Cell Potential: G and K: Videos & Practice Problems

Provide the balanced equation, standard cell potential, ΔG° and K at 298 K for the following reaction: The oxidation of chromium(II) ion in an acidic solution to chromium(III) ion by hypochlorous acid.

Cr³⁺(aq) + e⁻ → Cr²⁺(aq)                                                            E°_red = —0.50 V

2 HClO(aq) + 2 H⁺(aq) + 2 e⁻  → Cl₂(g) + 2 H₂O(l)     E°_red = 1.61 V

A certain voltaic cell uses the half-reactions shown below:

Anode: Zr(s) + 2 H₂O(l) → ZrO₂(s) + 4 H⁺(aq) + 4 e^–
Cathode: Mn²⁺(aq) + 2 e^– → Mn(s)

Using the thermodynamic values below at 25.0°C, calculate the cell potential (E°) and the equilibrium constant K for the overall cell reaction.

A rechargeable battery is classified as a secondary battery. Nickel-iron battery is an example of a secondary battery. Its half-reactions occur as follows:

Cathode:   NiO(OH) (s) + H₂O (l) + e⁻ → Ni(OH)₂ (s) + OH⁻ (aq)

Anode:      Fe (s) + 2 OH⁻ (aq) → Fe(OH)₂ (s) + 2 e⁻

Given the following data, determine the standard cell potential for the nickel-iron battery:

NiO(OH) (s) + H₂O (l) + e⁻ → Ni(OH)₂ (s) + OH⁻ (aq); E°_red = 0.52 V

Fe²⁺ (aq) + 2 e^– → Fe (s); E°_red = −0.447 V

Fe(OH)₂ (s) → Fe²⁺ (aq) + 2 OH^– (aq); K_sp = 4.87×10^–17

Refer to the following half-reactions and their E° values:

Bi⁺(aq) + e^– → Bi(s)                     E° = 0.240 V
W³⁺(aq) + 3 e^– → W(s)                E° = 0.100 V
Ga³⁺(aq) + 3 e^– → Ga(s)             E° = –0.549 V

For the combination of reactions that produces the largest voltage at 25°C, provide the overall cell reaction and determine the cell potential (E°), ΔG° (in kJ), and equilibrium constant (K).

Molten carbonate fuel cells (MCFC) are newly developed fuel cells that commonly use molten lithium and potassium carbonates as electrolytes. The half-reactions in the cell are shown below:

Anode:H₂(g) + CO₃^2–(l) → H₂O(l) +CO₂(g) + 2 e^–

Cathode: 1/2 O₂(g) + CO₂(g) + 2 e^– → CO₃^2–(l)

Using the thermodynamic values below, determine the cell potential (E°) and the equilibrium constant (K) for the overall reaction at 25°C. Identify whether the values of E° and K will increase, decrease or remain unchanged as the temperature decreases.

For the reaction 2 I^–(aq) + Hg²⁺(aq) → I₂(s) + Hg(l) at 298 K, calculate Eº_cell, K, ΔGº_rxn, and fill the table below.

A Nickel-Cadmium battery is rechargeable and is composed of a cadmium metal as an anode and a nickel(III) compound NiO(OH) supported on nickel metal as a cathode. This has an E° _cell of 1.2 V and uses the following reactions:

Anode: Cd (s) + 2 OH⁻ (aq) → Cd(OH)₂ (s) + 2e⁻
Cathode: 2 NiO(OH) (s) + 2 H₂O (l) + 2e⁻ → 2 Ni(OH)₂ (s) + 2 OH⁻ (aq)
Overall: 2 NiO(OH) (s) + Cd (s) + 2 H₂O (l) ⇌ 2 Ni(OH)₂ (s) + Cd(OH)₂ (s)

Find ΔG° (in kJ) and equilibrium constant K for the cell reaction at 25 °C.

The lead storage battery involves the following electrode half-reactions:

Anode: Pb (s) + HSO₄⁻ (aq) → PbSO₄ (s) + H⁺ (aq) + 2 e⁻                                      
(E° = 0.296 V)

Cathode: PbO₂ (s) + 3 H⁺ (aq) + HSO₄⁻ (aq) + 2 e⁻ → PbSO₄ (s) + 2 H₂O (l)  
(E° = 1.680 V)

Overall: PbO₂ (s) + Pb (s) +  2 H⁺ (aq) + 2 HSO₄⁻ (aq) → 2PbSO₄ (s) + 2 H₂O (l)  
(E° = 1.976 V)

Find the ΔG° (in kJ) and K at 25 °C.

What are the balanced equation, standard emf, ΔG°, and K value at 298 K for the oxidation of MnO₂(s) to MnO₄⁻(aq) by ClO⁻(aq) in basic solution?

What are the balanced equation, standard emf, ΔG°, and K value at 298 K for the oxidation of aqueous chloride ion by Hg₂²⁺(aq) to produce Cl₂(g)?

Determine K and ∆G°_rxn at 25.0 °C using tabulated electrode potentials for the reaction of HClO(aq) with  Cl^-(aq) to an acidic solution producing Cl₂(g).

Consider the reaction below: 

Pb(s) + 2 Ag⁺(aq) → Pb²⁺(aq) + 2 Ag(s)

Calculate the equilibrium constant using the reduction potentials. 

Silver is extracted from its ore via the leaching process for the cyanide ion in that ore. Shown below is the overall reaction.

4 Ag (s) + 8 CN⁻ (aq)  + O₂ (g) + 2 H₂O (l) → 4 [Ag(CN)₂]⁻ (aq) + 4 OH⁻ (aq)

Use the given data to calculate ΔG° for the above reaction at 25 °C.

Ag⁺ (aq) + 2 CN⁻ (aq) → Ag(CN)₂⁻ (aq);    K_f = 3.00×10²⁰

H₂O (l) ⇌ H⁺ (aq) + OH⁻ (aq);                   K_w = 1.00×10⁻¹⁴ 

O₂ (g) + 4 H⁺ (aq) + 4 e⁻ → 2 H₂O (l);        E° = 1.229 V

Ag⁺ (aq) + e⁻ → Ag (s);                              E° = 0.800 V

Which of the following conditions indicates a spontaneous reaction?

How is the equilibrium constant (K) related to the standard cell potential (E°) in a redox reaction?

What is the equation that relates standard cell potential (E°) to Gibbs free energy (ΔG°)?

Calculate the change in standard Gibbs free energy (ΔG°) for a reaction with n = 3 moles of electrons transferred and a standard cell potential (E°) of 0.50 V. (Faraday's constant = 96485 C/mol)

Which equation correctly relates Gibbs free energy (ΔG°) to the equilibrium constant (K)?

Calculate the equilibrium constant (K) for a reaction at 298 K if the change in standard Gibbs free energy (ΔG°) is -40 kJ/mol. (R = 8.314 J/mol·K)

A reaction has a standard cell potential of 0.20 V and n = 2 moles of electrons transferred. Compare the spontaneity of this reaction with one that has ΔG° = -35 kJ/mol and explain the relationship.