Question

A protein subunit from an enzyme is part of a research study and needs to be characterized. A total of 0.145 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 the protein is 12982.8 g/mol.

Explanation:

The osmptic pressure is given by:

π=MRT

Where,

M: is molarity of the solution

R: the ideal gas constant (0.0821 L·atm/mol·K)

T: the temperature in kelvins

Hence, we look for molarity:

$0.138 atm=M(0.0821\frac{l*atm}{mol*K} )(28+273K)$

$M=\frac{0.138atm}{(0.0821\frac{l*atm}{mol*K} )(301K)}$= =5.584×10⁻³mol/l

As we have 2 ml of solution, we can get the moles quantity:

Moles of protein: 5.584×10⁻³$\frac{mol}{l}\frac{1l}{1000ml}$×2ml=1.117×10⁻⁵mol

Finally, the moles quantity is the division between the mass of the protein and the molar mass of the protein, so:

Moles=Mass/Molar mass

Molar mass= Mass/Moles=$\frac{0.145g}{1.117*10^{-5}mol}$=12982.8 g/mol