Final answer:
Hydrogen gas will diffuse approximately 3.74 times more quickly than nitrogen gas due to its lower molar mass, as described by Graham's Law of Effusion.
Step-by-step explanation:
The question relates to the rate at which different gases diffuse, which is governed by Graham's Law of Effusion. According to this law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Since hydrogen (H2) has a much lower molar mass compared to nitrogen (N2), it will diffuse more quickly.
Specifically, if we look at the molar masses, hydrogen has a molar mass of approximately 2 g/mol, while nitrogen has a molar mass of approximately 28 g/mol.
Using Graham's Law, the rate of diffusion of hydrogen can be calculated in reference to nitrogen:
rH2 / rN2 = (MN2 / MH2)0.5
Where MN2 and MH2 are the molar masses of nitrogen and hydrogen, respectively. Plugging in the values:
rH2 / rN2 = (28 / 2)0.5 ≈ 3.74
Therefore, hydrogen gas will diffuse approximately 3.74 times more quickly than nitrogen gas at any given temperature and pressure.