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?

검증된 단계별 안내

insert step 1: Identify the half-reactions involved in the battery. The oxidation half-reaction is Mg -> Mg^{2+} + 2e^-, and the reduction half-reaction is Cu^{2+} + 2e^- -> Cu.

insert step 2: Determine the number of moles of electrons transferred per mole of reaction. In this case, 2 moles of electrons are transferred per mole of Mg oxidized and Cu^{2+} reduced.

insert step 3: Calculate the total charge (in coulombs) that can be delivered by the battery using the formula Q = n * F, where n is the number of moles of electrons and F is Faraday's constant (approximately 96485 C/mol).

insert step 4: Use the initial concentration of Cu^{2+} to find the limiting reactant. Since Cu^{2+} is in excess, calculate the moles of Mg available using its initial concentration and volume.

insert step 5: Calculate the time the battery can deliver 5.0 A using the formula t = Q / I, where Q is the total charge calculated in step 3 and I is the current (5.0 A).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Oxidation-Reduction Reactions

Oxidation-reduction (redox) reactions involve the transfer of electrons between two species. In this context, magnesium (Mg) is oxidized, losing electrons, while copper ions (Cu2+) are reduced, gaining electrons. Understanding these processes is crucial for analyzing how batteries generate electrical energy through chemical reactions.

Concentration and Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. In the given problem, the concentrations of Mg2+ and Cu2+ are provided in molarity, which is essential for calculating the total number of moles available for the redox reaction. This information is vital for determining how long the battery can operate.

Current and Charge

Current (measured in amperes) is the flow of electric charge, and it is related to the amount of charge (in coulombs) that passes through a circuit over time. The relationship between current, charge, and time is given by the equation Q = I × t, where Q is charge, I is current, and t is time. This concept is key to calculating how long the battery can deliver a specified current before the reactants are depleted.

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?