The molar conductivity of a weak electrolyte when plotted against the square root of its concentration, which of the following is expected to be observed ?

We need to describe how molar conductivity of a weak electrolyte varies with concentration.

We first recall the behavior of weak electrolytes. For weak electrolytes (like $$CH_3COOH$$, $$NH_4OH$$), the degree of dissociation $$\alpha$$ increases significantly as the solution becomes more dilute, following Ostwald’s dilution law: $$\alpha = \sqrt{K_a/c}$$ for dilute solutions.

Next, we consider the relationship between molar conductivity and concentration. Molar conductivity is given by $$\Lambda_m = \alpha \cdot \Lambda_m^\circ$$. As concentration increases, $$\alpha$$ decreases sharply (since $$\alpha \propto 1/\sqrt{c}$$), causing $$\Lambda_m$$ to decrease sharply.

Finally, when we examine the behavior plotted against $$\sqrt{c}$$, we see that unlike strong electrolytes (which show a linear decrease as per the Debye-Hückel-Onsager equation: $$\Lambda_m = \Lambda_m^\circ - A\sqrt{c}$$), weak electrolytes exhibit a sharp, non-linear decrease in molar conductivity with increasing concentration.

The correct answer is Option B) Molar conductivity decreases sharply with increase in concentration.