Question

Polystyrene (PS) is essentially insoluble in water, but dissolves in toluene readily. We have a PS-toluene solution at 27 C that is 10.0% by mass PS, has a solution density of 878.76 kg/m3, and a measured PS molecular weight of 190,000. Pure toluene has a density of 860.52 kg/m3.  What is the specific gravity of the PS-toluene solution? What is the molarity of the PS-toluene solution?

Answer 1

specific gravity of the PS-toluene solution

= density of the PS-toluene solution/density of water

= 878.76 / 1000

= 0.87876

For 100 kg solution

Mass of PS = 10 kg

Molecular weight of PS = 190000 kg/kmol

Moles of PS = mass/molecular weight

= 10/190000

= 5.263 x 10^-5 kmol

Mass of toluene = 90 kg

Moles of toluene = 90/92.14 = 0.977 kmol

Mol fraction of PS, X1 = 5.386 x 10^-5

Mol fraction of toluene, X2 = 0.9999

Average molecular weight

M avg = X1 * M1 + X2 * M2

= 5.386 x 10^-5 x 190000 + 0.9999 x 92.14

= 102.28 kg/kmol

molarity of the PS-toluene solution

= (878.76 kg/m3)/(102.28 kg/kmol)

= 8.591 kmol/m3

= 8.591 mol/L

= 8.591 M