KINETIC THEORY AND THE STATES OF MATTER 2

 QUESTIONS AND ANSWERS: 

Q12: How do changes of state occur according to the kinetic theory? 

A12:

• Melting: When solids are heated, particles gain kinetic energy and vibrate more strongly. Attractive forces weaken, and particles become free to move around.
• Freezing: When liquids are cooled, particles lose kinetic energy. Attractive forces strengthen, causing particles to be restricted to a fixed position, moving only by vibration.
• Evaporation: Occurs when surface particles of a liquid gain enough kinetic energy to move faster and break away from intermolecular forces to form a vapour.
• Boiling: Rapid vaporisation anywhere in the bulk liquid at a fixed temperature (the boiling point).
• Condensation: The change from gaseous to liquid form when gas particles lose enough kinetic energy to form bonds and transition into a liquid, the reverse of vaporisation.

Q13: What is a 'Gas Law'? 

A13: A Gas Law is a mathematical relationship between the pressure, volume, temperature, and quantity of a gas.

Q14: What is Boyle's Law? 

A14: Boyle's Law states that the volume of a fixed mass of gas at constant temperature is inversely proportional to the pressure of that gas.

• Mathematical expression: P1V1 = P2V2.
• Variables related: Pressure (P) and Volume (V).
• Graphical representation: Shows an inverse relationship where as volume decreases, pressure increases.

Q15: What is Charles' Law? 

A15: Charles' Law states that the volume of a fixed mass of a gas at constant pressure is directly proportional to its absolute temperature.

• Mathematical expression: V1/T1 = V2/T2 (Temperature must always be converted to Kelvin).
• Variables related: Volume (V) and absolute Temperature (T).
• Graphical representation: Shows a direct relationship where as temperature increases, volume increases

Q16: What is Gay-Lussac's Law? 

A16: Gay-Lussac's Law states that for a fixed mass of gas at constant volume, the pressure of that gas is directly proportional to its absolute temperature (K).

• Mathematical expression: P₁/T₁ = P₂/T₂.
• Variables related: Pressure (P) and absolute Temperature (T).
• Graphical representation: Shows a direct relationship where as temperature increases, pressure increases.

Q17: What is the Combined Gas Law? 

A17: The Combined Gas Law is a combination of Boyle’s Law, Charles’ Law, and Gay-Lussac’s Law.

• Mathematical expression: (P₁V₁)/T₁ = (P₂V₂)/T₂.
• Note: Units chosen for each quantity must be consistent.

Q18: What is Avogadro's Law? 

A18: Avogadro's Law states that equal volumes of gases at the same temperature and pressure contain the same number of molecules or moles of gas.

• Mathematical expression: V/n = K (where V = Volume, n = number of moles, K = constant).
• Variables related: Volume (V) and number of moles (n).
• Graphical representation: Shows a direct relationship where as the number of moles increases, volume increases.

Q19: What is Graham's Law of Diffusion/Effusion? 

A19: Graham's Law states that the rate of diffusion, or effusion, for a gas is inversely proportional to the square root of its density at constant temperature and pressure.

• Mathematical expressions:
• R ∝ 1/√D
• R ∝ 1/√M (where R = Rate, D = Density, M = Molecular mass)
• For two gases: R₁/R₂ = √(D₂/D₁) = √(M₂/M₁)
• In terms of time: t₁/t₂ = √(M₂/M₁)
• In terms of volume: V₁/V₂ = √(M₂/M₁)
• Principle: Lighter gases or gases with lower molecular mass diffuse or effuse more rapidly than heavier gases.

Q20: What is Dalton's Law of Partial Pressures? 

A20: Dalton's Law of Partial Pressures states that, in a mixture of gases which do not react, the total pressure exerted is equal to the sum of the partial pressures of the individual gases at constant temperature.

• Mathematical expressions:
• P_T = P₁ + P₂ (where PT = total pressure, P₁ and P₂ are partial pressures).
• Partial pressure (Pi) = Mole fraction (Xi) × Total Pressure (PT).
• Mole fraction (Xi) = ni / (n₁ + n₂ + ...) (where ni = number of moles of component i).

Q21: What is the Ideal Gas Equation? 

A21: The Ideal Gas Equation, also known as the ideal gas law, is a fundamental equation that describes the behaviour of gases under certain conditions. It relates the Pressure (P), Volume (V), Temperature (T), and amount of gas in moles (n) of an ideal gas sample. It combines Boyle’s law, Charles’s Law and Avogadro’s law.

• Equation: PV = nRT.
• Variables:
• P = Pressure of gas (Pascals or atm or Torr).
• V = Volume of gas (m³ or Litres).
• n = Moles of gas (moles).
• T = Temperature of gas (Kelvin).
• R = Universal Gas Constant (molar physical quantity).
• Units of R: 8.314 J mol⁻¹ K⁻¹ (S.I. unit), 0.082057 L atm mol⁻¹ K⁻¹, 62.364 L Torr mol⁻¹ K⁻¹. It is crucial to match the units of P, V, n, and T with the chosen R value.

Q22: What are the assumptions of the Ideal Gas Law? 

A22:

1. Particles have zero volume: Gas particles are considered point particles with no volume.
2. No intermolecular forces: There are no attractive or repulsive forces between gas particles, so they move independently.
3. Large number of molecules: The gas consists of a large number of molecules in constant random motion.
4. Perfectly elastic collisions: Collisions between molecules (and with walls) lose no kinetic energy.
5. Negligible collision time: The duration of collisions is ignored compared to the time between collisions.
6. Newton's laws of motion: The motion of molecules follows Newton’s second law between collisions.

Q23: Under what conditions do real gases deviate from ideal behaviour, and why? 

A23: Real gases behave differently from ideal gases at high pressure and low temperature.

• High pressure: Real gases have an actual volume of molecules, which becomes significant at very high pressure, causing PV to be greater than the ideal value. Deviation increases with higher relative molecular mass. The volume of gas particles becomes a significant fraction of the container volume, reducing the free space for movement .
• Low temperature: At lower temperatures, the kinetic energy of molecules is reduced, allowing intermolecular forces to increase and become significant. These forces reduce the pressure, making the PV value less than the ideal value.
• Other factors: Large gas molecules and strong intermolecular forces also cause deviations. Polar molecules with hydrogen bonding, like ammonia, show higher deviation compared to non-polar molecules like neon or oxygen.

Q24: What is the Van der Waals equation, and how does it address the limitations of the Ideal Gas Law? 

A24: The Van der Waals equation is an equation of state that extends the ideal gas law to include the non-zero size of gas molecules and the interactions between them. It modifies the ideal gas law to describe real gases more accurately.

• Equation for one mole: (P + a/V²) (V – b) = RT.
• Equation for n moles: (P + an²/V²) (V – nb) = nRT.
• Significance of constants:
• 'a': A measure of the strength of the intermolecular forces. It corrects for the attractive forces between molecules, adding to the observed pressure.
• 'b': The excluded molar volume. It corrects for the non-zero volume of the gas particles themselves, subtracting from the total volume to represent the "free" volume available for particle movement.
• Difference from Ideal Gas Law: It accounts for molecular volume and intermolecular forces, which the ideal gas law assumes to be negligible.