Thermodynamics, Gibbs, and Spontaneity Cheat Sheet

A printable reference covering enthalpy, entropy, Gibbs free energy, equilibrium, and spontaneity for grades 11-12.

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Thermodynamics explains how energy changes determine whether chemical and physical processes are likely to occur. This cheat sheet helps students connect heat flow, disorder, temperature, and spontaneity in one organized reference. It is especially useful for predicting reactions using enthalpy, entropy, and Gibbs free energy. These ideas are central in chemistry, biology, environmental science, and engineering.

Key Facts

Gibbs free energy is calculated by $\Delta G = \Delta H - T\Delta S$ , where $T$ must be in kelvins.
A process is spontaneous at constant temperature and pressure when $\Delta G < 0$ .
A process is nonspontaneous at constant temperature and pressure when $\Delta G > 0$ .
A system is at equilibrium when $\Delta G = 0$ and there is no net change in reaction progress.
Entropy change can be estimated by $\Delta S = S_{\text{products}} - S_{\text{reactants}}$ using standard molar entropy values.
Standard Gibbs free energy and equilibrium are related by $\Delta G^\circ = -RT\ln K$ .
For nonstandard conditions, Gibbs free energy is calculated by $\Delta G = \Delta G^\circ + RT\ln Q$ .
A temperature threshold for spontaneity occurs when $\Delta G = 0$ , so $T = \frac{\Delta H}{\Delta S}$ if $\Delta H$ and $\Delta S$ use compatible units.

Vocabulary

Enthalpy: Enthalpy is the heat content of a system at constant pressure, represented by $H$ .
Entropy: Entropy is a measure of energy dispersal or disorder in a system, represented by $S$ .
Gibbs Free Energy: Gibbs free energy is the energy available to do useful work, represented by $G$ .
Spontaneous Process: A spontaneous process is one that can occur without continuous outside energy input when $\Delta G < 0$ .
Equilibrium Constant: The equilibrium constant $K$ compares product and reactant amounts at equilibrium for a reversible reaction.
Reaction Quotient: The reaction quotient $Q$ compares product and reactant amounts at any moment before equilibrium is reached.

Common Mistakes to Avoid

Using Celsius instead of kelvins in $\Delta G = \Delta H - T\Delta S$ is wrong because thermodynamic temperature must be absolute.
Forgetting to convert $\Delta S$ from $\text{J}\,\text{mol}^{-1}\,\text{K}^{-1}$ to $\text{kJ}\,\text{mol}^{-1}\,\text{K}^{-1}$ is wrong when $\Delta H$ is in $\text{kJ}\,\text{mol}^{-1}$ .
Assuming every exothermic reaction is spontaneous is wrong because entropy and temperature also affect $\Delta G$ .
Confusing $\Delta G$ with $\Delta G^\circ$ is wrong because $\Delta G^\circ$ applies only to standard-state conditions.
Treating a positive $\Delta S$ as always spontaneous is wrong because $\Delta H$ may still make $\Delta G$ positive at a given temperature.

Practice Questions

1 Calculate $\Delta G$ for a reaction with $\Delta H = -45.0\ \text{kJ}\,\text{mol}^{-1}$ , $\Delta S = -120\ \text{J}\,\text{mol}^{-1}\,\text{K}^{-1}$ , and $T = 298\ \text{K}$ .
2 Find the temperature at which a reaction changes spontaneity if $\Delta H = 80.0\ \text{kJ}\,\text{mol}^{-1}$ and $\Delta S = 200\ \text{J}\,\text{mol}^{-1}\,\text{K}^{-1}$ .
3 Use $\Delta G^\circ = -RT\ln K$ to determine whether $K$ is greater than $1$ or less than $1$ when $\Delta G^\circ = -12.5\ \text{kJ}\,\text{mol}^{-1}$ at $298\ \text{K}$ .
4 Explain why a reaction with $\Delta H > 0$ and $\Delta S > 0$ may be nonspontaneous at low temperature but spontaneous at high temperature.

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