Exactly 375.0 mg of an unknown protein is dissolved in enough water to give 50.00 mL of solution and the osmotic pressure determined as 3.25 mmHg at 298 K.Estimate the molar mass of this protein.
A)42,900 g/mol
B)3,600 g/mol
C)56,400 g/mol
D)139,000 g/mol

Question

Quizplus · Accepted Answer

The molar mass of the protein can be calculated using the formula for osmotic pressure: $\pi = \frac{n}{V}RT$, where $\pi$ is the osmotic pressure, $n$ is the number of moles of solute, $V$ is the volume of the solution in liters, $R$ is the ideal gas constant (0.0821 L·atm/K·mol), and $T$ is the temperature in Kelvin. Rearranging the formula to solve for $n$, we get $n = \frac{\pi V}{RT}$. The mass of the protein (375.0 mg or 0.375 g) divided by the number of moles $n$ gives the molar mass. Given that $\pi = 3.25$ mmHg (which is 0.00426 atm by converting mmHg to atm using the conversion factor 1 atm = 760 mmHg), $V = 0.05$ L, and $T = 298$ K, substituting these values into the formula gives a molar mass close to 42,900 g/mol.