19.2.5 The Nernst Equation

Question 1

The Nernst Equation

Answer 1

• The electromotive force (E ̊ cell ) is related to Gibbs free energy (ΔG ̊) by the formula ΔG ̊ = –n · F · E ̊ cell .
• The Nernst equation can be used to find the cell potential (E cell ) at non-standard state conditions.

Question 2

note

Answer 2

• Gibbs free energy (ΔG ̊) for an electrochemical reaction is equal to the maximum work that could be done by the electrochemical cell (w elec ). This provides the relationship between Gibbs free energy (ΔG ̊) and the electromotive force (cell potential, E ̊cell).
• ΔG ̊ = –n · F · E ̊ cell , where n is the number of moles of electrons transferred in the redox reaction, and F is the Faraday constant (96,485 C/mol).
• The Nernst equation relates the cell potential at any point to the electromotive force (the cell potential at standard state, E ̊ cell ).
• E cell = E ̊ cell – (R · T)/(n · F) · lnQ, where R is the
  universal gas constant (8.3145 J/mol·K), T is the temperature in kelvins, n is the number of moles of electrons transferred in the redox reaction, F is the Faraday constant (96,485 C/mol), and Q is the reaction quotient.
• At standard state, Q = 1, and the equation reduces to E cell = E ̊ cell .
• The Nernst equation can be used to calculate the cell potential of a galvanic cell given the concentrations of products and reactants, or to calculate the concentrations of products or reactants based on electrochemical measurements.

Question 3

Calculate the reduction potential for the Fe3+ / Fe2+ electrode at 25°C if the concentration of Fe2+ is four times that of Fe3+

Fe3+ + e− → Fe2+ E ° = +0.77 V

Answer 3

+0.734 V

Question 4

Calculate the standard Gibbs free energy change in J / mol at 25°C for the following reaction:

3Sn4+ + 2Cr -> 3Sn2+ + 2Cr3+

Answer 4

−5.2 × 10^5 J / mol

Question 5

Calculate the Ecell for a galvanic cell at 25°C with this net cell reaction
Cd(s) + Pb2+(aq) –> Cd2+(aq) + Pb(s)
In which the concentrations of ions are as follows
[Cd2+] = 0.015M and [Pb2+] = 0.120 M
half reaction E°
Cd2+ + 2e- –> Cd -0.40
PB2+ + 2e- –> Pb -0.13

Answer 5

+0.30 V

Question 6

The Nernst equation is useful in calculating the electrode or cell potential for concentrations and pressures other than standard state values. Many times, the temperature does not deviate from standard conditions. What part of the Nernst equation can be simplified at 25°C?

Answer 6

RT / F

Question 7

Which of the following choices represents the most complete and correct form for the Nernst equation for the reaction:
3PbSO4(s) + 2Cr(s) -> 3Pb(s) + 3SO42-(aq) + 2Cr3+(aq)

E°cell = +0.38

Answer 7

Ecell = 0.38V - 0.0592/6 * log([SO42-]^3[Cr3+]^2)

Question 8

Which of the following parts of the Nernst equation is incorrectly explained?
Ecell = E°cell - 2.303RT/nF logQ

Answer 8

Ecell = the standard potential

Question 9

Which relationship below does not accurately describe how experimental data can be used to calculate a value?

Answer 9

• Calorimetric data –> ΔG°
• Composition data –> Keq
• Electrochemical data –> E°cell
• All the above are correct

Question 10

Which of the following conditions of a forward reaction would not correspond to the values shown below? Assume all substances are at standard state conditions.

Answer 10

Reaction at equilibrium / ΔG° < 0