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Benzene and Toluene form ideal solution ...

Benzene and Toluene form ideal solution over the entire range of composition. The vapour pressure of pure benzene and toluene at 300 K are 50.71 mm of Hg and 32.06 mm of Hg respectively. Calculate the mole fraction of benzene in vapour phase if 80g of benzene is mixed with 100g of toluene.

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Molecular weight of benzene `(C_(6)H_(6))=78`
Molecular weight of Toluene `(C_(7)H_(8))=92`
`n_(C_(6)H_(6))=(80)/(78)=1.026`
`n_(C_(7)H_(8))=(100)/(92)=1.087`
`X_(C_(6)H_(6))=(1.026)/(1.026+1.087)=(1.026)/(2.113)=0.4855`
`X_(C_(7)H_(8))=1-0.4855=0.5145`
AC Cordin to Raoult's law
Partial pressure of benzene in solution
`P_(C_(6)H_(6))=P_(C_(6)H_(6))xxX_(C_(6)H_(6))`
`=50.71xx0.4855=24.61" mm"`
Partial pressure of Toluene in solution
`P_(GH_(8))=P_(G_(H_(8)))^(0)xxX_(C_(7)H_(8))=32.06xx0.5145=16.49" mm"`
Total vapour pressure of solution (P) `=24.61+16.49=41.1" mm"`
Mole fraction of benzene in vapour phase is
`=(X_(C_(6)H_(6))xxP_(C_(6)H_(6))^(0))/(P_("total"))=(0.4855xx50.71)/(41.1)=(24.61)/(41.1)=0.5987`
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