The vapour pressure of pure liquid solvent is 0.75 bar.When a nonvolatile solute is added to the solvent , the vapour pressure is reduced to 0.50 bar. The mole fraction of the solute is

To find the mole fraction of the solute when a nonvolatile solute is added to a pure solvent, we can use Raoult's Law. This law states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent. Let's break this down step by step.

Understanding the Problem

We know the following:

• The vapor pressure of the pure solvent (P₀) is 0.75 bar.
• The vapor pressure of the solution (P) after adding the solute is 0.50 bar.

Applying Raoult's Law

According to Raoult's Law, the relationship can be expressed as:

P = X_solvent * P₀

Where:

• P is the vapor pressure of the solution.
• X_solvent is the mole fraction of the solvent.
• P₀ is the vapor pressure of the pure solvent.

Calculating the Mole Fraction of the Solvent

We can rearrange the equation to find the mole fraction of the solvent:

X_solvent = P / P₀

Substituting the values we have:

X_solvent = 0.50 bar / 0.75 bar = 0.6667

Finding the Mole Fraction of the Solute

The mole fraction of the solute (X_solute) can be calculated using the relationship:

X_solute = 1 - X_solvent

Now, substituting the value we found:

X_solute = 1 - 0.6667 = 0.3333

Final Result

Thus, the mole fraction of the solute in the solution is approximately 0.3333. This means that for every part of the solute, there are about two parts of the solvent in the solution.

Real-World Application

This concept is crucial in various fields, including chemistry and engineering, especially when dealing with solutions and their properties. Understanding how solutes affect vapor pressure can help in processes like distillation, where separation of components based on their vapor pressures is essential.