Question

Benzene (C6H6) and cyclohexane (C6H12) form an ideal solution at 25°C. The density of benzene is 0.876 g/cm 3 and the density of cyclohexane is unknown.A liquid mixture is prepared by mixing 357 mL of benzene and 643 mL of cyclohexane. The vapor in equilibrium with this liquid has a mole fraction of benzene of 0.4. What is the density of cyclohexane in units of g/cm3?

Data:

Vapor pressure of benzene = 99 mmHg, at 25°C

Vapor pressure of cyclohexane = 100 mmHg, at 25°C

1) 0.70

2) 0.77

3) 0.87

4) 0.92

5) 1.07

Answer 1

Ans:- Here mole fraction of benzene _B = 0.4

Therefore mole fraction of cyclohexane _A = 1 - 0.4=0.6

Given Vapour pressure of Cyclohexane is ⁰_A = 100mmhg

Density of benzene = mass of benzene / volume

0.876                                     = mass of benzene _B / 357

_B = 31.27g

Molar mass of benzene _B = 78

Molar mass of cyclohexane = 84

Now , using raoults law for ideal solution

M_{B =} W_B x M_A / W_A x   X_A

78 = 31.27 x 84 / W_A x 0.6

W_A =46.8

density of cyclohexane = 46.8/64.3

                                   = 0.87 g/cm³

The option (3) is correct