Q.Assertion: Conductivity of all electrolytes decreases on dilution.
Reason: On dilution number of ions per unit volume decreases.

Concept: Molar Conductivity — the distinction between conductivity ($\kappa$) and molar conductivity ($\Lambda_m$).

Reasoning:

1. Assertion is true. Conductivity ($\kappa$) depends on the number of ions per unit volume. On dilution, the concentration of ions drops, so $\kappa$ decreases.

2. Reason is also true. Dilution increases the volume of solution, so the number of ions per unit volume indeed decreases.

3. The reason IS the correct explanation of the assertion. Conductivity $\kappa$ is, by definition, proportional to the number of charge carriers (ions) present per unit volume ($\kappa \propto n \times z \times u$). Diluting a fixed amount of electrolyte spreads the same ions over a larger volume, so $n$ (ions per unit volume) falls — and since this is the dominant factor (ion mobility $u$ only rises slightly), $\kappa$ falls with it. This is the direct, causal reason conductivity decreases, not a weaker restatement of the same …

Let’s unpack this carefully. The question tests a subtle but crucial distinction in electrochemistry — the difference between conductivity (κ) and molar conductivity (Λₘ). Many students mix them up, so let’s build the intuition first.

Conductivity (κ) measures how well a solution conducts electricity per unit volume. Think of it as the “crowdedness” of charge carriers. If you have more ions packed into each cubic centimetre, the conductivity is higher. When you dilute an electrolyte solution, you add more water — the same number of ions now occupy a larger volume. So the number of ions per unit volume definitely falls. That’s the reason given, and it’s perfectly correct.

Molar conductivity (Λₘ), on the other hand, is conductivity per mole of electrolyte. It’s κ divided by concentration. When you dilute, κ drops, but concentration drops even faster — so Λₘ actually increases on dilution (because ions move more freely when they’re less crowded). That’s the classic result you memorise: “molar conductivity increases on dilution.” But the assertion here is about conductivity, not molar conductivity. That’s the key.

Now let’s walk through the logic step by step.

1. What does conductivity depend on?

   Conductivity κ is proportional to:

   • The number of charge carriers per unit volume (n)
   • The charge on each carrier (z)
   • The mobility of each carrier (u) So κ ∝ n × z × u. On dilution, n decreases because the same number of ions spreads into a larger volume. Mobility u actually increases slightly (less interionic attraction), but the drop in n dominates. Hence κ decreases.

2. Why does the reason hold?

   The reason says “on dilution number of ions per unit volume decreases.” That’s a direct, factual statement. For a fixed amount of electrolyte, adding solvent increases total volume, so concentration (ions per unit volume) falls. This is the primary cause of the drop in conductivity. The reason is true. …

Method: Conceptual Analysis of Conductivity vs. Dilution

Step 1 — Understand the Assertion

• Conductivity ($\kappa$) is the conductance of a solution placed between electrodes 1 cm apart and 1 cm² area.
• On dilution, the number of ions per unit volume decreases.
• Therefore, $\kappa$ decreases on dilution.
• ✓ Assertion is true.

Step 2 — Understand the Reason

• The reason states: “On dilution number of ions per unit volume decreases.”
• This is factually correct — dilution increases volume, so ion concentration drops.
• ✓ Reason is true.

Step 3 — Check if Reason correctly explains Assertion

• The assertion is about conductivity ($\kappa$), which depends directly on ion concentration (ions per unit volume).
• Since dilution reduces ion concentration, conductivity must fall.
• The reason directly explains why conductivity decreases.
• ✓ Reason is the correct explanation. …

Here’s a breakdown of the common mistakes students make on this question, along with how to avoid each.

Mistake 1: Confusing Conductivity with Molar Conductivity

• The Error: Students often think that because molar conductivity increases on dilution, conductivity must also increase. They then mark the assertion as false.
• Why It’s Wrong: Conductivity ($\kappa$) measures the ability of a fixed volume of solution (say, 1 cm³) to conduct electricity. On dilution, the number of ions per unit volume decreases sharply, so $\kappa$ decreases.
• How to Avoid: Remember the definitions:
  • Conductivity ($\kappa$): Depends on the concentration of ions in a fixed volume. Dilution → fewer ions per unit volume → $\kappa$ decreases.
  • Molar Conductivity ($\Lambda_m$): Depends on the total ions produced by one mole of electrolyte. Dilution → ions move more freely (less interionic attraction) → $\Lambda_m$ increases.
• Key Takeaway: The assertion is true for conductivity, not for molar conductivity.

Mistake 2: Misinterpreting the Reason

• The Error: Students think the reason is false because they recall that “on dilution, the number of ions increases” (which is true for weak electrolytes, but only up to a point).
• Why It’s Wrong: The reason says “number of ions per unit volume decreases.” This is always true for any electrolyte on dilution. Even for a weak electrolyte, while the degree of dissociation increases, the total volume increases so much that the concentration (ions per unit volume) still drops.
• How to Avoid: Focus on the phrase “per unit volume.” Dilution means adding more solvent. Even if more molecules dissociate, the volume grows faster, so the density of ions in any given drop of solution goes down.
• Key Takeaway: The reason is true and directly explains why conductivity decreases.

Mistake 3: Thinking the Reason Does Not Explain the Assertion

• The Error: Students correctly identify both as true but choose option (ii) — “reason is not the correct explanation.”
• Why It’s Wrong: The assertion says “conductivity decreases.” The reason says “number of ions per unit volume decreases.” These are directly linked: fewer charge carriers per unit volume → lower conductivity. The reason is the direct cause.
• How to Avoid: Ask yourself: “Does the reason logically lead to the assertion?” If yes, it is the correct explanation. Here, the drop in ion density is the only reason conductivity falls.
• Key Takeaway: The correct answer is (i) — both are true, and the reason correctly explains the assertion.

Mistake 4: Forgetting the Distinction Between Strong and Weak Electrolytes

• The Error: Students think that for weak electrolytes, the number of ions increases on dilution (due to increased dissociation), so the reason must be false. …