Chemistry: Class 121 — Chapter 1: Solutions

Solutions can be classified into gaseous, liquid, or solid solutions depending on the physical state of the solvent:

• Gaseous Solutions: Solvent is a gas. Solutes can be gas (e.g., oxygen-nitrogen mixture), liquid (e.g., chloroform in nitrogen gas), or solid (e.g., camphor in nitrogen gas).
• Liquid Solutions: Solvent is a liquid. Solutes can be gas (e.g., oxygen in water), liquid (e.g., ethanol in water), or solid (e.g., glucose in water).
• Solid Solutions: Solvent is a solid. Solutes can be gas (e.g., hydrogen in palladium), liquid (e.g., mercury amalgam with sodium), or solid (e.g., copper dissolved in gold).

• Mass Percentage (w/w): The mass of a component per $100\text{ g}$ of solution.
  $$\text{Mass % of a component} = \frac{\text{Mass of the component in the solution}}{\text{Total mass of the solution}} \times 100$$
• Volume Percentage (V/V): The volume of a component per $100\text{ mL}$ of solution.
  $$\text{Volume % of a component} = \frac{\text{Volume of the component}}{\text{Total volume of solution}} \times 100$$
• Mass by Volume Percentage (w/V): The mass of solute dissolved in $100\text{ mL}$ of the solution, commonly used in medicine and pharmacy.
• Parts per Million (ppm): Used when a solute is present in trace quantities.
  $$\text{Parts per million} = \frac{\text{Number of parts of the component}}{\text{Total number of parts of all components of the solution}} \times 10^6$$
• Mole Fraction ($x$): The ratio of the number of moles of a component to the total number of moles of all components.
  $$x_A = \frac{n_A}{n_A + n_B}$$
  The sum of all mole fractions in a solution is always unity: $\sum x_i = 1$.
• Molarity ($M$): The number of moles of solute dissolved in one litre of solution.
  $$M = \frac{\text{Moles of solute}}{\text{Volume of solution in litres}}$$
  Molarity is temperature-dependent because volume changes with temperature.
• Molality ($m$): The number of moles of solute per kilogram of solvent.
  $$m = \frac{\text{Moles of solute}}{\text{Mass of solvent in kg}}$$
  Molality is temperature-independent as mass does not change with temperature.

Governed by the principle of "like dissolves like" (polar solutes dissolve in polar solvents, non-polar solutes in non-polar solvents).

• Dissolution and Crystallisation: When solute dissolves, its concentration increases (dissolution). Simultaneously, solute particles collide and separate out of solution (crystallisation). At dynamic equilibrium, both processes occur at the same rate.
• Saturated and Unsaturated Solutions: A saturated solution contains the maximum amount of solute at a given temperature and pressure. An unsaturated solution can dissolve more solute.
• Effect of Temperature: If the dissolution process is endothermic ($\Delta_{\text{sol}}H > 0$), solubility increases with temperature. If exothermic ($\Delta_{\text{sol}}H < 0$), solubility decreases.
• Effect of Pressure: Pressure has no significant effect on the solubility of solids in liquids because solids and liquids are highly incompressible.

Gas solubility is highly sensitive to pressure and temperature.

• Effect of Pressure (Henry's Law): At a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas present above the surface of the liquid or solution.
  $$p = K_H x$$
  where $p$ is the partial pressure of the gas, $x$ is its mole fraction in solution, and $K_H$ is the Henry's law constant. Higher $K_H$ values indicate lower solubility.
• Effect of Temperature: Gas solubility decreases with an increase in temperature because dissolution of gases is an exothermic process (similar to condensation).

For a solution of volatile liquids, the partial vapour pressure of each component is directly proportional to its mole fraction in the solution.

According to Dalton's law of partial pressures, the total pressure ($p_{\text{total}}$) is:

In both laws, partial pressure is proportional to mole fraction. In Raoult's law, the proportionality constant is $p_1^0$, while in Henry's law, it is $K_H$. Thus, Raoult's law becomes a special case of Henry's law when $K_H = p_1^0$.

When a non-volatile solute is added to a volatile solvent, the vapour pressure of the solution decreases because solute particles occupy part of the surface area, reducing the rate of solvent evaporation.

Solutions that obey Raoult's law over the entire range of concentration.

• Thermodynamic Properties: $\Delta_{\text{mix}}H = 0$ and $\Delta_{\text{mix}}V = 0$.
• Molecular Level: Intermolecular attractive forces between solute-solvent ($A-B$) are nearly equal to those between solvent-solvent ($A-A$) and solute-solute ($B-B$).
• Examples: n-hexane and n-heptane, bromoethane and chloroethane, benzene and toluene.

Solutions that do not obey Raoult's law and exhibit deviations.

• Positive Deviation: $A-B$ interactions are weaker than $A-A$ or $B-B$ interactions. Vapour pressure is higher than predicted. Examples: ethanol and acetone, carbon disulphide and acetone.
• Negative Deviation: $A-B$ interactions are stronger than $A-A$ or $B-B$ interactions. Vapour pressure is lower than predicted. Examples: phenol and aniline, chloroform and acetone.
• Azeotropes: Binary mixtures having the same composition in liquid and vapour phase that boil at a constant temperature. They cannot be separated by fractional distillation.
  • Minimum boiling azeotrope: Formed by solutions showing large positive deviation (e.g., $95\%$ ethanol-water mixture).
  • Maximum boiling azeotrope: Formed by solutions showing large negative deviation (e.g., $68\%$ nitric acid and $32\%$ water by mass).

The relative lowering of vapour pressure of a solvent is equal to the mole fraction of the non-volatile solute.

The boiling point of a solution containing a non-volatile solute is always higher than that of the pure solvent.

where $K_b$ is the molal elevation constant (Ebullioscopic Constant) and $m$ is the molality. The molar mass of the solute ($M_2$) is calculated as:

The freezing point of a solution containing a non-volatile solute is lower than that of the pure solvent.

where $K_f$ is the molal depression constant (Cryoscopic Constant). The molar mass of the solute ($M_2$) is calculated as:

Osmosis is the spontaneous flow of solvent molecules through a semipermeable membrane (SPM) from pure solvent to solution. Osmotic pressure ($\Pi$) is the excess pressure that must be applied to the solution side to stop osmosis.

The molar mass of the solute ($M_2$) is calculated as:

• Isotonic Solutions: Two solutions having the same osmotic pressure at a given temperature.
• Hypertonic and Hypotonic: A solution with higher osmotic pressure than another is hypertonic (causes cells to shrink); one with lower osmotic pressure is hypotonic (causes cells to swell).
• Reverse Osmosis: Occurs when a pressure larger than the osmotic pressure is applied to the solution, forcing solvent to flow from solution to pure solvent. Used in water purification and desalination.

Introduced to account for the extent of dissociation or association of a solute.

• For association (e.g., dimerisation of acetic acid in benzene), $i < 1$.
• For dissociation (e.g., NaCl, KCl in water), $i > 1$.

• Relative lowering of vapour pressure: $\frac{p_1^0 - p_1}{p_1^0} = i \frac{n_2}{n_1}$
• Elevation of Boiling point: $\Delta T_b = i K_b m$
• Depression of Freezing point: $\Delta T_f = i K_f m$
• Osmotic pressure: $\Pi = i \frac{n_2 R T}{V}$