An aqueous solution at 27°c contains 3.6 g of a protein in a 200 ml sample. the osmotic pressure is 0.0203 atm. what is the molar mass of the protein

In order to calculate the molar mass of the protein, we may manipulate the ideal gas equation:

PV = nRT, where n is the number of moles. We also know that:

n = m / Mr, where m is mass and Mr is molecular weight

Thus,

Mr = (mRT) / (PV)

Here, the mass is in grams, the temperature is in Kelvin, the pressure is in atm and the volume is in liters, so the molar gas constant is 0.082057.

Mr = (3.6 * 0.082057 * (27 + 273)) / (0.0203 * 0.2)

Mr = 21,828 g/mol

Thus, the Mr of the protein is 2.18 x 10⁴ g/mol