Equation (2.36) is also known as the mass action law , and therefore some authors

refer to the equilibrium constant K as the mass action constant. The equilibrium constant
represents the final expected distribution of mass between the reactants and products at a
given temperature and pressure. Depending on the reaction, we refer to the equilibrium
constant K as a) an acidity or dissociation constant in acid–base reactions (see Section 2.9),
b) a complexation constant in complexation reactions (see Section 2.8), c) a solubility
constant in solid dissolution reactions (see Section 2.7), d) an adsorption constant in
sorption reactions, or e) a Henry’s law constant in gas dissolution (see Section 14.1).
The values for these constants are typically derived from laboratory experiments and
thermodynamic calculations.

Example 2.6 Calculation of the equilibrium constant from Gibbs free energy data

Consider the reaction of calcite with carbon dioxide :
2+
CaCO + CO + H O ↔ Ca + 2 HCO -
3 2 2 3

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