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The molar volume of liquid benzene (dens...

The molar volume of liquid benzene (density `= 0.877 g mL^(-1))` increases by a factor of 2750 as it vaporizes at `20^(@)C` and that of liquid toluene (density `=0.867 g mL^(-1))` increases by a factor of 7720 at `20^(@)C` solution has a vapour pressure of `46.0` torr. Find the mole fraction of benzene in the above the solution.

Text Solution

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molar volume of benzene `=(78)/(0.877)ml`
molar volume of toluene `=(92)/(0.867)ml`
At `20^@C` volume of vapour of benzene and toluene
`V_B =(78)/(0.877)xx2750=244.58 ml`
`P_B^0=(RT)/(V_B), P_T^0=(RT)/(V_T), P_("total")=P_B^@chi_B +P_T^@chi_T`
`rArr (46)/(760)=chi_B((RT)/(V_B))+chi_T((RT)/(V_T))`
Substitute for `V_B and V_T and chi_T =1-chi_B`
`rArr chi_B=0.452`
Now find the vapour fraction of benzene.
`Chi_B^V =(P_B^0chi_B)/(P_("total"))=(0.452)/(46//760)((RT)/(V_B))=0.734`
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