An aqueous solution at 27^$\circ$C contains 3.60 g of a protein in a 200. mL sample. The osmotic pressure is 0.0203 atm. What is the molar mass of the protein?

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 solution in liters, $R$ is the gas constant (0.0821 L·atm/(K·mol)), and $T$ is the temperature in Kelvin. First, convert the temperature to Kelvin (273.15 + 10 = 283.15 K) and the volume to liters (200 mL = 0.200 L). The number of moles $n$ can be found by rearranging the formula to $n = \pi V / RT$. Substituting the given values, $n = (0.0203 atm \times 0.200 L) / (0.0821 L·atm/(K·mol) \times 283.15 K)$. The molar mass (M) is then the mass of the protein divided by the number of moles calculated. Given the mass of the protein is 3.60 g, the calculation will yield a molar mass in the range of $10^4$ g/mol, matching option E.

An Aqueous Solution at 27 ∘\circ∘ C Contains 3

An Aqueous Solution at 27^$\circ$C Contains 3