Why is Gibbs free energy zero at equilibrium?

1 Answer
Truong-Son N.
Jul 24, 2016

Because at equilibrium, everything that #G# depends on is constant.

The Gibbs' free energy may have been given to you without really emphasizing that it is actually a function of temperature, pressure, and the #"mol"#s of involved reactants and products:

#\mathbf(G = G(T,P,n_1,n_2, . . . , n_N))#

When we are at equilibrium, we really mean all of the following are occurring:

  • thermal equilibrium - the temperature is constant.
  • pressure equilibrium - the pressure is constant.
  • dynamic equilibrium - the concentration, and hence the #"mol"#s, of reactants and products is steady/constant (but may react if disturbed).

But when all those things are constant, the Gibbs' free energy simply isn't changing at all. If the variables on which #G# is dependent are constant, #G# (for a single state) is constant.

Obviously, #DeltaG = G_f - G_i#, but when #G# is constant, #G_f = G_i#.

Therefore, #\mathbf(DeltaG_"eq" = 0)#.

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