Mean free path, Avogadros number - Question Bank

1. In a gas at equilibrium, the mean free path is a statistical average. What is the typical order of magnitude for the mean free path of air molecules at atmospheric pressure and room temperature?
A) 10^-7 meters
B) 1 meter
C) 10^-2 meters
D) 10^-10 meters
2. Which of the following is a direct consequence of Avogadro's law?
A) The molar volume of all ideal gases is the same at the same temperature and pressure.
B) The pressure of an ideal gas is directly proportional to its temperature.
C) The average kinetic energy of gas molecules is directly proportional to the absolute temperature.
D) The mean free path depends only on temperature.
3. The mean free path is inversely proportional to the product of number density and collision cross-section. If the collision cross-section is doubled and the number density is halved, what is the net change in the mean free path?
A) It remains the same.
B) It doubles.
C) It halves.
D) It quadruples.
4. What is the standard condition for temperature and pressure (STP) as defined by IUPAC for molar volume calculations?
A) 0°C (273.15 K) and 100 kPa
B) 20°C (293.15 K) and 101.325 kPa
C) 0°C (273.15 K) and 101.325 kPa
D) 25°C (298.15 K) and 100 kPa
5. If the collision cross-section of gas molecules is increased (e.g., due to intermolecular forces becoming significant), what happens to the mean free path, assuming number density is constant?
A) It increases.
B) It decreases.
C) It remains the same.
D) It becomes zero.
6. Avogadro's number relates the number of particles to:
A) The amount of substance in moles.
B) The mass of the substance in grams.
C) The volume of the substance in liters.
D) The energy of the substance in joules.
7. Which of the following conditions would result in the longest mean free path for a given gas?
A) Low pressure and high temperature.
B) High pressure and low temperature.
C) Low pressure and low temperature.
D) High pressure and high temperature.
8. In the context of the kinetic theory of gases, what is the primary assumption regarding the volume of the gas molecules themselves compared to the volume of the container?
A) The volume of the molecules is negligible compared to the container volume.
B) The volume of the molecules is equal to the container volume.
C) The volume of the molecules is significantly larger than the container volume.
D) The volume of the molecules is half the container volume.
9. The mass of one molecule of a substance can be calculated using its molar mass (M) and Avogadro's number (N_A) as:
A) M / N_A
B) N_A / M
C) M * N_A
D) 1 / (M * N_A)
10. If the number density of a gas is halved, while keeping the molecular size constant, what happens to the mean free path?
A) It halves.
B) It doubles.
C) It remains the same.
D) It quadruples.
11. Which of the following is a direct consequence of a high collision frequency among gas molecules?
A) Short mean free path.
B) Long mean free path.
C) Low pressure.
D) High temperature.
12. Avogadro's number is approximately 6.022 x 10^23. This means that in 12 grams of Carbon-12, there are this many:
A) Atoms
B) Molecules
C) Neutrons
D) Protons
13. If the number of moles of a gas in a container is constant, and the temperature is increased, how does the mean free path change?
A) It increases.
B) It decreases.
C) It remains constant.
D) It doubles.
14. What is the physical significance of the factor √2 in the mean free path formula λ = 1 / (√2 * n * σ)?
A) It accounts for the relative motion of colliding molecules.
B) It accounts for the size of the container.
C) It accounts for the temperature of the gas.
D) It is a statistical average of collision angles.
15. Consider two ideal gases, Gas A and Gas B, at the same temperature and pressure. If the molecules of Gas A are smaller than the molecules of Gas B, what can be said about their mean free paths?
A) λ_A > λ_B
B) λ_A < λ_B
C) λ_A = λ_B
D) The relationship depends on the density.
16. Avogadro's number is a bridge between the microscopic world of atoms and molecules and the macroscopic world we observe. It is used to define:
A) The mole.
B) The atom.
C) The molecule.
D) The electron.
17. Which quantity is directly proportional to the mean free path?
A) The average distance between molecules.
B) The pressure of the gas.
C) The number density of the gas.
D) The square of the molecular diameter.
18. The kinetic theory of gases assumes that molecules collide elastically. What does this imply for the total kinetic energy of the molecules during a collision?
A) It remains conserved.
B) It increases.
C) It decreases.
D) It is converted into potential energy.
19. If a gas expands adiabatically, the temperature decreases, and the number density decreases. What is the combined effect on the mean free path?
A) It increases.
B) It decreases.
C) It remains the same.
D) The effect is indeterminate without more information.
20. Which of the following statements about mean free path is INCORRECT?
A) It is the average distance between successive collisions.
B) It increases with temperature at constant pressure.
C) It decreases with pressure at constant temperature.
D) It depends on the size of the molecules.
21. Avogadro's number is approximately 6.022 x 10^23 mol^-1. This number represents:
A) The number of entities in one mole.
B) The number of moles in one gram.
C) The number of atoms in a cubic meter.
D) The energy of one mole of photons.
22. If a gas is compressed isothermally, the number density (n) increases. Consequently, the mean free path (λ) will:
A) Increase
B) Decrease
C) Remain constant
D) Fluctuate unpredictably
23. What is the molar volume of an ideal gas at Standard Temperature and Pressure (STP)?
A) 22.4 liters
B) 11.2 liters
C) 44.8 liters
D) 8.31 liters
24. The concept of mean free path is crucial for understanding transport phenomena in gases, such as diffusion and viscosity. What is the primary reason for molecular collisions?
A) The finite size of molecules and their random motion.
