Equal masses of `H_(2)`, `O_(2)` and methane have been taken in a container of volume `V` at temperature `27^(@)C` in identical conditions. The ratio of the volume of gases `H_(2) : O_(2)` : methane would be

Options

A. `8:16:1`
B. `16:8:1`
C. `16:1:2`
D. `8:1:2`

Answer

C

Explanation

According to Avogadro's hypothesis,
Volume of a gas `(V)prop` number of moles (n)
Therefore, the ratio of the volumes of gases can be determined in terms of their moles.
`therefore"The ratio of volumes of "H_(2):O_(2):"methane"(CH_(4)) "is given by"`
`V_(H_(2)):V_(O_(2)):V_(CH_(4))=n_(H_(2)):n_(O_(2)):n_(CH_(4))`
`rArr" "V_(H_(2)):V_(O_(2)):V_(CH_(4)): =(m_(H_(2)))/(M_(H_(2))):(m_(O_(2)))/(M_(O_(2))):(m_(CH_(4)))/(M_(CH_(4)))`
Given, `m_(H_(2))=m_(O_(2))=m_(CH_(4))=m`
`" "[becausen=("mass")/("molar mass"]]`
Thus, `V_(H_(2)):V_(O_(2)):V_(CH_(4))=(m)/(2):(m)/(32):(m)/(16)=16:1:2`