Question

Four rubber tubes are respectively filled with ${{H}_{2}}$,${{O}_{2}}$, ${{N}_{2}}$ and He. The tube which will be reinflated first is :
(A) ${{H}_{2}}$ filled tube
(B) ${{O}_{2}}$ filled tube
(C) ${{N}_{2}}$ filled tube
(D) He filled tube

Answer 1

The gaseous particles are in constant random motion and they tend to undergo diffusion since they have kinetic energy. At higher temperatures, the diffusion is quicker since the gas molecules have greater kinetic energy and the process of effusion refers to the movement of gas particles through a small hole.

Complete step by step solution:
- Let's start with the concept of diffusion and effusion. Diffusion is the phenomenon in which there is a movement of one material from a high concentration region to a low concentration area through the process of spreading of particles across the medium.
- The effusion is a process in which the air leaks or escapes through a hole whose diameter is less than the mean free path of the molecules. The relationship between the rate of diffusion and molar mass is referred to as Graham’s law and according to this law, the rate of diffusion of a gaseous substance is inversely proportional to the square root of its molar mass. The law can be mathematically represented as follows
$r\propto \sqrt{\dfrac{1}{M}}$
Where M is the molar mass and r is the rate of diffusion.
- Among the four given compounds (${{H}_{2}}$,${{O}_{2}}$, ${{N}_{2}}$ and He) , the molar mass of hydrogen is minimum and thus the hydrogen filled tube will be reinflated first as the rate of diffusion of hydrogen is maximum due to the lowest molar mass.

Therefore the answer is option (A) ${{H}_{2}}$ filled tube.

Note: Keep in mind that the Graham’s law is commonly used to compare the rates of two different gases at equal pressures and temperatures and the reason why most gas molecules that are lighter will travel faster than the heavier gas molecules can be explained by this law.