Question

A 275−mL benzene solution containing 2.13 g of an organic polymer has an osmotic pressure of 7.77 mm Hg at 21°C. Calculate the molar mass of the polymer. g/mol

Answer 1

osmotic pressure π= MRT

Where, M = Molarity; R = Universal Gas Constant; T = Temperature In Kelvins

We have , π = (7.77 mm Hg)x (1atm /760 mmHg)=0.01022 atm
T = 21 + 273 =294 K

R = 0.08206 atm/mol.K

Therefore, osmotic pressure π= MRT

0.01022 atm = M x (0.08206 atm/mol.K) x 294 K

M = 0.000424 moles/L

No. Moles of Polymer = Molarity x Volume in L

                                                = (0.000424 moles/L) x (0.275 L )

                                                = 0.000117 moles

Molar Mass of Polymer = grams of polymer/No. moles of polymer

                                                = 2.13 g/0.000117 moles

                                                = 18205 g/mol

Molar mass of polymer = 18205 g/mol = 1.8 x 10⁴ g/mol