## Effects Of Temperature And Pressure On Equilibrium

Equilibrium constants vary with temperature and pressure in a way that can be predicted thermodynamically. The equilibrium constant is related to the standard free energy change of the process:

where AG° is the standard free energy change, T the absolute temperature, R the gas constant, AH° the standard enthalpy change, and AS° the standard entropy change, for the reaction. In simple terms, AH° is a measure of the change in energy (e.g., bond energies and other interaction energies), and AS° a measure of the change in the degrees of freedom. The change in ln K with temperature at constant pressure is easily seen by differentiating the expression for ln K (assuming that AH° and AS° are independent of T, as is normally a good approximation over reasonably small temperature ranges). That is, at constant pressure, r J \„ fl J A I_ro A CO A I_ro

Thus, the temperature variation of K depends on whether the enthalpy change of the process is negative (exothermic) or positive (endothermic). An exothermic heat of solution results in a decrease in solubility with increasing temperature. This is the case with CaC03, for example, which is less soluble in hot than in cold water. This property has consequences for carbonate solubility behavior in lakes and oceans. Values of the equilibrium constants used in this book refer to 25°C unless otherwise indicated.

The pressure variation of the equilibrium constant can be derived from the effect of pressure on AGO at constant temperature:

'd ln K |
d |
-AH° |
AS° |
AH° |

dT |
= dT |
RT |
T |
RT 2 |

where AV° is the standard volume change on reaction. For condensed (solid or liquid) systems, AV° is small; hence pressure effects are also small. However, pressures at the ocean's floor may exceed 200 atm, and this can have significant effects. For the dissolution of CaC03, AV° « —60cm3/mol (i.e., the volume decreases because of improved packing of water molecules around the ions), and thus CaCO3 should be more soluble in deep water than at the surface at the same temperature.

These effects can be predicted qualitatively from Le Chatelier's principle: when a system at equilibrium is perturbed by a change in concentration, temperature, or pressure, the equilibrium will shift in a way that tends to counteract the change.

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