Determining the Mole Fraction of Chloroform and Methylene Chloride in a Solution

When dealing with solutions composed of two volatile components, it is crucial to understand the mole fraction of each component. In this context, we will determine the mole fractions of chloroform (CHCl3) and methylene chloride (CH2Cl2) in a room temperature solution given their vapor pressures and the total vapor pressure of the solution.

Understanding the Problem

A solution contains a mixture of chloroform (CHCl3) and methylene chloride (CH2Cl2) at room temperature. The vapor pressure of the solution is 350 torr. The vapor pressure of pure methylene chloride is 431 torr. Our goal is to find the mole fraction of each component in the solution.

Using Raoult's Law

According to Raoult’s Law, the vapor pressure of a component in a solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution. The mathematical representation is:

RAUP_{solution} P_{CH_2Cl_2} cdot x_{CH_2Cl_2} P_{CHCl_3} cdot x_{CHCl_3}

Setting Up Equations

Let's denote:

xCH2Cl2 xCHCl3

where xCH2Cl2 is the mole fraction of methylene chloride and xCHCl3 is the mole fraction of chloroform.

From the mole fraction relationship, we have:

xCH2Cl2 xCHCl3 1

Therefore:

xCHCl3 1 - xCH2Cl2

Substituting into Raoult's Law:

Psolution PCH2Cl2 cdot xCH2Cl2 PCHCl3 cdot (1 - xCH2Cl2)

This simplifies to:

Psolution PCH2Cl2 cdot xCH2Cl2 PCHCl3 - PCHCl3 cdot xCH2Cl2

Which further simplifies to:

Psolution PCH2Cl2 - PCHCl3 cdot xCH2Cl2

Solving for xCH2Cl2

Rearranging the equation to solve for xCH2Cl2 gives:

xCH2Cl2 frac{Psolution - PCHCl3}{PCH2Cl2 - PCHCl3}

We need the vapor pressure of pure chloroform (PCHCl3) for this calculation. Let's assume it is around 200 torr (a typical value).

Substituting Values

Psolution 350 torr PCH2Cl2 431 torr PCHCl3 200 torr (our assumption)

Substituting into the equation:

xCH2Cl2 frac{350 - 200}{431 - 200} frac{150}{231} approx 0.649

Calculating xCHCl3

Using the mole fraction relationship:

xCHCl3 1 - xCH2Cl2

xCHCl3 1 - 0.649 approx 0.351

Final Results

Mole fraction of methylene chloride (CH2Cl2): xCH2Cl2 approx 0.649 Mole fraction of chloroform (CHCl3): xCHCl3 approx 0.351

These mole fractions indicate the relative amounts of each component in the solution based on the provided vapor pressures. Understanding and correctly applying Raoult's Law is essential for accurately determining the mole fractions in similar scenarios.