Finding the total vapor pressure?

Question

A solution is 40.0% by volume benzene (C6H6) in carbon tetrachloride at 20°C. The vapor pressure of pure benzene at this temperature is 74.61 mmHg and its density is 0.87865 g/cm^3 the vapor pressure of pure carbon tetrachloride is 91.32 mmHg and its density is 1.5940 g/cm^3 . If this solution is ideal, its total vapor pressure at 20°C is

84.64 mmHg.

84.30 mmHg.

82.96 mmHg.

81.63 mmHg.

165.93 mmHg.

Answer 1

Favorite Answer

84.30 mmHg, answer 2.

According to Raoult's law, Ptot = Σ(μi*Pi), where μi is the "mole fraction" of substance i, or the ratio of moles of i divided by total moles, and Pi is substance i's vapor pressure.

Givens:

MW1 = 78, MW2 = 153.82

P1 = 74.61, P2 = 91.32

d1 = 0.87865, d2 = 1.594

Relative mole contributions:

relmol1 = 0.4*d1/MW1 = 4.50589743589744D-03

relmol2 = 0.6*d2/MW2 = 6.21765700169029D-03

Mole fractions:

μ1 = relmol1/(relmol1+relmol2) = 0.420186931685968

μ2 = relmol2/(relmol1+relmol2) = 0.579813068314032

Partial pressures:

PP1 = μ1P1 = 31.3501469730901 mmHg

PP2 = μ2P2 = 52.9485293984374 mmHg

Ptot is sum of partial pressures:

Ptot = PP1+PP2 = 84.2986763715275 mmHg

Source(s): http://en.wikipedia.org/wiki/Vapor_pressure#Mixtur...