nsulin is a hormone responsible for the regulation of glucose levels in the blood. An aqueous solution of insulin has an osmotic pressure of \(2.5 \mathrm{~mm} \mathrm{Hg}\) at \(25^{\circ} \mathrm{C}\). It is prepared by dissolving \(0.100 \mathrm{~g}\) of insulin in enough water to make \(125 \mathrm{~mL}\) of solution. What is the molar mass of insulin?

Osmotic pressure is a fundamental concept in chemistry that deals with the pressure required to stop the flow of a solvent into a solution through a semipermeable membrane. This flow is due to the natural tendency of a system to balance concentrations on either side of the membrane, a process known as osmosis. When a solution is separated from a pure solvent by a membrane that only allows the solvent to pass through, the solvent naturally moves into the solution. The osmotic pressure \( \Pi \) can be quantified using a formula derived from the ideal gas law: \( \Pi = nRT/V \), where \( n \) is the number of moles of solute, \( R \) is the gas constant, \( T \) is temperature in Kelvin, and \( V \) is the volume of the solution in liters.

Understanding osmotic pressure is crucial for biological and chemical sciences, as it's involved in many physiological processes, such as the regulation of blood glucose levels by insulin. In laboratory settings, measuring the osmotic pressure of a solution can help determine the molar mass of an unknown solute, as illustrated in the exercise where we calculated the molar mass of insulin.

Colligative properties are the physical properties of solutions that depend on the number of particles (molecules or ions) present in the solution, rather than the identity of the solute particles. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.

For example, when a solute is dissolved in a solvent, the boiling point of the solution increases because the presence of solute particles interferes with the natural escape of solvent particles into the gas phase. Similarly, the freezing point of a solution is lower than that of the pure solvent because the solute disrupts the crystalline structure formation of the freezing solvent.

Osmotic pressure is also a colligative property and it’s used in the exercise to find the molar mass of insulin. This is because osmotic pressure is directly proportional to the number of solute particles, making it an invaluable tool for determining molecular quantities without needing to know the chemical identity of the solute.

The gas laws in chemistry describe the behavior of gases in relation to pressure, volume, and temperature. These laws are critical for understanding and predicting how gases will behave under different conditions. The ideal gas law, \( PV = nRT \), combines several simpler gas laws and relates the pressure (P), volume (V), moles of gas (n), temperature in Kelvin (T), and the universal gas constant (R).

In practice, the ideal gas law can be applied to situations where gases behave ideally, meaning there are no interactions between the gas particles and the volume of individual particles is negligible compared to the space the gas occupies. Although real gases do not always follow the ideal model perfectly, it provides a close approximation that is useful in many scenarios, including the calculation of osmotic pressure as shown in the molar mass determination of insulin.