Chapter 1: Solutions

Basic Formulas

• Mass percentage (w/w): (Mass of component / Total mass of solution) × 100
• Volume percentage (V/V): (Volume of component / Total volume of solution) × 100
• Parts per million (ppm): Used for trace quantities. (No. of parts of component / Total parts) × 10⁶
• Mole Fraction (x): No. of moles of component / Total no. of moles of all components. (Sum of all mole fractions = 1)

Molarity vs Molality

• Temperature Dependence: Molarity depends on temperature because volume changes with temperature. Molality is independent of temperature because mass does not change with temperature.

Solid in Liquid

• Effect of Temp: If dissolution is Endothermic (ΔH > 0), solubility increases with T. If Exothermic (ΔH < 0), solubility decreases with T (Le Chatelier's Principle).
• Effect of Pressure: No significant effect as solids and liquids are highly incompressible.

Gas in Liquid & Henry's Law

Solubility of gases in liquids decreases with increase in temperature. Solubility increases with increase in pressure.

Henry's Law: Partial pressure of the gas (p) in vapour phase is proportional to the mole fraction of the gas (x) in the solution.

• Higher the value of K_H at a given pressure, lower is the solubility of the gas.
• Applications:
  1. To increase solubility of CO₂ in soft drinks, bottles are sealed under high pressure.
  2. Scuba Divers (Bends): At high pressure underwater, N₂ dissolves in blood. Coming up rapidly releases N₂ bubbles, causing painful 'bends'. Tanks are diluted with Helium to avoid this.
  3. High Altitudes (Anoxia): Low partial pressure of O₂ leads to low oxygen in blood, causing weakness and inability to think clearly (Anoxia).

Raoult's Law for Volatile Liquids

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

Ideal vs Non-Ideal Solutions

• Ideal Solutions: Obey Raoult's law at all concentrations. ΔH_mix = 0, ΔV_mix = 0. A-B interactions are exactly equal to A-A and B-B interactions. (Ex: n-hexane + n-heptane).
• Positive Deviation (Non-Ideal): Vapour pressure is higher than expected. A-B interactions are weaker than A-A/B-B. ΔH > 0, ΔV > 0. (Ex: Ethanol + Acetone). Forms Minimum Boiling Azeotrope.
• Negative Deviation (Non-Ideal): Vapour pressure is lower than expected. A-B interactions are stronger than A-A/B-B. ΔH < 0, ΔV < 0. (Ex: Chloroform + Acetone due to H-bonding). Forms Maximum Boiling Azeotrope.

Azeotropes

Binary mixtures having the same composition in liquid and vapour phase and boil at a constant temperature. They cannot be separated by fractional distillation.

1. Relative Lowering of Vapour Pressure

When a non-volatile solute is added to a solvent, vapour pressure decreases.

2. Elevation of Boiling Point (ΔT_b)

• K_b = Molal elevation constant (Ebullioscopic constant).

3. Depression in Freezing Point (ΔT_f)

• K_f = Molal depression constant (Cryoscopic constant). Ex: Ethylene glycol is used as antifreeze in car radiators to depress freezing point of water.

4. Osmosis & Osmotic Pressure (π)

Flow of solvent from pure solvent to solution through a semi-permeable membrane (SPM).

• Reverse Osmosis (RO): If pressure applied is greater than osmotic pressure, solvent flows from solution to pure solvent. Used in desalination of sea water.
• Isotonic: Same osmotic pressure. Hypertonic: Higher π (Cell shrinks). Hypotonic: Lower π (Cell swells).

van't Hoff Factor (i)

Accounts for extent of dissociation or association.

• i = 1: No association/dissociation (Ex: Glucose, Urea).
• i > 1: Dissociation (Ex: NaCl, KCl). Molar mass appears less.
• i < 1: Association (Ex: Acetic acid in benzene forms dimers). Molar mass appears more.

Degree of Dissociation / Association

• For Dissociation (α): α = (i - 1) / (n - 1)
• For Association (α): α = (i - 1) / ((1/n) - 1)
• Modified Formulas: ΔT_b = i × K_b × m ; π = iCRT