Summary & Master Memory Capsule

The Whole Chapter in One Glance

This is your morning-of-the-exam capsule. Everything in Solutions hangs off a few core ideas: a solution is a homogeneous mixture; concentration can be expressed in many ways; gases follow Henry's law; liquid mixtures follow Raoult's law; and a non-volatile solute changes four colligative properties that let us find molar masses — with the van't Hoff factor correcting for ions and dimers.

Keep this map in your head; every number and concept slots into one of these five branches.

Master Formula Sheet

Concentration

• Mass %: $\dfrac{\text{mass of solute}}{\text{mass of solution}}\times100$
• Mole fraction: $x_B = \dfrac{n_B}{n_A+n_B}$, with $\sum x = 1$
• Molarity: $M = \dfrac{n_B}{V_{\text{solution (L)}}}$ (temperature-dependent)
• Molality: $m = \dfrac{n_B}{W_{A}\,(\text{kg})}$ (temperature-independent)

Henry's law: $p = K_H\,x$ (higher $K_H$ means lower solubility; $K_H$ increases with temperature)

Raoult's law: $p_A = p_A^0 x_A$; for two volatile liquids $p_{\text{total}}=p_A^0 x_A + p_B^0 x_B$; vapour composition $y_A = \dfrac{p_A}{p_{\text{total}}}$

Colligative properties

• Relative lowering: $\dfrac{p_A^0 - p_A}{p_A^0} = x_B$
• Boiling-point elevation: $\Delta T_b = K_b\, m$
• Freezing-point depression: $\Delta T_f = K_f\, m$
• Osmotic pressure: $\Pi = CRT$

With van't Hoff factor $i$ (multiply each): $\Delta T_b = iK_b m$, $\Delta T_f = iK_f m$, $\Pi = iCRT$, relative lowering $= i\,x_B$

• Dissociation: $i = 1+(n-1)\alpha$ ($i > 1$)
• Association: $i = 1-\alpha\left(1-\tfrac{1}{n}\right)$ ($i < 1$)
• $i = \dfrac{\text{normal molar mass}}{\text{observed molar mass}}$

Constants: $K_b$(water) $=0.52$, $K_f$(water) $=1.86$ K kg mol$^{-1}$; $R=0.0821$ L atm K$^{-1}$ mol$^{-1}$ $=0.083$ L bar K$^{-1}$ mol$^{-1}$.

Quick Comparison Tables

Ideal vs Non-ideal solutions

Feature	Ideal	Positive deviation	Negative deviation
Raoult's law	obeyed throughout	not obeyed (p higher)	not obeyed (p lower)
A-B forces vs A-A, B-B	equal	weaker	stronger
$\Delta_{mix}H$	0	> 0 (endothermic)	< 0 (exothermic)
$\Delta_{mix}V$	0	> 0	< 0
Example	benzene + toluene	ethanol + acetone	chloroform + acetone
Azeotrope	none	minimum-boiling	maximum-boiling

van't Hoff factor at a glance

Solute behaviour	$i$	Example	Effect on observed molar mass
No change	$= 1$	glucose, urea	normal
Dissociation	$> 1$	NaCl (2), CaCl$_2$ (3), Al$_2$(SO$_4$)$_3$ (5)	lower than true
Association	$< 1$	benzoic acid in benzene (0.5)	higher than true

Temperature dependence of concentration units

Unit	Temperature-dependent?
Mass %, mole fraction, molality	No
Molarity, normality, w/v %	Yes

Last-Minute Memory Hooks

• MolaRity → litRe of solution → changes with R (temperature). MolaLity → kiLogram of solvent → constant.
• Henry: big $K_H$ means low solubility. Warm drink = flat drink (gas less soluble when hot).
• Positive deviation = weaker forces = escape easier = higher vapour pressure = minimum-boiling azeotrope. (Ethanol-acetone.)
• Negative deviation = stronger forces (new H-bond) = lower vapour pressure = maximum-boiling azeotrope. (Chloroform-acetone, HNO$_3$-water.)
• Colligative properties count particles. Same moles of glucose and urea → same effect. NaCl → about double particles; CaCl$_2$ → about triple.
• Osmotic pressure is especially useful for very large molecules (proteins, polymers); $\Pi = CRT$, measured at a fixed temperature.
• $K_f > K_b$ for water (1.86 vs 0.52) → freezing-point method is more sensitive.
• $i$: dissociation pushes it above 1, association below 1, no change keeps it at 1.

One-line revision flow for the exam hall: Concentration → Henry (gases) → Raoult (liquids) → ideal/non-ideal & azeotropes → four colligative properties → van't Hoff correction. If you can recite that chain and the boxed formulas above, you have the chapter.