Solutions Question 260
Question: Phenol associates in benzene to a certain extent to form a dimer. A solution containing $ 20\times {10^{-3}} $ kg of phenol in 1.0 kg-of benzene has its freezing point depressed by 0.69 K. Calculate the fraction of phenol that has dimerised. ( $ K_{f} $ for benzene = 5.12 K kg $ mo{l^{-1}} $ )
Options:
A) 28.5%
B) 32.6%
C) 73.3%
D) 82%
Show Answer
Answer:
Correct Answer: C
Solution:
Observed mol. mass $ =\frac{100\times k_{f}\times w}{W\times \Delta T_{f}} $
$ =\frac{1000\times 5.12\times 20\times {10^{-3}}}{1\times 0.69}=148.4 $ Normal mol, mass of phenol=94 $ i=\frac{Normalmol\text{.}mass}{Observedmol\text{.}mass}=\frac{94}{148.4}=0.633 $ Since, phenol is dimerized
$ \therefore n=2 $ Also, $ i=1+[ \frac{1}{n}-1 ]\alpha =1+[ \frac{1}{2}-1 ]\alpha =1-\frac{\alpha }{2} $
$ \Rightarrow 0.633=1-\frac{\alpha }{2} $
$ \Rightarrow \frac{\alpha }{2}=0.367 $
$ \Rightarrow \alpha =0.733\times 100=73.3% $
