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Question
Derive the relationship between Gibbs energy of cell reaction and cell potential.
Solution
- The electrical work done in a galvanic cell is the electricity (charge) passed multiplied by the cell potential.
Electrical work = amount of charge × cell potential - Charge of one mole electrons is F coulombs.
For the cell reaction involving n moles of electrons,
Charge passed = nF coulombs - Hence, electrical work = nFEcell
Electrical work done in a galvanic cell is equal to the decrease in Gibbs energy, – ∆G, of cell reaction.
It then follows that
Electrical work done = − ∆G - Therefore, −∆G = nFEcell
or ∆G = − nFEcell
Under standard state conditions, we write
∆G° = `−"nFE"_"cell"^0`
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