Give reason : Reduction of `Cr_(2) O_(3)` with `Al` is thermodynamically feasible, yet it does no occur at room temperature.

Explanation

The interpretation of `Delta_(f) G^(Ө)` is dependent on `K(Delta G = - RT 1n K)` the equilibrium constant. Since in the abovementioned reaction all the reactants and products are solids at room temperature, there does not exist any equilibrium between the reactants and the products. That is why the reaction does not occur at room temperature. However, at higher temperature, when chromium `(Cr)` melts, value of `T Delta S` increases `(Delta_(f) G^(Ө) = Delta_(f) H^(Ө) - T Delta_(f) S^(Ө))`. As a result, `Delta_(f) G^(Ө)` becomes more negative and hence the reaction proceeds rapidly.