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The mass of carbon anode consumed (giving only carbon dioxide) in the production of $270 \mathrm{~kg}$ of a aluminium metal from bauxite by the Hall process is:
(Atomic mass : A1 = 27)
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(Atomic mass : A1 = 27)
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Verified Answer
The correct answer is:
$90 \mathrm{~kg}$
$3 \mathrm{C}+2 \mathrm{Al}_2 \mathrm{O}_3 \longrightarrow 4 \mathrm{Al}+3 \mathrm{CO}_2$
(from bauxite)
4 moles of $\mathrm{Al}$ is produced by 3 moles of $\mathrm{C}$
1 mole of $\mathrm{Al}$ is produced by $\frac{3}{4}$ mole of $\mathrm{C}$
$10^4$ moles of $\mathrm{Al}$ is produced by $\frac{3}{4} \times 10^4$ moles of $\mathrm{C}$
Amount of carbon used
$\begin{aligned}
& =\frac{3}{4} \times 10^4 \times 12 \mathrm{~g} \\
& =90000 \mathrm{~g}=90 \mathrm{~kg}
\end{aligned}$
(from bauxite)
4 moles of $\mathrm{Al}$ is produced by 3 moles of $\mathrm{C}$
1 mole of $\mathrm{Al}$ is produced by $\frac{3}{4}$ mole of $\mathrm{C}$
$10^4$ moles of $\mathrm{Al}$ is produced by $\frac{3}{4} \times 10^4$ moles of $\mathrm{C}$
Amount of carbon used
$\begin{aligned}
& =\frac{3}{4} \times 10^4 \times 12 \mathrm{~g} \\
& =90000 \mathrm{~g}=90 \mathrm{~kg}
\end{aligned}$
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