Which solution has the lower freezing point? $10 \mathrm{g}$ of methanol $\left({\mathrm{CH}}_3\mathrm{OH}\right)$ in $100 \mathrm{g}$ of water (or) $20 \mathrm{g}$ of ethanol $\left({\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}\right)$ in $200 \mathrm{g}$ of water.

1. Solution.

It is a homogeneous mixture of two or more chemically non-reacting substances whose composition can be varied within certain limits.

2. Solute and Solvent.

In a binary solution, the component present in smaller amount is called solute while the other present in larger amount is called solvent. If water is the solvent, solution is called aqueous solution.

3. Concentration of solutions

(i) $\text{Molarity }\left(\mathrm{M}\right)=\frac{\text{ Moles of solute }}{\text{ Vol. of solution (in mL) }}\times 1000$

(ii) $\text{Molality }\left(\mathrm{m}\right)=\frac{\text{ Moles of solute }}{\text{ Mass of solvent }\text{(in }\mathrm{g}\text{)}}\times 1000$

(iii) $\text{Mole fraction }\left(\mathrm{x}\right)=\frac{\text{ Moles of solute }}{\text{ Moles of solute}+\text{Moles of solvent }}$

$\text{Mole fraction of solute}+\text{mole fraction of solvent}=1$

4. Henry’s law:

The mass of the gas dissolved in a given volume of the liquid at constant temperature is directly proportional to the pressure of the gas in equilibrium with the liquid or for a mixture of gases in equilibrium with a liquid, the partial pressure of the gas is directly proportional to the mole fraction of the gas in the solution

m=k.por $\mathrm{p}={\mathrm{K}}_{\mathrm{H}}.\mathrm{x}$

${\mathrm{K}}_{\mathrm{H}}$ is Henry’s law constant.

5. Raoult’s law

Raoult’s law in its general form can be stated as, for any solution the partial vapour pressure of each volatile component in the solution is directly proportional to its mole fraction.

6. Colligative properties

(i) Relative lowering in vapour pressure:

$\frac{{\mathrm{p}}_1^{\mathrm{ }0}-{\mathrm{p}}_1}{{\mathrm{p}}_1^{\mathrm{ }0}}={\mathrm{x}}_2\text{and}{\mathrm{M}}_{\mathrm{2}}=\frac{{\mathrm{w}}_2{\mathrm{M}}_{\mathrm{1}}}{{\mathrm{w}}_1\times \left(\frac{{\mathrm{p}}_1^{\mathrm{ }0}-{\mathrm{p}}_1}{{\mathrm{p}}_1^{\mathrm{ }0}}\right)}$

(ii) $\text{Elevation in boiling point}\mathrm{ }{\mathrm{\Delta T}}_{\mathrm{b}}={\mathrm{K}}_{\mathrm{b}}\mathrm{ }\mathrm{m}\text{and}{\mathrm{M}}_{\mathrm{2}}=\frac{{\mathrm{K}}_{\mathrm{b}}\times {\mathrm{w}}_2\times 1000}{\mathrm{\Delta }{\mathrm{T}}_{\mathrm{b}}\times {\mathrm{w}}_1}$

(iii) $\text{Depression in freezing point}\mathrm{ }\mathrm{\Delta }{\mathrm{T}}_{\mathrm{f}}={\mathrm{K}}_{\mathrm{f}}\mathrm{m}\mathrm{ }\text{and }{\mathrm{M}}_2=\frac{{\mathrm{K}}_{\mathrm{f}}\times {\mathrm{w}}_2\times 1000}{\mathrm{\Delta }{\mathrm{T}}_{\mathrm{f}}\times {\mathrm{w}}_1}$

(iv) $\text{Osmotic pressure}\mathrm{ }\mathrm{\pi }=\mathrm{cRT} \text{or}\mathrm{\pi }=\frac{\mathrm{n}}{\mathrm{V}}\mathrm{RT}\text{and}\mathrm{ }{\mathrm{M}}_{\mathrm{2}}=\frac{{\mathrm{w}}_2\mathrm{RT}}{\mathrm{V\pi }}$

7. Abnormal colligative properties:

(i) For electrolytic solutions

$\text{V}\text{ant}\text{ Hoff factor,}\mathrm{ }\mathrm{i}=\frac{\text{Normal molar mass}}{\text{Abnormal molar mass}}=\frac{ \text{Observed colligative property} }{\mathrm{ }\text{Calcluated colligative property} }$

(ii) Relative lowering in vapour pressure $\frac{\mathrm{\Delta }\mathrm{p}}{\mathrm{p}}=\mathrm{i}\mathrm{ }{\mathrm{x}}_{\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{ }}$

(iii) Elevation in boiling point, $\mathrm{\Delta }{\mathrm{T}}_{\mathrm{b}}=\mathrm{i}\mathrm{ }{\mathrm{K}}_{\mathrm{b}}\mathrm{m}$

(iv) Depression in freezing point, $\mathrm{\Delta }{\mathrm{T}}_{\mathrm{f}}=\mathrm{i}\mathrm{ }{\mathrm{K}}_{\mathrm{f}}\mathrm{m}$

(v) Osmotic pressure, $\mathrm{\pi }=\mathrm{i}\mathrm{ }\frac{\mathrm{n}}{\mathrm{V}}\mathrm{RT}$