Question

I do not understand this " rate of diffusion of gases is inversely proportional to the square root of their molar masses provided that pressure and temperature remain constant. ?

Answer 1

Diffusion is the net movement of anything (for example, atoms, ions, molecules, and energy) from a higher to a lower concentration region. Diffusion is triggered by a concentration gradient. Many areas, including physics (particle diffusion), chemistry, biology, sociology, economics, and finance, employ the notion of diffusion (diffusion of people, ideas, and price values). The basic concept of diffusion, however, is the same in all of them: a material or collection that is experiencing diffusion expands out from a place or location where it has a larger concentration.

Complete answer:
Thomas Graham, a Scottish physical chemist, proposed Graham's law of effusion (also known as Graham's law of diffusion) in 1848. Graham discovered that a gas's rate of effusion is inversely related to the square root of its particles' molar mass. This formula is worded as follows:
$\dfrac{\text{Rat}{{\text{e}}_{1}}}{\text{Rat}{{\text{e}}_{2}}}=\sqrt{\dfrac{{{M}_{2}}}{{{M}_{1}}}}$
where $Rat{{e}_{1}}$ is the first gas's effusion rate. (the number of moles per unit of time or the volume of moles per unit of time)
The rate of effusion for the second gas is called $Rat{{e}_{2}}$ .
The molar mass of gas 1 is ${{M}_{1}}$ , while the molar mass of gas 2 is ${{M}_{2}}$ .
Graham's law says that a gas's rate of diffusion or effusion is inversely related to its molecular weight squared. If one gas has four times the molecular weight of another, it will diffuse through a porous plug or escape through a tiny puncture in a vessel at half the pace (heavier gases diffuse more slowly). Years later, the kinetic theory of gases offered a comprehensive theoretical explanation of Graham's law. Graham's law establishes a foundation for diffusing isotopes, a process that was important in the creation of the atomic bomb.

Note:
For molecular effusion, which includes the passage of one gas at a time through a hole, Graham's law is the most exact. Because these processes include the movement of more than one gas, it is only approximate for diffusion of one gas into another or in air.
The molar mass is related to the mass density at the same temperature and pressure. As a result, the square roots of the mass densities of various gases are inversely related to their diffusion rates.