CHEMISTRY · Multi-part · AP · Chemistry · Thermodynamics and Electrochemistry · Thermodynamics and Electrochemistry
Problem
Three identical electrolytic cells, each containing AgNO3 solution and identical inert electrodes, are connected in parallel across a regulated DC power supply that can provide a maximum output of 12.0A at 5.0V. The goal is to deposit exactly 1.00g of silver onto the cathode of each cell in 20.0min. Assume 100\% current efficiency, equal resistance in each branch, and that currents divide equally unless limited by the supply. Silver’s molar mass is 107.9g mol−1, and the Faraday constant is 96485C mol−1.
(a) For one cell, calculate the total charge required to deposit 1.00g of silver.
(b) Determine the minimum current that must flow through each individual cell to meet the 20.0min deadline.
(c) Using your result from part (b), evaluate whether the power supply can meet the combined current demand of the three parallel cells. Support your conclusion with numerical evidence.
(d) If the supply cannot deliver sufficient current, calculate the minimum time needed to produce the desired 1.00g of silver per cell when the power supply operates continuously at its 12.0A current limit.