A solution containing $\ce{HCl}$ and the weak acid $\ce{HClO2}$ has a pH of 2.4. Enough $\ce{KOH(aq)}$ is added to the solution to increase the pH to 10.5. The amount of which of the following species increases as the $\ce{KOH(aq)}$ is added?

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The strong base and acid will react and neutralize first:

$$\ce{KOH(aq) + HCl(aq) -> H2O(l) + K+(aq) + Cl-(aq)}$$

Since the solution becomes alkaline, we can infer that more strong base is added. The base would react with $\ce{HClO2}$:

$$\ce{KOH(aq) + HClO2(aq) -> H2O(l) + K+(aq) + ClO2-(aq) }$$

Note that there are two reasonable options that increase in solution: $\ce{Cl-(aq)}$ and $\ce{ClO2-(aq)}$. However, since we know that $\ce{HCl}$ is a stronger acid than $\ce{HClO2}$, the $\ce{Cl-}$ ions were already present in solution throughout the process. On the other hand, most of the $\ce{ClO2-(aq)}$ ions did not dissociate from the weak acid at the start of the reactions. It is only after the strong base liberates the proton do $\ce{ClO2-(aq)}$ ions noticeably increase.