Kinetic Molecular Theory of Gases - UNSOLVED PRACTICE SET
Chapter: States of Matter | Topic: Kinetic Molecular Theory of Gases
KINETIC MOLECULAR THEORY OF GASES - UNSOLVED PRACTICE SET
Topic: Kinetic Molecular Theory of Gases
Multiple Choice Questions
Q1. According to the Kinetic Molecular Theory, gas particles:
- Are stationary
- Move in straight lines with constant velocity
- Move randomly with a range of velocities
- Move in circular paths
Q2. The pressure exerted by a gas is due to:
- The mass of gas particles
- The collisions of gas particles with the walls of the container
- The attractive forces between gas particles
- The volume occupied by gas particles
Q3. The average kinetic energy of gas molecules is directly proportional to:
- Pressure
- Volume
- Absolute temperature
- Number of moles
Q4. The root mean square velocity (urms) of gas molecules is given by:
- √(3RT/M)
- √(3P/VM)
- 3RT/M
- 3P/VM
Q5. At the same temperature, which gas will have the highest root mean square velocity?
- H₂
- N₂
- O₂
- CO₂
Q6. The ratio of the root mean square velocities of two gases at the same temperature is equal to:
- The ratio of their molar masses
- The square root of the ratio of their molar masses
- The inverse square root of the ratio of their molar masses
- The inverse of the ratio of their molar masses
Short Answer Questions
Q7. State the five main postulates of the Kinetic Molecular Theory of gases.
Q8. Explain why the pressure of a gas increases when the temperature is increased at constant volume, using the Kinetic Molecular Theory.
Q9. Define root mean square velocity (urms). How does it differ from average velocity and most probable velocity?
Q10. At the same temperature, do all gas molecules have the same kinetic energy? Do they have the same velocity? Explain.
Q11. Explain why real gases deviate from ideal behaviour at high pressures and low temperatures, based on the assumptions of Kinetic Molecular Theory
Q12. Calculate the root mean square velocity of O₂ molecules at 300 K. (M of O₂ = 32 g/mol, R = 8.314 J/mol·K)
Long Answer Questions
Q13. (a) State the postulates of the Kinetic Molecular Theory of gases.
(b) Using the Kinetic Molecular Theory, derive the expression for the pressure of an ideal gas: P = (1/3)(mnurms²/V), where m is the mass of one molecule and n is the number of molecules.
(c) Show that the average kinetic energy of a gas molecule is (3/2)kBT, where kB is the Boltzmann constant.
Q14. (a) Define the following terms:
(i) Root mean square velocity (urms)
(ii) Average velocity (uav)
(iii) Most probable velocity (ump)
(b) Derive the relationship between these three velocities: ump : uav : urms = 1 : 1.128 : 1.224
(c) Calculate the three velocities for N₂ gas at 300 K. (M of N₂ = 28 g/mol)
Q15. (a) Explain Maxwell-Boltzmann distribution of molecular speeds. Draw a labelled diagram showing the distribution at two different temperatures.
(b) What happens to the distribution curve when:
(i) Temperature is increased?
(ii) Molar mass of the gas is increased?
(c) Explain why lighter gases effuse faster than heavier gases at the same temperature, using the concept of molecular speeds.
Numerical / Application-Based Problems
Q16. Calculate the following for O₂ gas at 300 K and 1.0 atm:
(M of O₂ = 32 g/mol, R = 8.314 J/mol·K, NA = 6.022 × 10²³)
(a) The root mean square velocity (urms)
(b) The average kinetic energy per molecule
(c) The total kinetic energy of 1 mole of O₂ gas
(d) The number of collisions per second made by one O₂ molecule with the walls of a 1.0 L container (approximate)
Q17. Consider the following gases at 300 K:
| Gas | Molar Mass (g/mol) |
|---|---|
| Data | 2 |
| Data | 4 |
| Data | 28 |
| Data | 32 |
| Data | 44 |
(a) Calculate the urms for each gas.
(b) Arrange the gases in order of increasing urms.
(c) Calculate the ratio of urms of H₂ to CO₂.
(d) At what temperature will the urms of O₂ be equal to the urms of H₂ at 300 K?
Q18. In India, the Kinetic Molecular Theory helps explain many everyday phenomena:
(a) A pressure cooker whistle releases steam when the pressure exceeds a limit. Explain using Kinetic Molecular Theory why increasing temperature increases the pressure inside the cooker.
(b) During summer, the smell of cooking spreads faster from the kitchen. Explain this using the concept of molecular velocities and the effect of temperature on urms.
(c) A balloon filled with helium rises in air, while one filled with CO₂ sinks. Explain this using the concept of average molecular speeds and densities. Calculate the ratio of urms of He to CO₂ at 300 K.
(d) In a school laboratory, a student compares the rates of effusion of H₂ and O₂ through a small hole. Calculate the ratio of their rates of effusion at the same temperature and pressure (Graham's Law). If 100 mL of H₂ effuses in 10 minutes, how much O₂ will effuse in the same time?