Which of the following increases with dilution?

Options

A. Conductivity
B. Molar conductivity
C. Equivalent conductivitiy
D. both (2) and (3)

Explanation

To solve the question "Which of the following increases with dilution?" we need to analyze the behavior of conductivity, molar conductivity, and equivalent conductivity when a solution is diluted.

### Step-by-Step Solution:

1. **Understanding Conductivity**:
- Conductivity (κ) is a measure of a solution's ability to conduct electricity, which depends on the concentration of ions in the solution.
- When a solution is diluted, the concentration of ions decreases because the same amount of solute is present in a larger volume.
- As a result, the conductivity decreases with dilution.

**Hint**: Remember that conductivity is directly related to the number of charge carriers (ions) in the solution.

2. **Understanding Molar Conductivity**:
- Molar conductivity (Λ_m) is defined as the conductivity of a solution divided by its molar concentration (C), i.e., Λ_m = κ/C.
- When the solution is diluted, while the conductivity (κ) decreases, the concentration (C) also decreases.
- However, the decrease in concentration is more significant than the decrease in conductivity. This means that the molar conductivity increases with dilution.

**Hint**: Consider how both conductivity and concentration change with dilution, and how their ratio behaves.

3. **Understanding Equivalent Conductivity**:
- Equivalent conductivity (Λ_e) is similar to molar conductivity but is based on the equivalent concentration of the solute.
- It is defined as Λ_e = κ/V, where V is the volume of the solution.
- As the solution is diluted, the volume (V) increases while the conductivity (κ) decreases. The increase in volume is more significant than the decrease in conductivity, leading to an increase in equivalent conductivity.

**Hint**: Focus on the relationship between conductivity and volume, and how their changes affect equivalent conductivity.

4. **Conclusion**:
- From the analysis, we find that:
- Conductivity decreases with dilution.
- Molar conductivity increases with dilution.
- Equivalent conductivity increases with dilution.
- Therefore, the correct options that increase with dilution are molar conductivity and equivalent conductivity.

### Final Answer:
The correct options that increase with dilution are **molar conductivity and equivalent conductivity** (options B and C). Thus, the answer is option D (both B and C are true).