The statement about molar conductivity being inversely proportional to dilution is actually incorrect. Molar conductivity, in fact, increases with dilution.
Here's the breakdown:
Dilution: When a solution is diluted, the total volume increases while the amount of solute (electrolyte) remains constant. This means the concentration of the solution decreases.
Molar conductivity: This quantity represents the ability of a solution containing one mole of electrolyte to conduct electricity. It's calculated by dividing the conductivity of the solution by its concentration.
Electrolytic conductivity: This simply refers to the conductivity of the solution itself, without any specific reference to the amount of electrolyte present.
Now, let's see how dilution affects each:
Conductivity: As the concentration decreases with dilution, conductivity also decreases because there are fewer ions per unit volume to carry the current.
Molar conductivity: Although the conductivity decreases, it's divided by a decreasing concentration (due to dilution) in the calculation of molar conductivity. This division ultimately results in an increase in molar conductivity.
Therefore, while the relationship between conductivity and dilution is inverse (they decrease together), the relationship between molar conductivity and dilution is direct (they increase together).
Here's an analogy: Imagine you have a group of people (ions) carrying buckets (conducting electricity). If you spread them out further by adding more empty space (dilution), the total amount of water they can carry (conductivity) decreases. However, the average water carrying capacity per person (molar conductivity) actually increases because each person has a smaller area to cover.