Class 11 Notes

Class 11 Chemistry Notes Chapter 5 (Chapter 5) – Examplar Problems (English) Book

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Philoid

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Examplar Problems (English)
Detailed Notes with MCQs of Chapter 5: States of Matter from your NCERT Exemplar. This chapter is fundamental for understanding the behaviour of substances around us and frequently appears in various government examinations. Pay close attention to the concepts, laws, and formulas.

Chapter 5: States of Matter - Detailed Notes

1. Introduction

  • Matter exists primarily in three states: Solid, Liquid, and Gas. A fourth state (Plasma) exists at very high temperatures, and a fifth (Bose-Einstein Condensate) at very low temperatures.
  • The state of a substance is determined by the balance between two opposing factors:
    • Intermolecular Forces (IMFs): Tend to keep molecules together.
    • Thermal Energy: Tends to keep molecules apart (related to kinetic energy and temperature).
  • Order of IMFs: Solids > Liquids > Gases
  • Order of Thermal Energy: Gases > Liquids > Solids

2. Intermolecular Forces (van der Waals Forces)

These are attractive forces between molecules (distinct from intramolecular forces like covalent bonds within a molecule).

  • (a) Dispersion Forces or London Forces:
    • Exist between all atoms and molecules, even non-polar ones (e.g., He, Cl₂, CH₄).
    • Arise due to temporary fluctuations in electron distribution, creating instantaneous dipoles that induce dipoles in neighbouring molecules.
    • Strength increases with:
      • Molecular size/mass (more electrons).
      • Surface area (more contact points, e.g., n-pentane has stronger forces than neopentane).
  • (b) Dipole-Dipole Forces:
    • Exist between polar molecules possessing permanent dipoles (e.g., HCl, SO₂).
    • Result from the attraction between the positive end of one molecule and the negative end of another.
    • Stronger than London forces for molecules of comparable size.
  • (c) Dipole-Induced Dipole Forces:
    • Exist between a polar molecule and a non-polar molecule.
    • The permanent dipole of the polar molecule induces a temporary dipole in the non-polar molecule.
    • Weaker than dipole-dipole forces.
  • (d) Hydrogen Bonding:
    • A special, stronger type of dipole-dipole interaction.
    • Occurs when hydrogen is bonded to a highly electronegative atom (F, O, or N) in one molecule and is attracted to another electronegative atom (F, O, or N) in a different molecule (or sometimes within the same large molecule).
    • Examples: H₂O, HF, NH₃, alcohols, carboxylic acids.
    • Significantly affects properties like boiling point and solubility.

3. The Gaseous State

Characterized by low density, high compressibility, indefinite shape and volume, and exertion of pressure.

  • Measurable Properties: Pressure (P), Volume (V), Temperature (T), Amount (n, moles).

    • Pressure: Force per unit area. Units: Pascal (Pa, SI unit), atm, bar, torr, mm Hg. (1 atm = 101325 Pa = 1.01325 bar = 760 torr = 760 mm Hg). Measured using a barometer (atmospheric) or manometer (gas).
    • Volume: Space occupied. Units: m³ (SI), L, mL, cm³. (1 m³ = 1000 L, 1 L = 1000 mL = 1000 cm³).
    • Temperature: Degree of hotness or coldness. Units: Kelvin (K, SI unit), degree Celsius (°C). (K = °C + 273.15). Always use Kelvin (Absolute Temperature) in gas law calculations.
    • Amount: Number of moles (n). n = mass (m) / Molar mass (M).

  • Gas Laws: Describe the relationships between P, V, T, and n for gases.

