The equilibrium constant for any reaction is related to the change in Gibbs Free Energy for that reaction under standard conditions by the equation
#K_(eq)=e^((-DeltaG^0)/(RT)#
where R is the universal gas constant (8.314 J/mol-K) and #T# is the absolute temperature in Kelvins.
Standard conditions means all reactants and products present in unit concentrations or pressures (e.g., 1 M, 1m or 1 bar) at the 'temperature of interest'. Most tables of thermodynamic values will give Gibbs Free Energy of formation for reactants and products at 298.15 K, so calculation of #K_(eq)# at this temperature is a simple matter of calculating #DeltaG^0# for reaction as the difference in Gibbs Free Energies of the products and reactants, and then using the equation above with #T=298.15K#.
Sometimes we need to calculate #K_(eq)# at a different temperature, and this involves a somewhat more complicated calculation:
First, calculate #DeltaH^0# for the reaction, taking the difference in standard enthalpies of formation of the products and reactants. Then calculate #DeltaS^0# by taking the difference in entropies of products and reactants. The #DeltaG^0# for reaction can then be calculated approximately from the equation
#DeltaG^0=DeltaH^0-TDeltaS^0#
Here, we can use any value of #T# because #DeltaH^0# and #DeltaS^0# are not strongly dependent on temperature. Finally, use the first equation (with the same value of #T# that you used in the second equation) to calculate #K_(eq)#.
Note that we cannot simply change #T# in the first equation because #DeltaG^0# is strongly dependent on temperature, as shown in the second equation.
