A conductivity cell with two electrodes (dark side) are half filled with infinitely dilute aqueous solution of a weak electrolyte. If volume is doubled by adding more water at constant temperature, the molar conductivity of the cell will -

Solution

Chemistry ma’am · 4 steps

Infinitely dilute means Λₘ is already at its limit, so more water has nothing left to change.

1. Already at the limit. At infinite dilution even a weak electrolyte is fully dissociated, and the ions are too far apart to pull on each other. So the molar conductivity has already reached its limiting value Λₘ°, and adding water cannot raise it any further.
2. Check with the cell. The number of ions stays the same. When the volume doubles, the concentration c halves, and the conductivity κ (ions per cm³) also halves. Their ratio does not change.

   Λₘ = κ/c → (κ/2)/(c/2) = κ/c

3. Measuring it. The cell goes from half full to full, so the wetted electrode area doubles while κ halves, and the conductance G = κ A/l also stays the same. With c close to zero, this conductance is tiny and very hard to measure accurately. That is why Λₘ° of a weak electrolyte is found with Kohlrausch's law, not read off a meter.
4. So. The molar conductivity stays the same, and in practice it cannot be measured accurately. The answer is (d).

The idea to keep. Dilution raises Λₘ only until it reaches Λₘ°. Once a solution is infinitely dilute, extra water changes nothing. For a weak electrolyte, get Λₘ° from Kohlrausch's law.

Answer from the NTA final answer key. Solution by PrepWiser.