Chapter 7.5, Problem 14E

To determine

To find: The quantity of water need to be add to the solution.

Answer to Problem 14E

The volume of water need to be add to the solution is $0.066$ litres.

Explanation of Solution

Given:

It is given $0.2$ litre of an acid solution whose acid concentration is $16$ moles per litre.

  

The given situation written in equation is as:

  $\begin{array}{l}12=\frac{16\cdot 0.2}{0.2+x}\left[x\text{is the volume of water that should add to the solution}\right]\\ \end{array}$

The solution is calculated as:

  $\begin{array}{c}12=\frac{16\cdot 0.2}{0.2+x}\\ 12\left(0.2+x\right)=3.2\left[\text{cross multiply}\right]\\ 2.4+12x=3.2\\ 12x=0.8\end{array}$

Further simplified as:

  $x\approx 0.066$

Check for $x\approx 0.066$ is the solution of the equation.

  $\begin{array}{c}12=\frac{16\cdot 0.2}{0.2+0.066}\\ 12\approx \frac{3.2}{0.2+0.066}\\ 12\approx 12.03\left[\text{true}\right]\end{array}$

Hence, the volume of water need to be add to the solution is $0.066$ litres.