Chemistry Chapter 1 Notes of CBSE Class 12

This unit covers the fundamental concepts of solutions. It begins by describing how different types of solutions are formed and how their composition can be expressed using various concentration units like mass percentage, volume percentage, parts per million, mole fraction, molarity, and molality. Key laws governing the behavior of solutions, such as Henry's Law for gas solubility and Raoult's Law for vapour pressure, are explained. The distinction between ideal and non-ideal solutions, including deviations from Raoult's law and azeotropes, is discussed. The note also details colligative properties – properties that depend on the number of solute particles – such as relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, and osmotic pressure, and how these can be used to determine molar masses. Finally, the concept of abnormal molar masses and the van't Hoff factor, which account for solute association or dissociation, is introduced.

1. Introduction to Solutions

• Definition: Solutions are homogeneous mixtures of two or more than two components.
• Homogeneous Mixture: Composition and properties are uniform throughout the mixture.
• Components:
  • Solvent: Present in the largest quantity. Determines the physical state of the solution.
  • Solute(s): One or more components present other than the solvent.
• Binary Solutions: Solutions consisting of two components.
• Importance: Most processes in the body occur in liquid solutions. Properties of mixtures like brass or German silver depend on their composition. Specific concentrations of substances like fluoride ions or salts in intravenous injections are critical for biological function.

2. Types of Solutions

Solutions can exist in different physical states depending on the solvent. Table 1.1 summarises types based on the state of solute and solvent:

3. Expressing Concentration of Solutions

Concentration describes the composition of a solution. It can be expressed qualitatively (dilute or concentrated) or quantitatively. Quantitative descriptions are needed for precision.

• Mass percentage (w/w):
  • Definition: Mass of the component in the solution divided by the total mass of the solution, multiplied by 100.
  • Formula: Mass % of a component = (Mass of component / Total mass of solution) * 100
  • Example: 10% glucose in water by mass means 10g glucose in 90g water (total 100g solution).
  • Use: Commonly used in industrial chemical applications.
• Volume percentage (V/V):
  • Definition: Volume of the component divided by the total volume of the solution, multiplied by 100.
  • Formula: Volume % of a component = (Volume of component / Total volume of solution) * 100
  • Example: 10% ethanol solution in water means 10 mL ethanol dissolved such that total volume is 100 mL.
  • Use: Commonly used for solutions containing liquids. Antifreeze is an example.
• Mass by volume percentage (w/V):
  • Definition: Mass of solute dissolved in 100 mL of the solution.
  • Use: Commonly used in medicine and pharmacy.
• Parts per million (ppm):
  • Definition: Used for trace quantities. Number of parts of the component divided by the total number of parts of all components, multiplied by 10^6.
  • Formula: Parts per million = (Number of parts of the component / Total number of parts of all components) * 10^6
  • Can be mass-to-mass, volume-to-volume, or mass-to-volume.
  • Use: Expressing concentration of pollutants in water or atmosphere (often in mg/mL or ppm).
  • Example: 5.8 ppm oxygen in seawater.
• Mole fraction (x):
  • Definition: Number of moles of the component divided by the total number of moles of all components.
  • Formula: Mole fraction of a component (xi) = ni / Σni
  • For a binary mixture of A and B: xA = nA / (nA + nB)
  • Sum of all mole fractions in a given solution is unity (1).
  • Use: Useful for relating physical properties (like vapour pressure) to concentration and in gas mixtures.
• Molarity (M):
  • Definition: Number of moles of solute dissolved in one litre (or one cubic decimetre) of solution.
  • Formula: Molarity = Moles of solute / Volume of solution in litre
  • Unit: mol L–1 or M or mol dm–3.
• Molality (m):
  • Definition: Number of moles of the solute per kilogram (kg) of the solvent.
  • Formula: Molality (m) = Moles of solute / Mass of solvent in kg
  • Unit: mol kg–1 or m.
• Temperature Dependence: Mass %, ppm, mole fraction, and molality are independent of temperature. Molarity is a function of temperature because volume depends on temperature.

4. Solubility

• Definition: Solubility is the maximum amount of a substance that can be dissolved in a specified amount of solvent at a specified temperature.
• Factors Affecting Solubility: Nature of solute and solvent, temperature, and pressure.

