College Algebra, Chapter 5, 5.5, Section 5.5, Problem 32

The pH readings for wines vary from 2.8 to 3.8. Determine the corresponding range of hydrogen ion concentrations.



Recall that pH scale is represented as

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

@ wines with pH $2.8$


$
\begin{equation}
\begin{aligned}

2.8 =& - \log [H^+]
&& \text{Multiply each side by } -1
\\
\\
-2.8 =& \log [H^+]
&& \text{Take anti log of each side}
\\
\\
10^{-2.8} =& H^+
&& \text{Solve for the hydrogen ion concentration } H^+
\\
\\
H^+ =& 1.58 \times 10^{-3} M

\end{aligned}
\end{equation}
$


@ wines with pH $3.8$


$
\begin{equation}
\begin{aligned}

3.8 =& - \log [H^+]
&& \text{Multiply each side by } -1
\\
\\
-3.8 =& \log [H^+]
&& \text{Take anti log on each side}
\\
\\
10^{-3.8} =& H^+
&& \text{Solve for the hydrogen ion concentration } H^+
\\
\\
H^+ =& 1.58 \times 10^{-4} M

\end{aligned}
\end{equation}
$


Thus, the corresponding range of hydrogen ion concentration is $1.58 \times 10^{-3} < H^+ < 1.58 \times 10^{-4}$.