If it took 976seconds for a sample of HCN to effuse, for which of the following would it require 2150seconds for the same number of moles to effuse?CH4NeNH3ArXeChemistry and Chemical ReactivityKotz and Treichel;Thomson PublishingChapter 12.7Lecture Help Main PageFeedback to Dr Van BramerFeedback to George Wiger

The question is asking to apply 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.

The formula for Graham's law of effusion is:

Rate1/Rate2 = sqrt(M2/M1)

Given that it took 976 seconds for HCN to effuse, we can find the rate of effusion for HCN as:

Rate1 = 1/976 moles/second

We are asked to find the gas that would take 2150 seconds to effuse the same number of moles, so the rate of effusion for this unknown gas is:

Rate2 = 1/2150 moles/second

Substituting these values into Graham's law of effusion gives:

1/976 / 1/2150 = sqrt(M2/M1)

Solving for M2 (the molar mass of the unknown gas) gives:

M2 = M1 * (2150/976)^2

The molar mass of HCN (M1) is approximately 27.03 g/mol. Substituting this value in gives:

M2 = 27.03 * (2150/976)^2 = 79.9 g/mol

Looking at the molar masses of the given gases, the one that is closest to 79.9 g/mol is Ar (argon), with a molar mass of approximately 39.95 g/mol. Therefore, the gas that would take 2150 seconds to effuse the same number of moles as HCN is Ar (argon).