Balance the following redox reactions occurring in acidic aqueous solution:

a) Al(s) + Fe²⁺(aq) → Al³⁺(aq) + Fe(s)

b) SO₃^2–(aq) + MnO₄^–(aq) → SO₄^2–(aq) + Mn²⁺(aq)

c) Cr₂O₇^2-(aq) + C₂O₂^2-(aq) → Cr³⁺(aq) + CO₂(g)

d) PbO₂(s) + Mn²⁺(aq) + SO₄^2-(aq) → PbSO₄(s) + MnO₄^–(aq)

e) MnO₄^–(aq) + H₂O₂(aq) → Mn²⁺(aq) + O₂(g)

Balance the following redox reactions occurring in basic aqueous solution:

a) Mn²⁺(aq) + ClO₃^–(aq) → MnO₂(s) + ClO₂(g)

b) MnO₄^–(aq) + Br^–(aq) → MnO₂ + BrO₃^–(aq)

c) MnO₄^–(aq)  + CN^–(aq) → CNO^–(aq)  + MnO₂(s)

d) H₂O₂(aq) + ClO₂(aq) → ClO₂^–(aq) + O₂(g)

e) MnO₄^–(aq) + Fe(OH)₂(s) → MnO₂(s) + Fe(OH)₃(s)

For each redox reaction, sketch a voltaic cell, label the anode and cathode, and indicate the half-reaction that occurs at each electrode. Show the direction of electron flow and the species present in each solution.

a) Cu²⁺(aq) + 2e^– → Cu(s)

Sn(s) → Sn²⁺(aq) + 2e^–

b) Cd²⁺(aq) + 2e^– → Cd(s)

Mn(s) → Mn²⁺(aq) + 2e^–

Given the values of standard reduction potentials, determine the redox reaction that will occur in a galvanic cell. Sketch a voltaic cell, label the anode and cathode, and indicate the half-reaction that occurs at each electrode. Show the direction of electron flow and the species present in each solution.

Pb²⁺(aq) + 2e^– → Pb(s) E^o = -0.13 V

Ag⁺(aq) + e^– → Ag(s) E^o = 0.80 V

Calculate the E°_cell for each balanced redox reaction and determine if the reaction is spontaneous as written.

a) Ni(s) + Mg²⁺(aq) → Ni²⁺(aq) + Mg(s)

b) 2Cl^–(aq) + Pb²⁺ (aq) → Cl₂(l) + Pb(s)

c) Cd(s) + Pb²⁺(aq) → Cd²⁺(aq) + Pb(s)

d) Fe(s) + 3Ag⁺(aq) → Fe³⁺(aq) + 3Ag(s)

e) Ca²⁺(aq) + Fe(s) → Ca(s) + Fe²⁺(aq)

Balance the following redox reaction occurring in acidic media, and using a table for standard electrode potentials, determine the E^o_cell at 25 ^oC.

Cd(s) + Cr₂O₇²⁻(aq) → Cd²⁺(aq) + Cr³⁺(aq)

Determine the balanced net reaction from the following two half-reactions and calculate the E^o_cell at 25 ^oC.

NO(g) + 2H₂O(l) ⟶ NO₃⁻(aq) + 4H⁺(aq) + 3e⁻ E° = -0.96 V

MnO₂(s) + 4H⁺(aq) + 2e⁻ ⟶ Mn²⁺(aq) + 2H₂O(l) E° = 1.21 V

Using a table for standard electrode potentials, find a metal that can be used to reduce Al³⁺ ions but not Na⁺ ions.

Using a table for standard electrode potentials, determine if Fe can be used to reduce the Sn²⁺ ion.

Using a table for standard electrode potentials, determine if H₂(g) is capable of reducing Cd²⁺(aq).

