Which form expresses the Gibbs free energy and when is a process spontaneous at constant temperature and pressure?

• A. ΔG = ΔH − TΔS; spontaneous when ΔG > 0
• B. ΔG = ΔH − TΔS; spontaneous when ΔG < 0
• C. ΔG = ΔS − TΔH; spontaneous when ΔG < 0
• D. ΔG = ΔU − TΔS; spontaneous when ΔG < 0

Answer: (B)

Gibbs free energy combines enthalpy and entropy to tell us if a process can happen on its own at constant temperature and pressure. Since G = H − TS, looking at changes under steady temperature means ΔG = ΔH − TΔS. Here, ΔH reflects heat exchanged at constant pressure, and ΔS is the system’s entropy change. If this ΔG becomes negative, the system can lower its free energy by proceeding, so the process is spontaneous under those conditions. If ΔG is positive, the process would require energy input and is not spontaneous; if ΔG is zero, the system is at equilibrium. The other forms mix up H, S, or U and give the wrong spontaneity criterion, so they don’t describe Gibbs free energy correctly or the correct sign for spontaneity.