Properties of solution that depend on the ratio of no: of solute particles to the total no: of particles in the solution.

**1. Relative lowering of vapour pressure:**

⇒ Vapour pressure of solvent in solution is less than that of pure solvent.

According to Raoult’s law

P_{A} = X_{A} x P°_{A}

⇒ So the reduction in vapour pressure is given as

Δ P_{A} = P°_{A} – P_{A}

i.e., Δ P_{A} = P°_{A} (1 – X_{A}) = P°_{A}X_{B}

i.e., therefore, relative lowering of vapour pressure Δ P_{A}/P_{A} is equal to mole fraction of solute X_{B.}

⇒ If two or more non-volatile solutes are present then it is equal to sum of the mole fraction of the solutes

\(\frac{\Delta {{P}_{A}}}{{{P}_{A}}}={{X}_{B}}+{{X}_{C}}+………+{{X}_{N}}\)** ****For dilute solutions:**

\(\frac{\Delta {{P}_{A}}}{{{P}_{A}}}={{X}_{B}}=\frac{{{n}_{2}}}{{{n}_{1}}}\) (As n₂ << n₁)

\(\frac{\Delta {{P}_{A}}}{{{P}_{A}}}=\frac{{{w}_{B}}\times {{M}_{A}}}{{{M}_{B}}\times {{w}_{A}}}\)Where, w_{A} = mass of solvent

M_{A} = Molar mass of solvent

W_{B} = mass of solute

M_{B} = Molar mass of solute

**2. Elevation of boiling point:**

⇒ A liquid boils at a temperature where its vapour pressure becomes equal to atmospheric pressure.

⇒ Since in a solution the vapour pressure of solvent is reduced, the temperature needs to be raised to increase the vapour pressure to atmospheric pressure.

⇒ Therefore, the boiling point of solution is always higher than that of pure solvent.

ΔT_{b} = T_{b} – T°_{b}

= elevation in boiling point

T_{b}= boiling point of solution

T_{b}^{0} = boiling point of pure solvent

**For dilute solutions:**

T_{b} α m

Δ T_{b} = K_{b} x m

m = molality

K_{b }= molal elevation constant (Ebullioscopic Constant). Units: K kg mol^{-1}

R = gas constant

M_{1} = molar mass of solvent

Δ_{vap}H = enthalpy of vaporization

**3. Depression of freezing point**

⇒ A solution freezes when its vapour pressure becomes equal to the vapour pressure of pure solid solvent.

⇒ As the vapour pressure of a solvent decreases when a non-volatile solute is added, the freezing point of solvent decreases.

ΔT_{f} = T°_{f} – T_{f}

ΔT_{f} = depression in freezing point

T°_{f} = freezing point of pure solvent

T_{f} = freezing point of solution

**For dilute solution:**

Δ T_{f} α m

Δ T_{f} = K_{f} x m

K_{f} = Molal depression constant (Cryoscopic constant). Units: K kg mol¯¹

R = gas constant

M_{1}= molar mass of solvent

Δ_{fus}H = enthalpy of fusion