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.
