The reaction,

Question:

The reaction,

$\mathrm{Cr}_{2} \mathrm{O}_{3}+2 \mathrm{Al} \longrightarrow \mathrm{Al}_{2} \mathrm{O}_{3}+2 \mathrm{Cr} \quad\left(\Delta G_{\mathrm{o}}=-421 \mathrm{~kJ}\right)$

is thermodynamically feasible as is apparent from the Gibbs energy value.

Why does it not take place at room temperature?

Solution:

The change in Gibbs energy is related to the equilibrium constant, K as

$\Delta G=-\mathrm{R} T \ln K$

At room temperature, all reactants and products of the given reaction are in the solid state. As a result, equilibrium does not exist between the reactants and the products. Hence, the reaction does not take place at room temperature. However, at a higher temperature, chromium melts and the reaction takes place.

We also know that according to the equation

$\Delta G=\Delta H-T \Delta S$,

Increasing the temperature increases the value of making the value of  more and more negative. Therefore, the reaction becomes more and more feasible as the temperature is increased.

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