The reaction,
Cr2O3 + 2Al → Al2O3 + 2Cr
(ΔGθ = -421kJ) is thermodynamically feasible as is apparent from the Gibbs energy value. Why does it not take place at room temperature?
Solution 1
The change in Gibbs energy is related to the equilibrium constant, K as
`triangleG = -RTInK`
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
`triangleG = triangleH-TtriangleS`
Increasing the temperature increases the value of `TtriangleS` making the value of `triangleG` more and more negative. Therefore, the reaction becomes more and more feasible as the temperature is increased.
Solution 2
This is explained on the basis of Keq, the equilibrium constant. In the given redox reaction, all reactants and products are solids at room temperature, so, there is no equilibrium between the reactants and products and hence the reactions does not occur at RT. At high temperature, Cr melts and values of TAS increases. As a result, the value of `triangle_rG^theta` becomes more negative and hence the reaction proceeds rapidlyt
