Question

List four properties of a solution that depend on the total concentration but not the type of particle or particles present as solute. Write the mathematical expression that describes how each of these properties depends on concentration.

Short answer

The four colligative properties of a solution are: 1. Vapor pressure lowering, 2. Boiling point elevation, 3. Freezing point depression, and 4. Osmotic pressure. The mathematical expressions for each property are: 1. Vapor pressure lowering: \(P_A = X_A P^\circ_A\) 2. Boiling point elevation: \(\Delta T_b = K_b \cdot i \cdot m\) 3. Freezing point depression: \(\Delta T_f = K_f \cdot i \cdot m\) 4. Osmotic pressure: \(\Pi= i \cdot M \cdot R \cdot T\)

Step-by-step solution

1. List the four colligative properties:

The four colligative properties of a solution are: 1. Vapor pressure lowering 2. Boiling point elevation 3. Freezing point depression 4. Osmotic pressure

2. Vapor pressure lowering:

According to Raoult's law, the vapor pressure lowering is proportional to the mole fraction of the solute. The mathematical expression can be written as: \(P_A = X_A P^\circ_A\) Here, \(P_A\) represents the vapor pressure of the solvent in the solution, \(X_A\) is the mole fraction of the solvent, and \(P^\circ_A\) is the vapor pressure of the pure solvent.

3. Boiling point elevation:

Boiling point elevation is the increase in the boiling point of a solvent due to the presence of a solute. The mathematical expression for boiling point elevation is given by: \(\Delta T_b = K_b \cdot i \cdot m \) Here, \(\Delta T_b\) is the increase in boiling point, \(K_b\) is the ebullioscopic constant for the solvent, \(i\) is the van't Hoff factor, and \(m\) is the molality of the solute.

4. Freezing point depression:

Freezing point depression is the decrease in the freezing point of a solvent due to the presence of a solute. The mathematical expression for freezing point depression is given by: \(\Delta T_f = K_f \cdot i \cdot m\) Here, \(\Delta T_f\) is the decrease in freezing point, \(K_f\) is the cryoscopic constant for the solvent, \(i\) is the van't Hoff factor, and \(m\) is the molality of the solute.

5. Osmotic pressure:

Osmotic pressure is the pressure required to prevent osmosis (movement of solvent molecules across a semipermeable membrane). The mathematical expression for osmotic pressure is given by: \(\Pi= i \cdot M \cdot R \cdot T\) Here, \(\Pi\) represents the osmotic pressure, \(i\) is the van't Hoff factor, \(M\) is the molarity of the solute, \(R\) is the ideal gas constant, and \(T\) is the temperature in Kelvin.