Chapter: Solutions – Detailed Notes for NEET/JEE Mains

1. Introduction to Solutions

• Solution: A homogeneous mixture of two or more non-reacting components whose composition can be varied within certain limits.
  • Homogeneous: The components are uniformly distributed throughout the mixture, and its properties are uniform throughout.
  • Components:
    • Solute: The component present in a smaller quantity, which dissolves in the solvent.
    • Solvent: The component present in a larger quantity, which dissolves the solute.
• Types of Solutions: Classified based on the physical state of the solute and solvent.

2. Expressing Concentration of Solutions

The concentration of a solution expresses the amount of solute present in a given quantity of solution or solvent.

1. Mass Percentage (% w/w):
   • Mass of solute per 100 parts by mass of solution.
   • \text{Mass % of solute} = \frac{\text{Mass of solute}}{\text{Mass of solution}} \times 100
2. Volume Percentage (% v/v):
   • Volume of solute per 100 parts by volume of solution.
   • \text{Volume % of solute} = \frac{\text{Volume of solute}}{\text{Volume of solution}} \times 100 (Used for liquid-liquid solutions)
3. Mass by Volume Percentage (% w/v):
   • Mass of solute per 100 mL of solution.
   • \text{Mass by Volume % of solute} = \frac{\text{Mass of solute}}{\text{Volume of solution (mL)}} \times 100 (Common in medicine and pharmacy)
4. Parts per Million (ppm):
   • Used for very dilute solutions.
   • ppm=Mass of solutionMass of solute​×106 (For mass)
   • ppm=Volume of solutionVolume of solute​×106 (For volume)
5. Mole Fraction (χ):
   • Ratio of the number of moles of one component to the total number of moles of all components in the solution.
   • For a binary solution with components A and B:
     • χA​=nA​+nB​nA​​
     • χB​=nA​+nB​nB​​
   • Sum of mole fractions of all components is always 1 (χA​+χB​=1).
   • Temperature independent.
6. Molarity (M):
   • Number of moles of solute dissolved per litre (or dm3) of solution.
   • Molarity (M)=Volume of solution (L)Moles of solute​
   • Units: mol L−1 or M.
   • Temperature dependent (as volume changes with temperature).
7. Molality (m):
   • Number of moles of solute dissolved per kilogram of solvent.
   • Molality (m)=Mass of solvent (kg)Moles of solute​
   • Units: mol kg−1 or m.
   • Temperature independent (as mass does not change with temperature). Molality is preferred for colligative property calculations.

3. Solubility

• Solubility: The maximum amount of solute that can be dissolved in a given amount of solvent at a specific temperature to form a saturated solution.
• Saturated Solution: A solution in which no more solute can be dissolved at a given temperature.
• Unsaturated Solution: A solution in which more solute can be dissolved at a given temperature.
• Supersaturated Solution: A solution containing more solute than required to saturate it at a given temperature. It’s unstable.
• Factors Affecting Solubility:
  • Nature of Solute and Solvent (“Like dissolves like”):
    • Polar solutes dissolve in polar solvents (e.g., NaCl in water).
    • Non-polar solutes dissolve in non-polar solvents (e.g., Naphthalene in benzene).
    • This is due to the principle that intermolecular forces similar to those being broken (solute-solute, solvent-solvent) are formed (solute-solvent).
  • Effect of Temperature:
    • Solids in Liquids:
      • For endothermic dissolution (ΔHsol​>0), solubility increases with temperature (e.g., sugar in water).
      • For exothermic dissolution (ΔHsol​<0), solubility decreases with temperature (e.g., Ce2​(SO4​)3​ in water).
    • Gases in Liquids:
      • Solubility of gases in liquids decreases with increasing temperature (exothermic process).
  • Effect of Pressure:
    • Solids in Liquids: Pressure has negligible effect.
    • Gases in Liquids: Pressure has a significant effect. Solubility of a gas in a liquid increases with increasing pressure. This is explained by Henry’s Law.
• Henry’s Law: “The partial pressure of the gas in vapor phase (p) is proportional to the mole fraction of the gas (χ) in the solution.”
  • p=KH​×χ
  • Where KH​ is Henry’s Law constant.
  • Higher the value of KH​ at a given temperature, the lower is the solubility of the gas in the liquid.
  • Applications: In soda water bottles (high CO2​ pressure), deep-sea diving (bends), high altitude (anoxia).

