CBSE · Class 12 · Chemistry · Chapter 1

Solutions — Formula Sheet

Board Formulas

10 formulas

1.Molarity (M)★
$M = \frac{n _{solute}}{V _{solution} ( L )} = \frac{w _{B} \times 1000}{M _{B} \times V ( mL )}$
$n_{solute}$ : Moles of solute (mol) · $w_{B}$ : Mass of solute (g) · $M_{B}$ : Molar mass of solute (g/mol) · $V$ : Volume of solution (L or mL as noted)
Moles of solute per litre of SOLUTION. Temperature-dependent because volume changes.
2.Molality (m)★
$m = \frac{n _{solute}}{W _{solvent} ( kg )} = \frac{w _{B} \times 1000}{M _{B} \times W _{A} ( g )}$
Moles of solute per kg of SOLVENT. Temperature-independent — preferred for colligative properties.
3.Mole Fraction
$x_{A} = \frac{n _{A}}{n _{A} + n _{B}}, x_{A} + x_{B} = 1$
Ratio of moles of one component to total moles. Dimensionless. Sum of all mole fractions = 1.
4.Raoult's Law (volatile solvent, non-volatile solute)★
$\frac{p _{A}^{\circ} - p _{A}}{p _{A}^{\circ}} = x_{B}$
Relative lowering of vapour pressure equals mole fraction of solute. Used to find molar mass of unknown solute.
5.Raoult's Law (binary volatile mixture)
$p_{total} = p_{A}^{\circ} x_{A} + p_{B}^{\circ} x_{B}$
Total pressure over an ideal binary solution equals sum of partial pressures. Ideal solution obeys this at all compositions.
6.Elevation of Boiling Point★
$Δ T_{b} = K_{b} \cdot m \cdot i$
$Δ T_{b}$ : T_b(solution) − T_b(pure solvent) in K · $K_{b}$ : Molal elevation constant (K·kg/mol) · $m$ : Molality of solute (mol/kg) · $i$ : Van't Hoff factor (=1 for non-electrolyte)
Kb = molal elevation constant (ebullioscopic). For water Kb = 0.52 K·kg/mol.
7.Depression of Freezing Point★
$Δ T_{f} = K_{f} \cdot m \cdot i$
Kf = molal depression constant (cryoscopic). For water Kf = 1.86 K·kg/mol.
8.Osmotic Pressure (van't Hoff equation)★
$π = C R T \cdot i = \frac{n}{V} R T \cdot i$
Pressure required to prevent osmosis. C = molar concentration (mol/L). Use for determining molar mass of macromolecules.
9.Van't Hoff Factor (i)
$i = \frac{observed colligative property}{calculated colligative property} = 1 + (n - 1) α$
$i$ : Van't Hoff factor (dimensionless) · $n$ : Number of particles produced per formula unit · $α$ : Degree of dissociation (0 to 1)
For dissociation into n ions with degree α, i = 1+(n−1)α. For association of n molecules into one, i = 1−(n−1)α/n. Non-electrolyte i = 1.
10.Henry's Law
$p = K_{H} \cdot x$
Partial pressure of a gas above solution ∝ its mole fraction in solution. K_H = Henry's constant (larger K_H ⇒ lower solubility).