Question

A friend tells you “Free energy G and pressure P are directly related by the equation

$\mathbf{G}\mathbf{=}\mathbf{G}\mathbf{°}\mathbf{+}\mathbf{RTln}\mathbf{\left(}\mathbf{P}\mathbf{\right)}$

Also, G is related to the equilibrium constant K in that when G_products = G_reactants, the system is at equilibrium. Therefore, it must be true that a system is at equilibrium when all pressures are equal.” Do you agree with this friend? Explain.

Short answer

No, I wouldn’t agree because at equilibrium, free energy change is zero not the value of free energy.

Step-by-step solution

Relationship between Gibbs Free Energy change and Equilibrium Constant   

At Equilibrium change in Gibbs free energy is zero, i.e,

$\mathbf{\Delta G}\mathbf{=}{\mathbf{G}}_{\mathbf{products}}\mathbf{-}{\mathbf{G}}_{\mathbf{reactants}}\mathbf{=}\mathbf{0}$

So that

$\begin{array}{l}\mathbf{\Delta G}\mathbf{=}\mathbf{\Delta G}\mathbf{°}\mathbf{-}\mathbf{RTlnK}\mathbf{=}\mathbf{0}\\ \mathbf{\Delta G}\mathbf{°}\mathbf{=}\mathbf{RTlnK}\end{array}$

Equilibrium and Pressure

So we can say from the equation that free energy change is zero at equilibrium not the value of free energy so we cannot say that for equilibrium pressure of all part must be equal.