Question

In an effusion experiment, it was determined that nitrogen gas, N₂, effused at a rate 1.812 times faster than an unknown gas. What is the molar mass of the unknown gas?

Answer 1

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:

$r=\sqrt {\frac {1}{M}}$

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:

$\frac {r_1}{r_2}=\sqrt {\frac {M_2}{M_1}}$

So,  

For nitrogen gas :

$r_1$ = 1.812*$r_2$

$M_1$ = 28 g/mol

For unknown gas:

$r_2$

$M_2$ = ? g/mol

$\frac {1.812\times r_2}{r_2}=\sqrt {\frac {M_2}{28\ g/mol}}$

$M_2=\left(1.812\times \sqrt{28\:}\right)^2\ g/mol= 91.93\ g/mol$

Molar mass of unknown gas = 91.93 g/mol