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

Answer

D

Explanation

Given, number of moles of hydrogen `(n_(H_(2)))` and that of oxygen `(n_(O_(2))` are equal.
`therefore` We have, the relation between ratio of number of moles escaped and ratio of molecular mass.
`(n_(O_(2)))/(n_(H_(2)))=sqrt((M_(H_(2)))/(M_(O_(2))))`
where, M = Molecular mass of the molecule.
`rArr" "(n_(O_(2)))/(n_(H_(2)))=sqrt((2)/(36))`
`rArr" "(n_(O_(2)))/(n_(H_(2)))=sqrt((1)/(16))`
`rArr" "(n_(O_(2)))/(0.5)=(1)/(4)`
`rArr" "n_(O_(2))=(0.5)/(4)=(1)/(8)`