Factors affecting Equilibrium Constant

The value of equilibrium constant depends on the nature of reactants and products, the temperature of reaction mixture, stoichiometry of balanced chemical equation for the reaction and direction of the reaction considered.

Nature of Reactants and Products

Consider the reactions,

(ce{CO(g) + 2H2(g) <=> CH3OH(g)}); (K_c = {[CH_3OH] over {[H_2]^2[CO]}})

(ce{CO(g) + H2(g) <=> HCHO(g)}); (K_c = {[HCHO] over {[H_2][CO]}})

The equilibrium constants in the two chemical reactions are different.

Temperature of Equilibrium Mixture

Let, the equilibrium constants at two temperatures (T_1) and (T_2) for an equilibrium are (K_1) and (K_2) respectively. The relation between them is given by:

(log{K_2 over K_1} ) = ( {Delta H over {2.303 R}})(left ( {1 over T_1} – {1 over T_2} right ))

The equation is derived by the help of the Arrehenius equation (Chemical Kinetics).

Stoichiometry of balanced chemical equation

For the stoichiometric coefficients of a balanced chemical equation, (ce {CO(g) + 2H2(g) <=> CH3OH(g)});

((K_c)_{old} = {[CH_3OH] over {[H_2]^2[CO]}})

For a different stoichiometric coefficients in balanced chemical equation for the same chemical reaction, (ce {nCO(g) + $2n$H2(g) <=> nCH3OH(g)});

((K_c)_{new} = {[CH_3OH]^n over {[H_2]^{2n}[CO]^n}})

((K_c)_{new}) = ({(K_c)^n_{old}})

Direction of the reaction considered

If the forward direction of a reaction is represented as (ce {CO(g) + 2H2(g) <=> CH3OH(g)});

((K_c)_{old} = {[CH_3OH] over {[H_2]^2[CO]}})

But if the reaction has started from the products of the above chemical reaction, the forward direction is represented as:

(ce{CH3OH(g) <=> CO(g) + 2H2(g)}); and the ((K_c)_{new} = {{[H_2]^2[CO]} over [CH_3OH]})

((K_c)_{new}) = (1 over {(K_c)_{old}})