class 12 notes

Class 12 Chemistry Notes Chapter 2 (Solutions) – Chemistry-I Book

Philoid

Philoid

— 10 min read

Chemistry-I
Alright everyone, let's focus on Chapter 2: Solutions from your NCERT Class 12 Chemistry-I book. This is a crucial chapter, not just for board exams but also frequently tested in various government exams. We'll cover the key concepts, definitions, laws, and formulas you need to master.

Chapter 2: Solutions - Detailed Notes for Exam Preparation

1. Introduction

  • Solution: A homogeneous mixture of two or more substances whose composition can be varied within certain limits.
  • Components:
    • Solute: The substance present in a smaller amount, which gets dissolved.
    • Solvent: The substance present in a larger amount, in which the solute dissolves. The physical state of the solvent usually determines the physical state of the solution.
  • Types of Solutions: Based on the physical state of solute and solvent (Total 9 types, e.g., Gas in Gas - Air; Liquid in Gas - Chloroform in N2; Solid in Gas - Camphor in N2; Gas in Liquid - O2 in water; Liquid in Liquid - Ethanol in water; Solid in Liquid - Sugar in water; Gas in Solid - H2 in Palladium; Liquid in Solid - Amalgam of Hg with Na; Solid in Solid - Alloys like Brass).

2. Expressing Concentration of Solutions

This section is vital for numerical problems.

  • (a) Mass Percentage (w/w):
    • Mass % of component = (Mass of the component in the solution / Total mass of the solution) × 100
    • Unitless. Independent of temperature.
  • (b) Volume Percentage (v/v):
    • Volume % of component = (Volume of the component / Total volume of the solution) × 100
    • Unitless. Used mainly for liquid-in-liquid solutions. Temperature dependent.
  • (c) Mass by Volume Percentage (w/v):
    • Mass by Volume % = (Mass of solute (in g) / Volume of solution (in mL)) × 100
    • Commonly used in medicine and pharmacy. Temperature dependent.
  • (d) Parts Per Million (ppm):
    • Used for very dilute solutions, especially for pollutants in air or water.
    • ppm = (Number of parts of the component / Total number of parts of all components in the solution) × 10^6
    • Can be expressed as mass/mass, volume/volume, or mass/volume.
    • ppm (w/w) = (Mass of solute / Mass of solution) × 10^6
    • ppm (v/v) = (Volume of solute / Volume of solution) × 10^6
  • (e) Mole Fraction (χ):
    • Mole fraction of component A (χ_A) = (Number of moles of A) / (Total number of moles of all components)
    • χ_A = n_A / (n_A + n_B) (for a binary solution)
    • χ_A + χ_B = 1
    • Unitless. Independent of temperature.
  • (f) Molarity (M):
    • Molarity (M) = (Moles of solute) / (Volume of solution in Litres)
    • Units: mol L⁻¹ or M.
    • Temperature dependent (as volume changes with temperature).
  • (g) Molality (m):
    • Molality (m) = (Moles of solute) / (Mass of solvent in kg)
    • Units: mol kg⁻¹ or m.
    • Temperature independent (as mass does not change with temperature). Preferred for studies involving temperature changes.

3. Solubility

  • Solubility: Maximum amount of solute that can be dissolved in a specified amount of solvent at a specific temperature and pressure.

  • Saturated Solution: A solution in which no more solute can be dissolved at the same temperature and pressure.

  • Unsaturated Solution: A solution containing less solute than the saturated solution at a given temperature and pressure.

  • Supersaturated Solution: A solution that contains more solute than required for saturation at a given temperature (unstable).

  • (a) Solubility of a Solid in a Liquid:

    • Nature of Solute and Solvent: "Like dissolves like" (Polar solutes dissolve in polar solvents, non-polar solutes dissolve in non-polar solvents).
    • Temperature:
      • If dissolution is endothermic (ΔsolH > 0), solubility increases with increasing temperature (Le Chatelier's Principle). Ex: NaCl, KNO3.
      • If dissolution is exothermic (ΔsolH < 0), solubility decreases with increasing temperature. Ex: Li2SO4, Ce2(SO4)3.
    • Pressure: Has negligible effect on the solubility of solids in liquids.

  • (b) Solubility of a Gas in a Liquid:

    • Nature of Gas and Solvent: Gases capable of forming ions or hydrogen bonds with the solvent are more soluble (e.g., HCl, NH3 in water).
    • Temperature: Solubility of gases in liquids decreases with an increase in temperature (dissolution is generally exothermic). This is why aquatic life is more comfortable in cold water.
    • 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."
      • Mathematically: p = K_H × χ
        • p = Partial pressure of the gas in the vapour phase.
        • χ = Mole fraction of the gas in the solution.
        • K_H = Henry's Law constant (depends on the nature of the gas and solvent, and temperature).
      • Higher the value of KH at a given pressure, the lower is the solubility of the gas in the liquid.
      • KH increases with an increase in temperature, indicating lower solubility at higher temperatures.
    • Applications of Henry's Law:
      • Production of carbonated beverages (CO2 dissolved under high pressure).
      • Scuba diving: To avoid "bends" (decompression sickness), tanks are filled with air diluted with Helium (He is less soluble in blood than N2).
      • High altitudes: Lower partial pressure of O2 leads to lower concentration in blood, causing "anoxia" (symptoms like weakness, inability to think clearly).

