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phenol associates in benzene to a certai...

phenol associates in benzene to a certain extent in dimerisation reaction. A solution containing 0.02 kg of phenol in 1.0 kg of benzene has its freezing point depressed 0.69 k. [`K_(f)(C_(6)H_(6)) =5.12 k kg"mol"^(-1)`]. The degree of association:

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`M_(2)` (observed) `=(K_(f) xx 1000 xx W_(2))/(DeltaT_(f) xx W_(1))`
Here, `W_(2) = 20g, W_(1) = 1.0 kg = 1000 g `
`DeltaT_(f) = 0.69K`
`K_(f) = 5.1 Km^(-1)`
Normal mol. wt. of phenol
`(C_(6)H_(5)OH) = (12xx6) +(1xx5) +16 +1=94" g mol"^(-1)`
Substituting the values, `M_(2)` (observed)
`=(5.1 xx 1000 xx 20)/(0.69 xx 1000)=147.82`
van.t Hoff factor .i. `=("Normal mol. wt.")/("Observed mol. wt.")=(94)/(147.82)=0.635`
Since phenol associates as a dimer, n = 2.
Degree of association,
`alpha=(1-i)/(1-1//n)=(1-0.635)/(1-1//2) = (0.365)/(0.5) =0.73 =73%`
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