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Question

Phenol associates in benzene to a certain extent for a dimer. A solution containing 20×103 kg of phenol in 1 kg of benzene has its freezing point decreased by 0.7 K
Calculate the fraction of the phenol that has dimerised
Given :
(Kf)Benzene=5.12 K kg mol1

A
0.72
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B
0.29
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C
0.91
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D
0.09
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Solution

The correct option is A 0.72
Weight of phenol(w)=20×103 kg=20 g Weight of benzene(W)=1 kgΔTf=0.7 K

Let mobs be observed molecular mass of phenol

mobs=Kf×wW×ΔTmobs=5.12×201×0.7=146.3 g mol1
Theoretical molecular mass of phenol (C6H5OH)=94 g mol1
So, i=Theoretical molecular massObserved molecular mass=94146.3=0.64

Degree of association (β) :
β=(i1)×n(1n)
Since phenol dimerises, so n=2
Putting the values:
β=(0.641)×2(12)β=0.72

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