Question

A protein subunit from an enzyme is part of a research study and needs to be characterized. A total of 0.155 g of this subunit was dissolved in enough water to produce 2.00 mL of solution. At 28 ∘C the osmotic pressure produced by the solution was 0.138 atm. What is the molar mass of the protein?

Answer 1

Answer : The molar mass of protein is, $1.38\times 10^4g/mol$

Explanation :

Formula used :

$\pi =CRT\\\\\pi=\frac{w\times 1000}{M\times V}RT$

where,

$\pi$ = osmotic pressure  = 0.138 atm

C = concentration

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

T = temperature  = $28^oC=273+28=301K$

w = mass of protein subunit = 0.155 g

M = molar mass of protein subunit = ?

V = volume of solution  = 2.00 mL

Now put all the given values in the above formula, we get:

$\pi=\frac{w\times 1000}{M\times V}RT$

$0.138atm=\frac{0.155g\times 1000}{M\times 2.00ml}\times (0.0821L.atm/mole.K)\times (301K)$

$M=13878.17g/mol=1.38\times 10^4g/mol$

Therefore, the molar mass of protein is, $1.38\times 10^4g/mol$