Aluminium oxide may be electrolysed at $1000^{\circ} \mathrm{C}$ to furnish aluminium metal (Atomic mass…

Aluminium oxide may be electrolysed at $1000^{\circ} \mathrm{C}$ to furnish aluminium metal (Atomic mass $=27$ amu; 1 Faraday $=96,500$ Coulombs). The cathode reaction is $\mathrm{Al}^{3+}+3 \mathrm{e}^{-} \longrightarrow \mathrm{Al}^{\circ}$ To prepare $5.12 \mathrm{~kg}$ of aluminium metal by this method would require
  1. $5.49 \times 10^7 \mathrm{C}$ of electricity
  2. $1.83 \times 10^7$ C of electricity
  3. $5.49 \times 10^4 \mathrm{C}$ of electricity
  4. $5.49 \times 10^1 \mathrm{C}$ of electricity

Solution

$ \begin{aligned} & \mathrm{Q}=\frac{\mathrm{mFZ}}{\mathrm{M}}=\frac{5.12 \times 10^5 \times 96500 \times 3}{27} \\ & =5.49 \times 10^7 \mathrm{C} \end{aligned} $

Asked in: JEE Main 2005

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