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?

Osmotic pressure is a fundamental concept in chemistry and biology, particularly when studying solutions and their behaviors. It is defined as the pressure required to prevent the solvent's flow across a semipermeable membrane, which separates a solution from the pure solvent.

Consider a solution where the solvent is moving from a lower concentration region to a higher concentration region; osmotic pressure is what would need to be applied to stop this natural process. Essentially, it reflects a solution’s tendency to draw in water (or another solvent), and is influenced by factors such as the concentration of solute particles that cannot cross the membrane.

In the context of the exercise, understanding osmotic pressure is critical for calculating the molar mass of substances like lysozyme. It is used in the formula \(\Pi = MRT\), where \(\Pi\) represents the osmotic pressure, M is molarity of the solution, R is the ideal gas constant, and T is the temperature in Kelvin. This formula assumes that the solute does not dissociate or associate in the solution, hence the term 'non-electrolyte' is often associated with such substances.

Molarity is a measure of concentration in chemistry, representing the number of moles of solute per liter of solution. This value, often denoted as M, is a key component in various calculations involving chemical reactions, solutions, and their properties.

It's important to differentiate molarity from molality, another concentration measure, which is defined as moles of solute per kilogram of solvent. Being volume-based, molarity is temperature-dependent because liquid volumes change with temperature.

Students should note that when converting osmotic pressure into molarity, as seen in the provided exercise, the conversion facilitates the determination of how many moles of the solute—in this case, lysozyme—are present in a specific volume of solution. This step is crucial before progressing to calculate the molar mass of the solute. A solid grasp on molarity allows students to understand the stoichiometry of reactions in a solution and the solution’s colligative properties, such as osmotic pressure.

The lysozyme enzyme is an important protein that functions to protect the body by degrading bacterial cell walls, causing bacteria to lyse, or break apart. This natural defense mechanism is found in various bodily secretions like saliva and tears. Understanding proteins such as lysozyme is fundamental in biochemistry and molecular biology.

Lysozymes are a perfect example of a biomolecule that can be studied through their osmotic pressure in a solution. The enzyme itself is a high-molecular-weight substance, hence in the exercise, the calculated molar mass is quite large (around 13,300 g/mol). Such enzymes are typically non-electrolytic; they do not disassociate into ions in solution, a factor that simplifies the calculation of their molar mass through osmotic pressure data.

The application of the molar mass calculation to biochemically relevant substances like lysozyme bridges the gap between theoretical chemistry and practical biological phenomena. This underscores the essential nature of understanding these concepts and their interrelatedness in the real world.