Step 1: Understanding the Concept:
Electrolytic conductivity (\( \kappa \)), also known as specific conductance, is the measure of a solution's ability to conduct electricity per unit volume.
Electricity in solutions is carried by ions. Therefore, the conductivity depends directly on the concentration of ions (number of ions per unit volume).
As a solution is diluted (volume increases for a fixed amount of solute), the number of ions per unit volume decreases, and hence the specific conductivity (\( \kappa \)) decreases.
To find the maximum conductivity, we must find the solution with the highest molarity (concentration).
Step 2: Key Formula or Approach:
The concentration or Molarity (\( M \)) is given by:
\[ M = \frac{\text{moles of solute}}{\text{volume in Liters}} \]
We will calculate \( M \) for all four options.
Step 3: Detailed Explanation:
Let's compute the molarities:
1. Solution (1): \( 0.2 \text{ mol} / 0.250 \text{ L} = 0.8 \text{ M} \)
2. Solution (2): \( 0.3 \text{ mol} / 0.600 \text{ L} = 0.5 \text{ M} \)
3. Solution (3): \( 0.6 \text{ mol} / 1.000 \text{ L} = 0.6 \text{ M} \)
4. Solution (4): \( 0.8 \text{ mol} / 2.000 \text{ L} = 0.4 \text{ M} \)
Comparing these values: \( 0.8 \text{ M}>0.6 \text{ M}>0.5 \text{ M}>0.4 \text{ M} \).
Solution (1) is the most concentrated, meaning it has the highest density of ions available to carry charge per unit volume.
Step 4: Final Answer:
Since conductivity is directly proportional to the concentration of ions for a given electrolyte, the solution with 0.8 M concentration will have the maximum conductivity.
The correct option is (A).