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.

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