Q.Solutions of two electrolytes 'A' and 'B' are diluted. The $\Lambda_m$ of 'B' increases 1.5 times while that of 'A' increases 25 times. Which of the two is a strong electrolyte? Justify your answer.

Concept: Molar Conductivity — For strong electrolytes, $\Lambda_m$ increases only slightly on dilution (due to reduced ion-ion interactions), while for weak electrolytes, $\Lambda_m$ increases sharply (due to increased dissociation).

Reasoning:

1. Strong electrolytes are fully dissociated even at moderate concentrations. Dilution reduces interionic attraction, so $\Lambda_m$ rises only modestly.
2. Weak electrolytes are partially dissociated. Dilution shifts the equilibrium toward greater dissociation, producing many more ions, so $\Lambda_m$ rises steeply. …

The key to this question lies in understanding what molar conductivity ($\Lambda_m$) actually measures and how it behaves when you dilute an electrolyte solution.

Molar conductivity is the conductivity of a solution containing one mole of electrolyte, placed between electrodes 1 cm apart. When you dilute a solution, the number of ions per unit volume drops — so you might expect conductivity to fall. But $\Lambda_m$ often increases on dilution. Why? Because dilution affects how freely ions can move and, for weak electrolytes, how many ions actually exist.

For a strong electrolyte (like NaCl, HCl, KOH), the salt is fully dissociated into ions even at high concentration. Dilution doesn't create more ions — it just separates the existing ones further apart, reducing interionic attractions. This gives a modest increase in $\Lambda_m$ as ions move more freely. The change is small.

For a weak electrolyte (like acetic acid, NH₄OH), the salt is mostly undissociated at higher concentrations. On dilution, the equilibrium shifts toward more dissociation (Le Chatelier's principle), so the number of charge carriers increases dramatically. This causes a large jump in $\Lambda_m$.

Now let's apply this to the numbers given.

1. Electrolyte B shows a 1.5× increase in $\Lambda_m$ on dilution. This is a small change. It means B was already nearly fully dissociated even before dilution — dilution just slightly improves ion mobility. This is the hallmark of a strong electrolyte.

2. Electrolyte A shows a 25× increase — a huge jump. Such a large rise cannot come from mobility changes alone. It signals that A was poorly dissociated at higher concentration, and dilution caused a massive surge in the number of ions. This is characteristic of a weak electrolyte. …

Method: Variation of Molar Conductivity with Dilution (Kohlrausch's Law & Weak/Strong Electrolyte Behaviour)

Step 1 — Recall the key concept

• Strong electrolytes are fully dissociated even at moderate concentrations. On dilution, $\Lambda_m$ increases only slightly because interionic attractions decrease.
• Weak electrolytes are partially dissociated. On dilution, dissociation increases sharply, so $\Lambda_m$ increases dramatically.

Step 2 — Compare the given data

• For electrolyte A: $\Lambda_m$ increases 25 times → very large increase.
• For electrolyte B: $\Lambda_m$ increases 1.5 times → small increase.

Step 3 — Apply the reasoning

• A small increase (like 1.5×) is characteristic of a strong electrolyte — already nearly fully dissociated, dilution only reduces ion-ion interactions slightly. …

Here’s a breakdown of the common mistakes students make on this specific Molar Conductivity question, and how to avoid each one.

Mistake 1: Confusing the magnitude of change with the type of electrolyte

The Error:

Students see that the molar conductivity ($\Lambda_m$) of 'A' increases by 25 times (a huge jump) and think, "Wow, that's a strong electrolyte because it conducts so much more!" They associate a large increase with high strength.

The Correct Concept (Why this is wrong):

• Strong electrolytes (like NaCl, HCl) are fully dissociated in solution. Diluting them doesn't create more ions; it just spreads the existing ions further apart. This reduces inter-ionic attractions, causing a small increase in $\Lambda_m$.
• Weak electrolytes (like CH₃COOH, NH₄OH) are partially dissociated. Dilution shifts the equilibrium towards more dissociation ($\alpha \to 1$), creating many new ions. This causes a large increase in $\Lambda_m$.

How to Avoid:

• Memorise the trend: Strong = small increase on dilution. Weak = large increase on dilution.
• Think of the cause: The increase is due to new ions being created (weak) vs. existing ions moving more freely (strong). Creating 25x more ions is a weak electrolyte behaviour.

Answer for the question: 'B' is the strong electrolyte because its $\Lambda_m$ increases only 1.5 times (a small change), indicating it was already fully dissociated.

Mistake 2: Misinterpreting the "1.5 times" and "25 times" data

The Error:

Students try to compare the absolute values of $\Lambda_m$ (e.g., "A has a higher $\Lambda_m$ after dilution, so it's stronger"). The question only gives the ratio of change, not the actual values.

The Correct Concept:

The key is the relative change (factor of increase), not the final value. A strong electrolyte might have a high $\Lambda_m$ initially, but its increase factor is small. A weak electrolyte starts with a very low $\Lambda_m$ and increases dramatically.

How to Avoid:

• Focus on the factor: Ignore what the actual numbers might be. The factor (1.5 vs 25) is the only information you need.
• Use the formula: $\Lambda_m = \kappa \times \frac{1000}{C}$. For a weak electrolyte, as $C \to 0$, $\Lambda_m \to \Lambda_m^\infty$ (a large increase). For a strong electrolyte, $\Lambda_m$ is already close to $\Lambda_m^\infty$ at moderate concentrations.

Mistake 3: Forgetting the definition of Molar Conductivity ($\Lambda_m$)

The Error:

Students confuse $\Lambda_m$ with conductivity ($\kappa$). They think dilution always decreases conductivity (which is true for $\kappa$), and then get confused when the question talks about $\Lambda_m$ increasing.

The Correct Concept:

• Conductivity ($\kappa$): Conductance of a 1 cm³ solution. Decreases on dilution (fewer ions per unit volume). …