For the reaction at 298 K, 2A + B → C

= 400 kJ mol^–1 and = 0.2 kJ K^–1 mol^–1

At what temperature will the reaction become spontaneous considering and to be constant over the temperature range.

According to Gibbs Helmholtz equation

∆G = ∆H - T∆S, where

∆G = change in Gibbs energy

∆H = change in enthalpy, given as 400 kJ mol^-1

∆S = change in entropy, given as 0.2 kJ K^-1 mol^-1

T = temperature at which reaction occurs

For a reaction to be spontaneous, ∆G < 0, means it must be negative.

If ∆G = 0, it is in equilibrium.

So, for reaction to be spontaneous, ∆G < 0; ∆H - T∆S < 0; ∆H < T∆S;

(∆H / ∆S) < T; 400 / 0.2 = 2000 K < T

This implies that the temperature must be more than 2000K for the reaction to be spontaneous.