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

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.

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.