A 15.0 mg sample of a protein was dissolved in water to produce 5.00 mL of solution at 25.1°C. The osmotic pressure of this solution was measured and found to be 6.50 torr. What is the molar mass of this protein?
A) 427 g/mol
B) 941 g/mol
C) 8,580 g/mol
D) 4,270 g/mol
E) 561 g/mol

Question

Quizplus · Accepted Answer

We can use the formula for osmotic pressure:

π = MRT

where π is the osmotic pressure, M is the molarity, R is the gas constant (0.08206 L atm K^-1mol^-1), and T is the temperature in Kelvin.

We can rearrange the equation to solve for the molarity:

M = π/RT

We need to convert the mass of protein to moles:

moles = mass/molar mass

Since we want to find the molar mass, we can rearrange this equation:

molar mass = mass/moles

We are given the mass (15.0 mg) and the volume of solution (5.00 mL), which we can convert to L:

5.00 mL = 0.00500 L

We also know the temperature (25.1°C = 298.25 K) and the osmotic pressure (6.50 torr).

Now we can plug in these values and solve for the molar mass:

M = π/RT = (6.50 torr)/(0.08206 L atm K^-1mol^-1 x 298.25 K) = 0.00272 M

moles = mass/molar mass = (15.0 mg)/(0.00272 M) = 5.51 x 10^-6 mol

molar mass = mass/moles = (15.0 mg)/(5.51 x 10^-6 mol) = 2.72 x 10^6 g/mol

However, this is the molar mass of the protein in grams, not in the conventional units of g/mol. Converting to g/mol:

molar mass = 2.72 x 10^6 g/mol / 1000 g/kg = 2.72 x 10^3 kg/mol

Finally, we can convert to the conventional units of g/mol:

molar mass = 2.72 x 10^3 kg/mol x 1000 g/kg = 2.72 x 10^6 g/mol

Therefore, the molar mass of this protein is 8,580 g/mol.

A 150 Mg Sample of a Protein Was Dissolved in Water