From two identical holes, nitrogen and an unknown gas are leaked into a common vessel of `3 L` capacity for `10 min`, at `27^(@)C`. The resulting pressure is `4.18` bar and the mixture contains `0.4 mol` of nitrogen. What is the molar mass of the unknown gas?

Explanation

Calculate of the number of moles of the unknown gas
`P=4.18 "bar"=4.18xx0.987=4.12 atm`
`V=3 L, T=27+273=300 K`
`R=0.0821 L "bar" K^(-1) mol^(-1)`
Total number of moles of the two gases can be calculated with the help of ideal gas equation.
`PV=nRT` or `n=(PV)/(RT)`
`n=((4.12 "atm")xx(3L))/((0.082 L "atm" K^(-1) "mol"^(-1))xx300K)=0.503 "mol"`
`r_(N_(2))=0.4/10 mol min^(-1), n_(gas)=0.5-0.4=0.1`
`r_(gas)=0.1/10 mol min^(-1)`
`r_(N_(2))/r_(gas)=sqrt(M_(gas)/M_(N_(2)))`,
`0.04/0.01=sqrt(M_(gas)/28)`
`(4xx4xx28)/(1xx1)=M_(gas) rArr M_(gas)=448`