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=(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{(r_1)/(r_2)}=(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{(3.2)/(4.5)}=(M_2)/(40)`

`M_2=28g/mol`