Q.Assertion: $\Lambda_m$ for weak electrolytes shows a sharp increase when the electrolytic solution is diluted.
Reason: For weak electrolytes degree of dissociation increases with dilution of solution.

The key idea is that molar conductivity ($\Lambda_m$) depends on both the number of ions and their mobility. For weak electrolytes, dilution increases the degree of dissociation ($\alpha$), which sharply raises the number of charge carriers.

• At infinite dilution, $\Lambda_m$ approaches $\Lambda_m^\infty$, but for weak electrolytes this limit is reached only at very high dilution because $\alpha$ grows rapidly. …

Why This Works

The key idea is molar conductivity ($\Lambda_m$) and how it behaves for weak electrolytes like acetic acid. Unlike strong electrolytes (which are fully dissociated even at moderate concentrations), weak electrolytes dissociate only partially. When you dilute the solution, the equilibrium shifts toward more dissociation — that’s Le Chatelier’s principle in action.

The sharp increase in $\Lambda_m$ on dilution is not because ions move faster; it’s because more ions are produced per mole of electrolyte. Let’s walk through it.

1. What is $\Lambda_m$? Molar conductivity is defined as:

where $\kappa$ is the specific conductivity and $c$ is the concentration in mol/L. For a weak electrolyte, $\kappa$ itself depends on the number of ions present. At higher concentration, dissociation is low, so $\kappa$ is small. On dilution, $c$ decreases, but the degree of dissociation $\alpha$ increases — so the number of ions per mole rises, and $\kappa$ does not drop as fast as $c$ does. The net effect: $\Lambda_m$ increases sharply.

2. Why does $\alpha$ increase with dilution? For a weak electrolyte $AB$ dissociating as $AB \rightleftharpoons A^+ + B^-$, the equilibrium constant $K$ is:

At a given temperature, $K$ is fixed. If you dilute (decrease $c$), the numerator $c \alpha^2$ must adjust to keep $K$ constant. The only way is for $\alpha$ to increase — because $\alpha^2$ appears in the numerator, a small drop in $c$ can be compensated by a rise in $\alpha$. This is a direct consequence of the equilibrium law.

3. The sharp increase — why “sharp”? For strong electrolytes, $\Lambda_m$ increases only gradually on dilution (due to reduced ion-ion interactions). For weak electrolytes, the increase is much steeper because the number of charge carriers itself multiplies. At very high dilution, $\alpha$ approaches 1, and $\Lambda_m$ approaches $\Lambda_m^\infty$, but the approach is rapid in the dilute region. …

Method: Conceptual Analysis of Molar Conductivity vs. Dilution

Step 1 – Understand the assertion

The assertion states that molar conductivity ($\Lambda_m$) for weak electrolytes shows a sharp increase when the solution is diluted.

This is true — for weak electrolytes like acetic acid, $\Lambda_m$ increases steeply at high dilutions.

Step 2 – Understand the reason

The reason says: For weak electrolytes, degree of dissociation ($\alpha$) increases with dilution.

This is also true — dilution shifts the equilibrium towards dissociation (Le Chatelier’s principle).

Step 3 – Connect the two

Molar conductivity is given by:

where $\Lambda_m^\infty$ is the limiting molar conductivity.

As dilution increases, $\alpha$ increases → $\Lambda_m$ increases sharply. …

Here’s a breakdown of the common mistakes students make on this assertion-reason question about molar conductivity of weak electrolytes, along with how to avoid each.

✗ Mistake 1: Thinking the assertion is false

What happens:

Some students believe that for weak electrolytes, dilution decreases conductivity because there are fewer ions per unit volume.

How to avoid:

• Remember: Molar conductivity ($\Lambda_m$) is not the same as conductivity ($\kappa$).
• On dilution, $\kappa$ (conductivity per unit volume) decreases, but $\Lambda_m$ increases because more ions are produced per mole due to increased dissociation.
• For weak electrolytes, the sharp rise in $\Lambda_m$ at high dilution is a signature behavior.

✗ Mistake 3: Misjudging the reason as false

What happens:

Students think “degree of dissociation” is constant or decreases with dilution.

How to avoid:

• Know Ostwald’s dilution law: For weak electrolytes, $\alpha \propto \frac{1}{\sqrt{C}}$.
• As dilution increases (concentration decreases), degree of dissociation ($\alpha$) increases.
• This is the direct cause of the sharp rise in $\Lambda_m$.

✗ Mistake 4: Choosing option (ii) instead of (i)

What happens: …