Chemistry · Applications of Thermodynamics · 14 min read · Updated 2026-05-11
Entropy and Gibbs Free Energy — AP Chemistry
AP Chemistry · Applications of Thermodynamics · 14 min read
1. Entropy, Second Law, and Predicting Entropy Changes★★☆☆☆⏱ 4 min
Entropy ($S$) is a thermodynamic state function that quantifies the degree of disorder, or the number of possible microstates available to a system. It is defined by Boltzmann’s formula:
S = k \ln W
where $k$ is the Boltzmann constant and $W$ is the number of distinct microstates a system can occupy. More microstates = higher entropy = greater disorder.
The third law of thermodynamics tells us that a perfect crystalline substance at 0 K has zero entropy, so all pure substances above 0 K have a positive standard molar entropy $S^\circ$ (entropy of 1 mole at 1 atm and 298 K). To predict the sign of $\Delta S_\text{sys}$, follow these general rules:
Gases have far higher entropy than liquids, which have higher entropy than solids
An increase in total moles of gas increases entropy
Dissolving a crystalline solid increases entropy
Increasing temperature increases entropy
2. Calculating Standard Entropy of Reaction★★☆☆☆⏱ 3 min
The standard entropy change for a reaction $\Delta S^\circ_{\text{rxn}}$ is calculated from tabulated standard molar entropies of reactants and products. A key difference from standard enthalpy of formation: unlike $\Delta H_f^\circ$, which is zero for elements in their standard state, $S^\circ$ is always positive for all substances (including elements) above 0 K. Never skip including $S^\circ$ for elements in your calculation. The formula is:
where $n$ and $m$ are the stoichiometric coefficients of products and reactants, respectively. $S^\circ$ is almost always reported in units of $\text{J/(mol·K)}$, which is important for later Gibbs free energy calculations where enthalpy uses kJ units.
3. Gibbs Free Energy and Spontaneity★★★☆☆⏱ 4 min
At constant temperature and pressure (the conditions for most chemical reactions), Gibbs free energy change combines enthalpy and entropy into a single value that directly predicts spontaneity. The core formula is:
\Delta G = \Delta H - T\Delta S
where $T$ is absolute temperature in Kelvin (always positive). The spontaneity rules are:
$\Delta G < 0$: Spontaneous in the forward direction
$\Delta G = 0$: Reaction is at equilibrium
$\Delta G > 0$: Non-spontaneous in the forward direction (spontaneous in reverse)
For standard state conditions, the formula becomes $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$. We can find the threshold temperature where a reaction switches spontaneity by setting $\Delta G^\circ = 0$, giving:
T = \frac{\Delta H^\circ}{\Delta S^\circ}
This is only useful when $\Delta H$ and $\Delta S$ have the same sign; if they have opposite signs, the reaction is always or never spontaneous regardless of temperature.
4. Relationship Between ΔG° and Equilibrium Constant K★★★☆☆⏱ 3 min
Gibbs free energy connects thermodynamics to chemical equilibrium: the standard Gibbs free energy change is directly related to the equilibrium constant $K$ of a reaction by:
\Delta G^\circ = -RT \ln K
where $R = 8.314 \text{ J/(mol·K)}$ (or $0.008314 \text{ kJ/(mol·K)}$) and $T$ is absolute temperature. The key interpretations are:
If $\Delta G^\circ < 0$, $\ln K > 0$, so $K > 1$: Products are favored at equilibrium
If $\Delta G^\circ = 0$, $\ln K = 0$, so $K = 1$: Products and reactants are equally favored at equilibrium
If $\Delta G^\circ > 0$, $\ln K < 0$, so $K < 1$: Reactants are favored at equilibrium
Common Pitfalls
Why: $\Delta S$ is always reported in J per mol-K, while $\Delta H$ is almost always reported in kJ per mol, leading to a 1000x error in $\Delta G$
Why: Students confuse the convention for enthalpy of formation with entropy, which is non-zero for all substances above 0 K
Why: Solids and liquids have negligible entropy compared to gases, so total moles can give the wrong sign
Why: Students confuse thermodynamic spontaneity with reaction kinetics
Why: Students confuse standard state $\Delta G^\circ$ with non-standard $\Delta G$, which depends on reactant/product concentrations