4.1 Solubility of a Solid in a Liquid

• "Like dissolves like": Polar solutes dissolve in polar solvents, and non-polar solutes dissolve in non-polar solvents. Intermolecular interactions should be similar.
• Dissolution: Solute dissolves in solvent.
• Crystallisation: Solute particles separate out of solution.
• Dynamic Equilibrium: Rate of dissolution equals rate of crystallisation.
  • Solute + Solvent ⇌ Solution
  • Concentration of solute is constant at this stage under given conditions.
• Saturated Solution: Solution in dynamic equilibrium with undissolved solute, contains maximum amount of solute dissolved at that temperature and pressure. Concentration of solute in a saturated solution is its solubility.
• Unsaturated Solution: More solute can be dissolved at the same temperature.
• Effect of Temperature: Solubility of a solid in a liquid is significantly affected by temperature.
  • Follows Le Chatelier's Principle.
  • If dissolution is endothermic (Δsol H > 0), solubility increases with temperature rise.
  • If dissolution is exothermic (Δsol H < 0), solubility decreases with temperature rise.
• Effect of Pressure: Pressure has no significant effect on solubility of solids in liquids because solids and liquids are highly incompressible.

4.2 Solubility of a Gas in a Liquid

• Many gases dissolve in water (e.g., oxygen sustains aquatic life, HCl is highly soluble).
• Solubility of gases in liquids is greatly affected by pressure and temperature.
• Effect of Pressure: Solubility of gases increases with increase of pressure. Increased pressure increases the number of gas particles per unit volume over the solution, increasing the rate they strike and enter the solution surface.

5. Henry's Law

• Statement: 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.
• Alternative Statement (using mole fraction): The partial pressure of the gas in vapour phase (p) is proportional to the mole fraction of the gas (x) in the solution.
• Equation: p = KH x
  • p: partial pressure of the gas.
  • x: mole fraction of the gas in the solution.
  • KH: Henry's law constant.
• Henry's Law Constant (KH):
  • Different gases have different KH values at the same temperature.
  • KH is a function of the nature of the gas.
  • Higher the value of KH at a given pressure, the lower is the solubility of the gas in the liquid.
• Effect of Temperature on KH: KH values for N2 and O2 increase with temperature. This indicates that the solubility of gases increases with decrease of temperature. This is why aquatic life is more comfortable in cold water. Dissolution of gases is exothermic, so solubility decreases with increasing temperature (Le Chatelier's Principle).
• Applications of Henry's Law:
  • To increase CO2 solubility in soft drinks and soda water, bottled under high pressure.
  • Scuba Divers: Breathing air at high pressure underwater increases solubility of atmospheric gases in blood. Decreasing pressure during ascent releases dissolved gases, forming nitrogen bubbles which cause bends (painful, dangerous condition). To avoid this, scuba tanks use air diluted with helium (11.7% He, 56.2% N2, 32.1% O2) as helium is less soluble.
  • High Altitudes: Lower partial pressure of oxygen leads to low oxygen concentration in blood/tissues, causing anoxia (climbers become weak, unable to think clearly).

6. Vapour Pressure of Liquid Solutions

6.1 Vapour Pressure of Liquid-Liquid Solutions

• Consider a binary solution of two volatile liquids (components 1 and 2) in a closed vessel.
• An equilibrium is established between vapour phase and liquid phase.
• Raoult's Law (for volatile liquids): The partial vapour pressure of each component of the solution is directly proportional to its mole fraction present in solution.
  • For component 1: p1 µ x1 and p1 = p1^0 x1
  • For component 2: p2 µ x2 and p2 = p2^0 x2
  • p1^0 and p2^0 are vapour pressures of pure components 1 and 2 at the same temperature.
• Dalton's Law of Partial Pressures: The total pressure over the solution is the sum of the partial pressures.
  • ptotal = p1 + p2
  • Substituting Raoult's Law: ptotal = x1 p1^0 + x2 p2^0
  • Since x1 + x2 = 1, ptotal = (1 – x2) p1^0 + x2 p2^0 or ptotal = p1^0 + (p2^0 – p1^0) x2
• Conclusions from ptotal equation:
  • Total vapour pressure relates to mole fraction of any one component.
  • Total vapour pressure varies linearly with the mole fraction of component 2 (or component 1).
  • Total vapour pressure changes depending on the pure component vapour pressures as mole fraction changes.
• Vapour Phase Composition: If y1 and y2 are mole fractions in the vapour phase, by Dalton's Law:
  • p1 = y1 ptotal and p2 = y2 ptotal
  • In general: pi = yi ptotal
  • The vapour phase is always richer in the component which is more volatile (higher pure vapour pressure).

