# A mixture of benzene and toluene contains 30% by mass of toluene. At 30 °C, vapour pressure of pure toluene is 36.7 mm Hg and that of pure benzene is 118.2 mm Hg. Assuming that the two liquids form ideal solutions, calculate the total pressure and partial pressure of each constituent above the solution at 30 °C.

### Solution

##### Given: Mass percentage of toluene = 30 %W/WVapour pressure of liquid toluene $\left({\text{P}}_{1}^{0}\right)$ = 36.7 mm HgVapour pressure of liquid benzene $\left({\text{P}}_{2}^{0}\right)$ = 118.2 mm HgTo find: 1. Partial pressures of each constituent2. Total pressureFormulae: 1. ${\text{P}}_{1}={\text{P}}_{1}^{0}{\text{x}}_{1}\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}{\text{P}}_{2}={\text{P}}_{2}^{0}{\text{x}}_{2}$,2. P = P1 + P2Calculation: Molar mass of toluene, C7H8 = (7 ×12) + (8 × 1) = 92 g mol-1Molar mass of benzene, C6H6 = (6 ×12) + (6 × 1) = 78 g mol-1Now, 30 % W/W toluene means 30 g toluene in 100 g solution.Thus, mass of benzene = 100 – 30 = 70 gNumber of moles of toluene, C7H8 =  = 0.326 molNumber of moles of benzene, C6H6 = ${\text{n}}_{\text{B}}=\frac{\text{70 g}}{78\text{mol}}$ = 0.897 molTotal number of moles  = 1.223 molMole fraction of toluene $\left({\text{x}}_{{\text{C}}_{7}{\text{H}}_{6}}\right)=\frac{{\text{n}}_{\text{A}}}{{\text{n}}_{\text{A}}+{\text{n}}_{\text{B}}}=\frac{0.326}{1.223}=0.2666$Mole fraction of benzene $\left({\text{x}}_{{\text{C}}_{6}{\text{H}}_{6}}\right)$ = 1.0 - 0.2666 = 0.7334Now, using formula (i),${\text{P}}_{{\text{C}}_{7}{\text{H}}_{8}}={\text{P}}_{{\text{C}}_{7}{\text{H}}_{8}}^{0}×{\text{x}}_{{\text{C}}_{7}{\text{H}}_{8}}$ = 36.7 mm Hg × 0.2666 = 9.78 mm Hg${\text{P}}_{{\text{C}}_{6}{\text{H}}_{6}}={\text{P}}_{{\text{C}}_{6}{\text{H}}_{6}}^{0}×{\text{x}}_{{\text{C}}_{6}{\text{H}}_{6}}$ = 118.2 mm Hg × 0.7334 = 86.7 mm Hg Now, using formula (ii),Vapour pressure of the solution,P = ${\text{P}}_{{\text{C}}_{7}{\text{H}}_{8}}+{\text{P}}_{{\text{C}}_{6}{\text{H}}_{6}}=9.78+86.7=96.48=96.5$ mm Hg∴ Partial pressures of toluene and benzene are 9.78 mm Hg and 86.7 mm Hg, respectively.∴ Total pressure above the solution is 96.5 mm Hg.

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