What is the equation relating ∆G, ∆H, and ∆S?

What is the equation relating ∆G, ∆H, and ∆S?

• A. ∆G = ∆H + T∆S
• B. ∆G = ∆S - T∆H
• C. ∆G = ∆H - T∆S
• D. ∆G = ∆H / T∆S

Answer: (C)

The relation shows how energy available to do work at constant pressure and temperature is determined by enthalpy change and the temperature-scaled entropy change. Gibbs free energy tells you whether a process can occur on its own: negative ΔG means spontaneous. Enthalpy change reflects heat absorbed or released, while entropy change reflects changes in disorder. The key is the minus sign in front of TΔS: as entropy increases (positive ΔS), the TΔS term lowers ΔG, making the process more favorable at a given temperature. Temperature matters because it scales how much entropy contributes. If ΔH is positive, a large positive ΔS at sufficiently high T can still yield a negative ΔG. This is captured by the equation ΔG = ΔH − TΔS.

The relation shows how energy available to do work at constant pressure and temperature is determined by enthalpy change and the temperature-scaled entropy change. Gibbs free energy tells you whether a process can occur on its own: negative ΔG means spontaneous. Enthalpy change reflects heat absorbed or released, while entropy change reflects changes in disorder. The key is the minus sign in front of TΔS: as entropy increases (positive ΔS), the TΔS term lowers ΔG, making the process more favorable at a given temperature. Temperature matters because it scales how much entropy contributes. If ΔH is positive, a large positive ΔS at sufficiently high T can still yield a negative ΔG. This is captured by the equation ΔG = ΔH − TΔS.