# Colligative Properties

### Colligative Properties

Those properties of ideal solutions which depend only on the number of solute particles but do not depend on the nature of solute are called colligative properties.

The important colligative properties are :

#### Relative lowering of vapour pressure

$$~\chi _{B}=\frac{P_{A}^{o}-P_{A}}{P_{A}^{o}}$$

In this expression, $$\Delta P_{A}=P_{A}^{o}-P_{A}$$ expresses the lowering of vapour pressure while $$\frac{P_{A}^{o}-P_{A}}{P_{A}^{o}}$$ is called relative lowering in vapour pressure and χB represents mole fraction of the solute in solution.

$$\frac{W_{B}~\times ~M_{A}}{M_{B}~\times ~W_{A}}=\frac{P_{A}^{o}-P_{A}}{P_{A}^{o}}$$

#### Elevation in Boiling Point

The boiling point of liquid is the temperature at which the vapour pressure of the liquid becomes equal to the atmospheric pressure.

The elevation in boiling point (ΔTb) depends on molal concentration (m) of solute in solution.

###### ΔTb ∝ m     or    ΔTb = Kb × m

Where Kb is called the molal elevation constant or ebullioscopic constant and ‘m’ is the molality.

$$\Delta T_{b}=K_{b}\times \frac{W_{B}~\times ~1000}{M_{B}~\times W_{solvent~in~gm}}$$

Note: $$\Delta T_{b}=T_{b}-T_{b}^{o}$$

#### Depression in Freezing Point

Freezing point of a substance is the temperature at which the solid and liquid forms of the substance have same vapour pressure. It is found that the freezing point of the solution is always lower than that of pure of solvent.

The depression in freezing point (ΔTf) depends on molal concentration (m) of solute in solution.

###### ΔTf ∝ m     or    ΔTf = Kf × m

Where Kf is called molal depression constant or cryoscopic constant and ‘m’ is the molality.

$$\Delta T_{f}=K_{f}\times \frac{W_{B}~\times ~1000}{M_{B}~\times W_{solvent~in~gm}}$$

Note: $$\Delta T_{f}=T_{f}^{o}-T_{f}$$

#### Osmotic Pressure

Osmosis is the spontaneous process of movement of solvent only, from its higher concentration to lower concentration through semi-permeable membrane.

Osmotic Pressure :

It can be defined as the additional pressure applied on the solution to prevent the entry of the solvent into the solution through semi-permeable membrane. It is represented by ‘π.

Osmotic pressure (π) of a solution is found to be directly proportional to molar concentration (C) of the solution and its temperature (T).

π ∝ C —(i)                 π ∝ T —(ii)

Compare the equation (i) and (ii)

π ∝ CT        or         π = RCT

Where ‘R’ is a constant and its value is found to be same as that of the ‘Gas constant’. ‘C’ is molar concentration (n/V). ‘n’ is number of moles of solute and ‘V’ is the volume of solution in litre. The above equation is usually written as :

$$\pi = \frac{n}{V}.RT~~~or~~~\pi V=nRT$$

Determination of Molecular mass from Osmotic Pressure :

$$\left [ n=\frac{W_{B}}{M _{B}} \right ] ~~~~~~~ \pi V = \frac{W_{B}}{M _{B}}.RT$$

or

$$M _{B}=\frac{W_{B}\times RT}{\pi~ \times V}$$