The osmotic pressure of solutions of PVC in cyclohexanone at 300 K are plotted on the graph.
The molar mass of PVC is ____________ g mol⁻¹ (Nearest integer)
(Given : R = 0.083 L atm K⁻¹ mol⁻¹)

Solution

Chemistry ma’am · 4 steps

The graph hands you π/C directly, and van't Hoff says π/C is RT/M, so M is one division away.

1. Van't Hoff in grams. With C in g L⁻¹, the molar concentration is C/M, so π = C/MRT. Divide both sides by C to get π/C = RT/M.

   M = RT/(π / C)

2. Read the graph. The y-axis is π/C in atm/(g L⁻¹), and the quoted slope 6 × 10⁻⁴ is the value of π/C that you need. Take π/C = 6 × 10⁻⁴ atm L g⁻¹.
3. Put in numbers. RT = 0.083 × 300 = 24.9 L atm mol⁻¹. Then M = 24.9/(6 × 10⁻⁴) = 4.15 × 10⁴ g mol⁻¹.
4. So. The molar mass of PVC is 41500 g mol⁻¹.

The common slip: 138. Leaving out T and dividing only R by 6 × 10⁻⁴ gives 138, not 41500. The product RT must go on top.

The idea to keep. When concentration is given in g L⁻¹, write π = C/MRT. The ratio π/C is then RT/M, and that is how osmometry finds the large molar masses of polymers.

Answer from the NTA final answer key. Solution by PrepWiser.