6.2 Raoult's Law as a Special Case of Henry's Law

• Comparing p = KH x (Henry's Law) and pi = xi pi^0 (Raoult's Law):
• Both state that partial pressure is proportional to mole fraction.
• The proportionality constant differs: KH for Henry's, pi^0 for Raoult's.
• Raoult's law becomes a special case of Henry's law when the Henry's law constant KH is equal to the vapour pressure of the pure component pi^0.

6.3 Vapour Pressure of Solutions of Solids in Liquids

• Examples: NaCl, glucose, urea in water; iodine, sulphur in carbon disulphide.
• Non-volatile solute: If the solute is non-volatile, only the solvent contributes to the vapour pressure of the solution.
• Lowering of Vapour Pressure: The vapour pressure of the solution is lower than the vapour pressure of the pure solvent at the same temperature.
  • Reason: Non-volatile solute molecules occupy part of the surface area, reducing the fraction covered by solvent molecules. Fewer solvent molecules can escape into the vapour phase.
  • The decrease in vapour pressure depends on the quantity of non-volatile solute, not its nature.
• Raoult's Law (for non-volatile solute): The partial vapour pressure of the solvent in the solution is directly proportional to its mole fraction.
  • Let solvent be 1, solute be 2. p1 = x1 p1^0
• Relative Lowering of Vapour Pressure:
  • Reduction in vapour pressure: Δp1 = p1^0 – p1 = p1^0 (1 – x1)
  • Since x1 + x2 = 1, 1 – x1 = x2. So, Δp1 = x2 p1^0.
  • Relative lowering of vapour pressure: (p1^0 – p1) / p1^0 = Δp1 / p1^0.
  • Δp1 / p1^0 = x2
  • The relative lowering of vapour pressure is equal to the mole fraction of the solute.
  • For dilute solutions (n2 << n1): (p1^0 – p1) / p1^0 = n2 / n1.
  • Relating to masses and molar masses: (p1^0 – p1) / p1^0 = (w2/M2) / (w1/M1). This equation can be used to calculate the molar mass of the solute (M2).

7. Ideal and Non-ideal Solutions

Based on Raoult's law, liquid-liquid solutions are classified.

7.1 Ideal Solutions

• Definition: Solutions that obey Raoult’s law over the entire range of concentration.
• Other Important Properties:
  • Enthalpy of mixing (ΔmixH) is zero: No heat absorbed or evolved on mixing.
  • Volume of mixing (ΔmixV) is zero: Volume of solution equals the sum of volumes of components.
• Molecular Level Explanation: Intermolecular attractive interactions between A-A and B-B are nearly equal to those between A-B.
• Examples: n-hexane and n-heptane, bromoethane and chloroethane, benzene and toluene. Perfectly ideal solutions are rare, but some are nearly ideal.

7.2 Non-ideal Solutions

• Definition: Solutions that do not obey Raoult’s law over the entire range of concentration.
• Vapour pressure is either higher or lower than predicted by Raoult's law.
• Cause of Deviations: The nature of interactions at the molecular level.

Comparison of Positive and Negative Deviations:

• Azeotropes: Binary mixtures that have the same composition in liquid and vapour phases and boil at a constant temperature. Cannot be separated by fractional distillation. Arise due to very large deviations from Raoult's law.
  • Minimum Boiling Azeotrope: Formed by solutions showing large positive deviation. Example: Ethanol-water (approx. 95% ethanol by volume).
  • Maximum Boiling Azeotrope: Formed by solutions showing large negative deviation. Example: Nitric acid-water (approx. 68% nitric acid by mass, b.p. 393.5 K).

8. Colligative Properties

• Definition: Properties of solutions that depend on the number of solute particles irrespective of their nature relative to the total number of particles in the solution.
• Connected with the decrease of vapour pressure when a non-volatile solute is added.
• Types:
  1. Relative lowering of vapour pressure of the solvent.
  2. Depression of freezing point of the solvent.
  3. Elevation of boiling point of the solvent.
  4. Osmotic pressure of the solution.

8.1 Relative Lowering of Vapour Pressure

• Already discussed under Vapour Pressure of Solutions of Solids in Liquids (Section 6.3).
• Δp1 / p1^0 = x2.
• This property can be used to determine the molar mass of the solute.

