Chemical Thermodynamics

A thermodynamic system is the part of the universe under study; everything else is the surroundings.

Exothermic reactions release heat ($\Delta H < 0$). Endothermic reactions absorb heat ($\Delta H > 0$).

Energy is measured in joules (J) or calories (1 cal = 4.184 J).

The first law states that energy is conserved: $\Delta U = Q - W$ (or $Q + W$ depending on sign convention).

At constant pressure, the heat exchanged equals the enthalpy change: $\Delta H = Q_P$.

Standard enthalpy of formation $\Delta H_f^\circ$: the enthalpy change when 1 mole of a compound is formed from its elements in their standard states.

Hess's law: the enthalpy change of a reaction depends only on the initial and final states, not on the pathway. Therefore, we can sum the enthalpies of intermediate steps: $$\Delta H^\circ_{rxn} = \sum \nu_i \Delta H_{f}^\circ(\text{products}) - \sum \nu_i \Delta H_f^\circ(\text{reactants})$$

The second law: the entropy ($S$) of the universe increases in spontaneous processes. Entropy is a measure of disorder.

The third law: the entropy of a perfect crystal at $T=0\,\mathrm{K}$ is zero.

Standard molar entropies $S^\circ$ are tabulated. The entropy change of a reaction: $$\Delta S^\circ_{rxn} = \sum \nu_i S^\circ(\text{products}) - \sum \nu_i S^\circ(\text{reactants})$$

The Gibbs free energy combines enthalpy and entropy: $G = H - TS$. At constant $T$: $$\Delta G = \Delta H - T\Delta S$$

Spontaneity criteria:

• $\Delta G < 0$: spontaneous (exergonic)
• $\Delta G > 0$: non-spontaneous (endergonic)
• $\Delta G = 0$: equilibrium

The transition temperature where $\Delta G = 0$: $T_{trans} = \Delta H / \Delta S$.