CBSE Class 12 Chemistry Chapter 2 Notes: Solutions

Understanding Solutions and Concentration Terms

A solution is a homogeneous mixture of two or more chemically non-reacting substances whose composition can be varied within certain limits. It consists of a solute (minor component) dissolved in a solvent (major component). The concentration of a solution is a measure of the amount of solute present in a given amount of solution or solvent. Various ways to express concentration are vital for quantitative analysis:

• Mass percentage (% w/w): (Mass of solute / Mass of solution) × 100. Useful when dealing with solids in solids or solids in liquids where masses are easily measured.
• Volume percentage (% v/v): (Volume of solute / Volume of solution) × 100. Commonly used for liquid-liquid solutions, such as alcohol in water.
• Mass by volume percentage (% w/v): (Mass of solute / Volume of solution) × 100. Often used in medicine and pharmacy.
• Parts per million (ppm): (Mass of solute / Mass of solution) × 10⁶. Used for very dilute solutions, like pollutants in water or air.
• Mole fraction (χ): Moles of a component / Total moles of all components. It's a ratio, hence dimensionless, and the sum of mole fractions of all components in a solution is always 1.
• Molarity (M): Moles of solute / Volume of solution in Litres. Temperature-dependent due to volume expansion/contraction. It's crucial for volumetric titrations.
• Molality (m): Moles of solute / Mass of solvent in kg. Temperature-independent as it relies on mass, making it preferred for colligative property calculations.

Solubility: Henry's Law and Raoult's Law

Solubility is the maximum amount of solute that can dissolve in a given amount of solvent at a specific temperature and pressure. It depends on the nature of solute/solvent, temperature, and pressure.

• Henry's Law: States that the partial pressure of the gas in vapor phase (p) is proportional to the mole fraction of the gas (χ) in the solution. Mathematically, p = K_H * χ, where K_H is Henry's Law constant. Higher K_H at a given temperature implies lower solubility of the gas. Increased temperature decreases the solubility of gases in liquids (e.g., carbonated drinks become flat when warm).

• Raoult's Law: For a solution of volatile liquids, the partial vapor pressure of each component in the solution is directly proportional to its mole fraction in the solution. For component 'i', p_i = p_i° χ_i, where p_i° is the vapor pressure of the pure component. For a solution of a non-volatile solute in a volatile solvent, the vapor pressure of the solution is directly proportional to the mole fraction of the solvent: p_solution = p_solvent° χ_solvent.

Key Colligative Properties and Their Formulas

• Colligative Properties: Properties of solutions that depend only on the number of solute particles, not on their nature. They are primarily observed in dilute solutions.
• 1. Relative Lowering of Vapor Pressure (RLVP): (p° - p) / p° = χ_solute. Here, p° is vapor pressure of pure solvent, p is vapor pressure of solution.
• 2. Elevation in Boiling Point (ΔT_b): ΔT_b = K_b * m. Where ΔT_b is the increase in boiling point, K_b is molal elevation constant (ebullioscopic constant), and m is molality of solution.
• 3. Depression in Freezing Point (ΔT_f): ΔT_f = K_f * m. Where ΔT_f is the decrease in freezing point, K_f is molal depression constant (cryoscopic constant), and m is molality of solution.
• 4. Osmotic Pressure (Π): Π = CRT. Where Π is osmotic pressure, C is molarity (mol L⁻¹), R is gas constant (0.0821 L atm mol⁻¹ K⁻¹ or 8.314 J K⁻¹ mol⁻¹), and T is temperature in Kelvin.
• Van't Hoff Factor (i): Accounts for dissociation/association of solute particles in solution. i = (Normal molar mass / Abnormal molar mass) = (Observed colligative property / Calculated colligative property assuming no association/dissociation).
• For dissociation, i > 1; for association, i < 1; for non-electrolytes, i = 1.
• Modified colligative property formulas with 'i': RLVP = i χ_solute, ΔT_b = i K_b m, ΔT_f = i K_f m, Π = i CRT.

