Cornell Note: Enthalpy and the $\Delta n_g$ Rule

Definition of H | $H = U + PV$ . For ideal gases: $\Delta H = \Delta U + \Delta(nRT) = \Delta U + \Delta n_g RT$

$\Delta n_g$ rule | Count ONLY gaseous species: $\Delta n_g =$ (moles gas product) $-$ (moles gas reactant). Solids and liquids contribute zero.

When $\Delta H > \Delta U$ | When $\Delta n_g > 0$ (more gas produced): $\Delta H = \Delta U + \Delta n_g RT > \Delta U$

When $\Delta H < \Delta U$ | When $\Delta n_g < 0$ (less gas in products): $\Delta H < \Delta U$

Classic NEET trap | $CaCO_{3}$ (s) → CaO(s) + $CO_{2}$ (g): $\Delta n_g = 1$ (only $CO_{2}$ counts). Students often count the solids.

Units check | $\Delta n_g RT$ : mol × J/(mol·K) × K = J ✓

Reaction	Gas Products	Gas Reactants	$\Delta n_g$
$N_{2}$ + $3H_{2}$ → $2NH_{3}$	2	4	$-2$
$CaCO_{3}$ → CaO + $CO_{2}$	1	0	$+1$
$2H_{2}$ + $O_{2}$ → $2H_{2}$ O(l)	0	3	$-3$
$N_{2}$ + $O_{2}$ → 2NO	2	2	$0$

$\Delta H = \Delta U + \Delta n_g RT$ . Only gaseous moles matter. $\Delta n_g = 0$ means $\Delta H = \Delta U$ exactly.