Calculate \( \Delta_{f} H^{\circ} \) (in \( \mathrm{kJ} / \mathrm{mol} \) ) for \( \mathrm{Cr}_{...

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Calculate \( \Delta_{f} H^{\circ} \) (in \( \mathrm{kJ} / \mathrm{mol} \) ) for \( \mathrm{Cr}_{2} \mathrm{O}_{3} \) from the \( \Delta_{r} G^{\circ} \) and the \( S^{\circ} \) values provided at \( 27^{\circ} \mathrm{C} \)
\[
4 \mathrm{Cr}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Cr}_{2} \mathrm{O}_{3}(s) ; \quad \Delta_{r} G^{\circ}=-2093.4 \mathrm{~kJ} / \mathrm{mol}
\]
\( S^{\circ}(\mathrm{J} / \mathrm{K} \mathrm{mol}): S^{\circ}(\mathrm{Cr}, s)=24 ; \quad S^{\circ}\left(\mathrm{O}_{2}, g\right)=205 ; \quad S^{\circ}\left(\mathrm{Cr}_{2} \mathrm{O}_{3}, s\right)=81 \)
(a) \( -2258.1 \mathrm{~kJ} / \mathrm{mol} \)
(b) \( -1129.05 \mathrm{~kJ} / \mathrm{mol} \)
(c) \( -964.35 \mathrm{~kJ} / \mathrm{mol} \)
(d) None of these
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