A 226 mL solution containing 22 g of a protein in toluene has an osmotic pressure of 0.053 atm at 27 oC. What is the molar mass (in g/mol) of the protein

4.4 * 10⁴ g/mol

Explanation:

The osmotic pressure (π) is a colligative property that can be calculated using the following expression.

π = M * R * T

where,

M: molarity

R: ideal gas constant

T: absolute temperature (27°C + 273.15 = 300 K)

Let's use it to find the molarity of the protein.

M = π / R * T

M = 0.053 atm / (0.082 atm. L/mol. K) * 300 K

M = 2.2 * 10⁻³ M

The molarity of the protein is:

M = mass of the protein / molar mass of the protein * liters of solution

molar mass of the protein = mass of the protein / M * liters of solution

molar mass of the protein = 22 g / 2.2 * 10⁻³ mol/L * 0.226 L

molar mass of the protein = 4.4 * 10⁴ g/mol