Question

At 25°C, a saturated solution of pyrene in hexane is reported in the literature to contain a mole fraction of 0.0104 pyrene and 0.9896 hexane. The density of liquid hexane at this temperature is 0.659 g/mL. What mass of pyrene is required to make 5 mL of a saturated solution in hexane? If this mass were in the form of a cubic crystal, what would be the length of each side of the cube? The density of crystalline pyrene is 1.27 g/cm3 . If you add a crystal of pyrene to hexane that is ten times arger (in mass) than what you calculated above, what will be mole fraction of pyrene in the saturated solution?

Answer 1

Hexane and pyrene are ideal solutions

The density of liquid hexane at 25^OC temperature is 0.659 g/mL

The mass of hexane is 3.295gms

According to mole fraction

The function of the densities of ideal solutions and their volume participation, it is given as:

Total density=(mass of hexane(x)+mass of pyrene(1-x)).V

0.659+0.27=(3.259+1-x)5

the mass of pyrene is 3.33gms

the pyrene is in the form of FCC face centred cubic structure the effectiveness of FCC in a cubic structure is 33%.so it is FCC comparing the efficiency and mass.

mole fraction of pyrene in the saturated solution when you added a crystal of pyrene to hexane that is ten times larger (in mass) is

ρ =Σ χ i ρi

where ρ is the density of pyrene

X is the Mole fraction to be calculated

ρi is the mass of pyrene calculated above which is multiplied 10 times below because of condition

1.27=X*10(3.33)

X=1.27/33.3

X=0.038