Solutions

Chapter overview

A solution is a homogeneous mixture of two or more components. The component present in larger amount is usually called the solvent, and the component present in smaller amount is called the solute.

1. Types of solutions

2. Concentration terms

Mass percentage

$$\text{Mass percent} = \frac{\text{mass of solute}} {\text{mass of solution}} \times100$$

Volume percentage

$$\text{Volume percent} = \frac{\text{volume of solute}} {\text{volume of solution}} \times100$$

Mass by volume percentage

$$\frac{\text{mass of solute}} {\text{volume of solution}} \times100$$

Parts per million

$$ppm= \frac{\text{parts of solute}} {\text{parts of solution}} \times10^6$$

Mole fraction

$$X_A=\frac{n_A}{n_A+n_B}$$ $$X_A+X_B=1$$

Molarity

$$M= \frac{\text{moles of solute}} {\text{volume of solution in litre}}$$

Molality

$$m= \frac{\text{moles of solute}} {\text{mass of solvent in kg}}$$

3. Solubility

Solubility is the maximum amount of solute that can dissolve in a given amount of solvent at a particular temperature.

Factors affecting solubility:

• nature of solute,
• nature of solvent,
• temperature,
• pressure for gases.

4. Henry's law

Henry's law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.

$$p=K_Hx$$

where:

• $p$ = partial pressure of gas,
• $K_H$ = Henry's law constant,
• $x$ = mole fraction of gas.

Applications:

• soda bottles,
• deep sea diving,
• oxygen transport,
• high altitude breathing.

5. Vapour pressure of liquid solutions

Raoult's law for volatile components:

$$p_A=x_Ap_A^\circ$$ $$p_B=x_Bp_B^\circ$$

Total pressure:

$$p_{\text{total}}=p_A+p_B$$ $$p_{\text{total}} = x_Ap_A^\circ+x_Bp_B^\circ$$

6. Ideal solutions

An ideal solution obeys Raoult's law over the entire range of concentration.

Conditions:

$$\Delta H_{\text{mix}}=0$$ $$\Delta V_{\text{mix}}=0$$

Example:

• benzene + toluene
• n-hexane + n-heptane

7. Non-ideal solutions

Non-ideal solutions do not obey Raoult's law.

Positive deviation:

$$p_{\text{observed}}>p_{\text{Raoult}}$$

Negative deviation:

$$p_{\text{observed}}<p_{\text{Raoult}}$$

8. Azeotropes

Azeotropes are mixtures that boil at constant temperature and have same composition in liquid and vapour phase.

Types:

9. Colligative properties

Colligative properties depend on the number of solute particles, not their nature.

Types:

• relative lowering of vapour pressure,
• elevation of boiling point,
• depression of freezing point,
• osmotic pressure.

10. Relative lowering of vapour pressure

For a non-volatile solute:

$$\frac{p_A^\circ-p_A}{p_A^\circ} = x_B$$

For dilute solution:

$$\frac{p_A^\circ-p_A}{p_A^\circ} = \frac{n_B}{n_A}$$

11. Elevation of boiling point

$$\Delta T_b=T_b-T_b^\circ$$ $$\Delta T_b=K_bm$$

Molar mass of solute:

$$M_B= \frac{K_b\times w_B\times1000} {\Delta T_b\times w_A}$$

12. Depression of freezing point

$$\Delta T_f=T_f^\circ-T_f$$ $$\Delta T_f=K_fm$$

Molar mass:

$$M_B= \frac{K_f\times w_B\times1000} {\Delta T_f\times w_A}$$

13. Osmotic pressure

Osmosis is movement of solvent from dilute solution to concentrated solution through a semipermeable membrane.

Osmotic pressure:

$$\Pi=CRT$$

Also:

$$\Pi V=nRT$$

Molar mass:

$$M_B= \frac{w_BRT}{\Pi V}$$

14. van't Hoff factor

The van't Hoff factor accounts for association or dissociation of solute particles.

$$i= \frac{\text{observed colligative property}} {\text{normal colligative property}}$$

For dissociation:

$$i>1$$

For association:

$$i<1$$

Modified formulae:

$$\Delta T_b=iK_bm$$ $$\Delta T_f=iK_fm$$ $$\Pi=iCRT$$

15. Solved example

If $0.1$ mol solute is dissolved in $1$ kg water and $K_f=1.86$, then:

$$\Delta T_f=K_fm$$ $$\Delta T_f=1.86\times0.1=0.186\ K$$

16. Common mistakes

• Confusing molarity and molality.
• Forgetting molarity changes with temperature.
• Using wrong sign for $\Delta T_f$.
• Forgetting van't Hoff factor for electrolytes.
• Confusing positive and negative deviation.
• Treating all solutions as ideal.

17. Quick revision