The Solid State Class 12 – Notes, NCERT Solutions, Formulas & CBSE PYQs (Unit 1 Chemistry)

 

Unit 1 – The Solid State

1.1 General Characteristics of Solid State

1.2 Amorphous and Crystalline Solids

1.3 Classification of Crystalline Solids

1.4 Crystal Lattices and Unit Cells

1.5 Number of Atoms in a Unit Cell

1.6 Close Packed Structures

1.7 Packing Efficiency

1.8 Calculations Involving Unit Cell Dimensions

1.9 Imperfections in Solids

1.10 Electrical Properties

1.11 Magnetic Properties 

I. Fundamentals of Solutions

• Definition of Solution
  • A solution is a homogeneous mixture of two or more components.
  • "Homogeneous mixture" means that its composition and properties are uniform throughout.
• Components of a Solution
  • Solvent: The component present in the largest quantity. The solvent determines the physical state of the solution.
  • Solute(s): One or more components present in the solution other than the solvent.
• Types of Solutions
  • Solutions can be classified into solid, liquid, and gaseous solutions.
  • The sources primarily focus on liquid solutions.
  • Binary solutions, consisting of two components, are mainly considered.
  • Examples of Solution Types:
    • Gaseous Solutions:
      • Gas in Gas: Mixture of oxygen and nitrogen gases.
      • Liquid in Gas: Chloroform mixed with nitrogen gas.
      • Solid in Gas: Camphor in nitrogen gas.
    • Liquid Solutions: (Solvent is liquid)
      • Gas in Liquid: Oxygen dissolved in water.
      • Liquid in Liquid: Ethanol dissolved in water.
      • Solid in Liquid: Glucose dissolved in water.
    • Solid Solutions: (Solvent is solid)
      • Gas in Solid: Solution of hydrogen in palladium.
      • Liquid in Solid: Amalgam of mercury with sodium.
      • Solid in Solid: Copper dissolved in gold (e.g., bronze is a mixture of copper and tin; brass is a mixture of copper and zinc).
• Importance of Solutions in Daily Life
  • Most substances in normal life are mixtures.
  • Their utility depends on their composition.
  • Examples include brass, German silver, bronze, fluoride ion concentration in water (preventing tooth decay at 1 ppm, causing mottling at 1.5 ppm, or being poisonous at high concentrations), and intravenous injections (matching blood plasma ionic concentrations).
  • Almost all body processes occur in liquid solutions.

II. Expressing Concentration of Solutions

• Purpose of Expressing Concentration
  • Qualitative descriptions (dilute or concentrated) can cause confusion.
  • Quantitative descriptions are necessary for precision.
• Quantitative Units of Concentration
  • Mass percentage (w/w):
    • Defined as: (Mass of the component in the solution / Total mass of the solution) × 100.
    • Commonly used in industrial chemical applications (e.g., commercial bleaching solution with 3.62% sodium hypochlorite).
  • Volume percentage (V/V):
    • Defined as: (Volume of the component / Total volume of solution) × 100.
    • Commonly used for solutions containing liquids (e.g., 35% (v/v) ethylene glycol antifreeze).
  • Mass by volume percentage (w/V):
    • Defined as the mass of solute dissolved in 100 mL of the solution.
    • Commonly used in medicine and pharmacy.
  • Parts per million (ppm):
    • Used when solute is present in trace quantities.
    • Defined as: (Number of parts of the component / Total number of parts of all components of the solution) × 10^6.
    • Can be expressed as mass to mass, volume to volume, or mass to volume.
    • Example: 6 × 10^-3 g of dissolved oxygen in 1030 g of sea water is 5.8 ppm.
    • Often used for concentrations of pollutants in water or atmosphere.
  • Mole fraction (x):
    • Defined as: (Number of moles of the component / Total number of moles of all the components).
    • Symbol: 'x' with a subscript denoting the component (e.g., xA for component A).
    • In a solution with 'i' components, the sum of all mole fractions is unity (x1 + x2 + ... + xi = 1).
    • Useful for relating physical properties like vapor pressure and for gas mixture calculations.
  • Molarity (M):
    • Defined as the number of moles of solute dissolved in one liter (or one cubic decimeter) of solution.
    • Equation: Molarity = Moles of solute / Volume of solution in litre.
    • Temperature dependent because volume changes with temperature.
  • Molality (m):
    • Defined as the number of moles of the solute per kilogram (kg) of the solvent.
    • Equation: Molality (m) = Moles of solute / Mass of solvent in kg.
    • Independent of temperature because mass does not change with temperature.

