The vapour pressure of pure benzene and toluene are 160 and $60 \mathrm{~mm} \mathrm{Hg}$ respectively. The…

The vapour pressure of pure benzene and toluene are 160 and $60 \mathrm{~mm} \mathrm{Hg}$ respectively. The mole fraction of benzene in vapour phase in contact with equimolar solution of benzene and toluene is
  1. $0.073$
  2. $0.027$
  3. $0.27$
  4. $0.73$

Solution

For equimolar solution, $\begin{aligned} & \chi_b=\chi_t=0.5 \\ & \mathrm{p}_b=\chi_b \times \mathrm{p}_b^0=0.5 \times 160 \\ & =80 \mathrm{~mm} \\ & \mathrm{p}_b=\chi_t \times \mathrm{p}_b^0=0.5 \times 60 \\ & =30 \mathrm{~mm}\end{aligned}$ $\mathrm{p}_{\text {total }}=80+30=110 \mathrm{~mm}$ Mole fraction of benzene in vapour phase $=\frac{\mathrm{p}_b}{\mathrm{p}_{\text {total }}}=\frac{80}{110}=0.727=0.73$

Asked in: AP EAMCET 2016

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