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In pyro-metallurgy the metals are extracted from ores and concentrates by heat treatment. This involves conversion to metal oxide. This is followed by the reduction of the oxide to the metal using carbon or carbon monoxide.
$4 Cr (s) + 3 O_{2} (g) ⟶ 3 {Cr}_{2} O_{3} (s); Δ G^{\circ} = 1500 kJ / mol at 1200^{\circ} C$
$2 Mn (s) + O_{2} (g) ⟶ 2 MnO (s); Δ G^{\circ} = - 600 kJ / mol at 1200^{\circ} C$
$2 C (s) + O_{2} (g) ⟶ 2 CO (g); Δ G^{\circ} = - 550 kJ / mol at 1200^{\circ} C$
Select the correct statement.

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$C (s)$ can reduce $MnO (s)$ under given condition

$C (s)$ can reduce ${Cr}_{2} O_{3} (s)$ under given condition

Neither $MnO (s)$ nor ${Cr}_{2} O_{3} (s)$ be reduced by $C (s)$ under given condition

Both will be reduced simultaneously if carbon is passed over a mixture $MnO (s)$ and ${Cr}_{2} O_{3} (s)$

answer is B.

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Detailed Solution

For a reaction to occur $Δ G^{\circ} < 0$

$\begin{array}{l} 2 MnO + 2 C \to 2 Mn + CO \\ Δ G = 50 kJ / mol (not feasible) \\ \frac{2}{3} {Cr}_{2} O_{3} + 2 C \to \frac{4}{3} Cr + 2 CO \end{array}$

As the value of $Δ G$ is positive for the given reaction the reaction is feasible.

Hence, $C (s)$ can reduce and ${Cr}_{2} O_{3} (s)$ under given condition.

correct option is B.

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