Step 1: Identify the initial concentrations and relevant equilibrium. We have a weak dibasic acid $\text{H}_2\text{A}$ dissolved in a strong acid $\text{HCl}$. Initial concentration of $\text{H}_2\text{A} = \frac{0.1 \text{ mol}}{1 \text{ L}} = 0.1 \text{ M}$. Initial concentration of $\text{HCl} = 0.1 \text{ M}$. Since $\text{HCl}$ is a strong acid, it dissociates completely, providing $[\text{H}^{+}] = 0.1 \text{ M}$. The first ionization of $\text{H}_2\text{A}$ is: $$\text{H}_2\text{A} (aq) \rightleftharpoons \text{H}^{+} (aq) + \text{HA}^{-} (aq)$$ The equilibrium constant for this reaction is $K_{a1} = 8.1 \times 10^{-8}$. Step 2: Set up an ICE table for the first ionization and apply approximations. Initial concentrations: $[\text{H}_2\text{A}]_0 = 0.1 \text{ M}$ $[\text{H}^{+}]_0 = 0.1 \text{ M}$ (from $\text{HCl}$) $[\text{HA}^{-}]_0 = 0 \text{ M}$ Let $x$ be the concentration