Question

Calculate \(\mathrm{H}^{+}\) and \(\mathrm{OH}^{-}\) in solutions with the following \(\mathrm{pH}\). (a) 9.0 (b) 3.20 (c) -1.05 (d) 7.46

Short answer

Question: Calculate the concentrations of H⁺ and OH⁻ ions in solutions with the following pH values: (a) 9.0, (b) 3.20, (c) -1.05, and (d) 7.46. Answer: (a) [H⁺] = 1.0 × 10⁻⁹ M, [OH⁻] = 1.0 × 10⁻⁵ M (b) [H⁺] = 6.31 × 10⁻⁴ M, [OH⁻] = 1.59 × 10⁻¹¹ M (c) [H⁺] = 1.13 × 10¹ M, [OH⁻] = 8.85 × 10⁻¹⁶ M (d) [H⁺] = 3.47 × 10⁻⁸ M, [OH⁻] = 2.88 × 10⁻⁷ M

Step-by-step solution

Determine the \(\mathrm{H}^{+}\) concentration

We will begin by finding the concentration of \(\mathrm{H}^{+}\) ions using the formula: \(\mathrm{pH} = -\log{[\mathrm{H}^{+}]}\). To find the concentration of \(\mathrm{H}^{+}\), we'll rewrite this formula as \([\mathrm{H}^{+}] = 10^{-\mathrm{pH}}\).

Determine the \(\mathrm{OH}^{-}\) concentration

We will find the concentration of \(\mathrm{OH}^{-}\) ions using the ion product constant for water, \(K_\mathrm{w} = [\mathrm{H}^{+}][\mathrm{OH}^{-}] = 1.0 \times 10^{-14}\). By rearranging this formula, we can find the concentration of \(\mathrm{OH}^{-}\) ions: \([\mathrm{OH}^{-}] = \frac{K_\mathrm{w}}{[\mathrm{H}^{+}]}\). Now, we will apply these steps to find the concentrations of \(\mathrm{H}^{+}\) and \(\mathrm{OH}^{-}\) ions for each given \(\mathrm{pH}\) value. (a) \(\mathrm{pH} = 9.0\)

Calculate \(\mathrm{H}^{+}\) concentration in (a)

\([\mathrm{H}^{+}] = 10^{-9.0} = 1.0 \times 10^{-9}\,\mathrm{M}\)

Calculate \(\mathrm{OH}^{-}\) concentration in (a)

\([\mathrm{OH}^{-}] =\frac{1.0 \times 10^{-14}}{1.0 \times 10^{-9}} = 1.0 \times 10^{-5}\,\mathrm{M}\) (b) \(\mathrm{pH} = 3.20\)

Calculate \(\mathrm{H}^{+}\) concentration in (b)

\([\mathrm{H}^{+}] = 10^{-3.20} = 6.31 \times 10^{-4}\,\mathrm{M}\)

Calculate \(\mathrm{OH}^{-}\) concentration in (b)

\([\mathrm{OH}^{-}] =\frac{1.0 \times 10^{-14}}{6.31 \times 10^{-4}} = 1.59 \times 10^{-11}\,\mathrm{M}\) (c) \(\mathrm{pH} = -1.05\)

Calculate \(\mathrm{H}^{+}\) concentration in (c)

\([\mathrm{H}^{+}] = 10^{-(-1.05)} = 1.13 \times 10^1\,\mathrm{M}\)

Calculate \(\mathrm{OH}^{-}\) concentration in (c)

\([\mathrm{OH}^{-}] =\frac{1.0 \times 10^{-14}}{1.13 \times 10^1} = 8.85 \times 10^{-16}\,\mathrm{M}\) (d) \(\mathrm{pH} = 7.46\)

Calculate \(\mathrm{H}^{+}\) concentration in (d)

\([\mathrm{H}^{+}] = 10^{-7.46} = 3.47 \times 10^{-8}\,\mathrm{M}\)

Calculate \(\mathrm{OH}^{-}\) concentration in (d)

\([\mathrm{OH}^{-}] =\frac{1.0 \times 10^{-14}}{3.47 \times 10^{-8}} = 2.88 \times 10^{-7}\,\mathrm{M}\)