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.
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
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