How can i derive this Gibbs energy equation?

Click For Summary

Discussion Overview

The discussion revolves around deriving an expression that relates the standard state cell potential and the equilibrium constant for an electrochemical reaction. Participants explore the Gibbs free energy equations and their implications in the context of electrochemical cells.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant states the Gibbs free energy for an electrochemical cell is given by G = -nFE and suggests mixing equations involving ΔG and standard state free energy.
  • Another participant questions the values of ΔG and Q at equilibrium and their relationship to standard cell potential Eθ.
  • A participant asserts that at equilibrium, Q equals K and reiterates that G equals -nFE.
  • Further clarification is provided that ΔGθ equals nFEθ, prompting a discussion about the net free energy change for forward and reverse reactions at equilibrium.

Areas of Agreement / Disagreement

Participants express uncertainty about the derivation process, and while some agree on the relationships between ΔG, Q, and K, the overall discussion remains unresolved with multiple viewpoints on how to proceed with the derivation.

Contextual Notes

Participants have not fully resolved the assumptions regarding the relationships between the Gibbs free energy equations and the equilibrium constant, nor have they clarified the mathematical steps needed to derive the expression.

lioric
Messages
335
Reaction score
26

Homework Statement



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


Homework Equations



ΔG=-nFE and ΔG=ΔGθ + RT lnQ

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
 
Physics news on Phys.org
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?
 
Q would be K G would be-nFE
 
lioric said:
Q would be K G would be-nFE

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.:wink:
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 4 ·
Replies
4
Views
4K
Replies
1
Views
3K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
Replies
1
Views
3K