Answer: The molar mass of the protein is 244678.2 g/mol
Explanation:
To calculate the concentration of solute, we use the equation for osmotic pressure, which is:
[tex]\pi=icRT[/tex]
where,
[tex]\pi[/tex] = osmotic pressure of the solution = 0.001 atm
i = Van't hoff factor = 1 (for non-electrolytes)
c = molarity of solute = ?
R = Gas constant = [tex]0.0821\text{ L atm }mol^{-1}K^{-1}[/tex]
T = temperature of the solution = [tex]25^oC=[273+25]=298K[/tex]
Putting values in above equation, we get:
[tex]0.001atm=1\times c\times 0.0821\text{ L.atm }mol^{-1}K^{-1}\times 298K\\\\c=\frac{0.001}{1\times 0.0821\times 298}=4.087\times 10^{-5}M[/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 = [tex]4.087\times 10^{-5}M[/tex]
Given mass of protein = 1.0 grams
Volume of solution = 5.00 mL
Putting values in above equation, we get:
[tex]4.087\times 10^{-5}M=\frac{1.0\times 1000}{\text{Molar mass of protein}\times 100}\\\\\text{Molar mass of protein}=\frac{1\times 1000}{4.087\times 10^{-5}\times 100}=244678.2g/mol[/tex]
Hence, the molar mass of the protein is 244678.2 g/mol