8.2 Elevation of Boiling Point

• Boiling Point: Temperature at which vapour pressure equals atmospheric pressure.
• Adding a non-volatile solute decreases vapour pressure, so a higher temperature is needed to reach atmospheric pressure.
• Boiling point of a solution is always higher than that of the pure solvent.
• Elevation of Boiling Point (ΔTb): The increase in boiling point.
  • Formula: ΔTb = Tb – Tb^0 (where Tb^0 is pure solvent, Tb is solution).
• Relationship to Molality: For dilute solutions, ΔTb is directly proportional to the molal concentration (m) of the solute.
  • ΔTb µ m
  • ΔTb = Kb m
  • Kb: Boiling Point Elevation Constant or Molal Elevation Constant (Ebullioscopic Constant).
  • Unit of Kb: K kg mol–1. Kb depends on the nature of the solvent.
• Molar Mass Determination: ΔTb can be related to the mass of solute (w2), molar mass of solute (M2), mass of solvent (w1), and Kb.
  • m = (w2/M2) / (w1/1000).
  • ΔTb = Kb * (w2 * 1000) / (M2 * w1).
  • M2 = (Kb * w2 * 1000) / (ΔTb * w1)
  • Knowing w1, w2, ΔTb, and Kb, M2 can be calculated.

8.3 Depression of Freezing Point

• Freezing Point: Temperature at which the solid phase is in dynamic equilibrium with the liquid phase; vapour pressure of substance in liquid phase equals its vapour pressure in solid phase.
• Lowering of vapour pressure by adding non-volatile solute causes a lowering of the freezing point.
  • The solution freezes when its vapour pressure equals the vapour pressure of the pure solid solvent, which occurs at a lower temperature.
• Freezing point of the solvent decreases in a solution.
• Depression of Freezing Point (ΔTf): The decrease in freezing point.
  • Formula: ΔTf = Tf^0 – Tf (where Tf^0 is pure solvent, Tf is solution).
• Relationship to Molality: For dilute solutions, ΔTf is directly proportional to molality (m).
  • ΔTf µ m
  • ΔTf = Kf m
  • Kf: Freezing Point Depression Constant or Molal Depression Constant (Cryoscopic Constant).
  • Unit of Kf: K kg mol–1. Kf depends on the nature of the solvent.
• Molar Mass Determination: ΔTf can be related to w2, M2, w1, and Kf.
  • m = (w2/M2) / (w1/1000).
  • ΔTf = Kf * (w2 * 1000) / (M2 * w1).
  • M2 = (Kf * w2 * 1000) / (ΔTf * w1)
  • Knowing w1, w2, ΔTf, and Kf, M2 can be determined.
• Relation of Kf and Kb to Solvent Properties: Kf and Kb depend on the solvent's properties.
  • Kf = (R * M1 * Tf^2) / (1000 * ΔfusH)
  • Kb = (R * M1 * Tb^2) / (1000 * ΔvapH)
  • R: gas constant, M1: molar mass of solvent, Tf/Tb: freezing/boiling point of pure solvent (K), ΔfusH/ΔvapH: enthalpy of fusion/vapourisation of solvent.

8.4 Osmosis and Osmotic Pressure

• Observed Phenomena: Raw mangoes shrivel in brine, wilted flowers revive in water, blood cells collapse in saline water. These involve membranes.
• Semipermeable Membranes (SPM): Membranes (natural like pig's bladder or synthetic like cellophane) with submicroscopic pores. Allow small solvent molecules to pass through, but hinder larger solute molecules.
• Osmosis: The process of flow of solvent molecules through a semipermeable membrane from the pure solvent side to the solution side, or from a dilute solution to a concentrated solution. Flow continues until equilibrium. Solvent always flows from lower concentration to higher concentration of solution.
• Osmotic Pressure (P or Π): The excess pressure that must be applied to a solution to prevent osmosis, i.e., to stop the flow of solvent molecules through a semipermeable membrane into the solution.
• Colligative Property: Osmotic pressure depends on the number of solute molecules, not their identity.
• Relationship to Concentration (for dilute solutions): Osmotic pressure is proportional to the molarity (C) of the solution at a given temperature (T).
  • P = C R T
  • P: osmotic pressure, C: molarity (n2/V), R: gas constant, T: temperature (K).
  • P V = n2 R T.
  • Using n2 = w2/M2: P V = (w2/M2) R T.
  • M2 = (w2 R T) / (P V)
  • Knowing w2, T, P, and V, M2 can be calculated.
• Advantages of Osmotic Pressure Method for Molar Mass:
  • Measurement is around room temperature, suitable for biomolecules and polymers that are not stable at higher temperatures.
  • Uses molarity (C) instead of molality (m).
  • Magnitude of osmotic pressure is large even for very dilute solutions, allowing accurate measurement for macromolecules with poor solubility. Widely used for proteins, polymers, macromolecules.
• Isotonic Solutions: Solutions having the same osmotic pressure at a given temperature. No osmosis occurs when separated by SPM. Example: 0.9% (mass/volume) NaCl solution (normal saline) is isotonic with blood cells.
• Hypertonic Solution: Solution with higher osmotic pressure than another. If blood cells are placed in >0.9% NaCl solution, water flows out, and cells shrink.
• Hypotonic Solution: Solution with lower osmotic pressure than another. If blood cells are placed in <0.9% NaCl solution, water flows in, and cells swell.
• Other Osmosis Examples: Water movement from soil into plant roots, preservation of meat by salting (bacteria lose water and die), preservation of fruits by adding sugar.

