15.3 Determine the concentrations of hydronium and hydroxide ions in $$ 1.25 imes 10^{-3} \mathrm{M} $$ aqueous perchloric acid.

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15.3 Determine the concentrations of hydronium and hydroxide ions in $$ 1.25 	imes 10^{-3} \mathrm{M} $$ aqueous perchloric acid.

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The acid perchloric acid ($$ \mathrm{HClO_4} $$) is a strong acid, meaning it completely dissociates in water. Therefore, the concentration of hydronium ions ($$ \mathrm{H_3O^+} $$) is equal to the concentration of the acid:

$$
[\mathrm{H_3O^+}] = 1.25 \times 10^{-3}\,\mathrm{M}
$$

Next, we use the ion product of water:

$$
K_w = [\mathrm{H_3O^+}][\mathrm{OH^-}] = 1.0 \times 10^{-14}
$$

To find the hydroxide ion concentration ($$ [\mathrm{OH^-}] $$), we rearrange the equation:

$$
[\mathrm{OH^-}] = \frac{K_w}{[\mathrm{H_3O^+}]} = \frac{1.0 \times 10^{-14}}{1.25 \times 10^{-3}}
$$

Perform the division:

$$
[\mathrm{OH^-}] = 8.0 \times 10^{-12}\,\mathrm{M}
$$

Thus, the concentrations are:

$$
\begin{aligned}
[\mathrm{H_3O^+}] &= 1.25 \times 10^{-3}\,\mathrm{M} \
[\mathrm{OH^-}] &= 8.0 \times 10^{-12}\,\mathrm{M}
\end{aligned}
$$
The hydronium ion concentration is $$ 1.25 \times 10^{-3} \, \mathrm{M} $$ and the hydroxide ion concentration is $$ 8.0 \times 10^{-12} \, \mathrm{M} $$.

15.3 Determine the concentrations of hydronium and hydroxide ions in \( 1.25 \times 10^{-3} \mathrm{M} \) aqueous perchloric acid.

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