4. Vapour Pressure of Liquid Solutions

  • Vapour Pressure: The pressure exerted by the vapours of a liquid in equilibrium with its liquid phase at a given temperature in a closed container.

  • Factors affecting vapour pressure: Nature of liquid, Temperature.

  • (a) Vapour Pressure of Liquid-Liquid Solutions (Both components volatile):

    • Raoult's Law: "For a solution of volatile liquids, the partial vapour pressure of each component in the solution is directly proportional to its mole fraction present in the solution."
    • For component A: P_A = P_A° × χ_A
    • For component B: P_B = P_B° × χ_B
      • P_A, P_B = Partial vapour pressures of components A and B over the solution.
      • P_A°, P_B° = Vapour pressures of pure components A and B.
      • χ_A, χ_B = Mole fractions of components A and B in the solution.
    • Dalton's Law of Partial Pressures: Total vapour pressure over the solution (P_total) = P_A + P_B
    • P_total = P_A°χ_A + P_B°χ_B = P_A°(1 - χ_B) + P_B°χ_B = P_A° + (P_B° - P_A°)χ_B
    • Composition in Vapour Phase: If y_A and y_B are mole fractions in the vapour phase:
      • P_A = y_A × P_total => y_A = P_A / P_total
      • P_B = y_B × P_total => y_B = P_B / P_total

  • (b) Vapour Pressure of Solutions of Solids in Liquids (Non-volatile solute):

    • The vapour pressure of the solution is lower than that of the pure solvent because the non-volatile solute particles occupy some surface area, reducing the escaping tendency of solvent molecules.
    • Raoult's Law (for non-volatile solute): "The vapour pressure of a solution containing a non-volatile solute is directly proportional to the mole fraction of the solvent in the solution."
    • P_solution = P_solvent° × χ_solvent
    • Since χ_solvent = 1 - χ_solute
    • P_solution = P_solvent° (1 - χ_solute)
    • (P_solvent° - P_solution) / P_solvent° = χ_solute (This is Relative Lowering of Vapour Pressure - a colligative property).

5. Ideal and Non-Ideal Solutions

  • Ideal Solutions: Solutions that obey Raoult's Law over the entire range of concentration.

    • Conditions:
      • P_A = P_A°χ_A and P_B = P_B°χ_B
      • ΔH_mix = 0 (No heat evolved or absorbed on mixing)
      • ΔV_mix = 0 (Total volume is the sum of individual volumes)
    • Reason: Solute-solvent interactions (A-B) are nearly equal to solute-solute (A-A) and solvent-solvent (B-B) interactions.
    • Examples: n-hexane and n-heptane; Bromoethane and Chloroethane; Benzene and Toluene.

  • Non-Ideal Solutions: Solutions that do not obey Raoult's Law.

    • Reason: Solute-solvent interactions are different from solute-solute and solvent-solvent interactions.
    • ΔH_mix ≠ 0; ΔV_mix ≠ 0
    • (i) Positive Deviation from Raoult's Law:
      • P_A > P_A°χ_A; P_B > P_B°χ_B; P_total > P_A°χ_A + P_B°χ_B (Observed VP is higher than expected).
      • Reason: A-B interactions are weaker than A-A and B-B interactions. Molecules escape more easily.
      • ΔH_mix > 0 (Endothermic mixing - energy needed to overcome stronger initial interactions).
      • ΔV_mix > 0 (Volume expansion on mixing).
      • Examples: Ethanol and Acetone; Carbon disulphide and Acetone; Ethanol and Water.
      • Forms Minimum Boiling Azeotrope.
    • (ii) Negative Deviation from Raoult's Law:
      • P_A < P_A°χ_A; P_B < P_B°χ_B; P_total < P_A°χ_A + P_B°χ_B (Observed VP is lower than expected).
      • Reason: A-B interactions are stronger than A-A and B-B interactions (e.g., due to hydrogen bonding). Molecules escape less easily.
      • ΔH_mix < 0 (Exothermic mixing - energy released due to stronger bond formation).
      • ΔV_mix < 0 (Volume contraction on mixing).
      • Examples: Phenol and Aniline; Chloroform and Acetone; Nitric acid and Water.
      • Forms Maximum Boiling Azeotrope.

