Chapter 16.4, Problem 37SP

Interpretation Introduction

Interpretation: The mole fraction of each component in a solution containing $\text{50 g carbon tetrachloride( CCl4) }$ and $50.0\text{ g chloroform( CHCl3)}$ is to be determined.

Concept introduction: Mole fraction is the way of expressing the concentration of the solution. Mole fraction is defined as the ratio of the number of moles of one solute to that of the total number of moles of all the components present in the solution.

Answer to Problem 37SP

The mole fraction of carbon tetrachloride is $0.43$ and the mole fraction of chloroform is $0.57$ .

Explanation of Solution

There are two components present in the mixture and those are carbon tetrachloride and chloroform. The mole fraction of both components needs to be determined.

The data given in the question to determine the mole fraction of each component is as follows:

• $\text{50 g carbon tetrachloride( CCl4) }$
• $50.0\text{ g chloroform( CHCl3)}$

From the given mass, calculate the number of moles of both components.

The formula for the number of moles is as follows:

  $\text{Number of moles =}\frac{\text{Given mass}}{\text{Molar mass}}$

Substitute the value of the given mass and molar mass to calculate the number of moles of both components.

  $\begin{array}{l}\text{Number of moles of carbon tetrachloride= }\frac{\text{50}\text{.0 g}}{153.82\frac{g}{\text{mol}}}\\ \text{Number of moles = 0}\text{.32 moles}\end{array}$

  $\begin{array}{l}\text{Number of moles of chloroform= }\frac{50.0\text{ g}}{119.4\frac{g}{\text{mol}}}\\ \text{Number of moles = 0}\text{.42 moles}\end{array}$

Substitute the number of moles to calculate the mole fraction of both components.

The formula for the mole fraction is as follows:

  $\text{Mole fraction = }\frac{\text{Number of moles of one component}}{\text{Number of moles of all the components}}$

  $\begin{array}{l}\text{Mole fraction of carbon tetrachloride = }\frac{\text{0}\text{.32 moles}}{\text{0}\text{.32 moles + 0}\text{.42 moles}}\\ \text{Mole fraction of carbon tetrachloride = }\frac{\text{0}\text{.32 moles}}{\text{0}\text{.74 moles}}\\ \text{Mole fraction of carbon tetrachloride}=0.43\end{array}$

The total mole fraction of all the components in the solution is $1$ , therefore, the mole fraction of chloroform can be calculated as:

  $\begin{array}{l}\text{Mole fraction of chloroform = 1 - mole fraction of carbon tetrachloride}\\ \text{Mole fraction of chloroform = 1 - 0}\text{.43}\\ \text{Mole fraction of chloroform = 0}\text{.57}\end{array}$

Conclusion

The mole fraction of carbon tetrachloride is $0.43$ and the mole fraction of chloroform is $0.57$ .