For a given chemical reaction A → B at 300 K the free energy change is -49.4 kJ mol⁻¹ and the enthalpy of reaction is 51.4 kJ mol⁻¹. The entropy change of the reaction is _____________ JK⁻¹ mol⁻¹.

Solution

Chemistry ma’am · 4 steps

Rearrange Δ G = Δ H - TΔ S for Δ S, and keep the minus sign on Δ G in place.

1. Start from Gibbs. At constant temperature and pressure the three quantities are linked by one equation. Rearrange it to get Δ S alone.

   Δ S = (Δ H - Δ G)/T

2. Put in numbers. Δ H - Δ G = 51.4 - (-49.4) = 100.8 kJ mol⁻¹. Divide by T = 300 K to get Δ S = 0.336 kJ K⁻¹ mol⁻¹.
3. Convert units. The answer is asked in joules, so multiply by 1000: 0.336 × 1000 = 336 J K⁻¹ mol⁻¹.
4. So. The entropy change is 336 J K⁻¹ mol⁻¹. It is positive, which fits a reaction that is endothermic and still spontaneous.

The common slip: 6.67. Dropping the minus sign on Δ G gives (51.4 - 49.4)/300 kJ, which is about 6.67 J, not 336.

The idea to keep. An endothermic reaction can only be spontaneous if TΔ S beats Δ H, so expect a positive Δ S. Always subtract a negative Δ G with its sign.

Answer from the NTA final answer key. Solution by PrepWiser.