For dissolution endothermic with positive ΔS, how does ΔG° change with increasing temperature?

• A. Spontaneous at all temperatures
• B. Spontaneous at low temperatures
• C. Spontaneous at high temperatures
• D. Not spontaneous at any temperature

Answer: (C)

This question hinges on how temperature affects spontaneity through Gibbs free energy. For dissolution that is endothermic and increases disorder, ΔH° > 0 and ΔS° > 0. The relationship is ΔG° = ΔH° − TΔS°. Since ΔS° is positive, the term TΔS° grows with temperature and subtracts from the positive ΔH°. At low temperatures, ΔH° dominates and ΔG° remains positive, so dissolution isn’t spontaneous. As temperature increases, TΔS° can surpass ΔH°, making ΔG° negative and dissolution spontaneous. There is a threshold temperature T = ΔH°/ΔS° where this switch occurs. Hence, the process becomes spontaneous at high temperatures.