A sample of an unknown polymer weighing 0.0150 g is dissolved in 30.0 mL of water at 298 K. The osmotic pressure of the resulting solution is 0.142 atm. Assuming the solution behaves ideally, calculate the molar mass of the polymer.

hard 3 marks Class 12 · Chemistry · Solutions

Answer

86 g mol

^{- 1}

The correct answer is 86 g mol $^{- 1}$ — Step 4: Calculate molar mass $M = mass / n = 0.0150 g /0.000174 mol = 86 g mol^{- 1}$ .

Step-by-step solution

Step 1: Convert the volume of water to mass and then to kilograms: $30.0 mL = 30.0 g = 0.030 kg$ of solvent.
Step 2: Use the relation $P i = m R T$ to find the molality $m$ of the solution: $m = P i / (R T) = 0.142/ (0.082057 \times 298) = 0.00581 mol kg^{- 1}$ .
Step 3: Compute the number of moles of polymer: $n = m \times kg_{solvent} = 0.00581 \times 0.030 = 0.000174 mol$ .
Step 4: Calculate molar mass $M = mass / n = 0.0150 g /0.000174 mol = 86 g mol^{- 1}$ .

Common mistake: Using molarity instead of molality in the osmotic pressure formula

Concept tested: Osmotic pressure and molar mass