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Chapter 15 (Acids and Bases) of Holt High School Chemistry:

Neutralizing $\pu{5.00 L}$ of an acid rain sample required $\pu{11.3 mL}$ of $\pu{0.0102 M}\ \ce{KOH}$. Calculate the hydronium ion $[\ce{H3O+}]$ concentration in the rain sample.

We can derive the required concentration by substituting into:
$$c_1V_1 = c_2V_2,$$

Can we, after getting the concentration of $\ce{H3O+}$) use the equation with the ionization constant of water
$$K_\mathrm{w} = [\ce{H3O+}][\ce{OH-}]$$ to also get the $\ce{OH-}$ concentration?

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    $\begingroup$ Of course we can. $\endgroup$
    – Mithoron
    Sep 10, 2017 at 16:19

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Yes, that works. In fact, some textbooks and teachers ask this type of question (asking for the lesser ion of the autodeprotonation of water) to test which students actually read the question and which gloss over details. I fell into the trap of calculating the wrong one and stopping too early, too.

So if your question had asked for the hydroxide concentration, you would indeed calculate the hydronium concentration first (because that is actually accessible) and then invert and multiply $10^{-14}$ to get the desired one as you suggest.

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  • $\begingroup$ " you would indeed calculate the hydronium concentration first (because that is actually" Which balanced equation we can use in order to calculate $[\ce{H3O+}]$? $\endgroup$ May 4, 2021 at 18:56

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