Question

5gm of hydrogen diffused through a porus membrane
in 30 minutes. Find the time required to diffuse
the some amount of so2 gas at identhal conditions.​

Answer 1

169.71 minutes

Further explanation

Given

Rate of diffused of Hydrogen=5 gm/30 min

Required

The time required for SO₂

Solution

Graham's law: the rate of effusion of a gas is inversely proportional to the square root of its molar masses or  

the effusion rates of two gases = the square root of the inverse of their molar masses:  

$\tt \dfrac{r_1}{r_2}=\sqrt{\dfrac{M_2}{M_1} }$

r₁=5gm/30 min

M₁=molar weight of H₂-hydrogen= 2 g/mol

M₂=molar weight of SO₂-sulfur dioxide= 64 g/mol

$\tt \dfrac{5/30}{r_2}=\sqrt{\dfrac{64}{2} }\\\\\dfrac{5/30}{r_2}=4\sqrt{2}\\\\\dfrac{5}{30}=r_2.4\sqrt{2}\\\\r_2=\dfrac{5}{30\times 4\sqrt{2} }=\dfrac{\sqrt{2} }{48}$

the time required (for the same amount=5 gm) :

$\tt \dfrac{5}{x}=\dfrac{\sqrt{2} }{48}\rightarrow x=120\sqrt{2}=169.71 minute$