Ideal vs. Non-Ideal Solutions

Worked Examples

• Example 1: Molarity Calculation Q: Calculate the molarity of a solution containing 5 g of NaOH in 450 mL of solution. A: Molar mass of NaOH = 23+16+1 = 40 g/mol. Moles of NaOH = 5 g / 40 g/mol = 0.125 mol. Volume of solution = 450 mL = 0.450 L. Molarity = Moles / Volume (L) = 0.125 mol / 0.450 L = 0.278 M.
• Example 2: Osmotic Pressure Q: A 5% (w/v) solution of sucrose (Molar mass = 342 g/mol) is isotonic with another solution 'X'. Calculate the concentration of 'X' in g/L. A: For isotonic solutions, osmotic pressures are equal, hence molar concentrations are equal. Sucrose concentration (C) = 5% (w/v) = 5 g / 100 mL = 50 g/L. Molarity of sucrose solution = (50 g/L) / (342 g/mol) = 0.146 M. Since solution 'X' is isotonic, its molarity is also 0.146 M. If 'X' is a non-electrolyte, then its concentration in g/L will depend on its molar mass. If it's a generic comparison, simply stating molarity is sufficient. Assuming 'X' is also a non-electrolyte and its molarity is 0.146 M. The question asks for concentration in g/L, but without Molar Mass of X, we can't fully calculate it. However, if 'X' is also a sucrose solution, then it would also be 50 g/L. This question is slightly ambiguous without more info on X, so let's assume it wants the molarity of 'X' if it's isotonic to 5% sucrose: 0.146 M.

Key Definitions

Homogeneous Mixture

A mixture in which the components are uniformly distributed throughout the mixture, with no visible boundaries of separation.

Solubility

The maximum amount of solute that can be dissolved in a given amount of solvent at a specific temperature and pressure to form a saturated solution.

Azeotropes

Binary mixtures that boil at a constant temperature and distill without change in composition. They behave like pure liquids and cannot be separated by fractional distillation.

Isotonic Solutions

Solutions having the same osmotic pressure at a given temperature. They have the same molar concentration.

Ebullioscopic Constant (K_b)

The molal elevation constant; the elevation in boiling point when the molality of the solution is unity (1 molal).

Cryoscopic Constant (K_f)

The molal depression constant; the depression in freezing point when the molality of the solution is unity (1 molal).

Osmosis

The spontaneous net movement of solvent molecules through a selectively permeable membrane into a region of higher solute concentration, aiming to equalize solute concentrations on the two sides.

Exam Tip: Van't Hoff Factor & Colligative Properties

Always remember to incorporate the van't Hoff factor (i) when dealing with electrolyte solutions (which dissociate or associate). A common mistake is to forget 'i' in calculations involving colligative properties for ionic compounds like NaCl, CaCl₂, or K₂SO₄. For example, if you're calculating the boiling point elevation for a 0.1 m NaCl solution, i would be approximately 2 (since NaCl dissociates into Na⁺ and Cl⁻ ions). Ignoring i will lead to incorrect answers. Similarly, be mindful of units, especially for Molarity (L) vs. Molality (kg) and temperature in Kelvin for osmotic pressure.

Practice Questions with Solutions

• Q: Why is molality preferred over molarity for expressing the concentration of solutions in colligative property calculations? A: Molality is temperature-independent as it's based on mass of solvent, whereas molarity is temperature-dependent due to volume changes.
• Q: State Henry's Law. A: The partial pressure of the gas in vapor phase (p) is proportional to the mole fraction of the gas (χ) in the solution: p = K_H * χ.
• Q: What are azeotropes? Can they be separated by fractional distillation? A: Azeotropes are binary mixtures that boil at a constant temperature and have the same composition in liquid and vapor phases. They cannot be separated by fractional distillation.
• Q: How does the van't Hoff factor 'i' account for association of solute particles? A: For association, 'i' is less than 1, indicating that the observed number of particles in solution is less than the number of particles taken initially due to molecules combining.

Frequently Asked Questions