III. Solubility

• Definition of Solubility
  • 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.
  • Pressure.
• "Like Dissolves Like" Principle
  • Polar solutes dissolve in polar solvents, and non-polar solutes dissolve in non-polar solvents.
  • This occurs when intermolecular interactions are similar between the solute and solvent.
  • Examples: NaCl and sugar dissolve in water (polar), while naphthalene and anthracene dissolve in benzene (non-polar).
• Saturated vs. Unsaturated Solutions
  • Saturated Solution: A solution in which no more solute can be dissolved at the given temperature and pressure. It is in dynamic equilibrium with undissolved solute. The concentration of solute in a saturated solution is its solubility.
  • Unsaturated Solution: A solution in which more solute can be dissolved at the same temperature.

IV. Solubility of Gases in Liquids (Henry's Law)

• Effect of Pressure on Gas Solubility
  • Pressure has no significant effect on the solubility of solids in liquids because solids and liquids are highly incompressible.
  • Solubility of gases in liquids is greatly affected by pressure and temperature.
  • Solubility of gases increases with an increase in pressure.
  • Increasing pressure over a solution increases the number of gas particles striking the surface, leading to more dissolving until a new equilibrium is reached.
• 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.
  • Equation: p = KH x.
    • 'p' is the partial pressure of the gas in the vapor phase.
    • 'x' is the mole fraction of the gas in the solution (a measure of its solubility).
    • KH is Henry's law constant.
  • Henry's Law Constant (KH)
    • Different gases have different KH values at the same temperature, indicating that KH is a function of the nature of the gas.
    • Higher the KH value at a given pressure, the lower the solubility of the gas in the liquid.
• Applications of Henry's Law
  • Soft drinks and soda water: Bottles are sealed under high pressure to increase CO2 solubility.
  • Scuba diving: Increased underwater pressure increases dissolved atmospheric gases (like nitrogen) in blood. As divers ascend, pressure decreases, releasing nitrogen bubbles causing "bends" (painful and dangerous). Scuba tanks are filled with air diluted with helium (11.7% He, 56.2% N2, 32.1% O2) to avoid bends and nitrogen toxicity.
  • High altitudes (anoxia): Partial pressure of oxygen is lower, leading to low oxygen concentration in blood and tissues, causing weakness and unclear thinking.
• Effect of Temperature on Gas Solubility
  • Solubility of gases in liquids decreases with a rise in temperature.
  • Gas dissolution is generally an exothermic process (heat is evolved).
  • According to Le Chatelier's Principle, increasing temperature for an exothermic process shifts equilibrium to decrease solubility.

V. Vapour Pressure of Liquid Solutions (Raoult's Law)

• Vapour Pressure Defined
  • At a given temperature, the pressure exerted by the vapors of a liquid over the liquid phase under equilibrium conditions.
• Effect of Non-Volatile Solute on Vapour Pressure
  • Adding a non-volatile solute to a solvent lowers the vapour pressure of the solution compared to the pure solvent.
  • This is because solute molecules occupy part of the surface, reducing the fraction of solvent molecules that can escape into the vapor phase.
• Raoult's Law (for volatile liquids)
  • Statement: 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.
  • Equation: p1 = x1 p1^0.
    • 'p1' is the partial vapor pressure of component 1 in the solution.
    • 'x1' is the mole fraction of component 1 in the solution.
    • 'p1^0' is the vapor pressure of pure component 1.
  • Total Vapour Pressure (Dalton's Law of Partial Pressures):
    • ptotal = p1 + p2
    • For a binary solution of volatile liquids: ptotal = x1 p1^0 + x2 p2^0.
    • The total vapor pressure varies linearly with the mole fraction of any one component.
• Raoult's Law as a Special Case of Henry's Law
  • When a non-volatile solute is dissolved in a solvent, the solute does not contribute to the vapor pressure.
  • In this specific case, Raoult's law (p1 = x1 p1^0) resembles Henry's law (p = KH x), where the Henry's law constant (KH) becomes equal to the vapor pressure of the pure solvent (p1^0).

