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Question

Chemistry Question on Solutions

The vapour pressures of two liquids AA and BB in their pure states are in the ratio of 1:21 : 2. A binary solution of AA and BB contains AA and BB in the mole proportion of 1:21 : 2. The mole fraction of AA in the vapour phase of the solution will be

A

0.330.33

B

0.20.2

C

0.250.25

D

0.520.52

Answer

0.20.2

Explanation

Solution

Given, pA:PB=1:2p _{ A }: P _{ B }=1: 2
pB=2pA\therefore p _{ B }=2 p _{ A }

Similarly nAnB=12\frac{n_{A}}{n_{B}}=\frac{1}{2}
xA=11+2=13\therefore x_{A}=\frac{1}{1+2}=\frac{1}{3} and xB=21+2=23x_{B}=\frac{2}{1+2}=\frac{2}{3}

Total pressure, pT=PAxA+pBxBp _{ T }= P _{ A } x _{ A }+ p _{ B } x _{ B }
=pA×13+2pA×23=p_{A} \times \frac{1}{3}+2 p_{A} \times \frac{2}{3}
=13pA+43pA=\frac{1}{3} p_{A}+\frac{4}{3} p_{A}
=53pA=\frac{5}{3} p_{A}

Mole fraction in vapour phase

yA=pAxApry_{A}=\frac{p_{A} x_{A}}{p r}
=pA×1353pA=15=0.2=\frac{p_{A} \times \frac{1}{3}}{\frac{5}{3} p_{A}}=\frac{1}{5}=0.2