Chapter 17, Problem 99AE

(a)

Interpretation Introduction

Interpretation: The boiling point of an aqueous solution which has freezing point as -2.79°C needs to be determined.

Concept Introduction: Colligative properties are the properties of solution which depend on the number of particles present in the solution. Some common examples of colligative properties are depression in freezing point, elevation in boiling point, osmotic pressure, lowering in vapor pressure, etc. The number of particles is shown with the help of Van’t Hoff factor ‘i’.

The mathematical expression for depression in freezing point and elevation in boiling point are as given below:

  $\begin{array}{l}{\text{ΔT}}_{\text{f}}{\text{ = i × k}}_{\text{f}}\text{×m}\\ {\text{ΔT}}_{\text{b}}{\text{ = i × k}}_{\text{b}}\text{×m}\\ {\text{ΔT}}_{\text{f}}\text{ = Depression in freezing point}\\ {\text{ΔT}}_{\text{b}}\text{=Elevation in boiling point}\\ \text{i = van't Hoff factor}\\ {\text{k}}_{\text{b}}\text{=Molal elevation constant}\\ {\text{k}}_{\text{f}}=\text{Molal depression constant}\\ \text{m = Molality}\end{array}$

(b)

Interpretation Introduction

Interpretation: Thevapor pressure of solution at 25°C needs to be determined, if the vapor pressure of pure water is 23.76 mmHg at same temperature.

Concept Introduction:When a non-volatile solute is dissolve in solvent to get solution the vapor pressure decreases for the solution and it can be calculated with the help of Raoult’s law that states that the vapor pressure of solution is the product of mole fraction of solvent and vapor pressure of pure solvent. When a volatile solute is added to the solvent, the overall vapor pressure of solution will be the sum of vapor pressure contribution of individual component.

The mathematical expression can be written as:

  ${\text{P}}_{\text{solution }}{\text{= [χ}}_{\text{A}}{\text{× P}}_{\text{A}}]+{\text{[χ}}_{\text{B}}{\text{× P}}_{\text{B}}]$

(c)

Interpretation Introduction

Interpretation: The assumption made to calculate vapor pressure and boiling point of solution needs to be determined.

Concept Introduction:When a non-volatile solute is dissolve in solvent to get solution the vapor pressure decreases for the solution and it can be calculated with the help of Raoult’s law that states that the vapor pressure of solution is the product of mole fraction of solvent and vapor pressure of pure solvent. When a volatile solute is added to the solvent, the overall vapor pressure of solution will be the sum of vapor pressure contribution of individual component.

The mathematical expression can be written as:

  ${\text{P}}_{\text{solution }}{\text{= [χ}}_{\text{A}}{\text{× P}}_{\text{A}}]+{\text{[χ}}_{\text{B}}{\text{× P}}_{\text{B}}]$