An unknown gas effuses through a tiny hole at a rate that is 3.728 times higher

Question

An unknown gas effuses through a tiny hole at a rate that is 3.728 times higher than the rate at which nitrogen (N_2) gas effuses at the same temperature. The molar mass of the unknown gas is: 1.01 g middot mol^-1 2.02 g middot mol^-1 7.51 g middot mol^-1 14.51 g middot mol^-1 27.04 g middot mol^-1 52.22 g middot mol^-1 54.08 g middot mol^-1 104.43 g middot mol^-1 389.33 g middot mol^-1 None of the above; the correct molar mass is_g middot mol^-1 Based on the answer to Part i of this question, the unknown gas can be identified as_.

Explanation / Answer

m = 3.728 x higher rate than N2...

Apply Graham law of rates:

Rate 1 / Rate 2 = sqrt(MW2 / MW1)

assume 1 --> unkown

assume 2 --> N2, with molar mass of 28 g/mol

so..

Rate 1 = 3.6397*Rate 2

Rate 2 = Rate 2

MW1 =?

MW2 = 28 gmol

substitute

(3.6397*Rate 2)/(Rate2) = sqrt(28/MW1)

solve

(3.6397)^2 = 28/MW1

MW1 = 28/((3.6397)^2) = 2.1136 g/mol

nearest answer is B, which is most likely H2 gas

since Helium is already 4 g/mol, which is too much... choose H2, hydrogen gas

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