Animated Solution for Chemistry - Electrochemistry: Given below are two statements. Statement I: The limiting molar conductivity of KCl (strong electrolyte) is higher compared to that of ${\text{CH}}_3\text{COOH}$ (weak electrolyte). Statement II: Molar conductivity decreases with decrease in concentration of electrolyte. In the light of the above statements, choose the most appropriate answer from the options given below

The world of electrochemistry is filled with fascinating counter-intuitive phenomena. When we hear the terms "strong" and "weak" electrolytes, our minds immediately jump to the conclusion that strong electrolytes must always be better conductors. But is that really the case at infinite dilution? Let's dive deep into this classic JEE problem and unravel the truth behind molar conductivity.

Statement I claims that the limiting molar conductivity of $\text{KCl}$ (a strong electrolyte) is higher than that of ${\text{CH}}_3\text{COOH}$ (a weak electrolyte). To verify this, we need to understand what happens at infinite dilution ($c\to 0$).

At infinite dilution, the solvent is so abundant that the ions are infinitely far apart. Because they don't interact with each other, even a weak electrolyte like acetic acid becomes 100% dissociated. This means the "weakness" of the electrolyte is no longer a factor. The conductivity now depends entirely on the nature of the individual ions.

According to Kohlrausch's Law of Independent Migration of Ions, the limiting molar conductivity (${\Lambda }_m^{\infty }$) is simply the sum of the limiting ionic conductivities of the cation and the anion.

For Potassium Chloride:

Now, let's look at Acetic Acid:

Here is where the magic happens. The hydrogen ion (${\text{H}}^{+}$) is essentially a bare proton. In water, it doesn't just swim through the liquid like other ions. Instead, it moves via the Grotthuss mechanism (or proton hopping). A proton attaches to a water molecule, and instantly, another proton detaches from the other side of the molecule. This relay race allows the charge to move incredibly fast, giving the ${\text{H}}^{+}$ ion an exceptionally high ionic conductivity ($\approx 349.8{\text{ S cm}}^2{\text{ mol}}^{-1}$).

Comparing the two, we clearly see that ${\Lambda }_m^{\infty }({\text{CH}}_3\text{COOH})>{\Lambda }_m^{\infty }(\text{KCl})$. Therefore, Statement I is absolutely false.

Statement II claims that molar conductivity decreases with a decrease in concentration. Let's test this. Decreasing the concentration means we are diluting the solution.

For weak electrolytes, dilution shifts the dissociation equilibrium forward (according to Ostwald's dilution law). More molecules break apart into ions, increasing the total number of charge carriers per mole of the electrolyte. Hence, the molar conductivity shoots up drastically.

For strong electrolytes, they are already fully dissociated. However, at higher concentrations, the ions are close together and experience strong interionic attractions (the electrophoretic and relaxation effects), which drag them down. When we dilute the solution, the ions move further apart, the drag decreases, and their mobility increases. Thus, the molar conductivity increases slightly.

In both scenarios, molar conductivity increases with a decrease in concentration. Therefore, Statement II is also false.

Both statements presented in the question are conceptually flawed. This problem serves as a brilliant reminder to never judge an electrolyte's limiting conductivity purely by its "strong" or "weak" label, and to always remember the unique behavior of the hydrogen ion!