8.5 Reverse Osmosis and Water Purification

• Reverse Osmosis: Occurs when a pressure larger than the osmotic pressure is applied to the solution side.
• Pure solvent (e.g., water) flows out of the solution through the semipermeable membrane.
• Practical Utility: Used in desalination of sea water to meet potable water requirements.
• Membrane: Cellulose acetate is a common porous membrane permeable to water but not impurities/ions. Pressure required is quite high.

9. Abnormal Molar Masses

• Colligative properties depend on the number of particles.
• If the solute undergoes dissociation into ions (e.g., KCl in water), the number of particles increases. The experimentally determined molar mass will be lower than the true value.
• If the solute undergoes association (e.g., ethanoic acid dimerising in benzene due to hydrogen bonding), the number of particles decreases. The experimentally determined molar mass will be higher than the true value.
• Abnormal Molar Mass: Molar mass that is lower or higher than the expected (normal) value.

9.1 van't Hoff Factor (i)

• Introduced by van't Hoff to account for the extent of dissociation or association.
• Definitions:
  • i = Normal molar mass / Abnormal molar mass
  • i = Observed colligative property / Calculated colligative property
  • i = Total number of moles of particles after association/dissociation / Number of moles of particles before association/dissociation
  • Observed colligative property is experimental; calculated assumes no association/dissociation.
• Value of i:
  • For association, i is less than unity (e.g., ~0.5 for ethanoic acid in benzene).
  • For dissociation, i is greater than unity (e.g., close to 2 for aqueous KCl).
  • For electrolytes undergoing complete dissociation, i equals the number of ions per formula unit (e.g., i=2 for NaCl/KCl, i=3 for K2SO4).
• Modified Equations for Colligative Properties (including van't Hoff factor):
  • Relative lowering of vapour pressure: (p1^0 – p1) / p1^0 = i * x2 [Equation derived from (1.26), (1.27), (1.28) and (1.25) combined with i, or directly from (1.25) as shown in the source: (p1^0 – p1) / p1^0 = i * n2 / (n1 + n2) for dilute solutions as shown in (1.27) becomes (p1^0 – p1) / p1^0 = i * n2 / n1]. The text simplifies this as (p1^0 – p1) / p1^0 = i * x2 or (p1^0 – p1) / p1^0 = i * n2/n1 for dilute solutions.
  • Elevation of Boiling point: ΔTb = i Kb m
  • Depression of Freezing point: ΔTf = i Kf m
  • Osmotic pressure: P = i (n2/V) R T (or P = i C R T or P V = i n2 R T)

Frequently Asked Questions:

1. What are colligative properties?
   Colligative properties are solution properties that depend solely on the number of solute particles, regardless of their identity. Examples include relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, and osmotic pressure. They are used to determine the molar mass of solutes.
   
   
2. State Henry's law and mention one important application.
   Henry's law states that at constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the solution. An important application is the use of high pressure to increase CO2 solubility in soft drinks.
   
   
3. What is the van't Hoff factor?
   The van't Hoff factor (i) accounts for the extent of solute dissociation or association in a solution. It is defined as the ratio of observed colligative property to the calculated property, or normal molar mass to abnormal molar mass. It is >1 for dissociation and <1 for association.