Phenol associates in benzene to a certain extent to form a dimer. A solution containing 20 g of phenol in 1.0 kg of benzene has its freezing point lowered by 0.69 K. Calculate the fraction of phenol that has dimerised.
[Given : `K_(f)` for benzene = 5.1 `Km^(-1)]`

Explanation

Association of phenol `C_(6)H_(5)OH (M_(B) = 94)`
`W_(B)=20` g ( Phenol )
`DeltaT_(f) `=0.69 K
`W_(A) =1` kg (Benzene fraction)
`K_(f) =5.1 km^(-1)`
Phenol dimerised
`DeltaT_(f)= iK_(f)m`
`0.69=ixx5.1xx(20)/(94xx1)`
`i =(94xx0.69)/(20xx5.1)`
`=(64.86)/(102.51)`
=0.63
`alpha=(i-1)/((1)/(n)-1)` (Association)
`=(0.63-1)/((1)/(2)-1)=(0.37)/(-0.5)`
`alpha=0.74`
or `= 74%`