Chapter 3.5, Problem 55E

To determine

Find ratio of hydrogen ion concentration of the apple juice to the drinking water

Answer to Problem 55E

The ratio of hydrogen ion concentration of the apple juice to the drinking water is $\left[H+\right]={10}^{-5.1}$

Explanation of Solution

Given:

Acidity model by $pH=–\log \left[H^{+}\right],$ where acidity (pH) is a measure of the hydrogen ion concentration $\left[H^{+}\right]$ (measured in moles of hydrogen per litre) of solution.

Apple juice has a $pH=2.9$

  $2.9=–log\left[H^{+}\right]$

Dividing both sides by $\left(–1\right)$

  $–2.9=log\left[H^{+}\right]$

Exponentiation of both the sides to the base 10

  ${10}^{-2.9}=10\log \left[H^{+}\right]$

Using the inverse property

  ${10}^{\log x}=x$

  ${10}^{-2.9}=\left[H^{+}\right]$

  $\left[H^{+}\right]={10}^{-2.9}$ moles/L

Drinking water has a

  $pH=8.0$ .

  $8.0=–log\left[H^{+}\right]$

Dividing both sides by $\left(–1\right)$

  $–8.0=\log \left[H^{+}\right]$

Exponentiation of both the sides to the base 10

  ${10}^{-8.0}=10\log \left[H^{+}\right]$

Using the inverse property ${10}^{\log x}=x$

  ${10}^{-8.0}=\left[H^{+}\right]$

  $\left[H^{+}\right]={10}^{-8.0}moles/L$

The ratio of hydrogen ion concentration of the apple juice to the drinking water is

  $\left[H^{+}\right]=\frac{{10}^{-2.9}}{{10}^{-8.0}}$

  $\left[H+\right]={10}^{-5.1}$