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.