Chemical Thermodynamics — Notes

The system is the part of the universe under study; the surroundings exchange energy with it across a boundary.

• Open: exchanges matter and energy (tea in an open cup).
• Closed: exchanges energy only (a sealed tube in a water bath).
• Isolated: exchanges neither (an ideal vacuum flask).

State functions ($p, V, T, U, H, S, G$) depend only on the present state, so their changes depend only on the initial and final states. Path functions ($q$, $w$) depend on the route.

Extensive properties depend on the amount ($m, V, U, H, S, G$); intensive ones do not ($T, p$, density, molar quantities). The ratio of two extensive properties is intensive.

IUPAC sign convention: viewed from the system, energy entering is positive. Work done on the system: $w > 0$. Work done by the system (expansion): $w < 0$. Heat absorbed: $q > 0$.

Pressure–volume work:

• Free expansion into vacuum: $w = 0$.
• Constant external pressure: $w = -p_\text{ex}\Delta V$ ($1\ \text{L bar} = 100\ \text{J}$).
• Isothermal reversible, ideal gas: $w = -2.303\,nRT\log(V_2/V_1)$; this is the maximum work obtainable.

First law: $\Delta U = q + w$. For an isolated system $\Delta U = 0$; for an adiabatic change $\Delta U = w$; for an isothermal change of an ideal gas $\Delta U = 0$, so $q = -w$.

Enthalpy $H = U + pV$ is a state function. At constant pressure $q_p = \Delta H$; at constant volume $q_V = \Delta U$.

For reactions involving gases: $\Delta H = \Delta U + \Delta n_g RT$, where $\Delta n_g$ is moles of gaseous products minus moles of gaseous reactants. If $\Delta n_g = 0$, $\Delta H = \Delta U$.

Heat capacity $C = q/\Delta T$ (extensive); molar heat capacity per mole, specific heat per gram. $\Delta U = nC_V\Delta T$, $\Delta H = nC_p\Delta T$, and for an ideal gas $C_p - C_V = R$.

Exothermic: $\Delta H < 0$ (products lower in enthalpy). Endothermic: $\Delta H > 0$.

Bomb calorimeter (constant volume) measures $\Delta U$; $q = C_\text{cal}\Delta T$; then convert with $\Delta H = \Delta U + \Delta n_g RT$. A constant-pressure (coffee-cup) calorimeter measures $\Delta H$: $q = mc\Delta T$.

Standard enthalpy changes (per mole, 1 bar, usually 298 K):

• Formation $\Delta_fH^\circ$: one mole of compound from elements in reference states; zero for an element.
• Combustion $\Delta_cH^\circ$: one mole burnt completely in oxygen; always negative.
• Atomisation $\Delta_aH^\circ$: one mole of gaseous atoms from the element (or compound).
• Sublimation, fusion, vaporisation (phase transitions): positive.
• Ionisation enthalpy: removing one electron from a gaseous atom (Na: +496 kJ mol⁻¹).
• Solution: dissolving one mole in a large excess of solvent (NaOH −44.5, NH₄NO₃ +25.7 kJ mol⁻¹).
• Dilution: enthalpy change on adding solvent to a solution.
• Neutralisation of a strong acid and strong base: about −57 kJ per mole of water.

Hess’s law: the enthalpy change of a reaction is the same whether it occurs in one step or in several, because $H$ is a state function. Reversing an equation changes the sign of $\Delta H$; multiplying scales it; equations and enthalpies can be added.

Bond enthalpy is the energy to break one mole of a bond in the gas phase (average value for many compounds). For gaseous reactions, $\Delta_rH \approx \sum(\text{bonds broken}) - \sum(\text{bonds formed})$. Typical values (kJ mol⁻¹): H–H 436, C–H 414, C–C 347, C=C 611, O=O 498, O–H 463, C=O (CO₂) 799, Cl–Cl 242, H–Cl 431.

Entropy $S$ is a measure of disorder, a state function. For a reversible process $\Delta S = q_\text{rev}/T$. Entropy rises on melting, boiling, dissolving and when the number of gas moles increases. Second law: $\Delta S_\text{total} = \Delta S_\text{sys} + \Delta S_\text{surr} > 0$ for a spontaneous process.

Gibbs energy: $\Delta G = \Delta H - T\Delta S$ (constant $T$, $p$). $\Delta G < 0$: spontaneous; $= 0$: equilibrium; $> 0$: non-spontaneous.

Equilibrium: $\Delta G^\circ = -2.303\,RT\log K$. If $\Delta G^\circ < 0$, $K > 1$.