During a classroom demonstration

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

Problem

During a classroom demonstration, an electrolytic cell is used to decompose water and collect hydrogen gas at the cathode. The instructor wants to generate

450\,\text{mL}

\text{H}_2\,

gas (measured at

25.0\,^{\circ}\!\text{C}

and

1.00\,\text{atm}

) in exactly

12.0\,\text{min}

. The cell is driven by a square-wave alternating current (AC) source for which the root-mean-square (rms) current equals 0.707 times the peak current. Assume 100\% current efficiency. The ideal-gas constant is

0.0821\,\text{L·atm·mol}^{-1}\text{K}^{-1}

and the Faraday constant is

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

. (a) Calculate the number of moles of hydrogen gas that must be produced. (b) Determine the total electrical charge required by the electrolytic cell to generate this amount of hydrogen. (c) Using the specified production time, calculate the necessary rms current. (d) Compute the corresponding peak current delivered by the AC source. (e) The demonstration circuit is protected by a

2.00\,\text{A}

fuse on the output side of the power supply. Assess, with quantitative justification, whether the planned experiment will blow the fuse.

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