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JEE Advanced levelNumerical answerDifficulty 3 of 3mt158

A Hall-Heroult cell is run at a steady current of $40.0 kA$ for $6.00$ hours with a current efficiency of $88.0%$ (only this fraction of the charge deposits aluminium). Taking Al = 27 and F = 96500 C/mol, calculate the mass of aluminium produced in kilograms (two decimals).

Numerical answer type, answer in kg, tolerance 0.01.

Answer: 70.91 kg

Charge passed is

40000 \times 21600 = 8.64 \times 1 0^{8} C

, of which

88.0%

is effective. Moles of electrons

= 8.64 \times 1 0^{8} \times 0.880/96500

and each Al needs

3

electrons (

Al X^{3 +} + 3 e X^{-} Al

). Mass of Al

= \frac{8.64 \times 1 0 ^{8} \times 0.880}{3 \times 96500} \times 27 = 70.91 kg

.

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