The reaction :
`Cr_(2)O_(3)+2Al to Al_(2)O_(3)+2Cr(triangleG^(0)= -421 kJ)`.
is thermodynamically feasible as is apparent from the gibbs energy value. Why does it not take place at room temperature ?

Explanation

In the given redox reaction, all the reactants and the products are solids at room temperature, therefore, there does not exist any equilibrium between the recatants and the products and hence the reaction does not occur at room temperature. The interpretation of `triangleG` is based on `K(triangleG^(0)= -RT ln K)` where K is the equilibrium constant. When there is no equilibrium in the solid state and the value of K becomes insignificant. However, at high temperature, when chromium melts, the value of `T triangle S` increases. As a result, the value of `triangle_(r )G^(0)` becomes more `-ve` and hence the reaction proceeds rapidly.