Chemical Thermodynamics — Formula Sheet

$W$: Work (J) · $P_{ext}$: Constant external pressure (Pa or bar) · $\Delta V$: Change in volume V₂ − V₁ (m³ or L)

Work against a constant external pressure. Expansion (ΔV > 0) gives W < 0; compression gives W > 0. Free expansion into vacuum (P_ext = 0) gives W = 0. 1 L bar = 100 J.

$n$: Amount of gas (mol) · $R$: Gas constant = 8.314 J K⁻¹ mol⁻¹ · $T$: Constant temperature (K) · $V_1,V_2$: Initial and final volumes

For n mol of an ideal gas at constant T on a reversible path. The work done by the gas has its largest possible magnitude. Use R = 8.314 J K⁻¹ mol⁻¹ to get W in joules.

At constant temperature Boyle's law gives V₂/V₁ = P₁/P₂. Note that the pressure ratio is initial over final.

$\Delta U$: Change in internal energy of the system (J) · $Q$: Heat exchanged; + when absorbed by the system (J) · $W$: Work; + when done on the system (J)

Sign convention used in the Maharashtra textbook (IUPAC): Q is positive when heat is absorbed by the system and negative when heat is released; W is positive when work is done ON the system and negative when work is done BY the system. Do not mix this with the older form ΔU = Q − W, in which W meant work done by the system.

U of an ideal gas depends only on T, so in isothermal expansion the heat absorbed equals the work done by the gas. In an adiabatic process work done on the system raises U (temperature rises); adiabatic expansion lowers U (temperature falls).

At constant volume no pressure–volume work is done, so the heat absorbed equals ΔU. At constant pressure part of the heat absorbed is used for expansion work.

At constant pressure the heat absorbed equals the enthalpy change. ΔH < 0 for exothermic and ΔH > 0 for endothermic processes.

$\Delta n_g$: Change in moles of gas (products − reactants) · $R$: 8.314 J K⁻¹ mol⁻¹ = 8.314 × 10⁻³ kJ K⁻¹ mol⁻¹

Δn_g = moles of gaseous products − moles of gaseous reactants; ignore solids and liquids. If Δn_g = 0, ΔH = ΔU. Equivalent form: Q_P = Q_V + Δn_g RT.

At constant T and P. If Δn_g > 0 the system expands and W is negative (work done by the system). If Δn_g < 0, W is positive (work done on the system).

Multiply each ΔfH° by its stoichiometric coefficient. ΔfH° of an element in its standard state (H₂(g), O₂(g), C(graphite)) is zero.

For reactions in the gas phase. The order is reactants − products, the opposite of the formation formula, because breaking bonds absorbs energy and forming bonds releases it.

Enthalpy is a state function, so ΔH is the same whether the change takes place in one step or several. Thermochemical equations can be added, subtracted and multiplied like algebraic equations. Example: ΔsubH = ΔfusH + ΔvapH.

Heat exchanged reversibly divided by the absolute temperature. Unit J K⁻¹ (J K⁻¹ mol⁻¹ for molar values). For a phase change at its transition temperature, ΔS = ΔH/T, e.g. ΔvapS = ΔvapH/T_b.

A process is spontaneous when the total entropy of system and surroundings increases; at equilibrium ΔS_total = 0. At constant T and P, ΔS_surr = −ΔH_sys/T.

At constant T and P. Use T in kelvin and express ΔS in kJ K⁻¹ when ΔH is in kJ. Standard form: ΔG° = ΔH° − TΔS°.

ΔH < 0, ΔS > 0: spontaneous at all T. ΔH > 0, ΔS < 0: non-spontaneous at all T. ΔH < 0, ΔS < 0: spontaneous below T = ΔH/ΔS. ΔH > 0, ΔS > 0: spontaneous above T = ΔH/ΔS. Assumes ΔH and ΔS do not change with T.

ΔG° < 0 means K > 1 (products favoured); ΔG° > 0 means K < 1. With R = 8.314 J K⁻¹ mol⁻¹, ΔG° must be in J mol⁻¹.