Page 43 - Soil and water contamination, 2nd edition

30 Soil and Water Contamination

The Gibbs free energies of formation for the reactants and reaction products at 25 °C are
ΔG 0 = –1128.8 kJ mol -1
f CaCO 3
ΔG 0 = –394.4 kJ mol -1
f CO 2
ΔG 0 = –237.1 kJ mol -1
f H 2 O
ΔG 0 2+ = –553.6 kJ mol -1
f Ca
ΔG 0 - = –586.8 kJ mol -1
f HCO 3
Calculate the equilibrium constant from the data given above.

Solution
The Gibbs free energy for the reaction is

0
ΔG = ΔG 0 2+ + 2 ΔG 0 - – ΔG 0 – ΔG 0 – ΔG 0
r f Ca f HCO 3 f CaCO 3 f CO 2 f H 2 O
0
ΔG = –553.6 – 2 × 586.8 + 1128.8 + 394.4 + 237.1 = 33.1 kJ mol -1
r
0
ΔG = –RT ln K
r
-3
33.1 = –(8.3144 · 10 )(298.15) ln K
ln K = –13.35

K = e -13.35 = 1.59 · 10 -6

Because natural environmental conditions usually deviate from the standard conditions
at 25 °C and 1 atmosphere pressure, the equilibrium constant K needs to be corrected.

Variations in pressure have only a small effect on the values of the equilibrium constant and
therefore these variations are generally neglected. However, variations in temperature have
a significant effect on the equilibrium constant. To correct the equilibrium constant K for
temperature, the Van ’t Hoff equation (which can be derived by combining Equations 2.7
and 2.36) is used:
d ln K H 0 r
(2.37)
dT RT 2
0
where K = equilibrium constant [-], T = absolute temperature (K), ΔH = the standard
r
-1
-1
-1
reaction enthalpy (kJ mol ), and R is the gas constant (J mol K ). Integration of Equation
(2.37) and conversion of the natural logarithm to a base -10 logarithm yields:
H 0 1 1
log K T log K 25 oC r (2.38)
. 2 303 R 298 . 15 T
where K = equilibrium constant at temperature T (in K) [-], T = absolute temperature [θ],
T
-1
0
0

ΔH = the standard reaction enthalpy (kJ mol ). The reaction enthalpy ΔH is negative
r r
for exothermic reactions and positive for endothermic reactions (see Table 2.4). For the
derivation of Equation (2.38), it was assumed that temperature variations have a negligible
effect on the reaction enthalpy, which is generally true for the temperature ranges normally

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