Lysozyme is an enzyme that breaks bacterial cell walls. A...

Lysozyme is an enzyme that breaks bacterial cell walls. A solution containing $0.150 \mathrm{~g}$ of this enzyme in $210 \mathrm{~mL}$ of solution has an osmotic pressure of 0.953 torr at $25^{\circ} \mathrm{C}$. What is the molar mass of lysozyme?

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Key Concepts

Osmotic Pressure

Osmotic pressure is a colligative property that depends on the concentration of solute particles in a solution. It is the pressure required to stop the net flow of solvent molecules through a semipermeable membrane from a region of low solute concentration to high solute concentration. Its measurement can provide valuable information about the concentration and size of solute molecules in solution.

Van’t Hoff Equation

The Van’t Hoff equation, ? = iMRT, relates osmotic pressure (?) to the molarity (M) of the solute, where i is the van’t Hoff factor, R is the ideal gas constant, and T is the absolute temperature. This equation is fundamental in using osmotic pressure measurements to calculate molar masses, particularly for large molecules like proteins that typically do not dissociate.

Molar Mass Determination Using Colligative Properties

Determining the molar mass of a solute from colligative properties involves measuring a property that is dependent on the number of particles present in a solution rather than their identity. By measuring the osmotic pressure of a solution and applying the Van't Hoff equation, one can calculate the moles of solute present in a given volume, and thereby determine the molar mass when the mass of solute is known.

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