Question

A 249−mL benzene solution containing 2.35 g of an organic polymer has an osmotic pressure of 7.91 mm Hg at 19°C. Calculate the molar mass of the polymer.

Answer 1

We Have

Osmotic Pressure P = 7.91 mm Hg = 7.91/760 = 0.0104 atm

Temperature T = 19⁰ C = 19 + 273 = 292 K

Volume = 249 mL = 0.249 L

mass of polymer = 2.35 g

R = Ideal Gas Constant = 0.082057 L atm mol^-1 K^-1

C = Molar Concentration = ?

So We know the formula

Osmotic Pressure = CRT

So

0.0104 atm = C 0.082057 L atm mol^-1 K^-1  292 K

C = 0.0104 atm/ 23.96 atm mol^-1 = 4.34 10^-4 M

Now Lets Calculate the number of moles by given volume

Moles of Polymer = 4.34 10^-4 M   0.249 L = 1.08   10^-4 mol

From this we can get Molar mass now

Molar mass of Polymer = mass of polymer / moles of Polymer = 2.35 g / 1.08   10^-4 mol

= 2.17   10⁴ g/mol

So Our Answer is = 2.17 10⁴ g/mol