Hydrolysis of salts Knowledge-Based Study

Study notes

1. What is Salt Hydrolysis?

   When an ionic compound (salt) dissolves in water, it dissociates completely into its constituent cations and anions. In many cases, these ions simply remain hydrated. However, certain ions can interact chemically with water molecules by donating or accepting protons ($\text{H}^+$). This chemical reaction between an ion and water is known as salt hydrolysis, and it affects the relative concentrations of hydronium ($\text{H}_3\text{O}^+$) and hydroxide ($\text{OH}^-$) ions, thereby altering the pH of the resulting solution.

   • Neutral Solutions: Formed when neither the cation nor the anion undergoes significant hydrolysis.
   • Acidic Solutions: Formed when the cation hydrolyzes to generate excess $\text{H}_3\text{O}^+$ ions.
   • Basic Solutions: Formed when the anion hydrolyzes to generate excess $\text{OH}^-$ ions.

   Neutral Salts

   Salts formed from the neutralization reaction between a strong acid and a strong base do not hydrolyze in aqueous solution.

   Consider sodium chloride ($\text{NaCl}$), which dissociates completely in water:

   $$\text{NaCl}(s) \rightarrow \text{Na}^+(aq) + \text{Cl}^-(aq)$$

   • The sodium cation ($\text{Na}^+$) is the conjugate acid of the strong base $\text{NaOH}$. Because $\text{NaOH}$ is strong, $\text{Na}^+$ is an extremely weak conjugate acid and does not accept or donate protons in water.
   • The chloride anion ($\text{Cl}^-$) is the conjugate base of the strong acid $\text{HCl}$. Because $\text{HCl}$ dissociates completely, $\text{Cl}^-$ has negligible base strength and cannot accept a proton from $\text{H}_2\text{O}$.

   Because neither ion reacts with water, the equilibrium of water autoionization remains undisturbed:

   $$[\text{H}_3\text{O}^+] = [\text{OH}^-] = 1.0 \times 10^{-7}\text{ M at } 25^\circ\text{C} \implies \text{pH} = 7.00$$

   Basic Salts

   When a salt formed from a weak acid and a strong base dissolves in water, the resulting solution is basic ($\text{pH} > 7$). This occurs because the anion acts as a Brønsted–Lowry base and undergoes hydrolysis.

   For example, in a solution of sodium acetate ($\text{CH}_3\text{COONa}$):

   $$\text{CH}_3\text{COONa}(s) \rightarrow \text{Na}^+(aq) + \text{CH}_3\text{COO}^-(aq)$$

   While $\text{Na}^+$ is a spectator ion, the acetate ion ($\text{CH}_3\text{COO}^-$) is the conjugate base of the weak acid acetic acid ($\text{CH}_3\text{COOH}$). It reacts reversibly with water:

   $$\text{CH}_3\text{COO}^-(aq) + \text{H}_2\text{O}(l) \rightleftharpoons \text{CH}_3\text{COOH}(aq) + \text{OH}^-(aq)$$

   This production of $\text{OH}^-$ ions raises the pH above 7. The equilibrium constant for this reaction is the base dissociation constant ($K_b$) of the acetate ion, related to the acid dissociation constant ($K_a$) of acetic acid by:

   $$K_b = \frac{K_w}{K_a}$$

   Acidic Salts

   Salts formed from the neutralization of a strong acid with a weak base produce acidic aqueous solutions ($\text{pH} < 7$). In this case, the cation hydrolyzes by donating a proton to water.

   A typical example is ammonium chloride ($\text{NH}_4\text{Cl}$):

   $$\text{NH}_4\text{Cl}(s) \rightarrow \text{NH}_4^+(aq) + \text{Cl}^-(aq)$$

   The chloride ion ($\text{Cl}^-$) is the conjugate base of a strong acid and does not hydrolyze. In contrast, the ammonium ion ($\text{NH}_4^+$) is the conjugate acid of the weak base ammonia ($\text{NH}_3$). It acts as a weak acid in water:

   $$\text{NH}_4^+(aq) + \text{H}_2\text{O}(l) \rightleftharpoons \text{NH}_3(aq) + \text{H}_3\text{O}^+(aq)$$

   The equilibrium generates hydronium ions, making the solution acidic. The acid dissociation constant ($K_a$) for the cation is calculated as:

   $$K_a = \frac{K_w}{K_b}$$

   where $K_b$ is the dissociation constant of the parent weak base.

   Competing Hydrolysis Equilibria

   When a salt contains both a cation derived from a weak base and an anion derived from a weak acid (such as ammonium acetate, $\text{NH}_4\text{CH}_3\text{COO}$, or ammonium nitrite, $\text{NH}_4\text{NO}_2$), both ions undergo hydrolysis simultaneously:

   • The cation hydrolyzes to yield $\text{H}_3\text{O}^+$, characterized by its constant $K_a = \frac{K_w}{K_b(\text{base})}$.
   • The anion hydrolyzes to yield $\text{OH}^-$, characterized by its constant $K_b = \frac{K_w}{K_a(\text{acid})}$.

   The overall acidity or basicity of the solution depends directly on the relative strengths of $K_a$ and $K_b$ of the hydrolyzing ions, or equivalently, on the $K_a$ of the parent weak acid versus the $K_b$ of the parent weak base:

   • If $K_a > K_b$, the cation hydrolyzes to a greater extent than the anion, so the solution is acidic ($\text{pH} < 7$).
   • If $K_b > K_a$, the anion hydrolyzes to a greater extent than the cation, so the solution is basic ($\text{pH} > 7$).
   • If $K_a = K_b$, hydrolysis proceeds equally in both directions, and the solution is neutral ($\text{pH} \approx 7$).