Question

Osmotic pressure of a solution containing 1g protein in 100ml solution at 300K is 1.66 bar. What is the molecular weight of protein?

Answer 1

Answer: The molecular weight of protein is 150.18 g/mol.

Explanation:

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

$\pi=iMRT$

or,

$\pi=i\times \frac{m_{solute}\times 1000}{M_{solute}\times V_{solution}\text{ (in mL)}}}\times RT$

where,

$\pi$ = osmotic pressure of the solution = 1.66 bar

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

$m_{solute}$ = mass of protein = 1 g

$M_{solute}$ = molar mass of protein = ?

$V_{solution}$ = Volume of solution = 100 mL

R = Gas constant = $0.0831\text{ L bar }mol^{-1}K^{-1}$

T = temperature of the solution = 300 K

Putting values in above equation, we get:

$1.66bar=1\times \frac{1g\times 1000}{M\times 100}\times 0.0831\text{ L. bar }mol^{-1}K^{-1}\times 300K\\\\M=150.18g/mol$

Hence, the molecular weight of protein is 150.18 g/mol.