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
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 0A = 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
MB = WB x MA / WA x XA
78 = 31.27 x 84 / WA x 0.6
WA =46.8
density of cyclohexane = 46.8/64.3
= 0.87 g/cm3
The option (3) is correct
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