Gibbs Free Energy and Thermodynamic Favorability — AP Chemistry
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:
\Delta G = \Delta H - T\Delta S
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:
\Delta G^\circ_{\text{rxn}} = \sum n\Delta G^\circ_f(\text{products}) - \sum m\Delta G^\circ_f(\text{reactants})
Exam tip: Remember the minus sign in the $\Delta G^\circ_{\text{rxn}}$ formula applies to the entire sum of reactants. If any $\Delta G^\circ_f$ 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:
\Delta G = \Delta G^\circ + RT \ln Q
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 = -RT \ln K
- $\Delta G^\circ < 0 \rightarrow \ln K > 0 \rightarrow K > 1$: Products are favored at equilibrium
- $\Delta G^\circ > 0 \rightarrow \ln K < 0 \rightarrow K < 1$: Reactants are favored at equilibrium
- $\Delta G^\circ = 0 \rightarrow \ln K = 0 \rightarrow K = 1$: 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.
Common Pitfalls
Why: AP questions almost always give ΔH in kJ and ΔS in J, so students plug in numbers without checking units
Why: Students confuse thermodynamic favorability with kinetic feasibility. ΔG only describes favorability, not how fast the reaction proceeds
Why: Students mix up the meaning of ΔG (any conditions) and ΔG° (only standard state)
Why: Students forget the second law refers to the entropy of the universe, not just the system
Why: Students remember R from gas law problems and use it by mistake
Why: Students forget the formula is products minus reactants, so a negative reactant ΔG°f becomes a positive term