A solution at `20^(@)C` is composed of 1.5 mol of benzene and 3.5 mol of toluene. If the vapour pressure of pure benzene and pure toluene at this temperature are 74.7 torr and 22.3 torr, respectively, then the total vapour pressure of the solution and the benzene mole fraction in equilibrium with it will be, respectively:

Options

A. 35.8 torr and 0.280
B. 38.0 torr and 0.589
C. 30.5 torr and 0.389
D. 30.5 torr and 0.480

Answer

B

Explanation

Total V.P. of solution `= P_A^@x_A + P_B^@x_B`
Given, `P_A^@ = 74.7 torr, P_B^@ = 22.3 "torr"`
`n_("benzene") = 1.5mo, n_("toluene") = 3.5 mol`
`n_("solution")=1.5 + 3.5 = 5mol`
`x_A =(n_("benzene"))/(n_("solution")) = 1.5/5`
Total V.P. of solution
`=(1.5/5xx74.7 +3.5/5xx22.3)"torr"`
`=15.6 + 22.4) " torr" = 38 "torr"`
Mole fractionof benzene in vapour form `= 22.4/38 = 0.589`