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 (r_1)/(r_2)=\sqrt{(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 (5/30)/(r_2)=\sqrt{(64)/(2) }\\\\(5/30)/(r_2)=4√(2)\\\\(5)/(30)=r_2.4√(2)\\\\r_2=(5)/(30* 4√(2) )=(√(2) )/(48)`

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

`\tt (5)/(x)=(√(2) )/(48)\rightarrow x=120√(2)=169.71 minute`