JEE Main - Mean free path and Avogadro’s number Online Test (MCQ Quiz)

1. 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.

2. 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

3. 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

4. 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)

5. 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.

6. 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.

7. 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

8. What is the SI unit for Avogadro's number?

A) mol^-1 B) mol C) particles/mol D) particles

9. 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.

10. 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.

11. 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

12. 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.

13. 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)

14. 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.

15. 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.

16. 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.

17. 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

18. 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

19. 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.

20. 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.

21. 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)

22. 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)

23. 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.

24. 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

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. At very low pressures, the mean free path of gas molecules becomes:

A) Very small. B) Very large. C) Zero. D) Constant.

27. 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

28. 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

29. 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.

30. 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.

31. 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

32. 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.

33. 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)

34. 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.

35. 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

36. 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.

37. 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

38. 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.

39. 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.

40. 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.

41. 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.

42. 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

43. 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.

44. Which of the following is a unit of number density?

A) m^3 B) m^-3 C) m D) mol

45. 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.

46. 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.

47. 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.

48. 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

49. 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.

Mean free path and Avogadro’s number - Online Test

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