VI. Ideal and Non-Ideal Solutions

• Ideal Solutions
  • Definition: Solutions that obey Raoult's law over the entire range of concentration.
  • Properties:
    • ΔmixH = 0: No heat is absorbed or evolved upon mixing (enthalpy of mixing is zero).
    • ΔmixV = 0: The volume of the solution is equal to the sum of the volumes of the components (volume of mixing is zero).
  • Molecular Level Explanation: Intermolecular attractive forces between A-A and B-B components are nearly equal to those between A-B components in the solution.
  • Examples: n-hexane and n-heptane, bromoethane and chloroethane, benzene and toluene.
• Non-Ideal Solutions
  • Definition: Solutions that do not obey Raoult's law over the entire range of concentration.
  • Deviations:
    • Positive Deviation: Vapour pressure is higher than predicted by Raoult's law.
      • Cause: A-B interactions are weaker than A-A or B-B interactions, making it easier for molecules to escape.
      • ΔmixH > 0 (endothermic process).
      • Examples: Ethanol and acetone (acetone breaks hydrogen bonds in ethanol), carbon disulfide and acetone (weaker dipolar interactions).
      • Can form minimum boiling azeotropes at a specific composition.
    • Negative Deviation: Vapour pressure is lower than predicted by Raoult's law.
      • Cause: A-B interactions are stronger than A-A or B-B interactions, decreasing the escaping tendency of molecules.
      • ΔmixH < 0 (exothermic process).
      • Can form maximum boiling azeotropes at a specific composition. Example: Nitric acid and water (68% nitric acid, 32% water by mass, boiling point 393.5 K).
• Azeotropes
  • Binary mixtures having the same composition in liquid and vapor phases and boiling at a constant temperature.
  • Components cannot be separated by fractional distillation.
  • Types: Minimum boiling azeotropes (from large positive deviation) and maximum boiling azeotropes (from large negative deviation).

VII. Colligative Properties

• Definition
  • Properties of solutions that depend on the number of solute particles (concentration) irrespective of their nature/chemical identity, relative to the total number of particles in the solution.
• Four Main Colligative Properties
  1. Relative Lowering of Vapour Pressure
     • The reduction in vapor pressure of the solvent (Δp1) is proportional to the mole fraction of the solute (x2) and the vapor pressure of the pure solvent (p1^0).
     • Equation: (p1^0 - p1) / p1^0 = x2. This is also known as the relative lowering of vapor pressure.
     • Used to determine the molar mass of the solute (M2).
  2. Elevation of Boiling Point
     • Definition: The boiling point of a solution is always higher than that of the pure solvent when a non-volatile solute is present.
     • ΔTb = Tb - Tb^0 where Tb^0 is the boiling point of pure solvent and Tb is that of the solution.
     • Proportionality: For dilute solutions, ΔTb is directly proportional to the molal concentration (m) of the solute.
     • Equation: ΔTb = Kb m.
       • Kb is the Boiling Point Elevation Constant (Ebullioscopic Constant), specific to the solvent.
     • Used to determine molar masses of solutes (M2).
  3. Depression of Freezing Point
     • Definition: The freezing point of a solution is lower than that of the pure solvent when a non-volatile solute is present.
     • ΔTf = Tf^0 - Tf where Tf^0 is the freezing point of pure solvent and Tf is that of the solution.
     • Proportionality: For dilute solutions, ΔTf is directly proportional to the molality (m) of the solution.
     • Equation: ΔTf = Kf m.
       • Kf is the Freezing Point Depression Constant (Cryoscopic Constant), specific to the solvent.
     • Used to determine molar masses of solutes (M2).
     • Constants (Kf, Kb) can be calculated from thermodynamic properties of the solvent.
  4. Osmotic Pressure
     • Membranes: Many natural (pig's bladder, parchment) or synthetic (cellophane) membranes contain submicroscopic pores. These are called semipermeable membranes (SPM), allowing small solvent molecules (like water) to pass but hindering larger solute molecules.
     • Osmosis: The flow of solvent molecules through a semipermeable membrane from pure solvent to a solution, or from a dilute solution to a more concentrated solution. This flow continues until equilibrium is attained.
     • Osmotic Pressure (P or Π): The excess pressure that must be applied to the solution side to prevent osmosis (to stop the net flow of solvent molecules into the solution).
     • Osmotic pressure is a colligative property.
     • Proportionality: For dilute solutions, osmotic pressure (P) is proportional to the molarity (C) of the solution at a given temperature (T).
     • Equation: P = C R T or ΠV = n2RT or M2 = (w2RT) / (ΠV).
       • R is the gas constant, V is solution volume in liters, n2 is moles of solute, w2 is mass of solute, M2 is molar mass of solute.
     • Applications: Widely used to determine molar masses of proteins, polymers, and other macromolecules due to large osmotic pressures even at low concentrations, which are stable at room temperature.
     • Isotonic Solutions: Solutions having the same osmotic pressure at a given temperature, causing no osmosis between them when separated by an SPM. Example: 0.9% (mass/volume) NaCl solution (normal saline) is isotonic with blood cells.
     • Hypertonic Solutions: Solutions with higher solute concentration (higher osmotic pressure) than cells, causing water to flow out of cells and shrink them (e.g., >0.9% NaCl solution).
     • Hypotonic Solutions: Solutions with lower solute concentration (lower osmotic pressure) than cells, causing water to flow into cells and swell them (e.g., <0.9% NaCl solution).
     • Reverse Osmosis: Occurs when a pressure greater than the osmotic pressure is applied to the solution side, forcing pure solvent out of the solution through the semipermeable membrane.
       • Application: Used in desalination of sea water. Cellulose acetate membranes are common for this purpose, permeable to water but impermeable to impurities and ions.

