Which combination corresponds to a thermally unfavorable (endothermic) but entropically favorable process?

Which combination corresponds to a thermally unfavorable (endothermic) but entropically favorable process?

• A. +ΔH and +ΔS
• B. -ΔH and -ΔS
• C. +ΔH and -ΔS
• D. -ΔH and +ΔS

Answer: (A)

The key idea is how Gibbs free energy dictates spontaneity: ΔG = ΔH − TΔS. A process that absorbs heat has a positive ΔH, while one that becomes more disordered has a positive ΔS. Because the −TΔS term subtracts more as temperature rises, a positive ΔS can overcome a positive ΔH at higher temperatures, making ΔG negative. So a thermally unfavorable (endothermic) process that is entropically favorable has +ΔH and +ΔS. This combination means the process isn’t favorable at low temperatures, but can become favorable at higher temperatures due to the large TΔS contribution. Other sign patterns either reinforce nonspontaneity at all temperatures or don’t allow the TΔS term to overcome ΔH.

The key idea is how Gibbs free energy dictates spontaneity: ΔG = ΔH − TΔS. A process that absorbs heat has a positive ΔH, while one that becomes more disordered has a positive ΔS. Because the −TΔS term subtracts more as temperature rises, a positive ΔS can overcome a positive ΔH at higher temperatures, making ΔG negative. So a thermally unfavorable (endothermic) process that is entropically favorable has +ΔH and +ΔS. This combination means the process isn’t favorable at low temperatures, but can become favorable at higher temperatures due to the large TΔS contribution. Other sign patterns either reinforce nonspontaneity at all temperatures or don’t allow the TΔS term to overcome ΔH.