Question

A macromolecule is added at a concentration of 18 g L−1 to water at a temperature of 10°C. If the resulting osmotic pressure of this solution is found to be equal to 12 mmHg, estimate the molecular weight of the macromolecule in grams per mole

Answer 1

Answer: 26138g/mol

Explanation:

$\pi =CRT$

$\pi$ = osmotic pressure = 12 mmHg =$\frac{1}{760}\times 12=0.016$ atm     (760 mmHg= 1atm)

C= concentration in Molarity

R= solution constant  = 0.0821 Latm/Kmol

T= temperature = $10^0C=(10+273)K=283K$

For the given solution: 18 g of macromolecule is dissolved to make 1 L of solution.

$Molarity=\frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{volume of solution in ml}}$

$C=\frac{18\times 1000}{M\times 1000ml}=\frac{18}{M}$

$0.016=\frac{18}{M}\times 0.0821\times 283}$

$M=26138g/mol$

The molecular weight of the macromolecule in grams per mole is 26138.