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 that depend on the total concentration of solute particles are: 1. Boiling Point Elevation: \(ΔT_b = K_b· molality\) 2. Freezing Point Depression: \(ΔT_f = K_f· molality\) 3. Vapor Pressure Lowering: \(P_s = X_aP_a^0\) (Raoult's Law) 4. Osmotic Pressure: \(Π = i·c·R·T\) (van't Hoff equation) These expressions describe the relationship between each property and the concentration of solute particles, irrespective of the type of particles.

Step-by-step solution

1. Boiling Point Elevation

Boiling point elevation refers to the increase in the boiling point of a solvent upon the addition of a solute. The higher the concentration of solute, the greater the boiling point elevation. The mathematical expression for boiling point elevation is given as: \[ ΔT_b = K_b· molality \] Here, \(ΔT_b\) represents the boiling point elevation, \(K_b\) is the ebullioscopic constant given for the solvent, and molality is the concentration of the solute particles.

2. Freezing Point Depression

Freezing point depression refers to the decrease in the freezing point of a solvent when a solute is added. The higher the concentration of solute, the greater the freezing point depression. The mathematical expression for freezing point depression is given as: \[ ΔT_f = K_f· molality \] Here, \(ΔT_f\) represents the freezing point depression, \(K_f\) is the cryoscopic constant given for the solvent, and molality is the concentration of the solute particles.

3. Vapor Pressure Lowering

Vapor pressure lowering is the decrease in vapor pressure of a solvent upon the addition of a solute. The higher the concentration of the solute, the greater the decrease in the vapor pressure. The mathematical expression for vapor pressure lowering can be described using Raoult's Law: \[ P_s = X_aP_a^0 \] Here, \(P_s\) is the vapor pressure of the solution, \(X_a\) represents the mole fraction of solvent in the solution, \(P_a^0\) is the vapor pressure of the pure solvent.

4. Osmotic Pressure

Osmotic pressure is the pressure required to prevent the flow of solvent into a solution through a semi-permeable membrane separating the two solutions. The higher the concentration of solute particles, the greater the osmotic pressure. The mathematical expression for osmotic pressure is given by the van't Hoff equation: \[ Π = i·c·R·T \] Here, \(Π\) represents the osmotic pressure, \(i\) is the van't Hoff factor (number of particles produced by each solute molecule), \(c\) is the molar concentration of the solute particles, \(R\) is the gas constant, and \(T\) is the temperature in Kelvin. These are the four properties of a solution that depend on the total concentration of solute particles and the mathematical expressions that describe their dependence on concentration.