The Gibbs free energy relation ΔG = ΔH - TΔS. If ΔH > 0 and ΔS > 0, the reaction is spontaneous at high temperature when?

• A. When T < ΔH/ΔS
• B. When T > ΔH/ΔS
• C. For any temperature
• D. Only at T = 0

Answer: (B)

Spontaneity at constant pressure and temperature is determined by ΔG being negative. With ΔG = ΔH − TΔS, if both ΔH and ΔS are positive, increasing temperature makes the TΔS term larger and more capable of overcoming ΔH. The temperature where ΔG changes sign is T = ΔH/ΔS. When T is greater than that value, ΔG becomes negative and the process is spontaneous; when T is below it, ΔG is positive and the process is not spontaneous. At T = ΔH/ΔS, ΔG is zero, indicating equilibrium. At T = 0, ΔG equals ΔH and remains positive. So spontaneity at high temperature corresponds to T > ΔH/ΔS.