Chemistry - Ideal Gas Question with Solution | TestHub

${\mathrm{x}}_{\mathrm{T}},{\mathrm{x}}_{\mathrm{B}}$ mole fraction of liquid Toluene and Benzene respectively $y_T,y_B$ mole fraction of vapour of Toluene and Benzene respectively (P) The vapour pressure of first vapour form is

$${\mathrm{P}}_{\text{total }}={\mathrm{x}}_{\mathrm{T}}{\mathrm{P}}_{\mathrm{T}}^{\circ }+{\mathrm{x}}_{\mathrm{B}}{\mathrm{P}}_{\mathrm{B}}^{\circ }=0.5\times 32+0.5\times 112=72\mathrm{mmHg}$$

(Q) Vapour pressure of the system when last trace of liquid will disappear is

$$\begin{array}{rlr}& \frac{1}{P_{\text{total }}}=\frac{1}{32}+\left(\frac{1}{112}-\frac{1}{32}\right)\times 0.5& P_{\text{total }}=49.78\mathrm{mmHg}\end{array}$$

(R) Vapour pressure of the system when half of total amount of liquid will vapourise

$${\mathrm{P}}_{\text{total }}=\sqrt{{\mathrm{P}}_{\mathrm{T}}^{\mathrm{O}}\times {\mathrm{P}}_{\mathrm{B}}^{\mathrm{O}}}=59.87\mathrm{mmHg}$$

(S) $59.87={\mathrm{x}}_{\mathrm{T}}\times 32+\left(1-{\mathrm{x}}_{\mathrm{T}}\right)\times 112$

${\mathrm{x}}_{\mathrm{T}}=0.65$