Respuesta :
The question is incomplete, here is the complete question:
0.100 g of an unknown protein are dissolved in enough solvent to make 5.00mL of solution. The osmotic pressure of this solution is measured to be 0.0604atm at 25.0°C. Calculate the molar mass of the protein. Be sure your answer has the correct number of significant digits.
Answer: The molar mass of the protein is 8097.2 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 = 0.0604 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]0.0604atm=1\times c\times 0.0821\text{ L.atm }mol^{-1}K^{-1}\times 298K\\\\c=0.00247M[/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 = 0.00247 M
Given mass of protein = 0.100 g
Volume of solution = 5.00 mL
Putting values in above equation, we get:
[tex]0.00247M=\frac{0.100\times 1000}{\text{Molar mass of protein}\times 5}\\\\\text{Molar mass of protein}=\frac{0.100\times 1000}{0.00247\times 5}=8097.2g/mol[/tex]
Hence, the molar mass of the protein is 8097.2 g/mol
