Benzoic acid completely dimerises is benzene. What will be the vapour pressure os a solution containing 61 g of benzonic acid per 500 g benzene when the vapour pressure of pure benzene at this temperature expermint is 66.6 torr ? What would be vapur pressure in the absence of dimerisation ?

Explanation

Calculation of Van't haff factor (i)
The association of benzoic acid is represented as: `2(C_(6)H_(5)COOH)hArr(C)(6)H_(5)COOH)_(2)`
Since association is complete, Van't Hoff factor (i)
= `("Normal molar mass")/("Observed molar mass")=((122g mol^(-1)))/((244g mol^(-1)))=0.5`
Calculation of vapour pressure of the solution `(P_(s))`
`(P_(A)^(@)-P__(S))/P_(S)=i(n_(B))/n_(A)=(ixxW_(B)xxM_(A))/(M_(B)xxW_(A))`
`i=0.5, W_(B)=61g, M_(B)=122g mol^(-1),W_(A)=500g, M_(A)-78g mol^(-1)`
`P_(A)^(@)66.6 torr `
`((66.6 torr-P_(S)))/P_(S)=(0.5xx(61g)xx(78g mol^(-1)))/((122g mol^(-1))xx(500g))=0.039`
`(66.6 torr)-P_(S)=(0.039)xxP_(S)`
`(1.039)xxP_(S)=66.6 torr or P_(S)=((66.6 torr))/((1.039))=64.1 torr`
Calculation of the vapour pressur of solution `(P_(S))` in the absence of dimersation
In the absence of dimersation i=1, and
`((66.6 torr-P_(S)))/P_(S)=0.039xx2=0.078 , 66.6 torr-P_(S)=(0.078)xxP_(S)`
` P_(S)=((66.6 tor))/((1.078))=61.78 torr`