I have a problem with the definition of the standard Gibbs energy and its connection to the equilibrium constants.
I think, that I've basically understood what the different equation mean but there is one thing, I'm unable to understand:
On the one hand:
One may describe a chemical reaction with $\Delta G=\Delta G^\circ + RT\ln{Q}$. In equilibrium $\Delta G = 0$ and the equation reads $\Delta G^\circ = -RT \ln{K}$.
On the other hand:
The definition of standard state is very clear: pressure = 1 bar and all reactants and products must have activity = 1.
If I consider these two aspects separately, everything seems to be fine. But these two concepts have to be valid at the same time, what leads to $\Delta G^\circ = 0$ (always), since $K=1$ (all activities are per definition = 1).
Therefore, $\Delta G^\circ$ would be always zero. I know that this isn't true, but I don't understand why.
Can anyone explain this to me?
Thanks!