Core Equations

$\boxed{\Delta U = q + w} \quad \text{(First Law, IUPAC)}$

$\boxed{\Delta H = H_{products} - H_{reactants} = \Delta U + \Delta n_g RT}$

$\boxed{\Delta G = \Delta H - T\Delta S} \quad \text{(Gibbs equation)}$

$\boxed{\Delta G^\circ = -RT\ln K = -2.303\,RT\log K}$

$\boxed{\Delta S = \frac{q_{rev}}{T}}$

Work Expressions

$w_{free} = 0 \quad (P_{ext} = 0)$

$w_{irrev} = -P_{ext}(V_2 - V_1) = -P_{ext}\,\Delta V$

$w_{rev} = -nRT\ln\frac{V_2}{V_1} = -2.303\,nRT\log\frac{V_2}{V_1}$

Enthalpy Relations

$\Delta H_{rxn}^\circ = \sum\Delta H_f^\circ(\text{products}) - \sum\Delta H_f^\circ(\text{reactants}) \quad \text{(Hess's Law)}$

$\Delta H_{bond} = \sum BE(\text{bonds broken}) - \sum BE(\text{bonds formed})$

Heat Capacities

$C_p - C_v = R \quad \text{(any ideal gas)}$

$q_v = nC_v\Delta T = \Delta U \quad \text{(isochoric)}$

$q_p = nC_p\Delta T = \Delta H \quad \text{(isobaric)}$

Heat Capacity Values

Spontaneity Crossover

$T_{crossover} = \frac{\Delta H}{\Delta S} \quad \text{(when both same sign)}$

Useful Constants

$R = 8.314\ \text{J/(mol·K)} = 0.0821\ \text{L·atm/(mol·K)}$ $1\ \text{L·atm} = 101.3\ \text{J}, \quad \ln 2 = 0.693, \quad \ln 10 = 2.303$