# How can i derive this Gibbs energy equation?

1. Apr 27, 2013

### lioric

1. The problem statement, all variables and given/known data

For an electrochemical cell Gibbs free energy is is given by G=-nFE
Gibbs free energy for a reaction at any moment in time and standard state free energy is given by G=Go + RT lnQ

Derive an expression relating standard state cell potential and equilibrium constant for a reaction

2. Relevant equations

ΔG=-nFE and ΔG=ΔGθ + RT lnQ

3. The attempt at a solution

I actually don t have an idea
But i m guessing that i have to mix both equations up since ΔG is common and then i'm totally clueless

2. Apr 27, 2013

### Sunil Simha

What will be the value of ΔG and Q at equilibrium? And if Eθ were the standard cell potential, how would it be related to ΔGθ?

3. Apr 28, 2013

### lioric

Q would be K G would be-nFE

4. Apr 28, 2013

### Sunil Simha

Q would be K. You are right there. However, ΔGθ=nFEθ (you have already written so). Now to the part which is key to solving this,

When you have the reactants and products at equilibrium, what do you think the net free energy change for the whole process ( forward +backward reactions) is?

Say A $\Leftrightarrow$ B. For the forward reaction, let ΔG be the free energy change. What will be the free energy change for the reverse reaction? So what will be net free energy change (free energy change for forward reaction + free energy change for the reverse reaction)?

If you figure this out, the answer to the original question just pops out.