Question

Under certain conditions argon (Ar) gas diffuses at a rate of 3.2 centimeters per second. Under the same conditions, an unknown gas diffuses at a rate of 4.5 centimeters per second. What is the approximate molar mass of the unknown gas?

a) 10 g/mol
b) 20 g/mol
c) 28 g/mol
d) 56 g/mol

Answer 1

According to Graham's law of diffusion/effusion, 
r₁ / r₂ = √m₂/m₁
3.2 / 4.5 = √m₂ / 38
m₂/38 = (3.2/4.5)²
m₂ / 38 = 0.50
m₂ = 0.50 * 38
m₂ = 19 ≈ 20 g/mol

In short, Your Answer would be Option B

Hope this helps!

Answer 2

Answer: c) 28 g/mol

Explanation: Rate of diffusion : It is defined as the volume of gas effused in a given time 't'.

Formula used : $Rate=\frac{Volume}{Time}$

According to Graham's law of diffusion, rate of diffusion is inversely proportional to the square root of the mass of the gas.

$\text{ Rate of diffusion}\propto \frac{1}{\sqrt{\text{ Mass of gas}}}$

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

where,

$r_1$ = rate of diffusion of argon gas = 3.2cm/sec

$r_2$ = rate of diffusion of unknown gas = 4.5 cm/sec

$M_1$ = Molar mass  of argon gas= 40g/mol

$M_2$ =  Molar mass  of unknown gas

$\sqrt{\frac{3.2}{4.5}}=\frac{M_2}{40}$

$M_2=28g/mol$