Salt Hydrolysis: Definition, Equation, Formula, Questions and Examples

Hydrolysis Of Salts

When a salt is added to water, ions of the salt interact with water to cause acidity or basicity in an aqueous solution. This ionic interaction is called salt hydrolysis. The interaction of a cation is cationic hydrolysis, and the interaction ofan anion is anionic hydrolysis.

• Hydrolysis is the reverse of neutralization and an endothermic process.
• If the hydrolysis constant is K_h and the neutralization constant is Kn. Then,
  Kn = 1/K_h
• A solution of the salt of a strong acid and a weak base is acidic and its pH < 7 or [H⁺] > 10^-7. For example, FeCl₃ (weak base + strong acid): The solution is acidic and involves cationic hydrolysis.
• A solution of the salt of a strong base and a weak acid is basic, and its pH > 7 or [H⁺] < 10^-7. For example, KCN (strong base + weak acid): The solution is basic and involves anionic hydrolysis.
• A solution of the salt of a weak acid and a weak base
  base, then:
  If K_a > K_b, it is acidic
  If K_a < K_b, it is basic
  If K_a = K_b, it is neutral
• CH₃COONH₄ (weak acid + weak base): The solution is neutral and involves both cationic and anionic hydrolysis.
• A solution of the salt of a strong acid and a strong base is neutral or pH = 7 or [H⁺] = 10^-7
• A salt of a strong acid and a strong base is never hydrolyzed; however, ions are hydrated. For example, K₂SO₄ (however, a strong base + a strong acid).

Degree of Hydrolysis

It is defined as the fraction of total salt that has undergone hydrolysis on attainment of equilibrium. It is denoted by h.
Let c be the concentration of salt and h be its degree of hydrolysis.

$\mathrm{A}^{-}+\mathrm{H}_2 \mathrm{O} \rightleftharpoons \mathrm{OH}^{-}+\mathrm{HA}$
c
c - ch ch ch

$\mathrm{K}_{\mathrm{h}}=\frac{\left[\mathrm{OH}^{-}\right][\mathrm{HA}]}{\left[\mathrm{A}^{-}\right]}=\frac{(\mathrm{ch})(\mathrm{ch})}{\mathrm{c}-\mathrm{ch}}=\frac{\mathrm{ch}^2}{1-\mathrm{h}}$

Hydrolysis Of Weak Acid And Strong Base

Such salts give alkaline solutions in water. Some of such salts are CH₃COONa, Na₂CO3, K₂CO₃, KCN, etc. For our discussion, we consider CH₃COONa (sodium acetate) in water. When CH₃COONa is put in water, it completely ionizes to give CH₃COO^- (acetate) ions and Na⁺ ions. Now acetate ions (CH₃COO^-) absorb some H⁺ ions from weakly dissociated H₂O molecules to form undissociated CH₃COOH. Na⁺ remains in the ionic state in water. Now for K_w (ionic product) of water to remain constant, H₂O further ionizes to produce more H⁺ and OH^- ions. H⁺ ions are taken up by CH₃COO^- ions leaving OH^- ions in excess and hence an alkaline solution is obtained.

Let BA represents such a salt. As it is put in water;
$\mathrm{BA}(\mathrm{aq})+\mathrm{H}_2 \mathrm{O}(\mathrm{aq}) \rightleftharpoons \mathrm{BOH}(\mathrm{aq})+\mathrm{HA}(\mathrm{aq})$

BA dissociates into ions and BOH being strong base also ionises.

$\mathrm{B}^{+}+\mathrm{A}^{-}+\mathrm{H}_2 \mathrm{O} \rightleftharpoons \mathrm{B}^{+}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq})+\mathrm{HA}(\mathrm{aq})$

Thus, the net reaction is:$\mathrm{A}^{-}(\mathrm{aq})+\mathrm{H}_2 \mathrm{O} \rightleftharpoons \mathrm{OH}^{-}(\mathrm{aq})+\mathrm{HA}(\mathrm{aq})$

Thus, the hydrolysis constant(K_h) is given as:$\mathrm{K}_{\mathrm{h}}=\frac{\left[\mathrm{OH}^{-}\right][\mathrm{HA}]}{\left[\mathrm{A}^{-}\right]}$

pH of Solution

pH of a basic solution is given as:

$\mathrm{pH}=14+\log \left[\mathrm{OH}^{-}\right]$and $\left[\mathrm{OH}^{-}\right]=\mathrm{ch}=\sqrt{\mathrm{K}_{\mathrm{h}} \mathrm{c}}$

Thus, substituting for K_h, we get:

