`CH_(3)COOH` is titrated with `NaOH` solution. Which of the following statements is true ?

Options

A. Conductance decreases upto equivalence point, after which it increases.
B. Conductance increases upto equivalence point,after which it decreases.
C. Conductance first decreases `(` but not rapidly`)` and then increases upto equibalence point and then increases rapidley after equivalence point.
D. None of these

Explanation

To solve the question regarding the titration of acetic acid (`CH₃COOH`) with sodium hydroxide (`NaOH`), we will analyze the process step by step.

### Step-by-Step Solution:

1. **Identify the Components**:
- We have a weak acid, acetic acid (`CH₃COOH`), and a strong base, sodium hydroxide (`NaOH`).

2. **Understand the Reaction**:
- When acetic acid is titrated with sodium hydroxide, they react to form sodium acetate (`CH₃COONa`) and water (`H₂O`).
- The balanced chemical equation for the reaction is:
\[ CH₃COOH + NaOH \rightarrow CH₃COONa + H₂O \]

3. **Analyze Conductance**:
- Conductance in a solution depends on the concentration of ions.
- Initially, as we start the titration, the concentration of acetic acid decreases as it reacts with NaOH, leading to an increase in the concentration of ions in the solution (Na⁺ and CH₃COO⁻). Therefore, conductance increases slowly.

4. **Equivalence Point**:
- The equivalence point is reached when the amount of NaOH added is stoichiometrically equivalent to the amount of acetic acid present. At this point, all the acetic acid has reacted with NaOH to form sodium acetate.
- At the equivalence point, the concentration of H⁺ ions is equal to the concentration of OH⁻ ions, resulting in a neutral solution.

5. **Post-Equivalence Point**:
- After the equivalence point, any additional NaOH will increase the concentration of OH⁻ ions in the solution. This leads to a rapid increase in the total ion concentration, which in turn causes a rapid increase in conductance.

6. **Conclusion**:
- Therefore, the correct statement regarding the conductance during the titration of acetic acid with sodium hydroxide is that conductance first increases slowly and then increases rapidly after the equivalence point.

### Final Answer:
Conductance first increases slowly and then increases rapidly after the equivalence point.