4. Vapour Pressure of Liquid Solutions

• Vapour Pressure: The pressure exerted by the vapor in equilibrium with its liquid phase at a given temperature.
• Factors affecting Vapour Pressure: Nature of liquid (weaker intermolecular forces, higher VP), temperature (higher T, higher VP).
• Raoult’s Law:
  • For volatile liquid-liquid solutions: For a solution of two volatile liquids A and B, the partial vapor pressure of each component in the solution is directly proportional to its mole fraction in the solution.
    • pA​=pA0​×χA​
    • pB​=pB0​×χB​
    • Where pA0​ and pB0​ are the vapor pressures of pure components A and B, respectively.
    • Total vapor pressure of solution (Ptotal​) = pA​+pB​=pA0​χA​+pB0​χB​ (Dalton’s Law of Partial Pressures).
  • For solutions of non-volatile solute in volatile solvent: The vapor pressure of the solution containing a non-volatile solute is directly proportional to the mole fraction of the solvent.
    • pA​=pA0​×χA​
    • Here, pA​ is the vapor pressure of the solution, and pA0​ is the vapor pressure of the pure solvent. The solute has no vapor pressure.
• Ideal Solutions:
  • Obey Raoult’s Law over the entire range of concentrations.
  • ΔHmix​=0 (no heat absorbed or released on mixing).
  • ΔVmix​=0 (no change in volume on mixing).
  • Intermolecular forces between A-A, B-B, and A-B are roughly similar.
  • Examples: n-hexane and n-heptane, bromoethane and chloroethane, benzene and toluene.
• Non-Ideal Solutions: Do not obey Raoult’s Law.
  • Positive Deviation from Raoult’s Law:
    • Ptotal​>pA0​χA​+pB0​χB​ (Observed VP is higher than expected).
    • A-B interactions are weaker than A-A and B-B interactions.
    • ΔHmix​>0 (Endothermic, heat absorbed).
    • ΔVmix​>0 (Volume increases on mixing).
    • Examples: Ethanol and acetone, carbon disulfide and acetone.
  • Negative Deviation from Raoult’s Law:
    • Ptotal​<pA0​χA​+pB0​χB​ (Observed VP is lower than expected).
    • A-B interactions are stronger than A-A and B-B interactions.
    • ΔHmix​<0 (Exothermic, heat released).
    • ΔVmix​<0 (Volume decreases on mixing).
    • Examples: Chloroform and acetone, nitric acid and water, HCl and water.
• Azeotropes: Binary mixtures that have the same composition in liquid and vapor phases and boil at a constant temperature. They cannot be separated by fractional distillation.
  • Minimum Boiling Azeotropes: Formed by solutions showing large positive deviation from Raoult’s Law (e.g., Ethanol-water mixture, 95.6% ethanol).
  • Maximum Boiling Azeotropes: Formed by solutions showing large negative deviation from Raoult’s Law (e.g., Nitric acid-water mixture, 68% nitric acid).

5. Colligative Properties

Properties of solutions that depend only on the number of solute particles (or moles of solute) present in the solution, irrespective of their nature. They depend on the ratio of the number of solute particles to the total number of particles in the solution.

