Question

A saturated solution is made by dissolving 0.327 g of a polypeptide (a substance formed by joining together in a chainlike fashion some number of amino acids) in water to give 1.70 L of solution. The solution has an osmotic pressure of 4.19 torr at 26 °C. What is the approximate molecular mass of the polypeptide?

Answer 1

Answer: The approximate molecular mass of the polypeptide is 856 g/mol

Explanation:

To calculate the concentration of solute, we use the equation for osmotic pressure, which is:

$\pi=iMRT$

Or,

$\pi=i\times \frac{\text{Mass of solute}}{\text{Molar mass of solute}\times \text{Volume of solution in L)}}\times RT$

where,

$\pi$ = osmotic pressure of the solution = 4.19 torr

i = Van't hoff factor = 1 (for non-electrolytes)

Mass of solute (polypeptide) = 0.327 g

Volume of solution = 1.70 L

R = Gas constant = $62.364\text{ L.torr }mol^{-1}K^{-1}$

T = temperature of the solution = $26^oC=[273+26]K=299K$

Putting values in above equation, we get:

$4.19torr=1\times \frac{0.327}{\text{Molar mass of solute}\times 1.70}\times 62.364\text{ L.mmHg }mol^{-1}K^{-1}\times 299K\\\\\text{molar mass of solute}=856g/mol$

Hence, the molar mass of the polypeptide is 856 g/mol