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The vapor pressure of water is 23.8 mm o...

The vapor pressure of water is `23.8 mm` of Hg at `25^(@)C`. If `28.5 g` of sucrose, `C_(12)H_(22)O_(11)` (molecular mass=`342u)` is dissolved in `100 g` of `H_(2)O`, then the vapor pressure of the resulting solution will be ___ mmHg

A

`32.5`

B

`20.6`

C

`23.2`

D

`19.8`

Text Solution

Verified by Experts

The correct Answer is:
3
since solute is nonvolatile, `P_(solu)=P_(solv)`. According to `2^(nd)` Raoult's law
`(P_(solv)^(0)-P_(solv))/P_(solv)^(0)=chi_(solute)=n_(solute)/(n_(solute)+n_(solv)) …(1)`
`n_(sucrose)=(mass_(sucrose))/(molar mass_(sucrose))`
`=(28.5 g)/(342 g mol^(-1))=0.083 mol`
`n_(H_(2)O)=(mass_(H_(2)O))/(molar mass_(H_(2)O))=(100g)/(18 g mol^(-1))`
`=5.55 mol`
Thus
`chi_(sucrose)=(0.083 mol)/(0.083 mol+5.55 mol)`
`=0.015`
Substituting this result into Equation (1), we get
`23.5-P_(solv)/23.5=0.015`
`23.5-P_(solv)=(0.015)(23.5)`
or `P_(solv)=23.1 mmHg`
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