Equal moles of hydrogen and oxygen gases are placed in a container with a pin-hole through which both can escape. What fraction of the oxygen escapes in the time required for one-half of the hydrogen to escape ?

Options

A. `3//8`
B. `1//2`
C. `1//8`
D. `1//4`

Answer

C

Explanation

Suppose the number of moles of each gas taken
=s moles
`H_(2)` escaped in time `t=(x)/(2)` mole
Suppose number of moles of `O_(2)` diffused in the same time=n times
Then `(r_(O_(2)))/(r_(H_(2)))=sqrt((M_(H_(2)))/(M_(O_(2))))`
i.e., `(n//t)/((x//2)//t)=sqrt((2)/(32))" or " (2n)/(x)=(1)/(4)" or " n=(1)/(8)x`
`:.` Fraction of `O_(2)` escaped`=(1)/(8)`.