VIII. Abnormal Molar Masses and van't Hoff Factor

• Abnormal Molar Mass
  • Occurs when solutes in solution undergo dissociation (breaking into more particles) or association (combining to form fewer particles).
  • If dissociation occurs, the observed colligative property is higher than expected, leading to a calculated molar mass that is lower than the actual molar mass.
  • If association occurs, the observed colligative property is lower than expected, leading to a calculated molar mass that is higher than the actual molar mass.
• van't Hoff Factor (i)
  • Introduced by van't Hoff to account for the extent of dissociation or association.
  • Definition 1: i = Normal molar mass / Abnormal molar mass.
  • Definition 2: i = Observed colligative property / Calculated colligative property.
  • Definition 3: i = Total number of moles of particles after association/dissociation / Number of moles of particles before association/dissociation.
  • Interpretation:
    • For association, i is less than unity (i < 1).
    • For dissociation, i is greater than unity (i > 1).
    • For non-dissociating/non-associating solutes (like glucose or urea), i = 1.
  • Example: For aqueous KCl, i values approach 2 as the solution becomes dilute (due to dissociation into K+ and Cl- ions).

Analogy for Solutions and Colligative Properties

Imagine a busy city street representing a pure solvent, with cars representing solvent molecules freely moving and interacting. The movement of cars in and out of the street represents the vapor pressure.

Now, if you add some large, non-volatile street vendors (solute particles) to this street, they occupy space and block some of the pathways for cars. Even if the cars still move, fewer of them can easily escape the street and get to other streets. This reduced "traffic" of escaping cars is analogous to the lowering of vapor pressure.

Because fewer cars can escape, you'd need to heat the street more to make them move faster and escape in the same numbers as before. This extra heating required to reach the "boiling point" is like the elevation of boiling point. Conversely, to make the cars "freeze" or solidify into a pattern, they'd have to slow down even more significantly due to the vendors obstructing their movement. This further cooling required is like the depression of freezing point.

Finally, imagine the street is separated from a car wash (pure solvent) by a special gate (semipermeable membrane) that only allows cars, not vendors, to pass. Cars will naturally flow from the car wash into the street to try and balance the "car density". To stop this flow, you'd have to apply external "pressure" on the street side. This "pressure" to prevent the natural flow of cars is the osmotic pressure. It highlights how the presence of the vendors (solute) influences the solvent's behavior.

Tags:

#TheSolidState, #Class12Chemistry, #CBSE2025, #NCERTSolutions, #ChemistryNotes, #SolidStateClass12, #PackingEfficiency, #ImperfectionsInSolids, #CrystalLattices, #CBSEBoardExam, #ScienceWithBYJUS, #NCERTClass12