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Second Law of Thermodynamics

The value of ...

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The value of $Δ_{f} G^{0}$ for formation of $C r_{2} O_{3}$ is $- 540 k J m o l^{- 1}$ and that of $A l_{2} O_{3}$ is $- 827 k J m o l^{- 1}$ . Is the reduction of $C r_{2} O_{3}$ possible with $A l$ ?

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Solution

$\frac{4}{2} A l + O_{2} \to \frac{2}{3} A l_{2} O_{3} Δ_{f} G^{o} (A l, A l_{2} O_{3} = - 827 k J / m o l)$ ......(i)

$\frac{4}{3} C r + O_{2} \to \frac{2}{3} C r_{2} O_{3} Δ_{f} G^{o} (C r, C r_{2} O_{3}) = - 540 k J / m o l$ ......(ii)

Subtract equation (ii) from equation (i), we get

$\frac{4}{3} A l + \frac{2}{3} C r_{2} O_{3} \to \frac{2}{3} A l_{2} O_{3} + \frac{4}{3} C r Δ_{r} G^{o} = - 287 k J / m o l$

Because, for the combined reaction, $Δ_{r} G^{o} < 0$ (negative), the reaction is spontaneous and the reduction of $C r_{2} O_{3}$ by $A l$ is possible.

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