Equal weight of `CH_(4) and H_(2)` are mixed in an empty container at `25^(@)C`. The fraction of the total pressure exerted by `H_(2)` is-

Options

A. `1/9`
B. `1/2`
C. `8/9`
D. `(16)/(17)`

Answer

C

Explanation

Gas mixture contains equal masses of `CH_(4) and H_(2)`. ltBrgt So, in the mixture, `n_(H_(2))=(w)/(2)mol,n_(CH_(4))=(w)/(16)` mol
`x_(H_(2))=(w//2)/((w)/(2)+(w)/(16))=(8)/(9) and x_(CH_(4))=1-x_(H_(2))=1-(8)/(9)=(1)/(9)`
`therefore`The partial presure of `H_(2),p_(H_(2))=x_(H_(2))xxP=(8)/(9)P`
[P=total pressure of the mixture]
`therefore (p_(H_(2)))/(P)=(8)/(9)`