# Regarding ΔG and equilibrium constant [duplicate]

We know that

$$ΔG = ΔG^\circ + RT\ln{Q} \tag{1}$$

where $$Q$$ is reaction quotient, and also that at equilibrium becomes

$$ΔG^\circ = -RT\ln{k} \tag{2}$$

I was trying to apply this equation to a reaction involving gaseous products and reactants.

If $$K_c = k$$ for concentration and $$K_p = k$$ for partial pressures, and assuming the gases are ideal, we get

$$K_p = K_c (RT)^x \label{eqn:3}\tag{3}$$

where $$x$$ is the sum coefficients of gaseous compounds on product side minus the same on reactant side. In general, $$x ≠ 0$$.

Now with this background, here is my question. At equilibrium, $$ΔG = 0$$ and $$Q = k$$. I am supposed to calculate $$k$$ from here in a question, but is this $$k$$ $$K_p$$ or $$K_c$$? From $$\eqref{eqn:3}$$ it is obvious that only one of the $$k$$'s can be unity in general. So which one is it?

• – andselisk Apr 1 '19 at 13:39