A liquid mixture of ' \(\mathrm{A}\) ' and 'B' (assume ideal solution) is placed in a cylinder and piston arrangement. The piston is slowly pulled out isothermally so that the volume of liquid decreases and that of the vapour increases. At the instant when the quantity of the liquid still remaining is negligibly small, the mole fraction of 'A' in the vapour is \(0.4\). If \(P_{\mathrm{A}}^{\circ}=0.4 \mathrm{~atm}\), \(P_{\mathrm{B}}^{\circ}=1.2 \mathrm{~atm}\) at this temperature, the total pressure at which the liquid has almost evaporated, is (a) \(0.667\) atm (b) \(1.5 \mathrm{~atm}\) (c) \(0.8 \mathrm{~atm}\) (d) \(0.545 \mathrm{~atm}\)

When we talk about an ideal solution, we are referring to a specific type of mixture where the interactions between the different types of molecules are the same as the interactions between molecules of the same kind. In essence, the mixing is perfect, and there are no changes in energy when the pure substances are mixed to form the solution. This concept is crucial in chemistry because it provides a simplified model that allows us to describe and predict the behavior of the solution.

For example, when a liquid mixture described as an ideal solution is vaporized, it obeys Raoult's Law. This law provides a link between the composition of the liquid and the resultant vapor pressures of its components when they are in equilibrium. In practice, an ideal solution is often an oversimplification, but it is useful for calculations because it simplifies the complex interactions in real solutions.

The concept of partial pressure is used to understand the contribution of each gas in a mixture of gases, such as the vapor above a liquid in a closed system. The partial pressure of a gas is the pressure it would exert if it were the only gas present in the entire volume of the mixture. According to Dalton's Law of partial pressures, the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases.

This is important in the context of Raoult's Law, which allows us to calculate the partial pressure of a component in an ideal solution. By multiplying the mole fraction of the component in the liquid phase by the vapor pressure of that pure component, we can determine its partial pressure in the vapor phase.

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. Vapor pressure is an intrinsic property of a substance, and it is dependent on temperature. Substances with high vapor pressure at normal temperatures are often referred to as volatile.

The vapor pressure of a pure substance is a key factor when using Raoult's Law to determine the partial pressures of components in an ideal solution. It represents the maximum pressure exerted by the vapor of a component when its molecules are escaping from the liquid phase into the vapor phase at a rate equal to the rate they are returning to the liquid.

The mole fraction is a way of expressing the concentration of a component in a mixture. It is defined as the ratio of the number of moles of the component to the total number of moles of all components in the mixture. Since it is a ratio, it has no units, and it can also be thought of as the fraction of molecules of a particular substance within the total mole count.

In the context of Raoult's Law, the mole fraction is used to predict the partial pressures of each substance in an ideal solution. The mole fraction in the vapor phase can be different from the liquid phase, but Raoult's Law establishes the relationship between the mole fraction in the liquid phase and the corresponding partial pressure in the vapor phase.