`3.7 gm` of gas at `25^(@)C` occupied the same volume as `0.184 gm` of hydrogen at `17^(@)C ` and at the same pressure. What is the molecular mass of the gas ?

Explanation

For hydrogen,
`w = 0.184 g , T = 17 + 273 = 290 K, M = 2`
We know that, `PV = (w)/(M) RT`
`= (0.184)/(2) xx R xx 290`.....(i)
For unknown gas,
`w = 3.7 g, T = 25 + 273 = 298 K, M = ?`
`PV = (3.7)/(M) xx R xx 298`....(ii)
Equating both the equations,
`(3.7)/(M) xx R xx 298 = (0.184)/(2) xx R xx 290`
or `M = (3.7 xx 298 xx 2)/(0.184 xx 290) = 41.33`