An industrial Hall–Héroult cell is scheduled to produce (8.00

CHEMISTRY · Multi-part · AP · Chemistry · Thermodynamics and Electrochemistry · Thermodynamics and Electrochemistry

Problem

An industrial Hall–Héroult cell is scheduled to produce

8.00\,\text{kg}

of aluminum metal over a 24.0-hour period. The process operates at 90.0\% current efficiency. Aluminum is formed by reduction of

\text{Al}^{3+}

ions according to the cathode half-reaction

\text{Al}^{3+}+3e^{-}\rightarrow \text{Al}

. Assume the cell voltage remains constant at

4.50\,\text{V}

throughout the run. The molar mass of aluminum is

26.98\,\text{g mol}^{-1}

, and the Faraday constant is

96\,485\,\text{C mol}^{-1}

. (a) Calculate the theoretical charge, in coulombs, required to produce

8.00\,\text{kg}

of aluminum at 100\% current efficiency. (b) Taking the 90.0\% current efficiency into account, determine the actual charge that must pass through the cell. (c) Compute the average current, in amperes, that the cell must draw to supply the charge calculated in part (b) over the 24.0-hour period. (d) Determine the total electrical energy, in kilowatt-hours, consumed during the 24.0-hour run. Express your answer to three significant figures. (e) A power supply rated at

150\,\text{kW}

is available for this cell. Critically evaluate whether this supply is adequate for continuous operation at the conditions specified, and justify your reasoning quantitatively.

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