Question

What is the relationship between the mass of a gas particle and the rate at which it diffuses through another gas?
A) The larger the particle, the faster it diffuses
B) There is no relationship
C) The larger the particle, the slower it diffuses
D) The more numerous the particle, the faster it diffuses

Answer 1

To solve this question, we need to know Graham's Laws of diffusion. This law gives us the relationship between the rate of diffusion and the Molecular Masses of the gases. These two terms are found to be inversely proportional to each other.

Complete answer:
Diffusion is termed as the movement of gaseous molecules from an area of high concentration to an area of low concentration. The rate of diffusion can be related to the Kinetic energy of a particle.
The kinetic energy can be given as the product of mass and the square of the velocity of the gas. Mathematically, Kinetic energy $K.E = \dfrac{1}{2}m{v^2}$ where m is the mass of the particle and v is the velocity.
Consider two gases A and B, such that A is heavier than B, at the same temperature. The Kinetic energy of both the gases will be same at the same temperature; i.e. $K.{E_A} = K.{E_B}$
Since, the mass of A is greater than B, to make the K.E same of both the gases, the velocity of A should be less than that of B. Therefore, we can infer that as the mass of the particle increases the velocity decreases. Low velocity means low rate of diffusion.
Hence the correct answer is C.

Note:
Graham's law states that, at constant pressure and temperature, molecules with lower molecular mass will diffuse faster than the molecules with higher molecular masses. He also related this to the rate of diffusion of gases. For two gases 1 and 2, the rate of diffusion of gases is inversely proportional to the square root of the molecular masses of the gases. It can be given gas: $\dfrac{{Rat{e_1}}}{{Rat{e_2}}} = \sqrt {\dfrac{{M.{M_2}}}{{M.{M_1}}}}$