An L.P.G. cylinder weight `14.8 kg` when empty. When full, it weighs `29 kg` and shows a pressure of `2.5 atm`. In the course of use at `27^(@)C`, the weight of the full cylinder reduced to `23.2 kg`. Find out the volume of `n-`butane in cubic metres used up at `27^(@)C` and `1 atm`. [Mol. mass of butane = `58`]

Explanation

Weight of LPG originally present
`=29.0-14.8`
`=14.2kg`
`"Pressure "="2.5 atm"`
Weight of L.P.G. present after use `=23.2-14.8`
`=8.4kg`
Since volume of the cylinder is constant, applying
`pV=nRT`
`(p_(1))/(p_(2))=(n_(1))/(n_(2))=(W_(1)//M)/(W_(2)//M)=(W_(1))/(W_(2))`
`(2.5)/(p_(2))=(14.2)/(8.4)`
`p_(2)=(2.5xx8.4)/(14.2)="1.48 atm"`
`"or Weight of used gas "=14.2-8.4=5.8 kg`
`"Moles of gas"=(5.8xx10^(3))/(58)="100 moles"`
Normal conditions
`p="1 atm,"`
`T=273+27=300`
`"Volume of 100 mL of LPG at 1 atm and 300 K"`
`V=(nRT)/(p)`
`=(100xx0.082xx300)/(1)="2463 litre"`
`V=2.463m^(3)`.