Metallrgical process can be explained in terms of thermodynamic principles. Reduction of `Cr_2O_3` by Aluminium metal is accompained by negative `DeltaG^@`value and is thermodynamically feasible. Why does this reaction fail at room temperature?

Explanation

Delta G_i^0=-RT. In .k_t,. where .k. is the equilibrium constant. In the given redox reaction. since all the reactants and products are solids at room temperature there exists.no equilibrium between the reactants and products, Hence the reaction does not occur at room temperature.
But at high temperature, when chromium melts .T Delta S. value increases. Hence in the equation
.Delta G=Delta H-T Delta S, Delta G. value becomes more nega tive and hence the reaction proceeds rapidly.