Chapter 3.5, Problem 55E

To determine

Find the hydrogen ion concentration relation between the apple juice and drinking water.

Answer to Problem 55E

The hydrogen ion concentration in apple juice is ${10}^{5.1}$ times the hydrogen ion concentration in drinking water.

Explanation of Solution

Given information:

The hydrogen ion concentration in apple juice is $2.9$ and the drinking water is $8.0$ .

Calculation:

Given

  ${\left[pH\right]}_j=2.9$

  ${\left[pH\right]}_w=8.0$

Use the model $\left[pH\right]=-\log \left[H^{+}\right]$ .

  $\begin{array}{l}\left[pH\right]=-\log \left[H^{+}\right]\\ \Rightarrow -\left[pH\right]=\log \left[H^{+}\right]\\ \Rightarrow \left[H^{+}\right]={10}^{-\left[pH\right]}\\ {\left[H^{+}\right]}_j={10}^{-2.9}\\ {\left[H^{+}\right]}_w={10}^{-8}\end{array}$

Now,

  $\begin{array}{l}\frac{{\left[H^{+}\right]}_j}{{\left[H^{+}\right]}_w}=\frac{{10}^{-2.9}}{{10}^{-8}}\\ \Rightarrow \frac{{\left[H^{+}\right]}_j}{{\left[H^{+}\right]}_w}={10}^{5.1}\\ \Rightarrow {\left[H^{+}\right]}_j={10}^{5.1}\cdot {\left[H^{+}\right]}_w\end{array}$

Hence the hydrogen ion concentration in apple juice is ${10}^{5.1}$ times the hydrogen ion concentration in drinking water.