Question

428. mg of an unknown protein are dissolved in enough solvent to make of solution. The osmotic pressure of this solution is measured to be at . Calculate the molar mass of the protein. Round your answer to significant digits.

Answer 1

The question is incomplete, here is the complete question:

428. mg of an unknown protein are dissolved in enough solvent to make 5.00 mL of solution. The osmotic pressure of this solution is measured to be 0.0766 atm at 25.0°C. Calculate the molar mass of the protein. Round your answer to 3 significant digits

Answer: The molar mass of protein is $27.3\times 10^3g/mol$

Explanation:

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

$\pi=iMRT$

Or,

$\pi=i\times \frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Volume of solution (in mL)}}\times RT$

where,

$\pi$ = osmotic pressure of the solution = 0.0766 atm

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

Mass of solute (protein) = 428 mg = 0.428 g   (Conversion factor: 1 g = 1000 mg)

Volume of solution = 5.00 mL

R = Gas constant = $0.0821\text{ L.atm }mol^{-1}K^{-1}$

T = temperature of the solution = $25^oC=[273+25]=298K$

Putting values in above equation, we get:

$0.0766=1\times \frac{0.428\times 1000}{\text{Molar mass of protein}\times 5}\times 0.0821\text{ L. atm }mol^{-1}K^{-1}\times 298K\\\\\text{Molar mass of protein}=\frac{1\times 0.428\times 1000\times 0.0821\times 298}{0.0766\times 5}=27340.4g/mol=27.3\times 10^3g/mol$

Hence, the molar mass of protein is $27.3\times 10^3g/mol$