# 26.5: Reaction Quotient and Equilibrium Constant Ratio Determines Reaction Direction

We developed the Gibbs free energy function to be able to predict which changes could occur spontaneously. If we start with a set of initial concentrations we can write them in a reaction quotient

\[Δ_rG = Δ_rG^o + RT \ln Q\]

if we subtract the equilibrium version of this expression:

\[0= Δ_rG^o + RT\ln K\]

we get

\[Δ_rG = RT \ln \left(\dfrac{Q}{K} \right)\]

That gives us the sign of \(Δ_rG\). If this is negative the reaction will spontaneously proceed from left to right as written, if positive it will run in reverse. In both case the value of \(Q\) will change until \(Q=K\) and equilibrium has been reached.

Note

Note that 'your' Δ_{r}G determines that, * not* the sign of Δ

_{r}G

^{o}(because that represents the decidedly non-equilibrium standard state!)