Question

Explain why the vapor pressure of a solvent is lowered by the presence of a nonvolatile solute.

Short answer

The vapor pressure of a solvent is lowered by a nonvolatile solute due to the solute reducing the number of solvent molecules able to vaporize.

Step-by-step solution

Understanding Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid form in a closed system. It is dependent on the temperature and the nature of the solvent, as well as the interaction between the solvent molecules in the liquid phase.

Effect of Nonvolatile Solute

When a nonvolatile solute is dissolved in a solvent, it does not vaporize. Its presence lowers the number of solvent molecules on the surface that can escape into the vapor phase, effectively decreasing the solvent's vapor pressure.

Raoult's Law Introduction

Raoult's Law states that the vapor pressure of a solvent in a solution is proportional to the mole fraction of the solvent. In other words, the more solute present, the lower the mole fraction of solvent, resulting in lower vapor pressure.

Entropic Explanation

The introduction of a nonvolatile solute leads to an increase in the entropy of the solution since there are more ways to arrange the solute and solvent molecules. This random distribution prevents some solvent molecules from escaping the liquid phase, thus decreasing vapor pressure.

Conclusion

Overall, the vapor pressure of a solvent is lowered by the presence of a nonvolatile solute because the solute decreases the number of solvent molecules available to escape into the vapor phase, as described by Raoult's Law.

Key concepts

Nonvolatile Solute

Imagine you're at a party, and everyone is trying to leave through a small door at the same time. The more people there, the harder it is to get outside quickly. In chemistry, a nonvolatile solute behaves similarly when dissolved in a solvent. It doesn't evaporate or "leave the party," if you will. Instead, it stays in the solution, creating fewer chances for the solvent molecules to escape into the vapor phase.
This is because nonvolatile solutes occupy space, reducing the number of solvent molecules at the surface of the liquid.

• They don't turn into gas easily or at all.
• They interfere with solvent molecules trying to evaporate.
• The result? A decrease in vapor pressure.

Raoult's Law

Raoult's Law offers a mathematical way to understand the relationship between the vapor pressure of a solution and the presence of a nonvolatile solute. It simply states that the vapor pressure of a solvent above a solution is directly proportional to the mole fraction of the solvent.
The law can be expressed with the equation:\[ P = P^0 X_s \]Where:

• \(P\) is the vapor pressure of the solvent in the solution.
• \(P^0\) is the vapor pressure of the pure solvent.
• \(X_s\) is the mole fraction of the solvent.

When a nonvolatile solute is added, the mole fraction \(X_s\) of the solvent is reduced, causing a proportional decrease in vapor pressure. Therefore, the more solute you add, the lower the vapor pressure becomes.
This principle assists scientists in predicting how adding different solutes affects a solvent's properties.

Entropy in Solutions

Entropy measures the randomness or disorder within a system. When a nonvolatile solute dissolves in a solvent, the system's entropy increases.
Let's break it down:

• Initially, the solvent molecules are quite orderly, similar to an organized dance of solvent pairs.
• Upon adding a solute, the orderly dance becomes chaotic, increasing the disorder in the solution.
• With greater entropy, it's more difficult for solvent molecules to line up at the surface and evaporate.

This heightened level of disorder means fewer solvent molecules break free to become vapor. Hence, the presence of a nonvolatile solute not only introduces new long-term interactions but also indirectly lowers the vapor pressure through increased entropy. Understanding entropy's role in solutions provides deeper insight into how solutes alter the physical properties of solvents.