Question

An ideal liquid solution has two volatile components. In the vapor in equilibrium with the solution, the mole fractions of the components are (a) both \(0.50 ;\) (b) equal, but not necessarily \(0.50 ;\) (c) not very likely to be equal; (d) 1.00 for the solvent and 0.00 for the solute.

Short answer

For case (a) and (b), the components have same volatilities but may not have equal molar quantities. For case (c), the components have different volatilities and hence different mole fractions in the vapor phase. In case (d), only the solvent is volatile and contributes to the total vapor pressure, while the solute does not.

Step-by-step solution

Case (a)

In this case, both components are said to be equally represented in the vapor phase with a mole fraction of 0.5. This means that both components are equally volatile and will have the same contribution to the total vapor pressure according to Dalton's law.

Case (b)

Here, the mole fractions of the components are equal, but not necessarily 0.5. This indicates that while the components might not have equal molar quantities, they contribute equally to the vapor pressure due to their identical volatilities.

Case (c)

This scenario refers to a case where it's likely that the mole fractions of the components are not equal. This would occur if the volatilities of the components differ significantly. The more volatile component will have a larger mole fraction in the vapor phase.

Case (d)

In the last case, the mole fraction of the solvent is 1.00, and the mole fraction of the solute is 0.00 in the vapor phase. In this scenario, only the solvent is volatile and so the total vapor pressure is due to the solvent alone. The solute does not contribute because it is not volatile.

Key concepts

Volatile Components

In an ideal liquid solution, volatile components are substances that can readily evaporate. This means they move easily from the liquid state to the gas phase under given conditions.
Such components significantly affect the vapor pressure of the solution, which is a measure of the tendency of particles to escape from the liquid phase into the gas phase.
Each volatile component contributes to the solution's total vapor pressure depending on its mole fraction and inherent volatility.

• In case (a), both components are equally volatile, leading to the same mole fractions in the vapor phase.
• For case (b), even though the mole fractions of the components are equal, they don't have to be at 0.5. Yet, similar volatilities lead to an equal contribution in vapor pressure.
• Case (c) highlights that differences in volatility result in unequal mole fractions in the vapor phase.
• Finally, case (d) illustrates a scenario where only the solvent is volatile, meaning the solute doesn’t evaporate and thus has no contribution to vapor pressure.

Mole Fractions

Mole fractions are a way of expressing the concentration of components in a solution. They are calculated as the ratio of moles of a particular component to the total moles of all components in the solution.
This concept helps understand how different components in a solution contribute to properties like vapor pressure.
The mole fraction is particularly useful in understanding ideal solutions where each component's contribution to vapor pressure is directly proportional to its mole fraction.

• In case (a), both components having a mole fraction of 0.5 indicates they contribute equally to the vapor phase.
• Case (b) represents equal mole fractions in the vapor phase, not necessarily starting at 0.5, due to equal volatility.
• For case (c), unequal mole fractions in the vapor phase suggest varying volatilities.
• Case (d) illustrates a situation where a solute's mole fraction is zero due to its lack of volatility.

Dalton's Law

Dalton's Law of Partial Pressures states that in a mixture of non-reacting gases, each gas contributes to the total pressure of the mixture in proportion to its partial pressure.
This law directly connects to vapor pressure in solutions, where each volatile component contributes to the overall vapor pressure according to its mole fraction.
In our ideal liquid solution scenario, Dalton's Law helps explain how the combination of volatilized components leads to the overall pressure measured in the vapor phase.

• With case (a), both components contribute equally to the vapor pressure due to the identical mole fractions and volatility.
• In case (b), equal contributions to vapor pressure arise from the same mole fractions and volatilities despite not being initially equal in liquid phase.
• Case (c) emphasizes that higher partial pressure corresponds to the more volatile component, resulting in a larger mole fraction in the vapor phase.
• For case (d), only the solvent's partial pressure matters, as the solute is non-volatile.

Vapor Pressure

Vapor Pressure is the pressure exerted by vapor in thermodynamic equilibrium with its liquid phase at a given temperature in a closed system.
It represents a critical aspect of understanding solutions, especially those with volatile components, as each component's volatility affects the overall pressure.
Higher volatility means a component is more likely to convert to gas, increasing its contribution to the vapor pressure.

• In case (a), both components contribute equally to vapor pressure due to equal volatilities.
• Case (b) shows equal volatilities with unspecified initial mole fractions leading to equal contributions in vapor phase.
• Case (c) describes different contributions to vapor pressure based on varying volatilities between components.
• Case (d) showcases a scenario where only the volatile solvent determines the vapor pressure.