Question

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 1

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

Step-by-step explanation:

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

`\pi=icRT`

where,

`\pi` = osmotic pressure of the solution = 0.0604 atm

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

c = molarity of solute = ?

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:

`0.0604atm=1* c* 0.0821\text{ L.atm }mol^(-1)K^(-1)* 298K\\\\c=0.00247M`

To calculate the molecular mass of solute, we use the equation used to calculate the molarity of solution:

`\text{Molarity of the solution}=\frac{\text{Mass of solute}* 1000}{\text{Molar mass of solute}* \text{Volume of solution (in mL)}}`

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:

`0.00247M=\frac{0.100* 1000}{\text{Molar mass of protein}* 5}\\\\\text{Molar mass of protein}=(0.100* 1000)/(0.00247* 5)=8097.2g/mol`

Hence, the molar mass of the protein is 8097.2 g/mol