1. Free Energy and Redox Reactions
The emf associated with any redox reaction can be calculated.
Eo = Eored (reduction) – Eored (oxidation)
Spontaneous redox reaction
positive Eo (standard conditions)
positive E (non-standard conditions)
negative DG
Non-spontaneous redox reactions:
negative Eo
negative E
positive DG

2. Free Energy and Redox Reactions
The change in Gibbs free energy is related to the emf of a redox reaction by the equation:
DG = -nFE
where DG = change in Gibbs free energy
n = number of electrons transferred
F = Faraday’s constant = 96,485 J/V.mol
E = emf under nonstandard conditions
(I will give you this equation and the value of F on your exam.)

3. Free Energy and Redox Reactions
Under standard conditions, this equation becomes:
DGo = -nFEo
where DGo = standard Gibbs free energy change
n = number of electrons transferred
F = Faraday’s constant = 96,485 J/V.mol
Eo = emf under standard conditions
(I will give you this equation and the value of F on your exam.)

4. Free Energy and Redox Reactions
You can use the value of Eo to calculate the value of DGo and the equilibrium constant, K, for the reaction.
DGo = -nFEo
DGo = -RTlnK

5. Free Energy and Redox Reactions
Example: Use the standard reduction potentials listed in Appendix E of your text to calculate the equilibrium constant for the following reaction at 298K.
3 Ce4+ (aq) + Bi(s) + H2O (l)  3 Ce3+ (aq) + BiO+ (aq) + 2 H+ (aq)
Step 1: Calculate the value for Eo:

6. Free Energy and Redox Reactions
Step 2: Calculate the value of DGo:
Step 3: Calculate the value of K:
Answer: x 1065

7. Free Energy and Redox Reactions
Example: What is the effect on the emf of the cell described by the following equation when the following changes are made:
2 Fe3+ (aq) + H2 (g)  2 Fe2+ (aq) H+ (aq)
The pressure of hydrogen gas in the anode compartment is increased?
Iron (III) nitrate is added to the cathode compartment?
Sodium hydroxide is added to the anode compartment?

8. Free Energy and Redox Reactions
The emf of a redox reaction varies with temperature and with the concentrations of reactants and products.
The Nernst equation relates the emf under nonstandard conditions to the standard emf and the reaction quotient.
E = Eo- (RT/nF)lnQ

9. Free Energy and Redox Reactions
Converting from natural log to log base 10 and assuming that T = 298 K, the Nernst Equation becomes:
E = Eo – log10 Q n
where n = the number of electrons transferred
Q = reaction quotient
(I will give you this equation. You need to be able to use this equation)

10. Free Energy and Redox Reactions
Example: Calculate the emf generated by the following reaction when [Al3+] = 4.0 x 10-3 M and [I-] = M at 298K.
2 Al (s) I2 (s)  2 Al3+ (aq) I- (aq)
Step 1: Calculate Eo

11. Free Energy and Redox Reactions
Step 2: Calculate Q
Step 3: Calculate E using the Nernst Eq’n:
Answer: E = 2.36 V