Chapter 14.4, Problem 49SSC

Interpretation Introduction

Interpretation:

Four colligative properties of solutionshave to be described.

Concept introduction:

Colligative properties are those properties of solutions, which entirely depend upon the number of solute particles (molecules or ions) dissolved in a known volume of solvent, but not at all on the nature (i.e., chemical composition or constitution) of those solute particles. Here the solute is invariably taken as non-volatile. There are four colligative properties, which are:

1. Lowering of vapor pressure
2. Osmotic pressure
3. Elevation of boiling point
4. Depression of freezing point

The colligative properties are essentially the properties of only dilute solution which are supposed to behave as ideal solution.

Answer to Problem 49SSC

Lowering of vapor pressure: the decrease in vapor pressure with increasing solute particles in solution.Osmotic pressure: the change in osmotic pressure with increasing solute particles in solution.Elevation of boiling point: the increase in boiling point with increasing solute particles in solution. Depression of freezing point: the decrease in freezing point with increasing solute particles in solution.

Colligative properties are entirely depend upon the number of solute particles. These four colligative properties lowering of vapor pressure, osmotic pressure, elevation of boiling point and depression of freezing point are valid under the following conditions:

1. The solution must be very dilute.
2. The solute must be non-volatile
3. The solute must be non-electrolyte, i.e., the solute does not undergo any type of dissociation or association.

Lowering of vapor pressure: When the solvent contains solute, a mix of solute and solvent particles occupies the surface area. With fewer solvent particles at the surface, fewer particles enter the gaseous state, and the vapor pressure is lowered. The greater the number of solute particles in a solvent, the lower the resulting vapor pressure. Thus, vapor pressure lowering is due to the number of solute particles in solution and is a colligative property of solutions.Osmotic pressure: Osmotic pressure is the equilibrium hydrostatic pressure of the column set up as a result of osmosis. It is the minimum pressure that must be applied on the solution to prevent the entry of the solvent into the solution through the semi­permeable membrane. It is the minimum pressure needed to apply on a solution to make its vapour pressure equal to vapour pressure of the solvent. It is denoted by P or p.

Van’t Hoff equation of osmotic pressure $\pi =CRT$

Where, C = Concentration of the solution in mol/litre

R = Gas constant

T = Absolute temperature in K

Elevation of boiling point: When a solute is added to a solvent, the vapor pressure of the resulting solution is less than the vapor pressure above the pure solvent. The boiling point of a solution, then, will be greater than the boiling point of the pure solvent because the solution (which has a lower vapor pressure) will need to be heated to a higher temperature in order for the vapor pressure to become equal to the external pressure (i.e., the boiling point).

For nonelectrolytes, the value of the boiling point elevation, which is symbolized ? T_b, is directly proportional to the solution’s molality.

Boiling point elevation $\Delta {\mathrm{T}}_b=K_b\times m$

Depression of freezing point: Freezing point is the temperature at which the liquid and the solid form of the same substance are in equilibrium and have the same vapor pressure. Due to lower vapor pressure of the solution, solid form of a solution separates out at a lower temperature. A solution’s freezing point depression, ? T_f, is the difference in temperature between its freezing point and the freezing point of its pure solvent. For nonelectrolytes, the value of the depression of freezing point, is directly proportional to the solution’s molality.

Depression of freezing point $\Delta T_f=K_f\times m$

Explanation of Solution

Colligative properties are entirely depend upon the number of solute particles. These four colligative properties lowering of vapor pressure, osmotic pressure, elevation of boiling point and depression of freezing point are valid under the following conditions:

1. The solution must be very dilute.
2. The solute must be non-volatile
3. The solute must be non-electrolyte, i.e., the solute does not undergo any type of dissociation or association.

Lowering of vapor pressure: When the solvent contains solute, a mix of solute and solvent particles occupies the surface area. With fewer solvent particles at the surface, fewer particles enter the gaseous state, and the vapor pressure is lowered. The greater the number of solute particles in a solvent, the lower the resulting vapor pressure. Thus, vapor pressure lowering is due to the number of solute particles in solution and is a colligative property of solutions.Osmotic pressure: Osmotic pressure is the equilibrium hydrostatic pressure of the column set up as a result of osmosis. It is the minimum pressure that must be applied on the solution to prevent the entry of the solvent into the solution through the semi­permeable membrane. It is the minimum pressure needed to apply on a solution to make its vapour pressure equal to vapour pressure of the solvent. It is denoted by P or p.

Van’t Hoff equation of osmotic pressure $\pi =CRT$

Where, C = Concentration of the solution in mol/litre

R = Gas constant

T = Absolute temperature in K

Elevation of boiling point: When a solute is added to a solvent, the vapor pressure of the resulting solution is less than the vapor pressure above the pure solvent. The boiling point of a solution, then, will be greater than the boiling point of the pure solvent because the solution (which has a lower vapor pressure) will need to be heated to a higher temperature in order for the vapor pressure to become equal to the external pressure (i.e., the boiling point).

For nonelectrolytes, the value of the boiling point elevation, which is symbolized ? T_b, is directly proportional to the solution’s molality.

Boiling point elevation $\Delta {\mathrm{T}}_b=K_b\times m$

Depression of freezing point: Freezing point is the temperature at which the liquid and the solid form of the same substance are in equilibrium and have the same vapor pressure. Due to lower vapor pressure of the solution, solid form of a solution separates out at a lower temperature. A solution’s freezing point depression, ? T_f, is the difference in temperature between its freezing point and the freezing point of its pure solvent. For nonelectrolytes, the value of the depression of freezing point, is directly proportional to the solution’s molality.

Depression of freezing point $\Delta T_f=K_f\times m$