  • Azeotropes (Constant Boiling Mixtures): Binary mixtures having the same composition in liquid and vapour phase and boil at a constant temperature. Components cannot be separated by fractional distillation.

    • Minimum Boiling Azeotrope: Formed by solutions showing large positive deviation (Boiling point is lower than either pure component). Ex: Ethanol-water (95% ethanol by volume).
    • Maximum Boiling Azeotrope: Formed by solutions showing large negative deviation (Boiling point is higher than either pure component). Ex: Nitric acid-water (68% nitric acid by mass).

6. Colligative Properties

Properties of solutions that depend only on the number of solute particles (concentration) relative to the total number of particles present in the solution, and not on the nature of the solute. Applicable to dilute solutions containing non-volatile solutes.

  • (a) Relative Lowering of Vapour Pressure (RLVP):
    • RLVP = (P_solvent° - P_solution) / P_solvent°
    • According to Raoult's Law: (P_solvent° - P_solution) / P_solvent° = χ_solute
    • χ_solute = n_solute / (n_solute + n_solvent)
    • For dilute solutions, n_solute << n_solvent, so n_solute + n_solvent ≈ n_solvent.
    • RLVP ≈ n_solute / n_solvent = (w_solute / M_solute) / (w_solvent / M_solvent)
    • Used to determine the molar mass of the solute (M_solute).
  • (b) Elevation in Boiling Point (ΔTb):
    • Boiling point of a liquid is the temperature at which its vapour pressure equals the external pressure.
    • Adding a non-volatile solute lowers the vapour pressure, so the solution must be heated to a higher temperature to make its VP equal to the external pressure.
    • ΔT_b = T_b (solution) - T_b° (pure solvent)
    • For dilute solutions: ΔT_b ∝ m (molality)
    • ΔT_b = K_b × m
      • K_b = Boiling Point Elevation Constant or Ebullioscopic Constant (depends only on the solvent). Units: K kg mol⁻¹.
      • m = Molality = (w_solute × 1000) / (M_solute × w_solvent (in g))
    • M_solute = (K_b × w_solute × 1000) / (ΔT_b × w_solvent (in g))
  • (c) Depression in Freezing Point (ΔTf):
    • Freezing point is the temperature at which the solid and liquid phases of a substance are in equilibrium (have the same vapour pressure).
    • Adding a non-volatile solute lowers the vapour pressure of the liquid phase, causing freezing to occur at a lower temperature.
    • ΔT_f = T_f° (pure solvent) - T_f (solution)
    • For dilute solutions: ΔT_f ∝ m
    • ΔT_f = K_f × m
      • K_f = Freezing Point Depression Constant or Cryoscopic Constant (depends only on the solvent). Units: K kg mol⁻¹.
      • m = Molality = (w_solute × 1000) / (M_solute × w_solvent (in g))
    • M_solute = (K_f × w_solute × 1000) / (ΔT_f × w_solvent (in g))
    • Application: Using ethylene glycol as antifreeze in car radiators; using NaCl or CaCl2 to clear snow from roads.
  • (d) Osmotic Pressure (π):
    • Osmosis: The spontaneous flow of solvent molecules from pure solvent to solution, or from a dilute solution to a concentrated solution, through a semipermeable membrane (SPM). SPM allows only solvent molecules to pass.
    • Osmotic Pressure (π): The excess pressure that must be applied on the solution side to just prevent the flow of solvent (osmosis) across the SPM.
    • π ∝ C (Molar concentration) at a given temperature T.
    • π ∝ T at a given concentration C.
    • π = C R T (Van't Hoff equation for dilute solutions)
      • C = Molarity (mol L⁻¹) = n_solute / V_solution (in L)
      • R = Universal Gas Constant (0.0821 L atm K⁻¹ mol⁻¹ or 8.314 J K⁻¹ mol⁻¹)
      • T = Temperature in Kelvin.
    • π = (n_solute / V) R T = (w_solute / M_solute) × (R T / V)
    • M_solute = (w_solute R T) / (π V)
    • Osmotic pressure is preferred for determining molar masses of macromolecules (polymers, proteins) because:
      • Magnitude of pressure is appreciable even for dilute solutions.
      • Measurements are done at room temperature (avoids thermal degradation).
      • Molarity is used instead of molality.
    • Isotonic Solutions: Two solutions having the same osmotic pressure at a given temperature (π₁ = π₂). No net osmosis occurs between them.
    • Hypertonic Solution: A solution with higher osmotic pressure compared to another.
    • Hypotonic Solution: A solution with lower osmotic pressure compared to another.
    • If a cell is placed in a hypertonic solution, water flows out (plasmolysis/shrinkage). If placed in a hypotonic solution, water flows in (swelling/bursting).
    • Reverse Osmosis (RO): If pressure greater than osmotic pressure is applied on the solution side, solvent flows from solution to pure solvent through SPM. Used for desalination of seawater.

