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COMEDK2025PhysicsKinetic Theory of GasesActual

What is the ratio of the mean free paths of the molecules of two gases A and B having the molecular diameters 2 ~A ^0 and 3 ~A ^0 respectively under the identical conditions of pressure, temperature and volume?

Options

  1. A_A _B =9: 4
  2. B_A _B =3: 2
  3. C_A _B =4: 9
  4. D_A _B =2: 3

Correct answer

A. _A _B =9: 4

Step-by-step solution

The mean free path of a gas molecule is given by the formula = k_B T 2 d^2 P , where k_B is the Boltzmann constant, T is the temperature, d is the molecular diameter, and P is the pressure. Under identical conditions of pressure, temperature, and volume, the variables k_B , T , and P are constant for both gases A and B . Therefore, the mean free path is inversely proportional to the square of the molecular diameter: 1 d^2 . Given the diameters d_A = 2 and d_B = 3 , the ratio of the mean free paths is: _A _B = d_B^2

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