Cheat Sheet — PC-05 Quick Revision — Notes

Formula	Expression	Key Variable
Henry's Law	$p = K_H \cdot x$	K_H ↑ with T → solubility ↓
Raoult's Law (volatile)	$P_T = x_A P^\circ_A + x_B P^\circ_B$	x = liquid mole fraction
Raoult's Law (non-volatile)	$\frac{\Delta P}{P^\circ} = x_{solute}$	x_solute = n_{2}/(n_{1}+n_{2})
Boiling point elevation	$\Delta T_b = iK_bm$	m = mol/kg solvent
Freezing point depression	$\Delta T_f = iK_fm$	Kf(water) = 1.86
Osmotic pressure	$\pi = iCRT$	C = mol/L; T in K
Molar mass ( $\Delta Tb$ )	$M_2 = \frac{K_b w_2 \times 1000}{\Delta T_b \cdot w_1}$	w in grams
Dissociation i	$i = 1 + (n-1)\alpha$	n = ions; α = fraction
Association i	$i = 1 - \frac{(n-1)}{n}\alpha$	n = monomers per cluster

Kb = 0.52 K·kg/mol | Kf = 1.86 K·kg/mol | Kf > Kb (remember: 1.86 > 0.52)
R = 0.0821 L·atm/(mol·K) for osmotic pressure

Solute	Dissociation/Association	i
Glucose, Urea, Sucrose	None	1
NaCl, KCl	2 ions	2
$K_{2}SO_{4}$ , $CaCl_{2}$ , $Na_{2}SO_{4}$	3 ions	3
$AlCl_{3}$ , $K_{3}PO_{4}$	4 ions	4
$CH_{3}COOH$ (benzene), Benzoic acid (benzene)	Dimer	0.5

Colligative properties → particle NUMBER, not nature or size
$\Delta Tb$ , $\Delta Tf$ use molality; π uses molarity; both use T in Kelvin for π
Association → i < 1 → apparent M > true M
Dissociation → i > 1 → apparent M < true M
Positive deviation → Min. boiling azeotrope | Negative deviation → Max. boiling azeotrope
Gas solubility decreases with temperature (K_H increases)
Kf(water) > Kb(water) because $\Delta Hf$ us < $\Delta Hv$ ap