$\begin{aligned} & {\left[\mathrm{OH}^{-}\right]=\sqrt{\frac{\mathrm{K}_{\mathrm{w}} \mathrm{c}}{\mathrm{K}_{\mathrm{a}}}}} \\ & \mathrm{pH}=14+\log _{10} \sqrt{\frac{\mathrm{K}_{\mathrm{w}} \mathrm{c}}{\mathrm{K}_{\mathrm{a}}}} \\ & \text { Thus, } \mathrm{pH}=\frac{1}{2}\left(\mathrm{pK}_{\mathrm{w}}+\mathrm{pK}_{\mathrm{a}}+\log _{10} \mathrm{c}\right) \\ & \text { Hence, } \mathrm{pH}=7+\frac{1}{2}\left(\mathrm{pK}_{\mathrm{a}}+\log _{10} \mathrm{c}\right)\end{aligned}$

Hydrolysis Of Weak Base And Strong Acid

Such salts give acidic solutions in water. Some of such salts are NH₄Cl, ZnCl₂, FeCl₃, etc. For the purpose of discussion, we will consider the hydrolysis of NH₄Cl. When NH₄Cl is put in water, it completely ionises in water to give NH₄⁺ and Cl^- ions. NH₄⁺ ions combine with OH^- ions furnished by weakly dissociated water to form NH₄OH (a weak base). Now for keeping K_w constant, water further ionises to give H⁺ and OH^- ions, where OH^- ions are consumed by NH₄⁺ ions leaving behind H⁺ ions in solution to give an acidic solution.
Let BA be one of such salts. When it is put into water, the reaction is as follows.$\mathrm{B}^{+}+\mathrm{A}^{-}+\mathrm{H}_2 \mathrm{O} \rightleftharpoons \mathrm{BOH}+\mathrm{H}^{+}(\mathrm{aq})+\mathrm{A}^{-}(\mathrm{aq})$

Thus the net reaction of hydrolysis is as follows:

$\mathrm{B}^{+}+\mathrm{H}_2 \mathrm{O} \rightleftharpoons \mathrm{BOH}(\mathrm{aq})+\mathrm{H}^{+}(\mathrm{aq})$
c - ch ch ch

$\begin{aligned} & \mathrm{K}_{\mathrm{h}}=\frac{[\mathrm{BOH}]\left[\mathrm{H}^{+}\right]}{\left[\mathrm{B}^{+}\right]}=\frac{(\mathrm{ch})(\mathrm{ch})}{\mathrm{c}-\mathrm{ch}}=\frac{\mathrm{ch}^2}{1-\mathrm{h}^2}=\mathrm{ch}^2 \quad(\text { assuming } \mathrm{h}<<1) \\ & \text { Thus, } \mathrm{h}=\sqrt{\frac{\mathrm{K}_{\mathrm{h}}}{\mathrm{c}}}\end{aligned}$

Considering ionisation of weak base BOH and H₂O.

$\begin{aligned} & \mathrm{BOH} \rightleftharpoons \mathrm{B}^{+}+\mathrm{OH}^{-} \quad \Rightarrow \quad \mathrm{K}_{\mathrm{b}}=\frac{\left[\mathrm{B}^{+}\right]\left[\mathrm{OH}^{-}\right]}{[\mathrm{BOH}]} \\ & \mathrm{H}_2 \mathrm{O} \rightleftharpoons \mathrm{H}^{+}+\mathrm{OH}^{-} \quad \Rightarrow \quad \mathrm{K}_{\mathrm{w}}=\left[\mathrm{H}^{+}\right]\left[\mathrm{OH}^{-}\right]\end{aligned}$

From expressions for K_h, K_b and K_w, we have :

$\mathrm{K}_{\mathrm{h}}=\frac{\mathrm{K}_{\mathrm{w}}}{\mathrm{K}_{\mathrm{b}}} \Rightarrow \mathrm{h}=\sqrt{\frac{\mathrm{K}_{\mathrm{w}}}{\mathrm{K}_{\mathrm{b}} \mathrm{c}}}$

pH of Solution

Now, pH = - log [H⁺]and $\left[\mathrm{H}^{+}\right]=\mathrm{ch}=\mathrm{c} \sqrt{\frac{\mathrm{K}_{\mathrm{h}}}{\mathrm{c}}}=\sqrt{\mathrm{K}_{\mathrm{h}} \mathrm{c}} \Rightarrow\left[\mathrm{H}^{+}\right]=\sqrt{\frac{\mathrm{K}_{\mathrm{W}} \mathrm{c}}{\mathrm{K}_{\mathrm{b}}}}$

$\Rightarrow \quad \mathrm{pH}=-\log _{10} \sqrt{\frac{\mathrm{K}_{\mathrm{w}} \mathrm{c}}{\mathrm{K}_{\mathrm{b}}}}$

$\Rightarrow \quad \mathrm{pH}=\frac{1}{2}\left(\mathrm{pK}_{\mathrm{w}}-\mathrm{pK}_{\mathrm{b}}-\log _{10} c\right)$

Hence, $\mathrm{pH}\left(\right.$ at $\left.25^{\circ} \mathrm{C}\right)=7-\frac{1}{2}\left(\mathrm{pK}_{\mathrm{b}}+\log _{10} c\right)$

Recommended topic video on (Salt Hydrolysis)

Some Solved Examples

Example 1: The definition of acids and bases as acids are substances that dissociate in water to give $H^{+}$ ions, and bases are substances that produce $O H^{-}$ ions was given by

1) (correct)Arrhenius

2)Lewis

3)Bronsted Lowry

4)None of these

Solution

The definition of acid and bases as acids are substances that dissociate in water to give $H^{+}$ ions and bases are substances that produce OH^- ions, was given by Arrhenius.

