Question

The osmotic pressure exerted by a 0.487-g sample of the polymer polystyrene in 41.06 mL of benzene at 25 °C is capable of supporting a column of solution (d = 0.88 g/mL) 5.9 mm in height. What is the molar mass of the polystyrene? Report the answer in kiloDaltons (abbreviated kD or kDa), but without units, to the nearest integer kD. 1kD = 1000 g/mol.

Answer 1

Column Solution density , d = 0.88 g/mL

Column Height , h = 5.9 mm

we have, Hg*h_Hg* g = sol.*h_sol* g

h_Hg = sol.*h_{sol /} h_Hg = 0.88 g/mL * 5.9 mm / 13.6 g/mL = 0.38 mmHg

Osmotic pressure : = 0.38 mmHg / 760 mmHg/atm = 0.0005 atm

Osmotic pressure : = C*RT

C = /RT = 0.0005 atm / (0.082 L-atm/K-mol*298 K ) = 2.05*10^-5 mol/L

==> 0.487-g sample of the polymer polystyrene in 41.06 mL of benzene at 25 °C

Solution Volume : 41.06 mL

Thus moles of polystyrene in this solution : 2.05*10^-5 mol/L*0.04106 L = 8.5*10^-7 moles

Thus molar mass of polystyrene : 0.487 g /8.5*10^-7 mole = 570468 g/mol

or    570 kD.