Relationship between equilibrium constant K, reaction quotient Q and Gibbs energy G

We know that if,

•  ΔG is negative, then the reaction is spontaneous and proceeds in the forward direction.
  
• ΔG is positive, then reaction is considered non-spontaneous. Instead, as reverse reaction would take place
  
•  ΔG is 0, reaction has achieved equilibrium; at this point, there is no longer any free energy left to drive the reaction.

A mathematical expression of this thermodynamic view of equilibrium can be described by the following equation:

ΔG = ΔG⁰ + RT ln Q

Where, G^⁰ is standard Gibbs energy.

At equilibrium, when ΔG = 0 and Q = K_c

ΔG = ΔG⁰ + RT ln K = 0

ΔG⁰ = -RT ln K

ln K = ΔG⁰ / RT

Taking antilog of both sides, we get,

K = e^{-ΔG⁰ /RT}

• If ΔG⁰ < 0, then –ΔG⁰/RT is positive, and e^{-ΔG⁰ /RT} >1, making K >1, which implies a spontaneous reaction or the reaction which proceeds in the forward direction to such an extent that the products are present predominantly.
  
• If ΔG⁰ > 0, then –ΔG⁰/RT is negative, and e^{-ΔG⁰ /RT} < 1, that is, K < 1, which implies a non-spontaneous reaction or a reaction which proceeds in the forward direction to such a small degree that only a very minute quantity of product is formed.