Answer :
Answer:
Molar mass of unknown gas = 91.93 g/mol
Explanation:
Scottish physicist Thomas Graham formulated a law known as Graham's law of effusion in 1848. He conducted an experiment and found the relationship between the rate of effusion of a gas and its molar mass as:
[tex]r=\sqrt {\frac {1}{M}}[/tex]
where,
r is the rate of effusion of a gas
M is the molar mass of the gas.
And for two gases taking different rate of effusion as r₁ and r₂ to effuse, the formula is:
[tex]\frac {r_1}{r_2}=\sqrt {\frac {M_2}{M_1}}[/tex]
So,
For nitrogen gas :
[tex]r_1[/tex] = 1.812*[tex]r_2[/tex]
[tex]M_1[/tex] = 28 g/mol
For unknown gas:
[tex]r_2[/tex]
[tex]M_2[/tex] = ? g/mol
[tex]\frac {1.812\times r_2}{r_2}=\sqrt {\frac {M_2}{28\ g/mol}}[/tex]
[tex]M_2=\left(1.812\times \sqrt{28\:}\right)^2\ g/mol= 91.93\ g/mol[/tex]
Molar mass of unknown gas = 91.93 g/mol