# Is it possible to calculated the concentration of hydroxide ions from the known concentration of hydronium ions?

I came across the following question in 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.

This is a reasonably straightforward question requiring substitution into the equation
$$c_1V_1 = c_2V_2,$$
which lets us derive the concentration of $\ce{H3O+}$.

I initially mis-read the question (which does not mention $\ce{H3O+}$) to read it as wanting the concentration of $\ce{OH-}$. However, had I not mis-read the question, would it be a valid question?

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

• Of course we can. – Mithoron Sep 10 '17 at 16:19

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.