Cell Potential, Free Energy, and the Equilibrium Constant

Use tabulated electrode potentials to calculate ΔG°_rxn for each reaction at 25 °C.

a) Zn(s) + Pb²⁺(aq) → Zn²⁺(aq) + Pb(s)

b) Sn²⁺(aq) + Mg(s) → Sn(s) + Mg²⁺(aq)

c) Br₂(l) + 2I^–(aq) → 2Br^–(aq) + I₂(s)

d) 2Al(s) + 3Cu²⁺(aq) → 2Al³⁺(aq) + 3Cu(s)

e) O₂(g) + 4H⁺(aq) + Cu(s) → Cu²⁺(aq) + 2H₂O(l)

f) MnO₂(s) + 4H⁺(aq) + Cd(s) → Mn²⁺(aq) + 2H₂O(l ) + Cd²⁺(aq)

Calculate the equilibrium constant for each redox reaction in problem 11.

a) Zn(s) + Pb²⁺(aq) → Zn²⁺(aq) + Pb(s)

b) Sn²⁺(aq) + Mg(s) → Sn(s) + Mg²⁺(aq)

c) Br₂(l) + 2I^–(aq) → 2Br^–(aq) + I₂(s)

d) 2Al(s) + 3Cu²⁺(aq) → 2Al³⁺(aq) + 3Cu(s)

e) O₂(g) + 4H⁺(aq) + Cu(s) → Cu²⁺(aq) + 2H₂O(l)

f) MnO₂(s) + 4H⁺(aq) + Cd(s) → Mn²⁺(aq) + 2H₂O(l ) + Cd²⁺(aq)

Use an appendix for the free energies of formation to calculate the standard cell potential for the oxidation reaction of ethylene, C₂H₄ by permanganate ion, MnO₄^–.

5C₂H₄(g) + 12MnO₄^–(aq) + 36H⁺(aq) → 10CO₂(g) + 12Mn²⁺(aq) + 28H₂O(l)

The standard free energy of formation for Mn²⁺ ions is -228 kJ/mol.

The Nernst Equation

A voltaic cell runs the following redox reaction:

Fe²⁺(aq) + Mg(s) → Mg²⁺(aq) + Fe(s)

Determine whether E_cell is larger or smaller than E°_cell and determine the E_cell for the following concentrations:

a) when [Fe²⁺] = 1.0 M and [Mg²⁺] = 2.5 M

b) when [Fe²⁺] = 3.0 M and [Mg²⁺] = 1.0 M

Calculate E°, E, and ΔG for the following cell reaction:

Mn(s) + Pb²⁺(aq) → Mn²⁺(aq) + Pb(s)

[Mn²⁺] = 0.164 M, [Pb²⁺] = 0.038 M 

A galvanic cell operates on the following redox reaction:

2MnO₄^–(aq) + 10Br^–(aq) + 16H⁺(aq) → 2Mn²⁺(aq) + 5Br₂(l) + 8H₂O(l)

Calculate the cell potential at 25 ^oC, given the concentrations of the aqueous components are: [MnO₄^–] = 0.0250 M, [Br^–] = 0.0150 M, [Mn²⁺] = 0.380 M, and [H⁺] = 0.64 M.

A voltaic cell consists of a Mg/Mg²⁺ half-cell and a Sn/Sn²⁺ half-cell at 25 °C. The initial concentrations of Sn²⁺ and Mg²⁺ are 1.80 M and 0.250 M, respectively.

a) Calculate the initial cell potential.

b) What is the cell potential when the concentration of Sn²⁺ dropped to 0.650 M?

c) Determine the concentrations of Sn²⁺ and Mg²⁺ ions when the cell potential falls to 2.15 V.

A voltaic cell consists of a Zn/Zn²⁺ half-cell and a H₂/H⁺ half-cell at 25 °C. Calculate the initial cell potential if [Zn²⁺] = 0.0250 M, [H⁺]  = 2.80 M, P(H₂) = 0.45 atm.

Determine the emf of a cell consisting of a Sn²⁺/Sn half-cell and a Pt/H⁺/H₂ half-cell if [Sn²⁺] = 0.12 M, [H⁺] = 0.0650 M, and P(H₂) = 1.25 atm?