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JEE Main 2018 · Chemistry · d- and f-Block Elements and Metallurgy · easy

Aluminium is produced in a Hall-Heroult cell run at a steady current of 50 kA with 90% current efficiency. The mass of aluminium (M=27) produced in…

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Aluminium is produced in a Hall-Heroult cell run at a steady current of 50 kA50\ \mathrm{kA} with 90%90\% current efficiency. The mass of aluminium (M=27M=27) produced in one hour is closest to (F=96500 C mol−1F=96500\ \mathrm{C\,mol^{-1}})
  1. A. 15.1 kg15.1\ \mathrm{kg}
  2. B. 16.8 kg16.8\ \mathrm{kg}
  3. C. 22.7 kg22.7\ \mathrm{kg}
  4. D. 45.3 kg45.3\ \mathrm{kg}
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Answer: (A) 15.1 kg15.1\ \mathrm{kg}

Useful charge =0.90×50000×3600=1.62×108=0.90\times50000\times3600=1.62\times10^8 C. Cathode reaction Al3++3e−→Al\mathrm{Al^{3+}+3e^-\to Al}, so moles of Al =1.62×1083×96500=559.6=\dfrac{1.62\times10^8}{3\times96500}=559.6 mol. Mass =559.6×27=15.1×103=559.6\times27=15.1\times10^3 g =15.1=15.1 kg. Ignoring the efficiency gives 16.816.8 kg; using n=2n=2 gives 22.722.7 kg and n=1n=1 gives 45.345.3 kg (with efficiency).
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