# 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' ΔrG determines that, not the sign of ΔrGo (because that represents the decidedly non-equilibrium standard state!)