Answer:
Molar mass of unknown gas = 4.0 g/mol
Explanation:
Based on the Graham's law of diffusion, if R1 and R2 are the diffusion rates for gas 1 and gas 2 with respective molar masses M1 and M2, the rates are related as:
[tex]\frac{R1}{R2} = \sqrt{\frac{M2}{M1} }[/tex] -----(1)
If R1 is the rate of diffusion of O2 and R2 that of the unknown gas, then as per the given information
R2 = 3(R1)
Now, molar mass of O2 = M1 = 32 g/mol. Based on eq(1), substituting for R1, M1 we get:
[tex]\frac{1}{3} = \sqrt{\frac{M2}{32} } \\\\M2 = \frac{32}{9} = 3.55 = 4 g/mol[/tex]
