The IUPAC form of the first law is $\Delta U =$ ___ $+$ ___. [q, w]

For free expansion, work $w =$ ___ because external pressure $P_{ext} =$ ___. [0, 0]

$\Delta H = \Delta U +$ ___ $\times RT$, where ___ counts only ___ moles. [$\Delta n_g$; $\Delta n_g$; gaseous]

$C_p - C_v =$ ___ for any ideal gas. [R]

Monoatomic gas: $C_v =$ ___, $C_p =$ ___, $\gamma =$ ___. [$\frac{3R}{2}$; $\frac{5R}{2}$; $\frac{5}{3}$]

Diatomic gas: $C_v =$ ___, $C_p =$ ___, $\gamma =$ ___. [$\frac{5R}{2}$; $\frac{7R}{2}$; $\frac{7}{5}$]

$\Delta G = \Delta H -$ ___ $\times \Delta S$. [T]

A reaction is spontaneous when $\Delta G$ ___ 0. [< ]

At equilibrium, $\Delta G =$ ___. [0]

$\Delta G^\circ = -RT\ln$ ___ $= -2.303 RT\log$ ___. [K; K]

The four cases of spontaneity: (a) $\Delta H(-), \Delta S(+)$: ___ spontaneous; (b) $\Delta H(+), \Delta S(-)$: ___ spontaneous; (c) $\Delta H(-), \Delta S(-)$: ___ T; (d) $\Delta H(+), \Delta S(+)$: ___ T. [always; never; low; high]

Hess's Law: $\Delta H_{rxn} = \Sigma\Delta H_f^\circ$(___) $- \Sigma\Delta H_f^\circ$(___). [products; reactants]

Bond enthalpy method: $\Delta H =$ ___(BE broken) $-$ ___(BE formed). [$\Sigma$; $\Sigma$]

Entropy of the universe is ___ for all spontaneous processes (second law). [positive / $> 0$]

$\Delta H_f^\circ$ of any element in standard state $=$ ___. [0]

Standard enthalpy of combustion is always ___ (sign). [negative]

Crossover temperature: $T =$ ___ / ___. [$\Delta H$; $\Delta S$]

For isochoric process: $w =$ ___, $\Delta U =$ ___. [0; $q_v$]

For adiabatic process: $q =$ ___, $\Delta U =$ ___. [0; $w$]

Entropy change: $\Delta S = q_{rev} /$ ___. [T]