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Ch.20 - Electrochemistry
Tro - Chemistry: A Molecular Approach 5th Edition
Tro5th EditionChemistry: A Molecular ApproachISBN: 9780134874371Not the one you use?Change textbook
All textbooksTro 5th EditionCh.20 - ElectrochemistryProblem 115a
Chapter 20, Problem 115a

A battery relies on the oxidation of magnesium and the reduction of Cu2+. The initial concentrations of Mg2+ and Cu2+ are 1.0 × 10–4 M and 1.5 M, respectively, in 1.0-liter half-cells. a. What is the initial voltage of the battery?

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Step 1: Identify the half-reactions. The oxidation half-reaction is Mg -> Mg2+ + 2e-, and the reduction half-reaction is Cu2+ + 2e- -> Cu.
Step 2: Use the Nernst equation to calculate the cell potential. The Nernst equation is E = E0 - (RT/nF) * ln(Q), where E is the cell potential, E0 is the standard cell potential, R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred in the balanced redox reaction, F is the Faraday constant, and Q is the reaction quotient.
Step 3: Determine the standard cell potential (E0). This is the difference between the standard reduction potentials of the two half-reactions. You can find these values in a standard reduction potentials table. Remember that the standard reduction potential for the oxidation half-reaction should be reversed because it is an oxidation, not a reduction.
Step 4: Calculate the reaction quotient (Q). This is the ratio of the concentrations of the products to the reactants, each raised to the power of its stoichiometric coefficient in the balanced chemical equation. In this case, Q = [Mg2+] / [Cu2+].
Step 5: Substitute the known values into the Nernst equation and solve for E. Remember to convert the temperature to Kelvin if it is given in degrees Celsius.

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Key Concepts

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

Oxidation and Reduction

Oxidation and reduction are fundamental concepts in redox reactions, where oxidation refers to the loss of electrons and reduction refers to the gain of electrons. In the context of a battery, magnesium (Mg) is oxidized, losing electrons, while copper ions (Cu2+) are reduced, gaining those electrons. Understanding these processes is crucial for analyzing how batteries generate electrical energy.
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Nernst Equation

The Nernst equation relates the concentration of reactants and products in a redox reaction to the cell potential (voltage). It allows us to calculate the voltage of a battery under non-standard conditions by taking into account the concentrations of the oxidized and reduced species. This equation is essential for determining the initial voltage of the battery in the given problem.
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Standard Electrode Potentials

Standard electrode potentials are measured voltages for half-reactions under standard conditions (1 M concentration, 1 atm pressure, and 25°C). These values help predict the direction of electron flow in a redox reaction and the overall voltage of the battery. Knowing the standard potentials for the oxidation of magnesium and the reduction of copper ions is necessary to calculate the initial voltage of the battery.
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Related Practice
Textbook Question

A battery relies on the oxidation of magnesium and the reduction of Cu2+. The initial concentrations of Mg2+ and Cu2+ are 1.0 × 10–4 M and 1.5 M, respectively, in 1.0-liter half-cells. b. What is the voltage of the battery after delivering 5.0 A for 8.0 h?

Textbook Question

A friend wants you to invest in a new battery she has designed that produces 24 V in a single voltaic cell. Why should you be wary of investing in such a battery?

Textbook Question

A battery relies on the oxidation of magnesium and the reduction of Cu2+. The initial concentrations of Mg2+ and Cu2+ are 1.0 × 10–4 M and 1.5 M, respectively, in 1.0-liter half-cells. c. How long can the battery deliver 5.0 A before going dead?

Textbook Question

The cell potential of this electrochemical cell depends on the gold concentration in the cathode half-cell. Pt(s) | H2(g, 1.0 atm) | H+(aq, 1.0 M) || Au3+(aq, ? M) | Au(s) What is the concentration of Au3+ in the solution if Ecell is 1.22 V?

Textbook Question

A rechargeable battery is constructed based on a concentration cell constructed of two Ag/Ag+ half-cells. The volume of each half-cell is 2.0 L, and the concentrations of Ag+ in the half-cells are 1.25 M and 1.0×10–3 M. a. How long can this battery deliver 2.5 Aof current before it goes dead?

Textbook Question

The cell potential of this electrochemical cell depends on the pH of the solution in the anode half-cell. Pt(s) | H2(g, 1 atm) | H+(aq, ? M) || Cu2+(aq, 1.0 M) | Cu(s) What is the pH of the solution if Ecell is 355 mV?

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