Equal weights of methane and hydrogen are mixed in an empty container at `25^(@)C`. The fraction of the total pressure exerted by hydrogen is

Options

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

Answer

A

Explanation

The fraction of the total pressure exerted by `H_(2)` gas is gieven by
`p_(f) = (p_(H_(2)))/(p_("total"))`
which is equal to the mole freaction of `H_(2)` gas . Let us assume that
`"Mass"_(H_(2)) = "Mass"_(CH_(4)) = mg`
Thus , `n_(H_(2)) = ("Mass"_(H_(2)))/("Molar mass" _(H_(2))) = (mg)/(2g "mol"^(-1))`
`n_(CH_(4)) = ("Mass"_(CH_(4)))/("Molar mass" _(CH_(4))) = (mg)/(16g "mol"^(-1))`
`chi_(H_(2)) = (n_(H_(2)))/(n_(H_(2)) + n_(CH_(4))) = (m//2)/((m)/(2) + (m)/(16))`
`= (m//2)/(9m//16) = (m)/(2) xx (16)/(9 m) = (8)/(9)`