Chapter 3.5, Problem 57E

To determine

To find that the hydrogen ion concentration of the glass of grape juice is how many times that of the baking soda solution by using the acidity model $\text{pH}=-{\log }_{10}\left[{\text{H}}^{+}\right]$ .

Answer to Problem 57E

The hydrogen ion concentration $\left[{\text{H}}^{+}\right]$ of the glass of grape juice is $79487.17$ times that of the baking soda solution.

Explanation of Solution

Given information:

A glass of grape juice has a $\text{pH}$ of $3.5$ and a baking soda solution has a $\text{pH}$ of $8.4$ .

Hydrogen ion concentration of Grape juice:

  $\begin{array}{l}\text{pH}=-{\log }_{10}\left[{\text{H}}^{+}\right]\\ 3.5=-{\log }_{10}\left[{\text{H}}^{+}\right]\\ \left[{\text{H}}^{+}\right]={10}^{-3.5}\\ \left[{\text{H}}^{+}\right]=0.00031=3.1\times {10}^{-4}\text{ M}\end{array}$

Hydrogen ion concentration of Baking soda solution:

  $\begin{array}{l}\text{pH}=-{\log }_{10}\left[{\text{H}}^{+}\right]\\ 8.4=-{\log }_{10}\left[{\text{H}}^{+}\right]\\ \left[{\text{H}}^{+}\right]={10}^{-8.4}\\ \left[{\text{H}}^{+}\right]=3.9\times {10}^{-9}\text{ M}\end{array}$

Let, the hydrogen ion concentration of the glass of grape juice is $x$ times that of the baking soda solution.

  $\begin{array}{l}\therefore 3.1\times {10}^{-4}=x\times \left(3.9\times {10}^{-9}\right)\\ \Rightarrow x=\frac{3.1\times {10}^{-4}}{3.9\times {10}^{-9}}=79487.17\end{array}$

Hence,

The hydrogen ion concentration $\left[{\text{H}}^{+}\right]$ of the glass of grape juice is $79487.17$ times that of the baking soda solution.