Maharashtra State Board · Class 12 · Chemistry · Chapter 2

Solutions — Formula Sheet

Board Formulas

12 formulas

1.Molarity
$M = \frac{n _{so l u t e}}{V _{so l u t i o n} ( L )}$
Moles of solute per litre of solution. Temperature-dependent because volume changes with T.
2.Molality★
$m = \frac{n _{so l u t e}}{w _{so l v e n t} ( kg )}$
Moles of solute per kilogram of solvent. Independent of temperature.
3.Mole Fraction
$x_{A} = \frac{n _{A}}{n _{A} + n _{B}}, x_{A} + x_{B} = 1$
Dimensionless. Used in Raoult's law.
4.Raoult's Law (volatile solute)★
$p_{A} = p_{A}^{\circ} x_{A}, p_{B} = p_{B}^{\circ} x_{B}$
Partial vapour pressure = pure vapour pressure × mole fraction. Total pressure p = p_A + p_B.
5.Raoult's Law (non-volatile solute)★
$\frac{p ^{\circ} - p}{p ^{\circ}} = x_{B}$
Relative lowering of vapour pressure = mole fraction of solute. Directly gives molar mass.
6.Elevation in Boiling Point
$Δ T_{b} = K_{b} m$
K_b = molal elevation constant of solvent (K·kg/mol). Colligative.
7.Depression in Freezing Point★
$Δ T_{f} = K_{f} m$
K_f = molal depression constant of solvent (K·kg/mol). Colligative.
8.Osmotic Pressure★
$π = C R T = \frac{n}{V} R T$
Van't Hoff equation for solutions (analogue of PV = nRT for gases). Useful for macromolecules.
9.van't Hoff Factor
$i = \frac{observed colligative property}{calculated colligative property} = \frac{normal molar mass}{abnormal molar mass}$
i > 1 for dissociation (NaCl → 2); i < 1 for association (dimer → ½).
10.Modified Colligative Property (with i)★
$Δ T_{f} = i K_{f} m, π = i C R T$
Multiply each colligative expression by van't Hoff factor to include electrolyte effect.
11.Degree of Dissociation from i
$α = \frac{i - 1}{n - 1}$
n = number of ions per formula unit of salt. e.g. NaCl → n = 2.
12.Henry's Law
$p = K_{H} x$
Partial pressure of a gas above liquid = K_H × its mole fraction in liquid.