A mixture of liquids \(A\) and \(B\) exhibits ideal behavior. At \(84^{\circ} \mathrm{C},\) the total vapor pressure of a solution containing 1.2 moles of \(A\) and 2,3 moles of \(B\) is 331 \(\mathrm{mmHg}\). Upon the addition of another mole of \(\mathrm{B}\) to the solution, the vapor pressure increases to 347 \(\mathrm{mmHg}\). Calculate the vapor pressures of pure \(\mathrm{A}\) and \(\mathrm{B}\) at \(84^{\circ} \mathrm{C}\)

Vapor pressure is an essential concept in understanding the behavior of liquids and solutions. It represents the pressure exerted by a vapor in equilibrium with its liquid or solid form at a given temperature. In the context of a closed system, vapor pressure is the point at which the rate of evaporation of a liquid equals the rate of condensation back into the liquid.

For instance, if we have a sealed container half-filled with water, the water molecules at the surface will escape into the air above as vapor. Over time, an equilibrium is reached where an equal number of molecules evaporate and condense, resulting in a constant vapor pressure.

Factors Affecting Vapor Pressure

Several factors influence this equilibrium and can alter the vapor pressure:

• Temperature: Increasing the temperature results in higher kinetic energy in the molecules, increasing the rate of evaporation, and thus the vapor pressure.
• Chemical Nature of the Liquid: Substances with weaker intermolecular forces generally have higher vapor pressures at the same temperature.

Understanding vapor pressure is crucial when studying distillation, evaporation, and other phase-transition phenomena. It also plays a pivotal role in Raoult's Law, which is used to calculate the pressures of mixtures.

Ideal solution behavior refers to a specific set of conditions and outcomes when different substances are mixed to form a solution. For a solution to be considered 'ideal', it must adhere to two primary criteria:

• It must show no change in enthalpy upon mixing – the process of combining the substances does not release or absorb heat.
• It must have the components mixed in such a way that their intermolecular forces (before and after mixing) are similar, meaning no significant change in the total volume of the solution.

In the realm of ideal solutions, Raoult's Law finds its most accurate application. According to this law, the partial vapor pressure of each component in an ideal solution is directly proportional to its mole fraction in the mixture. The law also implies that the total vapor pressure of the solution is the sum of the partial pressures of all components in the mixture.

This model helps us predict the behavior of each component in a mixture and the combined vapor pressure of the solution. However, it is important to note that many solutions do not exhibit ideal behavior, and various factors such as the difference in molecular size and intermolecular forces can lead to deviations.

Partial pressure is a cornerstone concept when dealing with gas mixtures. It is defined as the pressure that a single gas component in a mixture would exert if it occupied the entire volume of the container at the same temperature. In essence, it's a way of expressing how the total pressure of the mixture is divided among its various gaseous constituents.

The total pressure exerted by a gas mixture can be represented as the sum of its partial pressures. This principle is fundamental in Dalton's Law of Partial Pressures, which states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of individual gases. This also applies to the mixture of liquids, where Raoult's Law helps us calculate the partial pressure of each component based on its vapor pressure and mole fraction.

In the exercise provided, we use the concept of partial pressure to determine the vapor pressures of pure liquids from a mixture exhibiting ideal behavior. By applying Raoult's Law, we can calculate the individual contributions of each component to the total vapor pressure, ultimately understanding the properties of the substances within the solution.