Why don't we take activities in the rate law?

I am slightly confused by the fact that concentrations and not activities are taken in the rate law which is different to equilibrium and seems to lead to a discrepancy. For example, for the reaction $aA(g)+bB(aq)+cC(g)⇌eE(g)+fF(aq)+gG(aq)$, the value of $K\_{eq}$ is:- $$K\_{eq} = \frac{(P\_{\ce{E}})^e[\ce{F}]^f[\ce{G}]^g}{(P\_{\ce{A}})^a[\ce{B}]^b(P\_{\ce{C}})^c}$$


where all quantities are dimensionless.The above expression follows from the definitions of activities of gases and solutes.


Now, the rate law for the forward reaction will be $v\_f= K\_{fwd} [A]^a[B]^b [C]^c$ and for the backward reaction will be $v\_b= K\_{bwd} [E]^e [F]^f[G]^g$ where [X]=$ \frac{P\_x}{RT}$. Since, at equilibrium, $v\_f=v\_b$, so $K\_{fwd} [A]^a[B]^b [C]^c=K\_{bwd} [E]^e [F]^f[G]^g$. Since $K\_{eq}$=$\frac{K\_{fwd}}{K\_{bwd}}$ so we have $$K\_{eq} = \frac{[{\ce{E}}]^e[\ce{F}]^f[\ce{G}]^g}{[\ce{A}]^a[\ce{B}]^b[{\ce{C}}]^c}$$


which is incorrect. So, do we take activities in the rate law(and concentration is a common misquotation) or is there something else I'm missing?


