Mean free path and Avogadro’s number - Question Bank

1. The value of Avogadro's number is primarily determined by:
A) The mass of the Earth.
B) The speed of light.
C) Experimental measurements relating macroscopic properties to the number of particles.
D) The charge of an electron.
2. How many moles are there in 10 grams of water (Molar mass of H_2O = 18 g/mol)?
A) 10 / 18 moles
B) 18 / 10 moles
C) 10 * 18 moles
D) 1 / (10 * 18) moles
3. The mean free path formula λ = 1 / (√2 πnd²) is derived under the assumption that molecules are:
A) Point masses with no volume.
B) Rigid spheres of finite diameter.
C) Electrically charged particles.
D) Non-interacting particles.
4. If the temperature of a gas is increased at constant pressure, what happens to the number density (n) and thus the mean free path (λ)?
A) n increases, λ decreases.
B) n decreases, λ increases.
C) n and λ remain unchanged.
D) n decreases, λ decreases.
5. Avogadro's number is defined as the number of constituent particles (usually atoms or molecules) that are contained in one mole of a substance. What is the exact definition related to Carbon-12?
A) The number of atoms in 1 gram of Carbon-12.
B) The number of atoms in 12 grams of Carbon-12.
C) The number of molecules in 12 grams of Carbon-12.
D) The number of moles in 1 gram of Carbon-12.
6. Which of the following is a unit of number density?
A) m^3
B) m^-3
C) m
D) mol
7. The mean free path is dependent on the size of the molecules. Larger molecules generally have:
A) Shorter mean free paths.
B) Longer mean free paths.
C) Mean free paths independent of size.
D) Zero mean free paths.
8. What is the number of molecules in 1 mole of water (H_2O)?
A) Approximately 18
B) Approximately 6.022 x 10^23
C) Approximately 18 * 6.022 x 10^23
D) Approximately 1 gram
9. If the molecular diameter of gas molecules is very small, the mean free path would tend to be:
A) Very small.
B) Very large.
C) Zero.
D) Independent of diameter.
10. Avogadro's hypothesis states that equal volumes of all gases, at the same temperature and pressure, contain:
A) Equal masses.
B) Equal kinetic energies.
C) Equal numbers of molecules.
D) Equal densities.
11. The term 'collision frequency' in the context of gas molecules refers to:
A) The total number of collisions in the gas.
B) The number of collisions per unit time per molecule.
C) The time between two consecutive collisions.
D) The average distance between colliding molecules.
12. Consider a gas at constant temperature and volume. If the number of moles of gas is increased, the mean free path will:
A) Increase.
B) Decrease.
C) Remain the same.
D) Become zero.
13. What is the relationship between the number of molecules (N), Avogadro's number (N_A), and the number of moles (n)?
A) N = n * N_A
B) N = N_A / n
C) N = n / N_A
D) N = N_A + n
14. The mean free path (λ) is inversely proportional to the number density (n). If the number density is halved, the mean free path is:
A) Halved.
B) Doubled.
C) Quadrupled.
D) Unchanged.
15. Avogadro's number is approximately equal to the number of atoms in:
A) 1 gram of Hydrogen
B) 12 grams of Carbon-12
C) 1 gram of Oxygen
D) 1 gram of Helium
16. If the temperature of a gas is kept constant, but the pressure is increased, the number density (n) of molecules:
A) Decreases.
B) Increases.
C) Remains constant.
D) Becomes zero.
17. Which of the following is a correct expression for the number of moles (n) of a substance with mass (m) and molar mass (M)?
A) n = M / m
B) n = m * M
C) n = m / M
D) n = 1 / (m * M)
18. The mean free path is related to the average distance between molecules. If the average distance between molecules decreases, the mean free path generally:
A) Increases.
B) Decreases.
C) Remains constant.
D) Becomes zero.
19. What is the total number of molecules in 2 moles of any gas at STP?
A) 2 * N_A
B) N_A
C) N_A / 2
D) 4 * N_A
20. If the number density of a gas is constant, and the molecular diameter is doubled, the mean free path will:
A) Increase by a factor of 4.
B) Decrease by a factor of 4.
C) Increase by a factor of 2.
D) Decrease by a factor of 2.
21. The concept of mean free path is crucial in understanding phenomena like:
A) Gravitational attraction between molecules.
B) Electrical conductivity of metals.
C) Viscosity and diffusion of gases.
D) Blackbody radiation.
22. How many molecules are there in 1 gram of Hydrogen gas (Molar mass of H_2 = 2 g/mol), given Avogadro's number?
A) N_A / 2
B) N_A
C) 2 * N_A
D) N_A / 4
23. Which of the following is NOT a direct factor influencing the mean free path of gas molecules?
A) Temperature
B) Pressure
C) Molecular diameter
D) Molar mass
24. At very low pressures, the mean free path of gas molecules becomes:
A) Very small.
B) Very large.
C) Zero.
D) Constant.
25. In the formula for mean free path λ = 1 / (√2 πnd²), what does 'n' represent?
A) Number of moles
B) Number of molecules
C) Number density of molecules
D) Avogadro's number
26. Avogadro's number is a fundamental constant that bridges the macroscopic and microscopic worlds. It relates the number of entities to:
A) Mass
B) Volume
C) Amount of substance (moles)
D) Temperature
27. If the volume of a container holding a gas is decreased at constant temperature and number of moles, what happens to the mean free path?
