Question

Northern cod produce proteins that protect their cells from damage caused by subzero temperatures. Measurements of the osmotic pressure for two "antifreeze" proteins at 18°C yielded the data listed below. Use this information to calculate the molar mass for each of the proteins. Assume these proteins are nonelectrolytes and use the value i = 1.
Required:
If a 54.1 mg sample of protein A in 1.5 mL of water has an osmotic pressure of 0.285 atm, what is the molar mass of protein A?

Answer 1

Answer: The molar mass of protein A is 3023.41 g/mol.

Explanation:

To calculate the osmotic pressure, we use the formula:

$\pi=i\times M\times R\times T$

              OR

$\pi=i\times \frac{\text{Given mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Volume of solution}}\times R\times T$      .....(1)

Where,

$\pi$ = osmotic pressure = 0.285 atm

i = 1

Given mass of protien (solute) = 54.1 mg = 0.0541 g        (Conversion factor: 1 g = 1000 mg)

Volume of solution = 1.5 mL

R = Gas constant = 0.0821 L.atm/mol.K

T = temperature = $18^oC=[18+273]=291K$

Plugging values in equation 1:

$0.285atm=1\times \frac{0.0541\times 1000}{\text{Molar mass of protein}\times 1.5}\times 0.0821L.atm/mol.K\times 291K\\\\\text{Molar mass of protein}=\frac{1\times 0.0541\times 1000\times 0.0821\times 291}{0.285\times 1.5}\\\\\text{Molar mass of protein}=3023.41g/mol$

Hence, the molar mass of protein A is 3023.41 g/mol.