$word_{count}$: 230

Four colligative properties depend only on number of solute particles: (1) RLVP: $delta_P$/$P_{std}$ = i*$x_{solute}$ (non-volatile solutes only). (2) Boiling point elevation: $delta_{Tb}$ = iKbm. (3) Freezing point depression: $delta_{Tf}$ = iKfm. (4) Osmotic pressure: pi = iMRT. Key constants for water: Kb = 0.512 K.kg/mol, Kf = 1.86 K.kg/mol. Origin of constants: Kb = R$Tb^2$\frac{M_solvent}{1000*delta_H_vap}, Kf = R$Tf^2$\frac{M_solvent}{1000*delta_H_fus}. Kf > Kb because delta_H_{fus} < delta_H_{vap}. Solvents with high Kf: camphor (40), naphthalene (6.94), benzene (5.12). Molar mass determination: M = Kfw2*$\frac{1000}{delta_Tf*w1}$ or M = $\frac{wRT}{pi*V}$. Osmotic pressure is most sensitive — preferred for macromolecules. The van't Hoff factor i connects all four properties to electrolyte behaviour. For non-electrolytes: i = 1. For dissociation into n ions: i = 1 + (n-1)alpha. For association of n molecules: i = 1 - alpha(1-1/n). Abnormal molar mass: $M_{apparent}$ = $\frac{M_actual}{i}$. Dissociation (i>1) gives $M_{apparent}$ < $M_{actual}$. Association (i<1) gives $M_{apparent}$ > $M_{actual}$. When multiple solutes are present: $delta_{Tf}$ = Kf * sum($i_j$ * $m_j$). All colligative property formulas require correct i for accurate results.