Hydrolysis is an acid-basedreaction of a cation or anion or both ions of a salt with water, Resultan solution of hydrolysis may be acidic, basic or netural. The anion `A^(-)` which is a weakeer base than `OH^(-)` and which his its conjugate acid HA stronger then water but weaker than `H_(3)O` shown the phenomenon of hydrolysis Ex : `CH_(3)COO^(-),CN^(-),NO_(2)^(-)` etc.
The contion `B^(+)` which is a weaker acid than `H_(3)^(+)` which is a weaker acid then `H_(3)^(+)` and which has its conjugate base BOH stronger than water but weak than `OH^(-)` shown the phenmenon of hydrolysis Ex : `NH_(4)^(+)C_(6)H_(5)NH^(+),N_(2)H_(5)^(+)` etc.
The hydrolysis constant of anion and cation are given by
`A^(-)(aq.)+H_(2)O(l)hArrHA(aq.)+OH^(-)(aq)`
`" " K_(h)=(K_(w))/(K_(a))rArr([HA(aq.)][OH^(-)(aq.)])/([A^(-)(aq.)])`
`B^(+)(aq.)+H_(2)O(l)hArrBOH(aq.)+H^(+)(aq.)`
`" " K_(h)=(K_(w))/(K_(b))rArr([BOH(aq.)][H^(+)(aq.)])/([B^(-)(aq.)])`
select the correct statement :

Options

A. KCl undrgoes hydrolysis
B. `K_(h)=K_(b)(A^(-))` and `K_(h)=K_(a)(B^(+))`
C. 0.1 M solution of NACN is acidic
D. resultant solution of equal volume of 0.1 M `NH_(3)` and 0.1M HCl is basic

Answer

To solve the problem regarding hydrolysis and the nature of the resultant solutions, we will analyze the statements provided in the context of the hydrolysis of salts formed from strong acids and bases, as well as weak acids and bases.

### Step-by-Step Solution:

1. **Understanding Hydrolysis**: Hydrolysis is the reaction of a salt with water, resulting in the formation of an acidic or basic solution depending on the nature of the ions involved.

2. **Analyzing KCl Hydrolysis**: KCl is a salt formed from KOH (a strong base) and HCl (a strong acid). Since both the acid and base are strong, KCl does not undergo hydrolysis. Therefore, the solution remains neutral.

- **Conclusion**: The statement regarding KCl hydrolysis being incorrect is valid.

3. **Analyzing NaCN Hydrolysis**: NaCN is a salt formed from NaOH (a strong base) and HCN (a weak acid). In solution, Na⁺ does not hydrolyze, but CN⁻ does. The hydrolysis of CN⁻ can be represented as:
\[ CN^- + H_2O \rightleftharpoons HCN + OH^- \]
This reaction produces OH⁻ ions, indicating that the solution is basic.

- **Conclusion**: The statement claiming that 0.1 M NaCN is acidic is incorrect; it is basic.

4. **Analyzing the Mixture of NH₃ and HCl**: When equal volumes of 0.1 M NH₃ (a weak base) and 0.1 M HCl (a strong acid) are mixed, NH₃ will react with HCl to form NH₄⁺ and Cl⁻:
\[ NH_3 + HCl \rightarrow NH_4^+ + Cl^- \]
Cl⁻ comes from a strong acid and does not hydrolyze, while NH₄⁺ can hydrolyze:
\[ NH_4^+ + H_2O \rightleftharpoons NH_3 + H^+ \]
This reaction produces H⁺ ions, indicating that the solution is acidic.

- **Conclusion**: The statement claiming that the resultant solution is basic is incorrect; it is acidic.

5. **Final Evaluation**: Based on the analysis:
- The statement regarding KCl hydrolysis is correct.
- The statement regarding NaCN being acidic is incorrect; it is basic.
- The statement regarding the mixture of NH₃ and HCl being basic is incorrect; it is acidic.

### Correct Statement:
The only correct statement is regarding KCl hydrolysis, which does not occur, leading to a neutral solution.