Answer :
Answer: The molar mass of the protein is 13392.86 g/mol
Explanation:
To calculate the concentration of solute, we use the equation for osmotic pressure, which is:
[tex]\pi=iMRT[/tex]
where,
[tex]\pi[/tex] = osmotic pressure of the solution = 0.138 atm
i = Van't hoff factor = 1 (for non-electrolytes)
M = molarity of solute = ?
R = Gas constant = [tex]0.0820\text{ L atm }mol^{-1}K^{-1}[/tex]
T = temperature of the solution = [tex]28^oC=[273+28]=301K[/tex]
Putting values in above equation, we get:
[tex]0.138atm=1\times M\times 0.0820\text{ L.atm }mol^{-1}K^{-1}\times 301K\\\\c=0.0056M[/tex]
To calculate the molecular mass of solute, we use the equation used to calculate the molarity of solution:
[tex]\text{Molarity of the solution}=\frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Volume of solution (in mL)}}[/tex]
We are given:
Molarity of solution = 0.0056 M
Given mass of protein = 0.150 g
Volume of solution = 2 mL
Putting values in above equation, we get:
[tex]0.0056M=\frac{0.150\times 1000}{\text{Molar mass of protein}\times 2}\\\\\text{Molar mass of protein}=13392.86g/mol[/tex]
Hence, the molar mass of the protein is 13392.86 g/mol