A solution containing 27.55 mg of an unknown protein per 25.0 mL was found to have an osmotic pressure of 3.22 torr at 25 °C. What is the molar mass of the protein?

Verified step by step guidance

1. Convert the osmotic pressure from torr to atm using the conversion factor: 1 atm = 760 torr.
2. Use the osmotic pressure formula $\pi =iMRT$ where $\pi$ is the osmotic pressure in atm, $i$ is the van't Hoff factor (assumed to be 1 for non-electrolytes), $M$ is the molarity, $R$ is the ideal gas constant (0.0821 L·atm/mol·K), and $T$ is the temperature in Kelvin.
3. Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.
4. Rearrange the osmotic pressure formula to solve for molarity $M$: $M=\frac{\pi }{RT}$.
5. Calculate the molar mass of the protein using the formula: $\text{Molar Mass}=\frac{\text{mass of solute (g)}}{\text{moles of solute}}$, where moles of solute can be found from the molarity and volume of the solution.