Question

If a molecule of CH4 diffuses a distance of 0.530 m from a point source, calculate the distance (meters) that a molecule of N2 would diffuse under the same conditions for the same period of time (1 second).

Answer 1

The distance that a molecule of N2 would diffuse under the same conditions for the same period can be calculated using the ratio of the square roots of their molar masses.

Step-by-step explanation:

The diffusion rate of a gas is inversely proportional to the square root of its molar mass. Since methane (CH4) has a smaller molar mass compared to nitrogen (N2), it will diffuse faster. Let's assume that the molecule of CH4 diffused a distance of 0.530 m in 1 second. To calculate the distance that a molecule of N2 would diffuse under the same conditions, we can use the ratio of the square roots of their molar masses:

Distance(N2) = (√Molar Mass(CH4) / √Molar Mass(N2)) * Distance(CH4)

Using the molar masses of CH4 (16 g/mol) and N2 (28 g/mol), we can substitute these values into the equation:

Distance(N2) = (√16 g/mol / √28 g/mol) * 0.530 m = 0.530 m * 0.5 = 0.265 meters

Answer 2

Step-by-step explanation:

Assume the gases each diffuse in one second, in order to create a rate.

Set rate1 = N2 = x

Set rate2 = CH4 = 0.530 m/sThe molecular weight of N2 = 28.0

The molecular weight of CH4 = 16.0

Graham's Law is:

r1 over r2 = √MM2 over √MM1

Substituting, we have:

x / 0.530 = √(16.0 / 28.0)x = 0.400 m/s