Lysozyme is an enzyme that breaks bacterial cell walls. A solution containing 0.150 g of this enzyme in 210 mL of solution has an osmotic pressure of 0.953 torr at 25 °C. What is the molar mass of lysozyme?

Verified step by step guidance

1. Identify the formula for osmotic pressure: \( \Pi = iMRT \), where \( \Pi \) is the osmotic pressure, \( i \) is the van't Hoff factor (which is 1 for non-electrolytes like lysozyme), \( M \) is the molarity, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.
2. Convert the given osmotic pressure from torr to atm: \( 0.953 \text{ torr} \times \frac{1 \text{ atm}}{760 \text{ torr}} \).
3. Convert the temperature from Celsius to Kelvin: \( T = 25 + 273.15 \).
4. Rearrange the osmotic pressure formula to solve for molarity \( M \): \( M = \frac{\Pi}{RT} \).
5. Calculate the molar mass of lysozyme using the formula: \( \text{Molar mass} = \frac{\text{mass of solute (g)}}{\text{moles of solute}} \), where moles of solute can be found from \( M \times \text{volume of solution in liters} \).

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 related 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.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It can be determined by dividing the mass of the substance by the number of moles present. In the context of the question, calculating the molar mass of lysozyme involves using the osmotic pressure to find the number of moles in the solution and then relating that to the mass of the enzyme.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. Although it primarily applies to gases, it can be adapted for solutions in terms of osmotic pressure. Understanding this law is essential for converting osmotic pressure into molarity, which is necessary for calculating the molar mass of lysozyme in the given scenario.