Delta G = Delta H - T Delta S: Sign Table and What Delta G Means

Gibbs free energy combines enthalpy and entropy: ΔG = ΔH - TΔS, with T in kelvin.

What the sign of ΔG means

• ΔG < 0: spontaneous (exergonic) in the forward direction.
• ΔG > 0: not spontaneous (endergonic) as written; the reverse is favored.
• ΔG = 0: at equilibrium, with no net change.

Spontaneous means thermodynamically favorable. It says nothing about speed, which depends on activation energy.

Sign table

Temperature only matters when ΔH and ΔS have the same sign, because then the two terms compete.

Worked example

ΔH = -40 kJ/mol and ΔS = -100 J/(mol K) at 298 K.

• TΔS = 298 × (-0.100 kJ) = -29.8 kJ.
• ΔG = -40 - (-29.8) = -10.2 kJ/mol, spontaneous.
• The crossover temperature is ΔH / ΔS = -40 / -0.100 = 400 K. The reaction is spontaneous below 400 K.

Convert ΔS from J to kJ before combining it with ΔH.

Related equations

• ΔG = ΔG° + RT ln Q
• ΔG° = -RT ln K

Common traps

• Using Celsius for T.
• Mixing J and kJ.
• Reading positive ΔG as "never happens". It can be driven by coupling to a negative ΔG.

One-minute recap

• ΔG < 0 spontaneous; = 0 equilibrium.
• Same-sign ΔH and ΔS make temperature decisive.
• Spontaneous does not mean fast.