Benzene and toluene form an ideal solution over the entire range of composition. The vapour pressure of pure benzene and toluene at T( ~K ) are 50 ~mm Hg and 40 ~mm Hg respectively. What is the mole fraction of toluene in vapour phase when 117 ~g of benzene is mixed with 46 ~g of toluene? (molar mass of benzene and toluene are 78 and 92 ~g ~mol ⁻¹ respectively)

Step-by-step solution

p^ benzene p_ (b) ^ =50 ~mm Hg p^ toluene p_ (t) ^ =40 ~mm Hg Mass of benzene =117 ~g Mass of toluene =46 ~g Molar mass of benzene =78 ~g ~mol ⁻¹ Molar mass of toluene =92 ~g ~mol ⁻¹ Number of moles of benzene = 117 78 =1.5 ~mol Number of moles of toluene = 46 92 =0.5 ~mol Mole fraction of toluene ( _ (t) ) = Number of moles of toluene Total number of moles = 0.05 (1.5+0.5) = 0.5 2.0 =0.25 and of benzene _ (b) =0.75 Total vapour pressure (p_t ) aligned & =p_ (t) ^ _ (t) +p_ (b) ^ _ (b) & =p_ (toluene ) +p_ (benzene