Respuesta :
The question is incomplete, complete question is:
371 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 0.118 atm at 25°C .
Calculate the molar mass of the protein. Be sure your answer has the correct number of significant digits.
Answer:
The molar mass of unknown protein is 15,384.43 g/mol.
Explanation:
To calculate the molar mass of protein, we use the equation for osmotic pressure, which is:
[tex]\pi=icRT[/tex]
where,
[tex]\pi[/tex] = osmotic pressure of the solution = 0.118 atm
i = Van't hoff factor = 1 (for non-electrolytes)
c = concentration of solute = ?
R = Gas constant = [tex]0.0820\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]0.118 atm=1\times c\times 0.0821\text{ L.atm}mol^{-1}K^{-1}\times 298 K\\\\c=0.004823 mol/L[/tex]
[tex]concentration=\frac{Moles}{Volume (L)}[/tex]
[tex]0.004823 mol/L=\frac{n}{0.005 L}[/tex]
[tex]n=2.4115\times 10^{-5} mol[/tex]
To calculate the molecular mass of solute, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]
Moles of solute = [tex]2.4115\times 10^{-5} mol[/tex]
Given mass of solute = 371 mg = 0.371 g ( 1mg = 0.001 g)
Putting values in above equation, we get:
[tex]2.4115\times 10^{-5} mol=\frac{0.371 g}{\text{Molar mass of solute}}\\\\\text{Molar mass of solute}=15,384.43 g/mol[/tex]
Hence, the molar mass of unknown protein is 15,384.43 g/mol.
