Question

Pepsin is an enzyme involved in the process of digestion. Its molar mass is about \(3.50 \times 10^{4} \mathrm{~g} / \mathrm{mol}\). What is the osmotic pressure in \(\mathrm{mm} \mathrm{Hg}\) at \(30^{\circ} \mathrm{C}\) of a \(0.250-\mathrm{g}\) sample of pepsin in \(55.0 \mathrm{~mL}\) of an aqueous solution?

Short answer

Answer: The osmotic pressure of the pepsin solution at 30°C is 2.49 mm Hg.

Step-by-step solution

Convert the mass of pepsin to moles

Start by converting the given mass of pepsin (0.250 g) to moles using the molar mass of pepsin (3.50 x 10^4 g/mol): Number of moles (n) = (mass of pepsin) / (molar mass of pepsin) n = 0.250 g / (3.50 x 10^4 g/mol) = 7.14 × 10^(-6) mol

Calculate the molarity of the solution

Divide the moles of pepsin by the volume of the aqueous solution (55.0 mL) to obtain the molarity: Molarity (c) = (number of moles) / (volume in liters) c = (7.14 x 10^(-6) mol) / (0.055 L) = 1.30 x 10^(-4) mol/L

Convert the temperature to Kelvin

Add 273.15 to the given Celsius temperature (30°C) to convert it to Kelvin: Temperature (T) = 30°C + 273.15 = 303.15 K

Calculate the osmotic pressure

Using the osmotic pressure formula, we will now calculate the osmotic pressure (Π): Π = Molarity (c) × Gas constant (R) × Temperature (T) Π = (1.30 x 10^(-4) mol/L) × (62.36367 L mm Hg / K mol) × (303.15 K) Π = 2.49 mm Hg The osmotic pressure of the pepsin solution at 30°C is 2.49 mm Hg.

Key concepts

Molar Mass

Molar mass, often referred to as molecular weight, is a fundamental concept in chemistry that quantifies the weight of one mole of a substance. It is usually expressed in grams per mole (g/mol). This measurement is critical for converting between mass and moles, a common task in many chemistry problems, including the calculation of osmotic pressure.

Understanding molar mass allows us to determine how many moles are present in a given mass of substance. For instance, in the case of pepsin with a molar mass of about 35,000 g/mol, a 0.250-g sample is equivalent to approximately 7.14 x 10^-6 moles. This conversion is the first step to finding molarity, a piece of information necessary to find the osmotic pressure.

When improving exercises like the one with pepsin, emphasizing the significance of the molar mass in the context of the problem can foster a deeper understanding and highlight the importance of precision when weighing substances in the lab.

Enzyme Chemistry

Enzyme chemistry is a branch of biochemistry that focuses on the study of enzymes, which are biological catalysts accelerating biochemical reactions. Enzymes, like pepsin in the exercise, are crucial to various physiological processes, including digestion.

Each enzyme has a specific function, and pepsin, for example, breaks down proteins into peptides. This specificity is due to the unique three-dimensional structure of the enzyme, which provides the active site where the reaction takes place. While size (molar mass) is not usually critical to enzyme function, it is essential when studying enzymes in a controlled environment, such as calculating their effect on the osmotic pressure of a solution.

Including enzyme characteristics like function, specificity, and structure, can enhance a student's understanding when dealing with biochemical scenarios, offering a more comprehensive comprehension of how these biological molecules fit into the broader context of chemistry.

Colligative Properties

Colligative properties are physical properties of solutions that depend on the ratio of solute particles to solvent molecules, rather than the identity of the solute. Osmotic pressure is a crucial colligative property, especially in biological systems where it influences the movement of water across semi-permeable membranes.

Osmotic pressure is defined as the pressure required to prevent the flow of water into the solution through a semi-permeable membrane. It is determined by the molarity of the solution and can be calculated using the formula \[\Pi = cRT\], where \(\Pi\) denotes the osmotic pressure, \(c\) is the molarity, \(R\) is the gas constant, and \(T\) is the temperature in Kelvin.

When teaching about osmotic pressure, highlighting its role in maintaining cellular integrity and function can illustrate its importance in biology. Additionally, tying it back to the molar mass and the physical properties of enzymes provides students with a holistic view of how these concepts interact in biochemical solutions.