Vapour pressure of a solvent is 17.5 mm(Hg) while that of its dilute solution is 17.45. The mole fraction of the solvent is

To find the mole fraction of the solvent in a dilute solution, we can use Raoult's Law, which states that the vapor pressure of a solvent in a solution is equal to the vapor pressure of the pure solvent multiplied by its mole fraction in the solution. Let's break this down step by step.

Understanding the Given Values

We have the following information:

• Vapor pressure of the pure solvent (P_solvent) = 17.5 mmHg
• Vapor pressure of the dilute solution (P_solution) = 17.45 mmHg

Applying Raoult's Law

According to Raoult's Law, we can express the vapor pressure of the solution as:

P_solution = X_solvent × P_solvent

Where:

• X_solvent = mole fraction of the solvent
• P_solution = vapor pressure of the solution
• P_solvent = vapor pressure of the pure solvent

Rearranging the Equation

We can rearrange this equation to solve for the mole fraction of the solvent:

X_solvent = P_solution / P_solvent

Substituting the Values

Now, let's plug in the values we have:

X_solvent = 17.45 mmHg / 17.5 mmHg

Calculating the Mole Fraction

Performing the division gives us:

X_solvent = 0.9971 (approximately)

Interpreting the Result

This means that the mole fraction of the solvent in the dilute solution is about 0.9971. This indicates that the solution is indeed very dilute, as the mole fraction is very close to 1, suggesting that the majority of the solution is still composed of the solvent.

Final Thoughts

In summary, using Raoult's Law allows us to determine the mole fraction of a solvent in a dilute solution by comparing the vapor pressures of the pure solvent and the solution. In this case, the mole fraction of the solvent is approximately 0.9971, confirming that the solution is predominantly the solvent.