The increase in the value of molar conducitivity of acetic acid with dilution is due to

Options

A. Decrease in interionic forces and increases in `alpha`
B. Increase in the degree of ionization and interionic forces.
C. Increase in self ionization of water.
D. None of these

Explanation

To solve the question regarding the increase in the value of molar conductivity of acetic acid with dilution, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Molar Conductivity**: Molar conductivity (\( \Lambda_m \)) is defined as the conductivity of an electrolyte solution divided by its molar concentration. It is an important property that indicates how well an electrolyte conducts electricity.

2. **Weak Electrolytes and Ionization**: Acetic acid (\( CH_3COOH \)) is a weak electrolyte, meaning it does not completely dissociate into ions in solution. The degree of ionization (\( \alpha \)) is the fraction of the total number of acid molecules that dissociate into ions.

3. **Ostwald's Dilution Law**: According to Ostwald's dilution law, the dissociation constant (\( K_a \)) of a weak electrolyte can be expressed as:
\[ K_a = C \alpha^2 \]
where \( C \) is the concentration of the electrolyte and \( \alpha \) is the degree of ionization.

4. **Effect of Dilution**: When the concentration \( C \) decreases (i.e., when the solution is diluted), the degree of ionization \( \alpha \) increases. This can be derived from rearranging the equation:
\[ \alpha = \sqrt{\frac{K_a}{C}} \]
As \( C \) decreases, \( \alpha \) increases.

5. **Increase in Number of Ions**: As the degree of ionization \( \alpha \) increases, the number of ions produced in the solution also increases. This is because more acetic acid molecules are dissociating into ions.

6. **Relation to Molar Conductivity**: The molar conductivity of the solution is directly proportional to the number of ions present. Therefore, as the number of ions increases due to increased ionization, the molar conductivity of acetic acid also increases.

7. **Conclusion**: Thus, the increase in the value of molar conductivity of acetic acid with dilution is primarily due to the increase in the degree of ionization, which leads to a greater number of ions in the solution.

### Final Answer:
The increase in the value of molar conductivity of acetic acid with dilution is due to the increase in the degree of ionization of acetic acid, which results in a greater number of ions in the solution.

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