Why does it not take place at room temperature?

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The reaction,  Cr2O3 + 2 Al → Al2 O3 + 2 Cr (ΔG0 = – 421 kJ) Is thermodynamically feasible as is apparent from Gibbs energy value. The change in Gibbs free energy is related to the equilibrium constant, k as 

       ΔG = - RT ln K

A certain amount of energy activation is required even for such reactions which are thermodynamically feasible, therefore heating is required.

        ΔG = ΔH + S      

Increasing the temperature increases the value of TΔS, making the value of  ΔG more and more negative. Therefore, the reaction becomes more and more feasible as the temperature is increased.

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