Question

Sodium carbonate can be made by heating sodium bicarbonate:
2NaHCO3(s) → Na2CO3(s) + CO2(g) + H2O(g)

Given that ΔH° = 128.9 kJ and ΔG° = 33.1 kJ at25°C, above what minimum temperature will the reaction becomespontaneous under standard state conditions?

Answer 1

We know that, ΔG⁰ = ΔH⁰- TΔS⁰

  ΔH° = 128.9 kJ

  ΔG° = 33.1 kJ

   T = (25 + 273) K = 298 K

   ∴ 33.1 kJ = 128.9 kJ - 298(ΔS⁰)

        ΔS⁰ = 0.321 kJ /K

The temperature above which the reaction is spontaneouscan be obtained by setting ΔG°= 0

             ΔG⁰ = ΔH⁰ -TΔS⁰

                 0 = ΔH⁰ - TΔS⁰

                  T= ΔH⁰ / ΔS⁰

                    = 128.9 kJ / 0.321 kJ /K

                    =401.6 K

At a temperature above 401.6 K, TΔS⁰ hasa larger magnitude than ΔH⁰ andtherefore,  ΔG⁰ becomesnegative.

Thus, the reaction becomes spontaneous at 401.6 K