Equilibrium Constant: Valid under what conditions?

[Saladsamurai]

Hello all!

I am wondering: Since we derive the equilibrium constant by minimizing the Gibbs free energy, it means that me are taking advantage of the fact that at the minimum, we have $(dG)_{T,P,m}=0$. Does this mean that in order to determine the products of a reaction using the equilibrium constant then the reaction must take place at constant T, P, and m?

Thanks for your time!

 

[Yanick]

I know that Ka values can change at different temperatures and ∆G has a dependence on temperature based on ∆G=∆H - T∆S. So if you have ∆G = O at a certain temp and you change that temp then you are changing the (T∆S) term thereby making ∆G =/= 0. This moves the system away from equilibrium and it will then tend to the new minimum energy by the appropriate means.

EDIT: Let me say that I'm no expert by far and if you are looking for a definitive answer I'd wait for a true expert to come along. I'm wrong on plenty of things and although I think the overall answer is correct, the reasoning may be off or incomplete.

 

[Saladsamurai]

Thanks for replying Yanick I did some more thinking and research on this one. (dG)_T,P,m=0 is simply a relationship between state variables AT equilibrium. It does not matter HOW they got to equilibrium. If we know that a reaction has come to equilibrium and we are somehow able to specify T, P, and m, then the composition can be determined using the equilibrium constant. You are of course correct in that K varies with T (and P and m) for exactly the above reason.