The formula
- Definition
G = H - TS- Change at constant temperature
ΔG = ΔH - TΔS- Link to the equilibrium constant
ΔG° = -RT·ln K- Temperature where the sign flips
T = ΔH / ΔS when ΔG = 0
What the symbols mean
| Symbol | Meaning | Unit |
|---|---|---|
ΔG | Free energy change; negative is spontaneous, positive is not, zero is equilibrium | kJ/mol (or J/mol) |
ΔH | Enthalpy change; negative releases heat | kJ/mol |
ΔS | Entropy change; positive means more disorder | J/(mol·K) |
T | Absolute temperature | K |
R | Molar gas constant | 8.314 J/(mol·K) |
K | Equilibrium constant for the reaction | dimensionless |
° | Standard state marker: 1 bar and 1 M, at the stated temperature | dimensionless |
When it applies
- Temperature and pressure are constant, which is the situation almost every chemistry problem describes.
- ΔH and ΔS have to share units before subtracting. Tables give ΔH in kilojoules and ΔS in joules, so divide ΔS by 1000 or multiply ΔH by 1000 first.
- Spontaneous says nothing about speed. A reaction with a large negative ΔG can still be too slow to observe, which is what activation energy governs.
- When ΔH and ΔS share a sign, spontaneity depends on temperature, and T = ΔH/ΔS locates the crossover.
Worked example
Problem. Limestone decomposes as CaCO₃(s) → CaO(s) + CO₂(g), with ΔH° = +178.3 kJ/mol and ΔS° = +160.6 J/(mol·K). Is it spontaneous at 298 K, and above what temperature does that change?
- Match the units by converting the entropy term: ΔS° = 160.6 J/(mol·K) = 0.1606 kJ/(mol·K).
- Evaluate the entropy term at 298 K: TΔS° = 298 × 0.1606 = 47.86 kJ/mol.
- Subtract: ΔG° = 178.3 - 47.86 = 130.44 kJ/mol, which is +130.4 kJ/mol. Positive, so the decomposition is not spontaneous at room temperature.
- Both terms are positive, so raising the temperature eventually wins. Set ΔG° = 0: T = ΔH° / ΔS° = 178.3 / 0.1606 = 1110 K.
- Above about 1110 K the TΔS° term exceeds ΔH°, ΔG° turns negative, and the decomposition becomes spontaneous, which is why lime kilns run hot.
Answer. ΔG° = +130.4 kJ/mol at 298 K, so not spontaneous, becoming spontaneous above about 1110 K.
Common mistakes
- Subtracting joules from kilojoules. This single unit mismatch is the most common wrong answer on this equation, and it is off by a factor of a thousand.
- Using Celsius for T. The equation needs kelvin, and at 25 °C the difference is a factor of about twelve in the entropy term.
- Reading spontaneous as fast. Diamond turning into graphite has a negative ΔG and takes geological time.
- Assuming a positive ΔH always blocks a reaction. A large positive ΔS can overcome it once the temperature is high enough.
Related formulas
- Nernst equation:
E_cell = E°_cell - (RT / nF)·ln Q - Hess's law:
ΔH_reaction = ΣΔH_steps - Arrhenius equation:
k = A·e^(-Ea / RT)