Chapter 18, Problem 15STP

Interpretation Introduction

Interpretation:

Convert the concentrated $0.50\text{m}\text{N}\text{a}\text{O}\text{H}$ aqueous solution in terms of mole fraction.

Concept introduction:

Mole fraction is the fraction of the total number of moles.

If a solution has two components A and B, then mole fraction is calculated as,

  $\begin{array}{l}{\text{x}}_{\text{A}}=\frac{{\text{n}}_{\text{A}}}{{\text{n}}_{\text{A}}+{\text{n}}_{\text{B}}}\end{array}$

  $\begin{array}{c}{\text{x}}_{\text{B}}=\frac{{\text{n}}_{\text{B}}}{{\text{n}}_{\text{A}}+{\text{n}}_{\text{B}}}\end{array}$

  $\begin{array}{c}\text{w}\text{h}\text{e}\text{r}\text{e}\end{array}$

  $\begin{array}{c}{\text{x}}_{\text{A}}\text{i}\text{s}\text{m}\text{o}\text{l}\text{e}\text{f}\text{r}\text{a}\text{c}\text{t}\text{i}\text{o}\text{n}\text{o}\text{f}\text{A}\end{array}$

  $\begin{array}{c}{\text{x}}_{\text{B}}\text{i}\text{s}\text{m}\text{o}\text{l}\text{e}\text{f}\text{r}\text{a}\text{c}\text{t}\text{i}\text{o}\text{n}\text{o}\text{f}\text{B}\end{array}$

  $\begin{array}{c}{\text{n}}_{\text{A}}\text{i}\text{s}\text{n}\text{u}\text{m}\text{b}\text{e}\text{r}\text{o}\text{f}\text{m}\text{o}\text{l}\text{e}\text{s}\text{o}\text{f}\text{A}\end{array}$

  $\begin{array}{c}{\text{n}}_{\text{B}}\text{i}\text{s}\text{n}\text{u}\text{m}\text{b}\text{e}\text{r}\text{o}\text{f}\text{m}\text{o}\text{l}\text{e}\text{s}\text{o}\text{f}\text{B}\end{array}$

Answer to Problem 15STP

To convert $0.50\text{m}$ into a mole fraction, the number of moles of water is to be calculated in $1\text{k}\text{g}$ water. Then the mole fraction of solute is calculated by dividing the number of moles of a solute with the total number of moles of solute and water.

Explanation of Solution

Number of moles of water $\begin{array}{l}=\frac{1000\text{g}}{18\text{g}/\text{m}\text{o}\text{l}}\end{array}$

           $\begin{array}{c}=55.55\text{m}\text{o}\text{l}\end{array}$

Number of moles of $\text{N}\text{a}\text{O}\text{H}=0.50\text{m}$

$\begin{array}{c}{\text{x}}_{\text{A}}=\frac{0.50}{0.50+55.55}\end{array}$

  $\begin{array}{c}=0.009\end{array}$

Conclusion

Thus, the number of moles of solute and solvent is used to calculate the mole fraction of the solute and solvent.