Chapter 12, Problem 12.47QP

Interpretation Introduction

Interpretation:

The molality used for freezing point depression and boiling point elevation and molarity is used for osmotic pressure have to be explained.

Concept introduction

• Molality is the number of moles of solute present in one kilogram of solvent.

$\text{Molality (m) =}\frac{\text{Number}\text{of}\text{moles}\text{of}\text{solute}}{\text{1kg}\text{of}\text{solvent}}$

• Molarity is number of moles of the solute present in the one liter of the solution.
•  

  $\text{Molarity (M) =}\frac{\text{Number}\text{of}\text{moles}\text{of}\text{solute}}{\text{1}\text{liter}\text{of}\text{solution}}$

• Boiling point is the temperature at which liquid turns into a gas. Example: boiling point of water is $\text{100°C}$. That is water changes from liquid phase to gas phase.
•  

  ${\text{ΔT}}_{\text{b}}{\text{= T}}_{\text{b}}{\text{- T}}_{\text{b}}^{\text{°}}$

Where,

${\text{ΔT}}_{\text{b}}-$ Change in boiling point

${\text{T}}_{\text{b}}\text{ - }$ Boiling point of the solution

${\text{T}}_{\text{b}}^{\text{°}}\text{ - }$ Boiling point of pure solvent

• Boiling point elevation$(\Delta T_b)$  is distinction between boiling point of the pure solvent ${\text{(T}}_{\text{b}}^{\text{°}}\text{)}$ and the boiling point of the solution ${\text{(T}}_{\text{b}}\text{)}$.
•  

  ${\text{ΔT}}_{\text{b}}{\text{= K}}_{\text{b}}\text{m}$

Where,

${\text{ΔT}}_{\text{b}}-$ Change in boiling point

${\text{K}}_{\text{b}}-$ Molal boiling point constant

m- Molality of the solution

• Freezing point is the temperature at which liquid turns into solid.
• Freezing point depression ${\text{(ΔT}}_{\text{f}}\text{)}$ is distinction between freezing point of the pure solvent ${\text{(T}}_{\text{f}}^{\text{°}}\text{)}$ and the freezing point of the solution ${\text{(T}}_{\text{f}}\text{)}$.
•  

  ${\text{ΔT}}_{\text{f}}{\text{= K}}_{\text{f}}\text{m}$

Where,

${\text{ΔT}}_{\text{f}}-$ Change in freezing point

${\text{K}}_{\text{f}}-$ Molal freezing point constant

m- Molality of the solution

• Osmotic pressure is the pressure that is needed to stop osmosis. Osmotic pressure of the solution is directly proportional to the concentration of the solution.
•  

  Osmotic pressure $\text{(π) = MRT}$

  Where,

  M – Molarity of the solution (mole/L)

  R- Ideal gas constant (0.08206${\text{L atm mol}}^{\text{-1}}{\text{K}}^{\text{-1}}$)

  T-Temperature in Kelvin