With dilution the molar conductivity of a solution:

Question

Accepted Answer

With dilution, the molar conductivity of a solution increases. This is because molar conductivity ($\Lambda_m$) is defined as the conductivity of a solution divided by the molar concentration of the electrolyte. Mathematically, it is expressed as:

$$
\Lambda_m = \frac{\kappa}{c}
$$

where $\kappa$ is the conductivity and $c$ is the concentration of the solution.

1. **Explanation for Option 1 (Increases):**
   - As the solution is diluted, the concentration $c$ decreases. Since molar conductivity is inversely proportional to concentration, a decrease in concentration leads to an increase in molar conductivity.
   - Additionally, dilution reduces the inter-ionic interactions and increases the mobility of ions, as they have more space to move freely. This increased mobility contributes to an increase in molar conductivity.

2. **Explanation for why Option 2 (Decreases) is incorrect:**
   - If molar conductivity were to decrease with dilution, it would imply that ions become less mobile or that inter-ionic interactions increase, which is contrary to the observed behavior. In reality, ions move more freely with dilution, leading to increased molar conductivity.

3. **Explanation for why Option 3 (Remains constant) is incorrect:**
   - Molar conductivity cannot remain constant with dilution because the relationship between molar conductivity and concentration is not linear. As concentration decreases, the molar conductivity increases due to reduced ion interactions and increased ion mobility.

4. **Explanation for why Option 4 (First increases then decreases) is incorrect:**
   - Molar conductivity does not exhibit a trend where it first increases and then decreases with dilution. Instead, it consistently increases as the solution becomes more dilute. There is no point during dilution where molar conductivity decreases after initially increasing.

In conclusion, the correct answer is Option 1: With dilution, the molar conductivity of a solution increases due to decreased concentration and increased ion mobility.