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. b. What mass of silver is plated onto the cathode by running at 3.5 A for 5.5 h?

검증된 단계별 안내

Identify the half-reaction for the silver plating process: \( \text{Ag}^+ + e^- \rightarrow \text{Ag(s)} \).

Calculate the total charge (in coulombs) passed through the cell using the formula: \( Q = I \times t \), where \( I \) is the current in amperes and \( t \) is the time in seconds.

Convert the total charge to moles of electrons using Faraday's constant (\( 96485 \text{ C/mol} \)).

Use the stoichiometry of the half-reaction to determine the moles of silver plated, noting that 1 mole of electrons plates 1 mole of silver.

Convert the moles of silver to mass using the molar mass of silver (\( 107.87 \text{ g/mol} \)).

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주요 개념

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Electrochemical Cells

Electrochemical cells convert chemical energy into electrical energy through redox reactions. In a concentration cell, two half-cells with different ion concentrations generate a voltage due to the movement of ions from the higher concentration to the lower concentration. Understanding the principles of electrochemical cells is essential for analyzing how the battery operates and how current flows during the plating process.

Faraday's Law of Electrolysis

Faraday's Law states that the amount of substance deposited or dissolved during electrolysis is directly proportional to the electric charge passed through the cell. This law allows us to calculate the mass of silver plated onto the cathode by using the formula: mass = (current × time × molar mass) / (n × F), where n is the number of electrons transferred and F is Faraday's constant. This concept is crucial for determining the mass of silver deposited in the given scenario.

Current and Time Relationship

The relationship between current (measured in amperes) and time (measured in seconds) is fundamental in electrochemistry. The total charge (Q) passed through the cell can be calculated using the formula Q = I × t, where I is the current and t is the time. This relationship is vital for calculating the total charge that contributes to the electroplating process, enabling the determination of how much silver is deposited on the cathode.