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

Let the moles of each gas `= x`
Fraction `H_(2)` escaped `= y_(2)x`.
`(r_(O_(2)))/(r_(H_(2)))=sqrt((M_(H_(2)))/(M_(O_(2))))=(nO_(2)//t)/(x/2H_(2)//t) = sqrt((2)/(32)) = 1/4`
`n_(o_(2)) = 1/4 xx x/2 = x/8`
`n_(o_(2)) = (1)/(4) xx x/2 = x/8`
`:.` Fraction of `O_(2)` escaped `= 1//8`