7. Abnormal Molar Masses and Van't Hoff Factor (i)

  • Colligative properties depend on the number of solute particles.

  • When solutes dissociate (e.g., electrolytes like NaCl, MgCl2) or associate (e.g., ethanoic acid in benzene) in solution, the number of particles changes.

  • This leads to observed colligative properties being different from theoretical values calculated assuming no dissociation/association.

  • Consequently, the molar mass calculated from these observed colligative properties is different from the actual molar mass (termed "abnormal molar mass").

  • Van't Hoff Factor (i): Introduced to account for dissociation/association.

    • i = (Observed value of colligative property) / (Calculated value of colligative property)
    • i = (Normal molar mass) / (Abnormal molar mass)
    • i = (Total number of moles of particles after dissociation/association) / (Number of moles of particles before dissociation/association)

  • Values of i:

    • For non-electrolytes (no dissociation/association, e.g., glucose, urea, sucrose): i = 1
    • For solutes undergoing dissociation: i > 1 (e.g., NaCl → Na⁺ + Cl⁻, i ≈ 2; MgCl₂ → Mg²⁺ + 2Cl⁻, i ≈ 3)
    • For solutes undergoing association: i < 1 (e.g., 2CH₃COOH ⇌ (CH₃COOH)₂, i ≈ 0.5)

  • Modified Colligative Property Equations:

    • RLVP = (P° - P) / P° = i × χ_solute
    • ΔT_b = i × K_b × m
    • ΔT_f = i × K_f × m
    • π = i × C R T

  • Degree of Dissociation (α): α = (i - 1) / (n - 1), where 'n' is the number of ions produced per formula unit upon complete dissociation.

  • Degree of Association (α): α = (1 - i) / (1 - 1/n), where 'n' is the number of molecules associating to form one larger molecule.

10 Multiple Choice Questions (MCQs)

  1. Which of the following concentration units is independent of temperature?
    (a) Molarity
    (b) Molality
    (c) Normality
    (d) Mass by volume percentage

  2. According to Henry's law, the solubility of a gas in a liquid increases with:
    (a) Increase in temperature
    (b) Decrease in pressure
    (c) Increase in pressure
    (d) Decrease in KH value at constant pressure

  3. An ideal solution is formed when its components:
    (a) Have zero enthalpy of mixing (ΔHmix = 0)
    (b) Have zero volume change on mixing (ΔVmix = 0)
    (c) Obey Raoult's law over the entire range of concentration
    (d) All of the above

  4. A mixture of ethanol and acetone shows:
    (a) Positive deviation from Raoult's law
    (b) Negative deviation from Raoult's law
    (c) Ideal behaviour
    (d) No deviation from Raoult's law

  5. Which of the following colligative properties is most suitable for determining the molar mass of polymers?
    (a) Relative lowering of vapour pressure
    (b) Elevation in boiling point
    (c) Depression in freezing point
    (d) Osmotic pressure

  6. The Van't Hoff factor (i) for a dilute aqueous solution of BaCl2 (assuming complete dissociation) is:
    (a) 1
    (b) 2
    (c) 3
    (d) 0

  7. The relative lowering of vapour pressure of a solution containing a non-volatile solute is equal to:
    (a) Mole fraction of the solvent
    (b) Mole fraction of the solute
    (c) Molality of the solution
    (d) Molarity of the solution

  8. Kb (Ebullioscopic constant) depends on:
    (a) Nature of the solute
    (b) Nature of the solvent
    (c) Concentration of the solution
    (d) Temperature of the solution

  9. A liquid mixture boils without change in composition. This mixture is called:
    (a) Isotonic solution
    (b) Ideal solution
    (c) Azeotrope
    (d) Saturated solution

  10. The phenomenon of reverse osmosis is used in:
    (a) Preparation of carbonated drinks
    (b) Desalination of seawater
    (c) Functioning of kidneys
    (d) Preservation of fruits

Answers to MCQs:

  1. (b) Molality
  2. (c) Increase in pressure (and (d) is also correct as lower KH means higher solubility, but (c) is the direct statement of the law regarding pressure)
  3. (d) All of the above
  4. (a) Positive deviation from Raoult's law
  5. (d) Osmotic pressure
  6. (c) 3 (BaCl₂ → Ba²⁺ + 2Cl⁻, total 3 ions)
  7. (b) Mole fraction of the solute
  8. (b) Nature of the solvent
  9. (c) Azeotrope
  10. (b) Desalination of seawater

Make sure you understand the definitions, the conditions for laws like Henry's and Raoult's, the differences between ideal and non-ideal solutions, and how to apply the formulas for concentration and colligative properties, including the Van't Hoff factor. Good luck with your preparation!

Read more