    • (a) Boyle's Law (Pressure-Volume Relationship): At constant temperature (T) and amount (n), the pressure of a fixed amount of gas varies inversely with its volume.
      • Mathematically: P ∝ 1/V or PV = k (constant)
      • For two states: P₁V₁ = P₂V₂
      • Graphical Representation: P vs V is a hyperbola (isotherm); P vs 1/V is a straight line through the origin.
    • (b) Charles's Law (Temperature-Volume Relationship): At constant pressure (P) and amount (n), the volume of a fixed amount of gas is directly proportional to its absolute temperature (Kelvin).
      • Mathematically: V ∝ T or V/T = k' (constant)
      • For two states: V₁/T₁ = V₂/T₂
      • Graphical Representation: V vs T (in K) is a straight line passing through the origin (isobar). Extrapolating this line to zero volume gives Absolute Zero (-273.15 °C or 0 K).
    • (c) Gay Lussac's Law (Pressure-Temperature Relationship): At constant volume (V) and amount (n), the pressure of a fixed amount of gas is directly proportional to its absolute temperature (Kelvin).
      • Mathematically: P ∝ T or P/T = k'' (constant)
      • For two states: P₁/T₁ = P₂/T₂
      • Graphical Representation: P vs T (in K) is a straight line passing through the origin (isochore).
    • (d) Avogadro's Law (Volume-Amount Relationship): At constant temperature (T) and pressure (P), equal volumes of all gases contain an equal number of molecules (or moles).
      • Mathematically: V ∝ n or V/n = k''' (constant)
      • Standard Temperature and Pressure (STP): 0 °C (273.15 K) and 1 bar pressure. Molar volume of an ideal gas at STP = 22.71 L/mol.
      • Older convention (sometimes still used, check context): 0 °C (273.15 K) and 1 atm pressure. Molar volume = 22.41 L/mol.

  • Ideal Gas Equation: Combines Boyle's, Charles's, and Avogadro's Laws. Describes the behaviour of an ideal gas (hypothetical gas with no intermolecular forces and negligible molecular volume).

    • PV = nRT
    • Where:
      • P = Pressure
      • V = Volume
      • n = Number of moles
      • T = Absolute Temperature (Kelvin)
      • R = Universal Gas Constant. Its value depends on the units used for P and V:
        • R = 8.314 J K⁻¹ mol⁻¹ (SI units, P in Pa, V in m³)
        • R = 0.0821 L atm K⁻¹ mol⁻¹ (P in atm, V in L)
        • R ≈ 2 cal K⁻¹ mol⁻¹
    • Combined Gas Law (for a fixed amount of gas, n=constant): (P₁V₁)/T₁ = (P₂V₂)/T₂
    • Relation to Density (d): PV = (m/M)RT => P M = (m/V)RT => P M = d R T

  • Dalton's Law of Partial Pressures: The total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures that each gas would exert if it were present alone in the same volume and at the same temperature.

    • P_total = p₁ + p₂ + p₃ + ... (at constant V, T)
    • Partial Pressure (pᵢ): The pressure exerted by an individual gas component in the mixture.
    • Relationship with Mole Fraction (xᵢ): pᵢ = xᵢ * P_total
      • Where xᵢ = (moles of gas i) / (total moles of all gases)
    • Application: Calculating the pressure of a dry gas collected over water.
      • P_dry gas = P_total (observed) - Aqueous Tension
      • Aqueous Tension: The partial pressure exerted by water vapour, which depends only on temperature.

  • Graham's Law of Diffusion/Effusion:

    • Diffusion: The process of intermixing of gases.
    • Effusion: The escape of gas molecules through a tiny hole into a vacuum.
    • Law: At constant temperature and pressure, the rate of diffusion or effusion of a gas is inversely proportional to the square root of its density (d) or molar mass (M).
      • Rate ∝ 1/√d
      • Rate ∝ 1/√M
      • Comparing two gases: r₁/r₂ = √(d₂/d₁) = √(M₂/M₁)
      • Also related to time (t) taken for diffusion/effusion of same volume: r ∝ 1/t => t₁/t₂ = √(M₁/M₂)
      • Also related to distance travelled (l) in same time: r ∝ l => l₁/l₂ = √(M₂/M₁)

4. Kinetic Molecular Theory of Gases

Provides a microscopic explanation for the macroscopic behaviour of gases (gas laws).

  • Postulates:

    1. Gases consist of a large number of tiny particles (atoms/molecules) that are far apart relative to their size. The actual volume of the molecules is negligible compared to the total volume of the gas.
    2. There are no significant attractive or repulsive forces between gas molecules (ideal gas assumption).
    3. Gas particles are in continuous, random motion, colliding with each other and with the walls of the container.
    4. Collisions between gas particles and between particles and the container walls are perfectly elastic (no net loss of kinetic energy).
    5. The average kinetic energy of the gas molecules is directly proportional to the absolute temperature (Kelvin) of the gas. KE_avg ∝ T.

