A 0.10 M solution of which of the following salts is most basic? — Acids and Bases Chemistry Question

STEPS:

1. Understand the concept of salt hydrolysis: When an ionic salt dissolves in water, it dissociates completely into its component cations and anions. These ions can interact with water molecules in a reaction called hydrolysis, which can produce either hydronium ions ($\text{H}_3\text{O}^+$) or hydroxide ions ($\text{OH}^-$), altering the pH of the solution.
2. Classify the behavior of cations in water:
* Cations of strong bases (such as alkali metals like $\text{Li}^+$, $\text{Na}^+$, and $\text{K}^+$, and alkaline earth metals like $\text{Ca}^{2+}$) do not undergo hydrolysis and have no effect on pH (they are neutral).
* Highly charged, small transition or post-transition metal cations (like $\text{Al}^{3+}$) undergo acidic hydrolysis because they attract water molecules strongly, causing them to release $\text{H}^+$ ions into solution:
$$[\text{Al}(\text{H}_2\text{O})_6]^{3+}(aq) + \text{H}_2\text{O}(l) \rightleftharpoons [\text{Al}(\text{H}_2\text{O})_5(\text{OH})]^{2+}(aq) + \text{H}_3\text{O}^+(aq)$$
3. Classify the behavior of anions in water:
* Anions derived from strong acids (such as $\text{NO}_3^-$ and $\text{Cl}^-$) do not undergo hydrolysis and have no effect on pH (they are neutral).
* Anions derived from weak acids (such as $\text{SO}_4^{2-}$ and $\text{CO}_3^{2-}$) act as weak bases. They undergo basic hydrolysis by accepting protons from water molecules to produce hydroxide ions:
$$\text{Anion}^-(aq) + \text{H}_2\text{O}(l) \rightleftharpoons \text{Conjugate Acid}(aq) + \text{OH}^-(aq)$$
4. Compare the base strength of the hydrolyzing anions:
* The strength of a conjugate base is inversely related to the strength of its parent acid.
* The conjugate acid of the sulfate ion ($\text{SO}_4^{2-}$) is hydrogen sulfate ($\text{HSO}_4^-$), which is a relatively strong "weak acid" ($K_a \approx 1.2 \times 10^{-2}$). This makes $\text{SO}_4^{2-}$ an extremely weak base.
* The conjugate acid of the carbonate ion ($\text{CO}_3^{2-}$) is hydrogen carbonate ($\text{HCO}_3^-$), which is an exceptionally weak acid ($K_a \approx 4.7 \times 10^{-11}$). Because its parent acid is so weak, $\text{CO}_3^{2-}$ is a much stronger conjugate base.
5. Identify the most basic solution: Since potassium carbonate ($\text{K}_2\text{CO}_3$) consists of neutral $\text{K}^+$ ions and highly basic $\text{CO}_3^{2-}$ ions, it undergoes significant basic hydrolysis:
$$\text{CO}_3^{2-}(aq) + \text{H}_2\text{O}(l) \rightleftharpoons \text{HCO}_3^-(aq) + \text{OH}^-(aq)$$
This produces the highest concentration of $\text{OH}^-$ ions, making the $0.10\text{ M}$ solution of $\text{K}_2\text{CO}_3$ the most basic among the choices, which confirms Option E.

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WHY_OTHERS_WRONG:

• A is incorrect: Lithium nitrate ($\text{LiNO}_3$) dissociates into $\text{Li}^+$ (the conjugate of the strong base $\text{LiOH}$) and $\text{NO}_3^-$ (the conjugate of the strong acid $\text{HNO}_3$). Neither ion hydrolyzes water, resulting in a neutral solution (pH $\approx 7$).
• B is incorrect: Sodium sulfate ($\text{Na}_2\text{SO}_4$) contains neutral $\text{Na}^+$ ions and very weakly basic $\text{SO}_4^{2-}$ ions. Because $\text{HSO}_4^-$ is a strong weak acid, $\text{SO}_4^{2-}$ has negligible basicity in water, making the solution essentially neutral to only exceptionally slightly basic (far less basic than the carbonate solution).
• C is incorrect: Calcium chloride ($\text{CaCl}_2$) dissociates into $\text{Ca}^{2+}$ (the conjugate of the strong base $\text{Ca(OH)}_2$) and $\text{Cl}^-$ (the conjugate of the strong acid $\text{HCl}$). Neither ion hydrolyzes water, resulting in a neutral solution (pH $\approx 7$).
• D is incorrect: Aluminum nitrate ($\text{Al(NO}_3)_3$) contains neutral $\text{NO}_3^-$ ions and $\text{Al}^{3+}$ ions. The small, highly charged $\text{Al}^{3+}$ cation hydrolyzes water to release $\text{H}_3\text{O}^+$ ions, resulting in an acidic solution (pH < 7) rather than a basic one.