For the reaction at 298 K, 2 A+B → C, Δ H=400 kJ mol⁻¹ and Δ S=0.2 kJ mol⁻¹ K⁻¹. The reaction will become spontaneous above __________ K.

Solution

Chemistry ma’am · 3 steps

Set Δ G = 0 to find the crossover temperature, then check which side is spontaneous.

1. Read the signs. Both Δ H and Δ S are positive. In Δ G = Δ H - TΔ S, a positive Δ H works against the reaction and the TΔ S term works for it. So the reaction turns spontaneous only once T is high enough.
2. Find the boundary. The switch happens where Δ G = 0, that is, where Δ H = TΔ S. Both values are already in kJ, so the units match.

   T = (Δ H)/(Δ S) = (400 kJ mol⁻¹)/(0.2 kJ mol⁻¹ K⁻¹) = 2000 K

3. So. Above 2000 K, TΔ S exceeds Δ H, so Δ G becomes negative. The reaction becomes spontaneous above 2000 K.

The common slip: 2. Taking Δ H in kJ but Δ S as 200 J mol⁻¹ K⁻¹ gives 2 K, not 2000. Use the same energy unit for both.

The idea to keep. When Δ H and Δ S have the same sign, temperature decides spontaneity. The switch point is T = Δ H/Δ S. Put both in the same energy unit first.

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