Comprehensive Study Guide: ISC Class 12 Chemistry - Solutions

Overview of Solutions in Physical Chemistry

Solutions are homogeneous mixtures of two or more substances where the composition can vary within certain limits. In chemistry, particularly for class 12, the focus is on homogeneous mixtures that appear uniform throughout. Examples include air (gaseous solution), sugar or salt water (liquid solutions), and alloys like brass (solid solutions). A solution consists of two components: the Solute (the substance dissolved, usually in smaller quantity) and the Solvent (the dissolving medium, usually in larger quantity).

Types of Solutions based on Components

Solutions can be classified based on the number of components present:

  1. Binary Solutions: Contain two components (one solute and one solvent).

  2. Ternary Solutions: Contain three components (two solutes and one solvent).

  3. Quaternary Solutions: Contain four components (three solutes and one solvent).
    Note that while solutes can be multiple, there is typically only one solvent in a solution.

Physical States of Solutions

There are nine types of solutions based on the physical state of the solute and solvent. The final state of the solution is determined by the state of the solvent. Examples include:

  • Gaseous Solutions: Gas-Gas (Air), Liquid-Gas (Moisture in air), Solid-Gas (Camphor in Nitrogen gas).

  • Liquid Solutions: Gas-Liquid (Oxygen in water/Carbonated drinks), Liquid-Liquid (Ethanol in water), Solid-Liquid (Sugar in water).

  • Solid Solutions: Gas-Solid (Hydrogen in Palladium), Liquid-Solid (Amalgams of Mercury with Sodium), Solid-Solid (Alloys like Copper in Gold).

Concentration Units

Concentration expresses the amount of solute present in a given amount of solvent or solution. Key units include:

  • Mass Percentage (w/w): \text{Mass % of component} = \left( \frac{\text{Mass of component in solution}}{\text{Total mass of solution}} \right) \times 100

  • Mass by Volume Percentage (w/v): \text{Mass of solute (g)} / \text{Volume of solution (mL)} \times 100

  • Volume Percentage (v/v): \text{Volume of solute} / \text{Total volume of solution} \times 100

  • Molarity (M): The number of moles of solute dissolved in one liter of solution. (M = \frac{n}{V}) where V is in liters. This unit is temperature-dependent because volume changes with temperature.

  • Molality (m): The number of moles of solute per kilogram (1000g) of solvent. (m = \frac{n_{\text{solute}}}{\text{Mass of solvent in kg}}). Since mass does not change with temperature, molality is temperature independent.

  • Mole Fraction (x): The ratio of the number of moles of a particular component to the total number of moles of all components. For a binary solution: (xA = \frac{nA}{nA + nB}). The sum of all mole fractions in a system is always 1.

  • Parts Per Million (ppm): Used for very dilute solutions. \text{ppm} = (\text{Number of parts of component} / \text{Total parts of solution}) \times 10^6

Solubility and Factors Affecting It

Solubility is the maximum amount of solute that can be dissolved in a specified amount of solvent at a given temperature. Factors include:

  1. Nature of Solute and Solvent: Like dissolves like (polar solutes dissolve in polar solvents).

  2. Temperature:

    • For solids in liquids: Solubility usually increases with temperature if the dissolution is endothermic and decreases if exothermic.

    • For gases in liquids: Solubility decreases as temperature increases because the kinetic energy of gas molecules increases, causing them to escape the liquid.

  3. Pressure: Primarily affects gas solubility in liquids.

Henry's Law

Henry's Law states that at a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the surface of the liquid. The mathematical expression is: (P = KH \times x) where P is the partial pressure of the gas, x is the mole fraction of the gas in solution, and KH is the Henry's Law constant.

Vapor Pressure and Raoult's Law

Vapor pressure is the pressure exerted by the vapors of a liquid in equilibrium with the liquid at a given temperature in a closed system.

Raoult's Law (Volatile solutes): In a solution, the partial vapor pressure of each volatile component is directly proportional to its mole fraction. (PA = PA^0 \times xA) and total pressure (P{\text{total}} = PA + PB).

Raoult's Law (Non-volatile solutes): When a non-volatile solute is added to a solvent, the vapor pressure of the solution is solely due to the solvent. (P{\text{solution}} = P{\text{solvent}}^0 \times x{\text{solvent}}). This leads to the Relative Lowering of Vapor Pressure: \frac{P^0 - Ps}{P^0} = x_{\text{solute}}.

Ideal and Non-Ideal Solutions

  1. Ideal Solutions: Obey Raoult's Law over the entire range of concentration. \Delta H{\text{mix}} = 0 and \Delta V{\text{mix}} = 0. Intermolecular forces between A-B are similar to A-A and B-B.

  2. Non-Ideal Solutions: Do not obey Raoult's Law. They show:

    • Positive Deviation: A-B interactions are weaker than A-A/B-B. Vapor pressure is higher than expected. \Delta H_{\text{mix}} > 0.

    • Negative Deviation: A-B interactions are stronger than A-A/B-B. Vapor pressure is lower than expected. \Delta H_{\text{mix}} < 0.

Colligative Properties

These properties depend only on the number of solute particles, not their nature:

  1. Relative Lowering of Vapor Pressure: As described above, proportional to the mole fraction of the solute.

  2. Elevation of Boiling Point ($\Delta Tb$): Adding a non-volatile solute raises the boiling point. (\Delta Tb = Kb \times m), where Kb is the molal elevation constant (ebullioscopic constant).

  3. Depression of Freezing Point ($\Delta Tf$): Adding a non-volatile solute lowers the freezing point. (\Delta Tf = Kf \times m), where Kf is the molal depression constant (cryoscopic constant).

  4. Osmotic Pressure ($\pi$): The excess pressure applied to a solution to prevent the inward flow of solvent through a semipermeable membrane. According to the van't Hoff equation: (\pi = CRT) or (\pi V = nRT).

Van't Hoff Factor (i)

To account for association or dissociation of solute particles, the van't Hoff factor is used: (i = \frac{\text{Observed colligative property}}{\text{Calculated colligative property}}) or (i = \frac{\text{Normal molar mass}}{\text{Abnormal molar mass}}). For dissociation, i > 1; for association, i < 1.