The concentration of hydrogen ions in a water solution typically ranges from
\(10 \mathrm{M}\) to \(10^{-15} \mathrm{M}\). (One \(\mathrm{M}\) equals \(6.02 \cdot
10^{23}\) particles, such as atoms, ions, molecules, etc., per liter or 1 mole
per liter.) Because of this wide range, chemists use a logarithmic scale,
called the pH scale, to measure the concentration (see Exercise 12 of Section
4.6 ). The formal definition of \(\mathrm{pH}\) is \(\mathrm{pH}=-\log
\left[\mathrm{H}^{+}\right],\) where \(\left[\mathrm{H}^{+}\right]\) denotes the
concentration of hydrogen ions. Chemists use the symbol \(\mathrm{H}^{+}\) for
hydrogen ions, and the brackets [ ] mean "the concentration of."
a. Pure water at \(25^{\circ} \mathrm{C}\) has a hydrogen ion concentration of
\(10^{-7} \mathrm{M}\). What is the \(\mathrm{pH} ?\)
b. In orange juice, \(\left[\mathrm{H}^{+}\right] \approx 1.4 \cdot 10^{-3}
\mathrm{M}\). What is the \(\mathrm{pH}\) ?
c. Household ammonia has a pH of about \(11.5 .\) What is its
\(\left[\mathrm{H}^{+}\right] ?\)
d. Does a higher pH indicate a lower or a higher concentration of hydrogen
ions?
e. A solution with a \(\mathrm{pH}>7\) is called basic, one with a
\(\mathrm{pH}=7\) is called neutral, and one with a \(\mathrm{pH}<7\) is called
acidic. Identify pure water, orange juice, and household ammonia as either
acidic, neutral, or basic. Then plot their positions on the accompanying
scale, which shows both the \(\mathrm{pH}\) and the hydrogen ion concentration.
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