Explain Gibbs free energy and the sign that indicates spontaneity at constant T and P.

• A. ΔG = ΔH − TΔS; spontaneous if ΔG < 0.
• B. ΔG is always positive for spontaneous reactions.
• C. Spontaneity is determined by ΔS alone.
• D. ΔG = ΔS − TΔH.

Answer: (A)

Spontaneity at constant temperature and pressure is decided by Gibbs free energy. Gibbs free energy combines energy changes and the tendency toward disorder into a single quantity that tells us whether a process can proceed on its own. The rule is that a process will be spontaneous under these conditions if the change in Gibbs free energy is negative.

The relationship is ΔG = ΔH − TΔS, where ΔH is the enthalpy change, ΔS is the entropy change, and T is the absolute temperature. If the enthalpy decreases (ΔH negative) and/or the entropy increases (ΔS positive), ΔG tends to be negative, especially at higher temperatures since the TΔS term grows with T. When ΔG is negative, the process can proceed spontaneously; when ΔG is zero, it’s at equilibrium; when ΔG is positive, it is non-spontaneous under those conditions.

This is why the best answer states the correct formula and that spontaneity corresponds to ΔG < 0. The other statements either misstate the sign rule, claim ΔS alone decides spontaneity, or give an incorrect formula for ΔG.