The reaction, Cr_2O_3+2Al _2O_3+2Cr ( ^ =-421 kJ) is thermodynami… - Vidyadip

Question

The reaction, $\text{Cr}_2\text{O}_3+2\text{Al}\rightarrow\text{Al}_2\text{O}_3+2\text{Cr}\ \ \ \ \ (\Delta\text{G}^{\ominus}=-421\text{ kJ})$ is thermodynamically feasible as is apparent from the Gibbs energy value. Why does it not take place at room temperature?

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Answer

The change in Gibbs energy is related to the equilibrium constant, K as
$\Delta\text{G}=-\text{RTln}\Delta\text{G}=-\text{RT lnk}$
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. Certain amount of activation energy is essential even for such reactions which are thermodynamically feasible.

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