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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? |
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Answer» 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` |
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