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Q.

Use the relationship $, Δ G^{0}$ $= - n F {E^{0}}_{c e l l}$ to estimate the minimum voltage required to electrolyse $A l_{2} O_{3}$ in the Hall –Heroult process
$\begin{array}{l} Δ_{f} G^{0} (A l_{2} O_{3}) = - 1520 k J m o l^{- 1} \\ Δ_{f} G^{0} (C {O_{2}}_{}) = - 394 k J m o l^{- 1} \end{array}$

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An Intiative by Sri Chaitanya

a

0.8V

b

1.60V

c

2.8V

d

3.0V

answer is B.

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Detailed Solution

$\begin{array}{l} 2 A l_{2} O_{3} + 3 C \to 4 A l + 3 C O_{2} \\ Δ_{f} G^{0} 3 (C O_{2}) - 2 Δ G^{0} (A l_{2} O_{3}) \\ = 3 \times (- 394) - [2 \times (- 1520)] \\ = - 1858 k J = - 1858 \times 10^{3} J \\ ∴ n F E^{0} = 1858 \times 10^{3} (n = 12 e l e c t r o n s) \\ ∴ E^{0} = \frac{1858 \times 10^{3}}{12 \times 96500} = 1.60 V \end{array}$

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