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.

Key Concepts

Osmotic Pressure

Osmotic pressure is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane. It is directly proportional to the concentration of solute particles in the solution and can be calculated using the formula π = iCRT, where π is the osmotic pressure, i is the van 't Hoff factor, C is the molarity of the solution, R is the ideal gas constant, and T is the temperature in Kelvin.

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in moles per liter (mol/L). To find the molarity of the protein solution, the mass of the protein must be converted to moles using its molar mass, which is the unknown in this problem.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It can be calculated by dividing the mass of the solute by the number of moles present in a given volume of solution. In this case, the molar mass of the protein can be determined by rearranging the osmotic pressure equation to solve for the molar mass after calculating the number of moles from the given mass and volume.