Chapter 16.4, Problem 36SP

Interpretation Introduction

Interpretation: The mole fraction of each component in a solution prepared by mixing $300\text{ g ethanol }$ and $500\text{ g}$ of water 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 36SP

The mole fraction of each component in a solution prepared by mixing $300\text{ g ethanol }$ and $500\text{ g}$ of water is the mole fraction of ethanol is $0.19$ and the mole fraction of water is $0.82$ .

Explanation of Solution

There are two components present in the mixture such as ethanol and water. 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:

• Mass of solute( ethanol ) is $300\text{ g}$ .
• Mass of solvent( water) is $500\text{ g}$ .

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.

  $\begin{array}{l}\text{Number of moles of ethanol = }\frac{\text{300 g}}{46\frac{g}{\text{mol}}}\\ \text{Number of moles = 6}\text{.5 moles}\end{array}$

  $\begin{array}{l}\text{Number of moles of water= }\frac{500\text{ g}}{18\frac{g}{\text{mol}}}\\ \text{Number of moles = 28 moles}\end{array}$

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

The formula for the mole fraction is as follows:

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

  $\begin{array}{l}\text{Mole fraction of ethanol = }\frac{\text{6}\text{.5 moles}}{\text{6}\text{.5 moles + 28 moles}}\\ \text{Mole fraction of ethanol = }\frac{6.5\text{ moles}}{34.5\text{ moles}}\\ \text{Mole fraction of ethanol}=0.19\end{array}$

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

  $\begin{array}{l}\text{Mole fraction of water = 1 - mole fraction of ethanol}\\ \text{Mole fraction of water = 1 - 0}\text{.19}\\ \text{Mole fraction of water = 0}\text{.81}\end{array}$

Conclusion

The mole fraction of ethanol is $0.19$ and the mole fraction of water is $0.82$ .