Final answer:
Hydrogen (H₂) will diffuse approximately 3.74 times more quickly than nitrogen (N₂) at the same temperature and pressure, according to Graham's law of effusion.
Step-by-step explanation:
The rate at which one gas diffuses compared to another can be determined using Graham's law of effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Since the molar mass of hydrogen (H₂) is 2 g/mol and the molar mass of nitrogen (N₂) is 28 g/mol, we can calculate the relative rates of diffusion using the formula:
Rate of H₂ / Rate of N₂ = sqrt(Molar Mass of N₂ / Molar Mass of H₂)
So we calculate the square root of (28 / 2) which is approximately the square root of 14, giving us a factor of about 3.74. Therefore, hydrogen will diffuse approximately 3.74 times more quickly than nitrogen under the same conditions of temperature and pressure.