College Algebra, Chapter 5, 5.5, Section 5.5, Problem 30

The pH reading of a glass of liquid is given. Determine the hydrogen ion concentration of the liquid.

(a) Beer: pH = $4.6$

(b) Water: pH = $7.3$



Recall that pH scale is represented as

pH = $- \log [H^+]$ where $H^+ =$ hydrogen ion concentration measured in moles per liter (M)

a.) Beer:


$
\begin{equation}
\begin{aligned}

4.6 =& - \log [H^+]
&& \text{Multiply each side by } -1
\\
\\
-4.6 =& \log [H^+]
&& \text{Take antilog of each side}
\\
\\
10^{-4.6} =& H^+
&& \text{Solve for the hydrogen ion concentration } H^+
\\
\\
H^+ =& 2.51 \times 10^{-5} M

\end{aligned}
\end{equation}
$


b.) Water:


$
\begin{equation}
\begin{aligned}

7.3 =& - \log [H^+]
&& \text{Multiply each side by } -1
\\
\\
-7.3 =& \log [H^+]
&& \text{Take antilog on each side}
\\
\\
10^{-7.3} =& H^+
&& \text{Solve for the hydrogen ion concentration } H^+
\\
\\
H^+ =& 5.01 \times 10^{-8} M

\end{aligned}
\end{equation}
$