A) It increases.
B) It decreases.
C) It remains the same.
D) It becomes zero.
28. Which physical quantity is numerically equal to the number of particles per mole?
A) Universal Gas Constant (R)
B) Boltzmann Constant (k_B)
C) Avogadro's Number (N_A)
D) Planck's Constant (h)
29. The mean free path (λ) is directly proportional to the average speed of the molecules (ν_avg) and inversely proportional to the collision frequency (Z). What is the relation?
A) λ = ν_avg / Z
B) λ = Z / ν_avg
C) λ = ν_avg * Z
D) λ = 1 / (ν_avg * Z)
30. If the pressure of a gas is increased at constant temperature, what happens to the mean free path?
A) It increases.
B) It decreases.
C) It remains the same.
D) It becomes infinite.
31. Which of the following statements about Avogadro's number is INCORRECT?
A) It is the number of atoms in 12 grams of Carbon-12.
B) It is the number of molecules in one mole of any substance.
C) It is approximately 6.022 x 10^23.
D) It is denoted by N_A.
32. The total number of molecules in a given sample of gas is related to the number of moles (n) and Avogadro's number (N_A) by which formula?
A) N = n / N_A
B) N = N_A / n
C) N = n * N_A
D) N = n + N_A
33. What is the value of the Boltzmann constant (k_B) if the universal gas constant (R) is 8.314 J/(mol·K) and Avogadro's number (N_A) is 6.022 x 10^23 mol^-1?
A) 1.38 x 10^-23 J/K
B) 1.38 x 10^-21 J/K
C) 1.38 x 10^-19 J/K
D) 1.38 x 10^-25 J/K
34. The mean free path of gas molecules is inversely proportional to the square of the molecular diameter (d). If the diameter is halved, how does the mean free path change?
A) It halves.
B) It doubles.
C) It becomes one-fourth.
D) It becomes four times.
35. Consider two gases at the same temperature and pressure. If Gas A has smaller molecules than Gas B, what can be said about their mean free paths?
A) Gas A has a longer mean free path.
B) Gas B has a longer mean free path.
C) Their mean free paths are equal.
D) The mean free path depends on the molar mass, not molecular size.
36. If the temperature of a gas is increased at constant volume, what happens to the mean free path?
A) It increases.
B) It decreases.
C) It remains the same.
D) It becomes zero.
37. How is the number density (n) of gas molecules related to the total number of molecules (N) and the volume (V) they occupy?
A) n = N / V
B) n = V / N
C) n = N * V
D) n = √(N / V)
38. The molar mass of a substance is defined as:
A) The mass of one molecule of the substance.
B) The mass of one mole of the substance.
C) The number of moles in one gram of the substance.
D) The number of molecules in one gram of the substance.
39. What is the relationship between Avogadro's number (N_A) and the number of molecules (N) in 'n' moles of a substance?
A) N = N_A / n
B) N = n / N_A
C) N = n * N_A
D) N = N_A + n
40. If you have one mole of Helium gas and one mole of Oxygen gas at the same temperature and pressure, how do their number of molecules compare?
A) Helium has more molecules.
B) Oxygen has more molecules.
C) They have the same number of molecules.
D) The comparison depends on the volume.
41. Which of the following is a direct consequence of Avogadro's hypothesis?
A) Equal volumes of all gases at the same temperature and pressure contain the same number of molecules.
B) The pressure of a gas is directly proportional to its volume at constant temperature.
C) The average kinetic energy of gas molecules is directly proportional to the absolute temperature.
D) The mean free path is independent of the number of molecules.
42. What is the SI unit for Avogadro's number?
A) mol^-1
B) mol
C) particles/mol
D) particles
43. Avogadro's number (N_A) represents the number of particles (atoms or molecules) in one mole of a substance. What is its approximate value?
A) 6.022 x 10^20
B) 6.022 x 10^23
C) 6.022 x 10^26
D) 6.022 x 10^19
44. How does an increase in the absolute temperature affect the mean free path of gas molecules, assuming pressure and molecular diameter are constant?
A) It increases.
B) It decreases.
C) It remains unchanged.
D) It increases initially and then decreases.
45. If the number density of gas molecules in a container is doubled, how does the mean free path change, assuming temperature and molecular diameter remain constant?
A) It doubles.
B) It halves.
C) It remains the same.
D) It increases by a factor of four.
46. The formula for the mean free path (λ) of gas molecules, considering them as hard spheres of diameter 'd' and number density 'n', is approximately:
A) λ = √2 / (πnd²)
B) λ = 1 / (πnd²)
C) λ = √3 / (πnd²)
D) λ = 1 / (√2πnd²)
47. According to the kinetic theory of gases, the mean free path (λ) is inversely proportional to which quantity?
A) Absolute temperature (T)
B) Number density (n)
C) Molecular diameter (d)
D) Average kinetic energy
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 gas molecule?
A) The average distance traveled by a molecule between two consecutive collisions.
B) The total distance traveled by a molecule in a given time.
C) The distance between the centers of two colliding molecules.
D) The average distance a molecule travels before it completely stops.
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