Final answer:
Using Graham's law of effusion, hydrogen gas has been calculated to diffuse approximately 3.7 times more quickly than nitrogen gas because it has a much lower molar mass.
Step-by-step explanation:
The question requires us to compare the rate of diffusion of hydrogen gas (H2) to that of nitrogen gas (N2).
According to Graham's law of effusion, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass (M).
The formula is usually expressed as Rate1 / Rate2 = sqrt(M2 / M1), where Rate1 and Rate2 are the rates of effusion, and M1 and M2 are the molar masses of the two gases being compared.
For hydrogen, M1 = 2.0 g/mol, and for nitrogen, M2 = 28.0 g/mol.
Plugging these values into Graham's law gives us:
RateH2 / RateN2 = sqrt(28.0 / 2.0) = sqrt(14) = 3.74 (approximately).
Therefore, at any given temperature, hydrogen will diffuse approximately 3.7 times more quickly than nitrogen.