Mdtryhht

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 $Delta G=Delta G^circ + RTlnQ$. In equilibrium $Delta G = 0$ and the equation reads $Delta G^circ = -RT lnK$.

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!

As explained in the comments, the standard state conditions lead to $Q=1$ and therefore $$Delta G=Delta G^circ+ RTln1=Delta G^circ$$ On the other hand at equilibrium $Q=K$ and so $$Delta G=Delta G^circ + RTlnK$$ This of course leads to $Delta G^circ = -RTlnK$ since at equilibrium $Delta G=0$.

So you might want to think of it as three statements:

1. For the conversion of reactants to products in their standard states $Q=1$


2. At equilibrium $Delta G=0$
   


3. At equilibrium $Q=K$
   

The first statement is consistent with the definition of standard states.
The second statement follows from combination of the first and second laws of thermodynamics.
The third statement is a definition of $K$.

What you enter into $K$ are not the activities of the pure reactants and pure products at standard state (if you did then, yes, $K$ would be 1). Rather, it is their activities at equilibrium (raised, of course, to the power of their respective stochiometric coefficients). And, at equilibrium, these activities are generally not equal to one.