Equilibrium constant and Free Energy Change

For a chemical reaction:

A + B                                 C + D

The equilibrium constant is:

Keq = [C][D]^/[A][B]

where [A], [B] etc. are the concentrations at equilibrium

The standard free energy change for the reaction (D G^o) is the free energy of products minus the free energy of reactants under standard conditions  (298^oK, concentration of all reactants and products is 1 Molar).  Since all of molecules are present at the same concentration, (1 Molar)  D G^o  is really the free energy difference per molecule.  It is a measure of whether or not the reaction will go forward under standard conditions. If it is negative then the forward reaction is favorable and exergonic (releasing energy).  If it is positive then the forward reaction is unfavorable and requires the input of energy in order to go (endergonic).  In that case, the reverse reaction is favorable.  (That is because the D G^o for the reverse reaction equals -1 times the D G^o for the forward reaction.

 D G^o is related to the equilibrium constant:

D G^o = -RTlnKeq

or:

Keq = e^-DGo/RT

D G (without the ^o) takes into account the total free energy difference when there are NOT the same number of molecules of all types (i.e not under standard conditions).  It is a measure of whether or not the forward reaction is favorable at different concentrations.  If you know D G^o  you can calculate D G from the equation:

D G =  D G^o +RTln([C][D]^/[A][B])

Additivity of Free Energies

If the free energy change for reaction 1,  A → B,  is  D G^o1 and the free energy change for reaction 2,   B → C  is  D G^o2 then  the free energy change for reaction A → C   (which is the sum of reactions 1 and 2)  equals the sum of the free energies of the two reactions, i.e.   D G^o1  + D G^o2