Answer to Question #152190 in General Chemistry for Isbah

Question

400cm3 of helium gas effuses from a pourous container in 20 sec. How long will SO2 gas take to effuse from the same container?

Answer 1

Time taken for Helium gas to effuse = 10 sec

Pressure, Volume, Temperature is constant since the same container is used.

Molar mass of Helium = 4 g/mol

Molar mass of SO2 = 64g/mol

According to graham's law of diffusion/effusion

The rate of diffusion of a gas is proportional to the square root of the inverse of the molar mass.

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

$\dfrac{r_{He}}{r_{SO_2}} = \sqrt{\dfrac{M_{SO_2}}{M_{He}}}$

but, the rate is inversely proportional to time

$\dfrac{t_{SO_2}}{t_{He}} = \sqrt{\dfrac{M_{SO_2}}{M_{He}}}$

$\dfrac{t_{SO_2}}{10} = \sqrt{\dfrac{64}{4}}$

$\dfrac{t_{SO_2}}{10} = 4$

$t_{SO_2} = 40$

Therefore, it will take 40 seconds for $SO_2$ gas take to effuse from the same container.