Calculate the vapor pressure of a solution containing 24.5 g of glycerin(C3H8O3) in 135 mL of water at 30.0 C. The vapor pressure of pure water at this temperature is 31.8 torr. Assume that glycerin is not volatile and dissolves molecularly (that is, it is not ionic), and use a density of 1.00 g>mL for the water.

When it comes to understanding the behavior of solutions, Raoult's Law is a fundamental concept in chemistry. It's especially important when we want to calculate the vapor pressure of a solution. Simply put, Raoult's Law states that the vapor pressure of an ideal solution is directly proportional to the mole fraction of the solvent in the solution. This can be mathematically expressed as:

\( P_{solution} = X_{solvent} \cdot P^{\circ}_{solvent} \)

where \( P_{solution} \) is the vapor pressure of the solution, \( X_{solvent} \) is the mole fraction of the solvent, and \( P^{\circ}_{solvent} \) is the vapor pressure of the pure solvent. To apply Raoult's Law in a calculation, it's important to note that the substance must be a non-volatile solute like glycerin in our exercise. This is essential because non-volatile substances do not contribute to the vapor pressure of the solution, meaning they won't escape into the gas phase readily.

Molarity, denoted by \( M \) and also known as molar concentration, is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution. The formula to calculate molarity is:

\( M = \frac{moles \ of \ solute}{liters \ of \ solution} \)

Molarity is a critical concept in solution chemistry as it allows chemists to quantitatively describe how concentrated a solution is. In our textbook example, calculating the molarity of glycerin is a crucial step before applying Raoult’s Law because we need to find the mole fraction of the solvent (water), and to do that, we must know the amount of solute (glycerin) in moles.

At the heart of solution chemistry is the study of how substances dissolve and interact in a solvent to form a solution. Solutions are homogeneous mixtures consisting of two or more substances. The solvent is typically the substance present in greater amount, while the solutes are present in lesser amounts. In the context of our glycerin and water mixture, water acts as the solvent and glycerin is the solute.

Properties of Solutions

Key properties to consider include concentration, as discussed in molarity, and how the solute and solvent interact at a molecular level. It is these interactions that determine the behavior of the solution in terms of boiling point elevation, freezing point depression, and vapor pressure lowering, which are all colligative properties. Calculating these requires precise understanding and application of concepts like mole fractions and Raoult's Law.

Colligative properties are properties of solutions that depend on the ratio of the number of solute particles to the number of solvent molecules in a solution, and not on the type of chemical species present. An interesting aspect of colligative properties is that they are universal for all solvents, given equal concentration of solute particles.

The colligative properties include:

• Vapor Pressure Lowering
• Boiling Point Elevation
• Freezing Point Depression
• Osmotic Pressure

In our example with the glycerin-water solution, when Raoult's Law is applied, the vapor pressure lowering can be observed. This is because the addition of a non-volatile solute (glycerin) leads to a decrease in the vapor pressure of the solvent (water) due to the reduction in the mole fraction of the solvent in the solution. Understanding how colligative properties work is crucial in various scientific and industrial processes, including the one described in our exercise.