  • Kinetic Gas Equation: PV = (1/3) m N u²_rms

    • m = mass of one molecule
    • N = total number of molecules
    • u²_rms = mean square speed
    • Can also be written as PV = (1/3) M u²_rms (where M = mN = molar mass, if V is molar volume)

  • Kinetic Energy and Temperature:

    • Average KE per molecule = (3/2) k T (k = Boltzmann constant = R/N_A)
    • Average KE per mole = (3/2) R T
    • This shows KE depends only on temperature for an ideal gas.

  • Molecular Speeds: Due to collisions, molecules have different speeds.

    • Root Mean Square Speed (u_rms): √(3RT/M)
    • Average Speed (u_av): √(8RT/πM)
    • Most Probable Speed (u_mp): √(2RT/M)
    • Relationship: u_rms : u_av : u_mp ≈ 1.224 : 1.128 : 1.000 (or u_rms > u_av > u_mp)
    • Maxwell-Boltzmann Distribution: Shows the distribution of molecular speeds at a given temperature. The curve flattens and shifts to higher speeds as temperature increases.

5. Behaviour of Real Gases: Deviations from Ideal Behaviour

Real gases deviate from ideal behaviour because:

  1. Intermolecular forces are not zero.
  2. Molecular volume is not negligible, especially at high pressure.
  • Deviations are significant at:
    • High Pressure: Molecules are closer, volume is not negligible, repulsive forces dominate.
    • Low Temperature: Molecules move slower, intermolecular attractive forces become significant.
  • Compressibility Factor (Z): Measures the deviation from ideality.
    • Z = (PV)_real / (nRT) or Z = V_real / V_ideal (where V_ideal = nRT/P)
    • For an ideal gas, Z = 1 under all conditions.
    • For real gases:
      • Z < 1: Attractive forces dominate (gas is more compressible than ideal). Occurs at low/moderate pressures.
      • Z > 1: Repulsive forces dominate (molecular volume effect; gas is less compressible than ideal). Occurs at high pressures.
      • At very low pressures, Z approaches 1 (real gases behave ideally).
  • Van der Waals Equation: An equation of state for real gases that incorporates corrections for intermolecular forces and molecular volume.
    • [P + a(n/V)²] [V - nb] = nRT
    • For 1 mole: [P + a/Vₘ²] [Vₘ - b] = RT (Vₘ = molar volume)
    • 'a' (Correction for Intermolecular Forces): Represents the magnitude of attractive forces. Higher 'a' means stronger forces and easier liquefaction. Units: atm L² mol⁻² or Pa m⁶ mol⁻².
    • 'b' (Volume Correction or Excluded Volume): Represents the effective volume occupied by gas molecules. Related to molecular size. Units: L mol⁻¹ or m³ mol⁻¹. Approximately 4 times the actual molecular volume.

6. Liquefaction of Gases

  • Gases can be liquefied by increasing pressure and decreasing temperature.
  • Critical Temperature (T<0xE1><0xB5><0xA_): The maximum temperature above which a gas cannot be liquefied, no matter how much pressure is applied. T<0xE1><0xB5><0xA_ = 8a / 27Rb. Gases with higher T<0xE1><0xB5><0xA_ (stronger IMFs, higher 'a') are easier to liquefy.
  • Critical Pressure (P<0xE1><0xB5><0xA_): The minimum pressure required to liquefy a gas at its critical temperature. P<0xE1><0xB5><0xA_ = a / 27b².
  • Critical Volume (V<0xE1><0xB5><0xA_): The volume occupied by one mole of the gas at its critical temperature and critical pressure. V<0xE1><0xB5><0xA_ = 3b.

7. The Liquid State

Intermediate between gases and solids. Molecules are close together but can still move past one another. Definite volume, indefinite shape.

