1. Core Concepts: Gibbs Free Energy and Favorability★★☆☆☆⏱ 3 min

Gibbs free energy ($G$) is a combined thermodynamic state function that links enthalpy ($\Delta H$) and entropy ($\Delta S$) to predict whether a process will be thermodynamically favorable for reactions at constant temperature and pressure — the condition that describes almost all reactions studied in AP Chemistry.

By universal convention: a negative $\Delta G$ corresponds to a thermodynamically favorable process, while a positive $\Delta G$ corresponds to an unfavorable process. When $\Delta G=0$, the process is at equilibrium with no net change.

2. The Fundamental Equation: $\Delta G = \Delta H - T\Delta S$★★★☆☆⏱ 4 min

At constant temperature and pressure, the change in Gibbs free energy for any process is given by the equation:

Where $\Delta G$ = change in Gibbs free energy (kJ/mol), $\Delta H$ = enthalpy change (kJ/mol), $T$ = absolute temperature in Kelvin, and $\Delta S$ = entropy change of the system.

• If $\Delta H<0$ (exothermic) and $\Delta S>0$: $\Delta G<0$ at all temperatures (always favorable)

• If $\Delta H>0$ (endothermic) and $\Delta S<0$: $\Delta G>0$ at all temperatures (always unfavorable)

• If $\Delta H$ and $\Delta S$ have matching signs: temperature determines the sign of $\Delta G$ and thus favorability

Exam tip:

Always convert $\Delta S$ from J/mol·K to kJ/mol·K before plugging into the equation. AP exam questions almost always give $\Delta S$ in joules and $\Delta H$ in kilojoules, so missing this conversion will give you a wrong sign and incorrect answer.

3. Standard Gibbs Free Energy Calculations★★★☆☆⏱ 3 min

Standard Gibbs free energy change ($\Delta G^{\circ }$) is the change in Gibbs free energy when reactants in their standard states (1 atm pressure, 1 M concentration, pure solid/liquid, 298 K by default) are converted to products in their standard states. There are two common methods to calculate $\Delta G^{\circ }$:

When using standard free energies of formation, the reaction $\Delta G^{\circ }$ is calculated as:

Exam tip:

Remember the minus sign in the $\Delta G_{\text{rxn}}^{\circ }$ formula applies to the entire sum of reactants. If any $\Delta G_f^{\circ }$ of reactants is negative, you will subtract a negative which equals adding that value — always write out signs explicitly to avoid arithmetic errors.

4. $\Delta G$, $\Delta G^\circ$, and the Relationship to Equilibrium★★★★☆⏱ 4 min

$\Delta G^{\circ }$ only describes the Gibbs free energy change when the reaction is at standard state (all reactants and products at 1 M/1 atm, so $Q=1$). For any non-standard conditions, we calculate $\Delta G$ using:

When a reaction reaches equilibrium, $\Delta G=0$ (no net driving force) and $Q=K$ (the equilibrium constant). Substituting these values gives the key relationship connecting thermodynamics and equilibrium:

• $\Delta G^{\circ }<0\to \ln K>0\to K>1$: Products are favored at equilibrium

• $\Delta G^{\circ }>0\to \ln K<0\to K<1$: Reactants are favored at equilibrium

• $\Delta G^{\circ }=0\to \ln K=0\to K=1$: Equal amounts of reactants and products at equilibrium

Exam tip:

Always use $R=8.314$ J/mol·K for Gibbs free energy calculations, not $0.0821$ L·atm/mol·K (the gas constant used for ideal gas law problems). Using the wrong R will give you a K that is orders of magnitude off.