A reaction which is endothermic and has an overall increase in entropy is:

• A. spontaneous at low temperatures
• B. spontaneous at high temperatures
• C. always nonspontaneous
• D. always spontaneous

Answer: (B)

Verified step by step guidance

1. Recall the Gibbs free energy equation: \(\Delta G = \Delta H - T\Delta S\), where \(\Delta G\) determines spontaneity, \(\Delta H\) is the enthalpy change, \(T\) is the temperature in Kelvin, and \(\Delta S\) is the entropy change.
2. Identify the signs given: the reaction is endothermic, so \(\Delta H > 0\), and there is an overall increase in entropy, so \(\Delta S > 0\).
3. Analyze how temperature affects \(\Delta G\): since \(\Delta H\) is positive and \(\Delta S\) is positive, the term \(-T\Delta S\) becomes more negative as temperature increases.
4. At low temperatures, the positive \(\Delta H\) term dominates, making \(\Delta G\) positive (nonspontaneous). At high temperatures, the \(-T\Delta S\) term can outweigh \(\Delta H\), making \(\Delta G\) negative (spontaneous).
5. Conclude that the reaction is spontaneous at high temperatures because the entropy term drives the spontaneity when temperature is sufficiently high.