B) The attractive forces between molecules.
C) The repulsion forces between molecules.
D) The external electric field.
25. If the number of moles of a gas is increased while keeping temperature and volume constant, what happens to the mean free path?
A) It increases.
B) It decreases.
C) It remains unchanged.
D) It becomes infinite.
26. At very low pressures (like in a vacuum), the mean free path of molecules becomes very large. What is a practical application of this phenomenon?
A) Vacuum distillation.
B) High-pressure reactors.
C) Dense gas storage.
D) Superheated steam generation.
27. Which statement best describes Avogadro's hypothesis?
A) Equal volumes of all gases, at the same temperature and pressure, have the same number of molecules.
B) Equal masses of all gases, at the same temperature and pressure, have the same volume.
C) All molecules of a gas have the same velocity at a given temperature.
D) The pressure exerted by a gas is directly proportional to the number of moles.
28. How does the mean free path relate to the molecular diameter (d) and number density (n)?
A) λ ∝ 1 / (n * d^2)
B) λ ∝ n * d^2
C) λ ∝ 1 / (n^2 * d)
D) λ ∝ n / d^2
29. If the average distance between molecules in a gas is much larger than the mean free path, what does this imply about the gas's behavior?
A) It behaves like an ideal gas.
B) It behaves like a liquid.
C) It behaves like a solid.
D) It is undergoing a phase transition.
30. What is the SI unit for Avogadro's constant?
A) mol^-1
B) mol
C) J/mol
D) m^3/mol
31. The collision cross-section (σ) for a molecule is related to its size. For hard spheres, it is proportional to:
A) The square of the molecular diameter.
B) The molecular diameter.
C) The cube of the molecular diameter.
D) The inverse of the molecular diameter.
32. A gas is contained in a vessel. If the volume of the vessel is decreased while keeping the number of molecules and temperature constant, what happens to the mean free path?
A) It increases.
B) It decreases.
C) It remains the same.
D) It becomes zero.
33. If you have 2 moles of Helium gas, how many Helium atoms do you have?
A) 2 * N_A
B) N_A / 2
C) 2 / N_A
D) N_A
34. Avogadro's number is fundamental in relating macroscopic properties (like moles) to microscopic properties (like the number of atoms or molecules). What is its unit?
A) mol^-1
B) mol
C) g/mol
D) m^-3
35. Which of the following is a consequence of a shorter mean free path?
A) Increased rate of diffusion.
B) Decreased viscosity.
C) Increased thermal conductivity.
D) Reduced resistance to flow.
36. How does the average speed of gas molecules affect the mean free path?
A) Higher average speed leads to a longer mean free path.
B) Higher average speed leads to a shorter mean free path.
C) Average speed has no effect on the mean free path.
D) Average speed's effect depends on temperature only.
37. Consider two gases at the same temperature and pressure. Which gas is likely to have a larger mean free path, assuming similar molecular sizes?
A) The gas with a higher molar mass.
B) The gas with a lower molar mass.
C) The gas with a higher number density.
D) The gas with a lower number density.
38. If the number density (n) of gas molecules is high, what is the expected mean free path?
A) Long
B) Short
C) Infinite
D) Zero
39. The molar mass of a substance is the mass of how many moles of that substance?
A) One mole
B) Avogadro's number of moles
C) 1/N_A moles
D) Zero moles
40. What is the relationship between the total number of molecules (N) in a gas and the number of moles (n_moles)?
A) N = n_moles / N_A
B) N = n_moles * N_A
C) N = N_A / n_moles
D) N = n_moles + N_A
41. One mole of any substance contains Avogadro's number of elementary entities. What are these entities?
A) Atoms or molecules or ions or electrons, etc.
B) Only atoms.
C) Only molecules.
D) Only ions.
42. What is the approximate value of Avogadro's number?
A) 6.022 x 10^20
B) 6.022 x 10^23
C) 6.022 x 10^26
D) 6.022 x 10^19
43. Avogadro's number (N_A) is defined as:
A) The number of atoms in 12 grams of carbon-12.
B) The number of molecules in 1 liter of any gas at STP.
C) The number of electrons in a mole of any substance.
D) The number of protons in the nucleus of a helium atom.
44. How does the mean free path change with temperature at constant pressure?
A) It increases.
B) It decreases.
C) It remains constant.
D) It increases and then decreases.
45. If the pressure of a gas is doubled at constant temperature, what happens to the mean free path?
A) It doubles.
B) It halves.
C) It remains the same.
D) It quadruples.
46. The formula for the mean free path (λ) of molecules in a gas is approximately given by λ = 1 / (√2 * n * σ), where n is the number density and σ is the collision cross-section. What does σ represent?
A) The effective area of collision between two molecules.
B) The total surface area of a molecule.
C) The volume occupied by a molecule.
D) The average kinetic energy of a molecule.
47. According to the kinetic theory of gases, how does the mean free path relate to the number density (n) of molecules?
A) Mean free path is directly proportional to n.
B) Mean free path is inversely proportional to n.
C) Mean free path is proportional to n^2.
D) Mean free path is independent of n.
48. Which factor, when increased, leads to a decrease in the mean free path of gas molecules?
A) Temperature
B) Volume
C) Pressure
D) Average molecular speed
49. What is the definition of the mean free path of a molecule in a gas?
A) The average distance a molecule travels between successive collisions.
B) The total distance traveled by all molecules in a given time.
C) The distance between the container walls.
D) The average distance a molecule travels before escaping the container.
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