Question

A balloon filled with methane \[C{H_4}\] is pricked with a sharp point and quickly plunged into a tank of hydrogen at the same pressure. After some time the balloon will have?
A. Enlarged
B. Collapsed
C. Remained unchanged in size
D. Ethylene \[({C_2}{H_4})\] inside it

Answer 1

Hint:Gaseous particles tend to undergo diffusion because they have kinetic energy. Diffusion is faster at higher temperatures because the gas molecules have greater kinetic energy. The rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Gas with the lowest molar mass will have the highest rate of diffusion.

Formula used: \[r \propto \dfrac{1}{{\sqrt M }}\]

Complete step by step answer:
Graham’s Law states that the effusion rate of a gas is inversely proportional to the square root of the mass of its particles.
The value of compression of two gases, the rate of diffusion through a fine hole is given by:
 \[r \propto \dfrac{1}{{\sqrt M }}\] where r is the rate of diffusion and M is the molar mass.
The rate of diffusion depends on several factors such as the concentration gradient ( the increase or decrease in concentration from one point to another), the amount of surface area available for diffusion, and the distance the gas particles must travel.
The molecular weight \[C{H_4}\] is 16gm/mol, the molecular weight of hydrogen is 2gm/mol.
So, the ratio of the rate of diffusion of methane and hydrogen as follows,
 \[
  \dfrac{{{r_{{H_2}}}}}{{{r_{C{H_4}}}}} = \dfrac{{\sqrt {{M_{C{H_4}}}} }}{{\sqrt {{M_{{H_2}}}} }} \\
  \dfrac{{{r_{{H_2}}}}}{{{r_{C{H_4}}}}} = \dfrac{{\sqrt {16} }}{{\sqrt 2 }} \\
  {r_{{H_2}}} = \dfrac{4}{{\sqrt 2 }} \times {r_{C{H_4}}} \\
  {r_{{H_2}}} = 2\sqrt 2 \times {r_{C{H_4}}} \\
 \]
Therefore, the rate of diffusion of hydrogen is \[2\sqrt 2 \] times greater than methane. So, hydrogen will enter into the balloon and after some time the balloon will have enlarged.
So, the correct answer is A.

Note:Diffusion is inversely proportional to molecular weight. Therefore, \[N{H_3}\] has the highest diffusion rate, whereas, carbon dioxide has the greatest molecular mass and should be expected to diffuse the slowest.