Question

What is the effect of a nonvolatile solute on the vapor pressure of a liquid? Why is the vapor pressure of a solution different from the vapor pressure of the pure liquid solvent?

Short answer

The presence of a nonvolatile solute decreases the vapor pressure of the solution compared to the pure solvent due to a reduction in the mole fraction of the solvent.

Step-by-step solution

Understanding Raoult's Law

Raoult's Law states that the vapor pressure of a solvent above a solution is equal to the vapor pressure of the pure solvent times the mole fraction of the solvent in the solution. Mathematically, it can be expressed as: \( P_{solution} = \text{X}_{solvent} * P^0_{solvent} \), where \( P_{solution} \) is the vapor pressure of the solution, \( \text{X}_{solvent} \) is the mole fraction of the solvent, and \( P^0_{solvent} \) is the vapor pressure of the pure solvent.

Explaining the Effect of a Nonvolatile Solute

The presence of a nonvolatile solute lowers the mole fraction of the solvent due to the addition of solute particles. This in turn lowers the vapor pressure of the solution, as the product of mole fraction of solvent and vapor pressure of pure solvent (Raoult’s Law) will decrease. Since the nonvolatile solute does not contribute to the vapor pressure, only the solvent particles evaporate.

Comparing Vapor Pressure of Solution and Pure Solvent

The vapor pressure of the solution is lower than that of the pure solvent because the introduction of solute particles decreases the number of solvent molecules on the surface. This results in fewer solvent molecules escaping into the vapor phase, thus lowering the vapor pressure.

Key concepts

Vapor Pressure

Vapor pressure is a measure of a liquid's tendency to evaporate into a gaseous state. When a liquid is in a closed container, molecules at the surface escape into the air space above, creating pressure as they collide with the container's walls. This phenomenon establishes an equilibrium where an equal amount of molecules are evaporating as there are condensing, which results in a constant pressure known as the vapor pressure.

To understand this better, imagine a pot of water boiling on a stove. Before it reaches the boiling point, some of the water molecules at the surface have enough energy to escape as vapor. The warmer the liquid, the more molecules have the necessary energy to escape, thus increasing the vapor pressure. As the temperature rises, eventually the vapor pressure equals the atmospheric pressure and boiling occurs, allowing the molecules within the bulk of the liquid to also escape into the gas phase.

Nonvolatile Solute

Adding a nonvolatile solute to a solvent creates a solution that behaves differently than the pure solvent. A nonvolatile substance does not readily evaporate, meaning it has little to no vapor pressure at the same temperature as the volatile solvent. When dissolved, it affects the properties of the solvent, one of which is vapor pressure.

For example, when table salt (a nonvolatile solute) is dissolved in water (the solvent), the salt remains in the liquid phase even as the water evaporates. Because the salt molecules do not vaporize alongside the water molecules, they interrupt the process of evaporation by occupying space at the liquid surface, preventing some of the water molecules from escaping. This results in a decrease in the overall vapor pressure of the solution compared to the pure water.

Mole Fraction

Mole fraction is a way to express the concentration of a component in a mixture. It is defined as the number of moles of a particular substance divided by the total number of moles of all substances present, including itself.

If you consider a simple solution consisting of a solvent and a solute, the mole fraction of the solvent is calculated by dividing the number of moles of the solvent by the sum of the moles of both the solvent and the solute. This is an important concept when applying Raoult's Law as it helps us understand how the presence of a solute affects the properties of the solvent. The higher the amount of solute in a given amount of solvent, the lower the mole fraction of the solvent, which directly affects the vapor pressure of the solution.

Colligative Properties

Colligative properties are characteristics of solutions that depend on the ratio of the number of solute particles to solvent molecules, not on the nature of the chemical species present. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.

As demonstrated by Raoult's Law, the addition of a nonvolatile solute to a solvent leads to a lower vapor pressure compared to the pure solvent. This is a colligative property because it depends solely on the number of solute molecules present, not their identity. The reduced vapor pressure also influences the boiling and freezing points of the solution; the boiling point becomes higher and the freezing point becomes lower than that of the pure solvent. The impact of a nonvolatile solute on these physical properties is a key concept in understanding solutions and their behaviors.