To determine the molar mass of a protein, a 0.891 g sample of it is added to 5.00 g of water and the osmotic pressure is measured as 0.179 atm at 22.0°C, what is the molar mas of the protein? (The protein is non-ionizing)

MW = 24,097 g/mol

Explanation:

The osmotic pressure of a solution is given by the equation:

πV = nRT

where π is the osmotic pressure, V is the volume, R is the gas constant 0.08205 Latm/kmol, and T is the temperature.

n, the number of moles is equal to m/MW, substituting into the equation:

πV = (mass/MW) RT

MW = mass x R x T / (πV)

V is given by the density of solution assumed to be that of water:

d = m/v ⇒ v = m/d = 5.00 g / 1 g/mL = 5.00 mL

The volume we need to convert to liters for units consistency in the metric system:

5.00 mL x 1 L / 1000 mL = 5 x 10⁻³ L

solving for

MW = 0.891 g x 0.08205 Latm/Kmol x (22 + 273) K / (0.179 atm x 5 x 10⁻³ L)

= 24,097 g/mol