Hence, the answer is option(1).

Example 2: The pH of 0.1 M solution of the following salts increases in the order:

1)$\mathrm{NaCl}<\mathrm{NH}_4 \mathrm{Cl}<\mathrm{NaCN}<\mathrm{HCl}$

2) (correct)$\mathrm{HCl}<\mathrm{NH}_4 \mathrm{Cl}<\mathrm{NaCl}<\mathrm{NaCN}$

3)$\mathrm{HCl}<\mathrm{NaCl}<\mathrm{NaCN}<\mathrm{NH}_4 \mathrm{Cl}$

4)$\mathrm{NaCN}<\mathrm{NH}_4 \mathrm{Cl}<\mathrm{NaCl}<\mathrm{HCl}$

Solution

Solution of HCl and $\mathrm{NH}_4 \mathrm{Cl}$ will be acidic, NaCl solution of neutral whereas solution of NaCN will be basic.

Hence, the answer is option (2).

Example 3: An aqueous solution of aluminum sulfate would show:

1)Basic

2) (correct)Acidic

3)Neutral

4)Any of the above

Solution

$\mathrm{Al}_2\left(\mathrm{SO}_4\right)_3$ is a salt of $W_B / S_A \cdot\left[\mathrm{Al}(\mathrm{OH})_3+\mathrm{H}_2 \mathrm{SO}_4\right]$ it hydrolyses and gives the acidic solution.

Hence, the answer is option (2).

Example 4: A certain weak acid has K_a = 1.0 x 10^-4. Calculate the equilibrium constant for its reaction with a strong base.

1)10^-10

2) (correct)10¹⁰

3)10⁴

4)10⁸

Solution

Given,

$\mathrm{HA} \rightleftharpoons \mathrm{H}^{+}+\mathrm{A}^{-}, \mathrm{K}_{\mathrm{a}}=10^{-4}$

and we know that

$\mathrm{H}^{+}+\mathrm{OH}^{-} \rightleftharpoons \mathrm{H}_2 \mathrm{O}, \mathrm{K}=\frac{1}{\mathrm{~K}_{\mathrm{w}}}=10^{14}$

Adding the above two reactions we get

$\mathrm{HA}+\mathrm{OH}^{-} \rightleftharpoons \mathrm{A}^{-}+\mathrm{H}_2 \mathrm{O}, \mathrm{K}_{\mathrm{net}}=\frac{\mathrm{K}_{\mathrm{a}}}{\mathrm{K}_{\mathrm{w}}}$

$\therefore \mathrm{K}_{\text {net }}=\frac{\mathrm{K}_{\mathrm{a}}}{\mathrm{K}_{\mathrm{w}}}=\frac{10^{-4}}{10^{-14}}=10^{10}$

Hence, the answer is option (2).

Example 5: Which one of the following is not an acid salt?

1)$\mathrm{NaH}_2 \mathrm{PO}_4$

2)${ }^1 \mathrm{NaH}_2 \mathrm{PO}_3$

3)$\mathrm{Na}_2 \mathrm{SO}_3$

4) (correct)All of the above are acid salts

Solution

Salts of $S_B / W_A$ are called acid salts.
$\mathrm{NaH}_2 \mathrm{PO}_4$ ( Salt of $\left.\mathrm{NaOH}+\mathrm{H}_3 \mathrm{PO}_4\right)\left(S_B / W_A\right)$
$\mathrm{NaH}_2 \mathrm{PO}_2$ (Salt of $\left.\mathrm{NaOH}+\mathrm{H}_3 \mathrm{PO}_2\right)\left(S_B / W_A\right)$
$\mathrm{NaH}_2 \mathrm{PO}_3$ (Salt of $\left.\mathrm{NaOH}+\mathrm{H}_3 \mathrm{PO}_3\right)\left(S_B / W_A\right)$
All are acid salts.

Hence, the answer is option (4).

Practice More Questions With the Link Given Below

Summary

The acidic or basic solution are formed by the hydrolyze of acid and bases, depending on the nature of their salt. Acidic Salts formed from strong acids and weak bases are Useful in Buffer Solutions such as Acidic salts can help create buffer solutions that resist changes in pH. pH Adjustment in which can be used to acidify solutions in various industrial processes. acid-base hydrolysis has its application in corrosion control such that the Acidic conditions can be used in controlling corrosion rates in metal processing.

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