Lysozyme is an enzyme that cleaves cell walls. A 0.100-L...

Lysozyme is an enzyme that cleaves cell walls. A 0.100-L sample of a solution of lysozyme that contains $0.0750 \mathrm{g}$ of the enzyme exhibits an osmotic pressure of $1.32 \times 10^{-3}$ atm at $25^{\circ} \mathrm{C}$. Assuming ideal solution behavior, what is the molar mass of lysozyme?

Key Concepts

Colligative Properties

Colligative properties are characteristics of solutions that depend on the number of solute particles present rather than on the solute’s identity. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure, and they are especially useful for determining molar masses of solutes in dilute solutions.

Ideal Solution Behavior

Ideal solution behavior assumes that the interactions between all components in the solution are similar to those in a pure solvent, meaning that the solution adheres strictly to the ideal gas or ideal mixing laws. This assumption simplifies calculations because it allows the use of equations like the van’t Hoff equation without corrections for solute-solute or solute-solvent interactions.

Molar Mass Determination

Molar mass determination involves calculating the mass of a solute per mole of particles present in a solution. By using colligative properties such as osmotic pressure within the framework of the van’t Hoff equation, one can deduce the number of moles of solute in a known mass, and thereby determine the molar mass through the relationship between mass, moles, and concentration.

Osmotic Pressure

Osmotic pressure is a colligative property of solutions that reflects the tendency of solvent molecules to pass through a semipermeable membrane from a region of lower solute concentration to a region of higher solute concentration. It is directly proportional to the molar concentration of solute particles in the solution and is commonly used to determine molecular weights of large molecules by measuring the pressure required to counteract the flow of solvent.

Van’t Hoff Equation

The Van’t Hoff equation relates osmotic pressure to solute concentration in an ideal solution through the relation ? = cRT, where ? is the osmotic pressure, c is the molar concentration of the solute, R is the gas constant, and T is the temperature in Kelvin. This equation is fundamental in connecting measurable properties of a solution to the number of solute particles present.

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