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Gibb's Energy and Nernst Equation

The value of ...

Question

The value of $△_{f} G^{\circ}$ for formation of $C r_{2} O_{3}$ is - 540 KJ/mol and that of $A l_{2} O_{3}$ is - 827 kj/ mol. Is the reduction of $C r_{2} O_{3}$ possible with AI?

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Solution

The two thermochemical equations may be written as
$(i) \frac{4}{3} C r (s) + O_{2} (g) ⟶ \frac{2}{3} C r_{2} O_{3} (s)_{i} △_{f} G^{\circ} = - 540 k J (i i) \frac{4}{3} A I (s) + O_{2} (g) ⟶ \frac{2}{3} A l_{2} O_{3} (s)_{i} △_{f} G^{\circ} = - 827 k J$
Subtracting Eq. (i) from Eq. (ii) we get
$\frac{2}{3} C r_{2} O_{3} (s) + \frac{4}{3} a l (s) ⟶ \frac{2}{3} A l_{2} O_{3} (s) + \frac{4}{3} C r (s); △_{f} G^{\circ} = - 287 k J$

The value of $△_{f} G^{\circ}$ for formation of $C r_{2} O_{3}$ is - 540 kJ/mol is higher than Al2O3 is - 827 kJ/ mol. Therfore, the reduction of $C r_{2} O_{3}$ with AI is possible.

As $△_{f} G^{\circ}$ comes out to be negative, the reaction is feasible, i.e., Al can be used for the reduction of $C r_{2} O_{3}$

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