1. Relative Lowering of Vapour Pressure (RLVP):
   • Adding a non-volatile solute lowers the vapor pressure of the solvent.
   • pA0​pA0​−pA​​=χB​=nA​+nB​nB​​ (where B is solute, A is solvent)
   • For dilute solutions (nB​≪nA​), pA0​pA0​−pA​​≈nA​nB​​=wA​/MA​wB​/MB​​
     • Can be used to determine molar mass of non-volatile solute (MB​).
2. Elevation in Boiling Point (ΔTb​):
   • Adding a non-volatile solute increases the boiling point of the solvent.
   • ΔTb​=Tb​−Tb0​ (where Tb​ is BP of solution, Tb0​ is BP of pure solvent)
   • ΔTb​=Kb​×m (where m is molality of solute)
   • Kb​ (Molal Elevation Constant or Ebullioscopic Constant): Elevation in boiling point when molality is 1. Units: K kg mol−1.
   • MB​=ΔTb​×wA​Kb​×wB​×1000​ (for determining molar mass of solute)
3. Depression in Freezing Point (ΔTf​):
   • Adding a non-volatile solute decreases the freezing point of the solvent.
   • ΔTf​=Tf0​−Tf​ (where Tf0​ is FP of pure solvent, Tf​ is FP of solution)
   • ΔTf​=Kf​×m
   • Kf​ (Molal Depression Constant or Cryoscopic Constant): Depression in freezing point when molality is 1. Units: K kg mol−1.
   • MB​=ΔTf​×wA​Kf​×wB​×1000​ (for determining molar mass of solute)
4. Osmotic Pressure (π):
   • Osmosis: The spontaneous net flow of solvent molecules from a region of lower solute concentration (higher solvent concentration) to a region of higher solute concentration (lower solvent concentration) through a semi-permeable membrane.
   • Semi-permeable Membrane (SPM): A membrane that allows solvent molecules to pass through but prevents the passage of solute molecules.
   • Osmotic Pressure (π): The excess pressure that must be applied to the solution side to prevent the net flow of solvent into the solution through the SPM.
   • π=CRT (van’t Hoff equation for dilute solutions)
     • C = Molar concentration of solute (mol L−1)
     • R = Gas constant (0.0821 L atm K−1 mol−1 or 8.314 J K−1 mol−1)
     • T = Temperature in Kelvin (K)
   • π=VnB​​RT⇒MB​=πVwB​RT​ (for determining molar mass of solute, especially for polymers and proteins).
   • Isotonic Solutions: Solutions having the same osmotic pressure at a given temperature. They have the same molar concentration. (e.g., 0.9% NaCl solution with blood cells).
   • Hypotonic Solution: A solution with lower osmotic pressure than another solution (e.g., cells swell in hypotonic solution).
   • Hypertonic Solution: A solution with higher osmotic pressure than another solution (e.g., cells shrink in hypertonic solution).
   • Reverse Osmosis (RO): If a pressure greater than the osmotic pressure is applied to the solution side, the solvent starts flowing from the solution to the solvent side through the SPM. Used in desalination of seawater.

6. Abnormal Molar Masses (van’t Hoff Factor, i)

• Colligative properties depend on the number of particles. If the solute undergoes association (molecules combine) or dissociation (molecules break into ions) in the solution, the observed molar mass (calculated from colligative properties) will be abnormal.
• Association: Observed molar mass > Normal molar mass. The number of particles decreases.
• Dissociation: Observed molar mass < Normal molar mass. The number of particles increases.
• van’t Hoff Factor (i): A measure of the extent of dissociation or association of a solute in solution.
  • i=Observed molar massNormal molar mass​=Calculated colligative property (assuming no diss./assoc.)Observed colligative property​=Number of moles of particles before diss./assoc.Total number of moles of particles after diss./assoc.​
• Modified Colligative Property Equations (with i):
  1. RLVP: pA0​pA0​−pA​​=i×χB​
  2. Elevation in Boiling Point: ΔTb​=i×Kb​×m
  3. Depression in Freezing Point: ΔTf​=i×Kf​×m
  4. Osmotic Pressure: π=i×CRT
• For Dissociation:
  • Let ‘n’ be the number of ions/particles produced from one molecule of solute.
  • Let ‘α’ be the degree of dissociation.
  • i=1+(n−1)α
• For Association:
  • Let ‘n’ be the number of molecules that associate to form one larger particle.
  • Let ‘α’ be the degree of association.
  • i=1+(n1​−1)α (or i=1−α+nα​)
  • Example: Dimerization of carboxylic acids in benzene (n=2). i=1−α+α/2=1−α/2.