The degree of dissociation of `Ca(NO_(3))_(2)` in a dilute aqueous solution, containing `7.0 g` of the salt per `100 g` of water at `100^(@)C` is `70%`. If the vapour pressure of water at `100^(@)C` is `760 mm`, calculate the vapour pressure of the solution.

Options

A. 746.3 mm of Hg
B. 757.5 mm of Hg
C. 740.9 mm of Hg
D. 750 mm of Hg

Answer

A

Explanation

No. Of moles of `Ca(NO_(3))_(2)=(14)/(40+2xx14+6xx16)`
`=7//0.82`
No. Of moles of water = 200/18 = 100/9
Moles fraction of salt X = `(7//0.82)/(7//0.82+100//9)=0.008`
`Ca(NO_(3))_(2)iffCa^(2+)+2NO_(3)^(-)`
`{:("Initial",alpha,0,0),("Final",1-alpha,alpha,2alpha):}`
`i=1-alpha+alpha+2alpha=1+2alpha`
`i=1+2xx0.7(alpha=70%)`
`i=2.4`
`(P_(o)-P_(s))/(P_(o))=i.Ximplies(760-P_(s))/(760)=2.4xx0.008`
`P_(s)~~746mm` of Hg.