Colligative properties
Colligative properties
- Definition: Properties of solution which depends only on the number of particles not on their nature.
- Use: Colligative properties used to determine the molecular mass of solute
- Types:
a. Relative lowering of vapor pressure
b. Elevation of boiling point
c. Depression of freezing point
d. Osmotic pressure
a. Relative lowering of vapor pressure:
Addition of a non-volatile solute to the pure solvent decreases its vapor pressure because some of the solvent particles from the surface are replaced by non-volatile solute, which do not vaporize. Therefore, number of particles escaping from the surface decreases which causes the decrease of vapor pressure. The decrease in vapor pressure of pure solvent by the addition of a non-volatile solute is known as lowering of vapor pressure. The ratio of lowering of vapor pressure to the vapor pressure of pure solvent is known as relative lowering of vapor pressure.
$$\text{RLVP} = \dfrac{P^o-P}{P^o}$$
$$P^o = \text{Vapor pressure of pure solvent}$$
$$P = \text{Vapor pressure of solution}$$
Raoult’s law: Relative lowering of vapor pressure is equal to the mole fraction of the solute.
$$\dfrac{P^o-P}{P^o} = \chi_B$$
$$\chi_B = \text{Mole fraction of solute}$$
b. Elevation of boiling point
Increase in boiling point of a pure solvent by the addition of non-volatile solute to it is known as elevation of boiling point.
$$\Delta T_b = T_b – T^o_b$$
$$\Delta T_b = \text{Elevation of boiling point}$$
$$T_b = \text{Boiling point of solution}$$
$$T^o_b = \text{Boiling point of pure solvent}$$
$$\Delta T_b = \dfrac{K_b \times w_B \times 1000}{m_B \times W_A(g)}$$
$$K_b = \text{Molal elevation constant}$$
$$w_B = \text{Mass of solute}$$
$$m_B = \text{Molecular mass of solute}$$
$$W_A = \text{Mass of solvent}$$
c. Depression of freezing point
Decrease in Freezing point of a pure solvent by the addition of non-volatile solute to it is known as depression of boiling point.
$$\Delta T_f = T^o_f – T_f$$
$$\Delta T_f =\text{Depression of freezing point}$$
$$T_f = \text{Freezing point of solution}$$
$$T^o_f = \text{Freezing point of pure solvent}$$
$$\Delta T_f = \dfrac{K_f \times w_B \times 1000}{m_B \times W_A(g)}$$
$$K_f = \text{Molal depressionconstant}$$
$$w_B = \text{Mass of solute}$$
$$m_B = \text{Molecular mass of solute}$$
$$W_A = \text{Mass of solvent}$$
d. Osmotic pressure
Osmotic pressure is the pressure that must be applied to a solution to prevent the flow of solvent molecules through a semipermeable membrane into the solution.
$$\pi =C\times R \times \ T$$
$$\pi \times V = n \times R\times T$$
$$\pi = \text{Osmotic pressure in atm}$$
$$n = \text{moles of solute}$$
$$V = \text{Volume of solution in L.}$$
$$R = \text{Gas constant} = 0.0821 \text{L.atmmol-1 K-1}$$
$$T = \text{Absolute temperature in K}$$
Note: Osmotic pressure is a suitable colligative property to determine Molecular mass of macro molecules like Proteins.