Thermodynamics of Chemical Equilibrium:
The relation between the Gibbs energy and the equilibrium constant can be found by considering chemical potentials.At constant temperature and pressure, the Gibbs free energy, G, for the reaction depends only on the extent of reaction: ξ (Greek letter xi), and can only decrease according to the second law of thermodynamics. It means that the derivative of G with ξ must be negative if the reaction happens; at the equilibrium the derivative being equal to zero.
- : equilibrium
In this article only the constant pressure case is considered. The constant volume case is important in geochemistry and atmospheric chemistry where pressure variations are significant. Note that, if reactants and products were in standard state (completely pure), then there would be no reversibility and no equilibrium. The mixing of the products and reactants contributes a large entropy (known as entropy of mixing) to states containing equal mixture of products and reactants. The combination of the standard Gibbs energy change and the Gibbs energy of mixing determines the equilibrium state.
In general an equilibrium system is defined by writing an equilibrium equation for the reaction
- , ( is the standard chemical potential ).
- in the case of a closed system.
- ( corresponds to the Stoichiometric coefficient and is the differential of the extent of reaction ).
- which corresponds to the Gibbs free energy change for the reaction .
- .
- ,
-
- : which is the standard Gibbs energy change for the reaction. It is a constant at a given temperature, which can be calculated, using thermodynamical tables.
-
- ( is the reaction quotient when the system is not at equilibrium ).
-
- ; the reaction quotient becomes equal to the equilibrium constant.
Addition of reactants or products
For a reactional system at equilibrium: ; .- If are modified activities of constituents, the value of the reaction quotient changes and becomes different from the equilibrium constant:
and
then
- If activity of a reagent increases
- then
- If activity of a product increases
- then
Note that activities and equilibrium constants are dimensionless numbers.
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