Question

When 0.873 grams of a protein were dissolved in 48.6 mL of solution at 15.6 degrees C, the osmotic pressure was found to be 0.061 atm. Calculate the molar mass of the protein.

Answer 1

Answer:

697 g / mol

Explanation:

The osmotic pressure of a protein ( non electrolyte ) is given by:

π V= nRT where  V is the volume, n is the number of moles, R is the gas constant ( 0.08206 L·atm/Kmol ), and T is the temperature (K).

n= mass/ MW protein ⇒ MW protein = mass / n

Thus,

π V = ( mass/ MW ) RT

MW = mass x R xT/ ( π V )

mass = 0.873 g

R = 0.08206 L·atm/K·mol

T = ( 15.6 + 273 ) K= 288.6 K

π  = 0.061 atm

V = 48.6 mL = 48.6 mL x ( 1 L/ 1000 mL ) = 0.0486 L

We just need to plug our values into the aqbove equation for MW:

MW = 0.873 g x 0.08205 L· atm /K·mol x 288.6 K / ( 0.061 atm x0.0486 L )

       = 697 g/mol