  • Vapour Pressure: The pressure exerted by the vapour of a liquid in equilibrium with its liquid phase in a closed container at a given temperature.
    • Increases with temperature.
    • Depends on the nature of the liquid (weaker IMFs = higher vapour pressure).
    • Boiling Point: The temperature at which the vapour pressure of a liquid equals the external pressure.
      • Normal Boiling Point: Boiling point at 1 atm external pressure.
      • Standard Boiling Point: Boiling point at 1 bar external pressure.
  • Surface Tension: The energy required to increase the surface area of a liquid by one unit. Arises from unbalanced intermolecular forces at the liquid surface, pulling molecules inward and minimizing surface area.
    • Units: N m⁻¹ or J m⁻².
    • Decreases with increasing temperature (increased KE overcomes IMFs).
    • Leads to spherical shape of drops, capillary rise/fall.
  • Viscosity: The measure of a liquid's resistance to flow. Arises from intermolecular forces hindering the movement of layers past one another.
    • Units: N s m⁻² or Pa s (SI), poise (1 poise = 0.1 Pa s).
    • Decreases rapidly with increasing temperature.
    • Increases with stronger intermolecular forces and larger/irregular molecular shapes.

Multiple Choice Questions (MCQs)

  1. Which of the following exhibits the weakest intermolecular forces?
    (a) NH₃
    (b) HCl
    (c) He
    (d) H₂O

  2. According to Boyle's law, if the pressure of a gas is doubled at constant temperature, its volume becomes:
    (a) Double
    (b) Half
    (c) Four times
    (d) Remains unchanged

  3. The value of the universal gas constant (R) depends upon the:
    (a) Temperature of the gas
    (b) Volume of the gas
    (c) Number of moles of the gas
    (d) Units of pressure and volume

  4. A mixture of gases contains H₂ and O₂ gases in the ratio of 1:4 (w/w). What is the molar ratio of the two gases in the mixture?
    (a) 1:4
    (b) 4:1
    (c) 16:1
    (d) 2:1

  5. The rate of diffusion of methane (CH₄) is twice that of gas X. The molar mass of X is:
    (a) 64.0 g/mol
    (b) 32.0 g/mol
    (c) 4.0 g/mol
    (d) 8.0 g/mol

  6. According to the kinetic theory of gases, the average kinetic energy of gas molecules is directly proportional to:
    (a) Pressure
    (b) Volume
    (c) Absolute temperature
    (d) Molar mass

  7. For a real gas, the compressibility factor Z has a value less than 1 at low pressures. This is because:
    (a) The volume occupied by molecules is significant.
    (b) Repulsive forces dominate.
    (c) Attractive forces dominate over repulsive forces.
    (d) The gas behaves ideally.

  8. The van der Waals constant 'a' is a measure of:
    (a) Mean free path
    (b) Intermolecular attraction
    (c) Volume occupied by molecules
    (d) Mean molecular speed

  9. Which condition is necessary for the liquefaction of a gas?
    (a) High temperature and low pressure
    (b) Low temperature and high pressure
    (c) High temperature and high pressure
    (d) Low temperature and low pressure

  10. The property of a liquid that causes drops to assume a spherical shape is:
    (a) Viscosity
    (b) Vapour pressure
    (c) Surface tension
    (d) Density

Answers to MCQs:

  1. (c) He (Helium is a non-polar monoatomic gas with only weak London dispersion forces)
  2. (b) Half (P₁V₁ = P₂V₂ => P₁V₁ = (2P₁)V₂ => V₂ = V₁/2)
  3. (d) Units of pressure and volume (e.g., 0.0821 L atm K⁻¹ mol⁻¹ vs 8.314 J K⁻¹ mol⁻¹)
  4. (b) 4:1 (Let mass of H₂ be w, mass of O₂ be 4w. Moles H₂ = w/2. Moles O₂ = 4w/32 = w/8. Ratio = (w/2) : (w/8) = 1/2 : 1/8 = 4:1)
  5. (a) 64.0 g/mol (r_CH₄ / r_X = √(M_X / M_CH₄) => 2 = √(M_X / 16) => 4 = M_X / 16 => M_X = 64 g/mol)
  6. (c) Absolute temperature (KE_avg = 3/2 kT)
  7. (c) Attractive forces dominate over repulsive forces (Attractive forces make the gas more compressible than ideal)
  8. (b) Intermolecular attraction
  9. (b) Low temperature and high pressure (Low T reduces KE, High P brings molecules closer, favouring IMFs)
  10. (c) Surface tension (Minimizes surface area for a given volume)

Study these notes thoroughly. Focus on understanding the underlying principles behind the laws and equations. Practice numerical problems based on the gas laws, ideal gas equation, Dalton's law, and Graham's law. Good luck with your preparation!

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