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A solution containing 6 g of benzoic aci...

A solution containing 6 g of benzoic acid, `C_(6)H_(5)COOH` in 50 g of diethy 1 ether, `C_(2)H_(5)OC_(2)H_(5)`, has a vapour pressure of 410 mm Hg at 293 K. Calculate the molar mass of the benzoic acid. Vapour pressure of diethy1 eth at 293 K is 442 mm Hg.

Text Solution

Verified by Experts

The correct Answer is:
113.8 g `mol^(-1)`
`P_(A)^(@)=442" mm Hg",P_(S)=410" mm Hg", W_(B)=6 g , W_(A)=50g,`
`M_(A)(C_(2)H_(5)-O-C_(2)H_(5))=74" g mol"^(-1)`
According to Raoult's Law (solution is non-ideal),
`(P_(A)^(@)-P_(S))/P_(S)=n_(B)/n_(A)=W_(B)/M_(B)xxM_(A)/W_(A)`
`((442-410)mm)/(410 mm)=((6g))/((M_(B)))xx((74" g mol"^(-1)))/((50 g))`
`M_(B)=((6g)xx(74" g mol"^(-1)))/((50g))xx((410 mm))/((32mm))=113.8" g mol"^(-1)`.
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