A voltaic cell is constructed from an Ni²⁺(aq) / Ni(s) half-cell and an Ag⁺(aq) / Ag(s) half-cell. The initial concentration of Ni²⁺(aq) in the Ni²⁺ - Ni half-cell is [Ni²⁺] = 0.0100 M. The initial cell voltage is +1.12 V. (a) By using data in Appendix E, calculate the standard emf of this voltaic cell.

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Identify the half-reactions for the voltaic cell: Ni^{2+} + 2e^- \rightarrow Ni(s) and Ag^+ + e^- \rightarrow Ag(s).

Look up the standard reduction potentials (E^\circ) for each half-reaction from Appendix E: E^\circ_{Ni^{2+}/Ni} and E^\circ_{Ag^+/Ag}.

Calculate the standard cell potential (E^\circ_{cell}) using the formula: E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}.

Determine which half-reaction is the cathode and which is the anode based on their standard reduction potentials (the more positive potential is the cathode).

Substitute the standard reduction potentials into the formula to find the standard emf of the cell.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Voltaic Cell

A voltaic cell, also known as a galvanic cell, is an electrochemical cell that converts chemical energy into electrical energy through spontaneous redox reactions. It consists of two half-cells, each containing an electrode and an electrolyte. The flow of electrons from the anode to the cathode generates an electric current, and the cell's voltage is determined by the difference in reduction potentials of the two half-reactions.

Standard Electrode Potential

The standard electrode potential (E°) is a measure of the tendency of a chemical species to be reduced, measured under standard conditions (1 M concentration, 1 atm pressure, and 25°C). Each half-cell in a voltaic cell has a specific standard electrode potential, which can be found in electrochemical series tables. The overall cell potential can be calculated by subtracting the anode potential from the cathode potential, providing insight into the cell's voltage and spontaneity.

Nernst Equation

The Nernst equation relates the cell potential to the concentrations of the reactants and products in a redox reaction. It allows for the calculation of the cell voltage under non-standard conditions by incorporating the reaction quotient (Q) and the number of electrons transferred (n). This equation is crucial for understanding how changes in concentration affect the emf of the cell, particularly when the concentrations deviate from standard conditions.

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The Nernst Equation

Related Practice

Textbook Question

Predict whether the following reactions will be spontaneous in acidic solution under standard conditions: (a) oxidation of Sn to Sn²⁺ by I₂ (to form I^-), (b) reduction of Ni²⁺ to Ni by I^- (to form I₂), (c) reduction of Ce⁴⁺ to Ce³⁺ by H₂O₂, (d) reduction of Cu²⁺ to Cu by Sn²⁺ (to form Sn⁴⁺).

Textbook Question

Gold exists in two common positive oxidation states, +1 and +3. The standard reduction potentials for these oxidation states are Au+1aq2 + e- ¡ Au1s2 Ered ° = +1.69 V Au3+1aq2 + 3 e- ¡ Au1s2 Ered ° = +1.50 V (c) Miners obtain gold by soaking gold-containing ores in an aqueous solution of sodium cyanide. A very soluble complex ion of gold forms in the aqueous solution because of the redox reaction 4 Au1s2 + 8 NaCN1aq2 + 2 H2O1l2 + O21g2 ¡ 4 Na3Au1CN2241aq2 + 4 NaOH1aq2 What is being oxidized, and what is being reduced in this reaction?

Textbook Question

A voltaic cell is constructed that uses the following half-cell reactions:

Cu⁺(aq) + e^- → Cu(s)

I₂(s) + 2 e^- → 2 I^-(aq)

The cell is operated at 298 K with [Cu⁺] = 0.25 M and [I^-] = 0.035 M.

(a) Determine E for the cell at these concentrations.

Textbook Question

A voltaic cell is constructed that uses the following half-cell reactions:

Cu⁺(aq) + e^- → Cu(s)

I₂(s) + 2 e^- → 2 I^-(aq)

The cell is operated at 298 K with [Cu⁺] = 0.25 M and [I^-] = 0.035 M.

(b) Which electrode is the anode of the cell?

Textbook Question

The capacity of batteries such as the typical AA alkaline battery is expressed in units of milliamp-hours (mAh). An AA alkaline battery yields a nominal capacity of 2850 mAh. (b) The starting voltage of a fresh alkaline battery is 1.55 V. The voltage decreases during discharge and is 0.80 V when the battery has delivered its rated capacity. If we assume that the voltage declines linearly as current is withdrawn, estimate the total maximum electrical work the battery could perform during discharge.

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