Q.Why does the conductivity of a solution decrease with dilution?

Concept: Molar Conductivity — the conductivity per unit concentration, which reveals how dilution affects ion mobility.

Conductivity ($\kappa$) depends on the number of charge carriers per unit volume. When you dilute a solution, the concentration of ions drops. Since $\kappa = \frac{1}{R} \cdot \frac{l}{A}$, fewer ions per cm³ means fewer carriers to conduct current, so $\kappa$ falls.

However, molar conductivity ($\Lambda_m = \frac{\kappa}{c}$) behaves differently — it increases on dilution because ions move more freely when interionic attractions weaken. The decrease in $\kappa$ is simply a concentration effect, not a loss of conducting ability per mole.

The Core Idea: What Conductivity Actually Measures

Conductivity ($\kappa$) is the ability of a solution to conduct electricity. It depends on two things: how many ions are present in a given volume, and how fast those ions can move under an electric field.

When you dilute a solution, you add more solvent. The total number of ions in the entire solution stays the same (assuming no dissociation changes), but the volume increases. So the concentration of ions — ions per cubic centimetre — goes down. Fewer ions per unit volume means fewer charge carriers available to move current through that volume. That’s the primary reason conductivity falls.

But there’s a subtle twist: as you dilute, ions get more room to move. Interionic attractions weaken, so each ion can move a little faster. This effect (increase in ionic mobility) tries to raise conductivity. However, the drop in ion concentration is far more dramatic, so the net effect is a decrease.

Step-by-Step Reasoning

1. Define conductivity in terms of charge carriers

Conductivity $\kappa$ is given by:

where $n_i$ is the number of ions of type $i$ per unit volume, $q_i$ is their charge, and $\mu_i$ is their mobility (speed per unit electric field). For a simple salt like NaCl, this becomes:

Since the solution is electrically neutral, $n_+ = n_- = n$, so:

2. What happens to $n$ upon dilution?

Suppose you start with a solution of concentration $c$ (mol/L). The number of ions per unit volume is $n = c \times N_A$ (Avogadro’s number). When you dilute by adding solvent, $c$ decreases. For example, if you double the volume, $c$ halves, and so $n$ halves. This is a direct, proportional drop.

3. What happens to $\mu_+$ and $\mu_-$ upon dilution?

In a concentrated solution, ions are close together. Their mutual electrostatic attractions slow them down — a positive ion is pulled back by nearby negative ions. As you dilute, the average distance between ions increases. These attractions weaken, so each ion can move more freely. Hence, mobilities $\mu_+$ and $\mu_-$ increase slightly with dilution.

4. Which effect wins?

The concentration $n$ drops linearly with dilution (factor of 2, 10, 100…). The mobilities increase, but only by a small amount — typically a few percent over a tenfold dilution. The product $n \times (\mu_+ + \mu_-)$ is dominated by the drop in $n$. So $\kappa$ decreases.

5. A concrete example

Take 0.1 M KCl solution. Its conductivity is about 1.29 S/m. Dilute it to 0.01 M (tenfold dilution). The new conductivity is about 0.141 S/m — roughly one-tenth. The slight increase in mobility makes it a bit more than one-tenth (0.129 vs 0.141), but the dominant factor is the tenfold drop in ion concentration.

6. The limiting case: infinite dilution

As you keep diluting, $\kappa$ approaches zero. At infinite dilution, there are effectively no ions per unit volume, so conductivity is zero. The mobilities approach their maximum values (the limiting molar conductivities), but with no ions to carry current, $\kappa$ is zero.

The Classic Pitfall

Students often think: “Dilution makes ions move faster, so conductivity should increase.” That’s wrong because they forget that conductivity is a per-volume property. Imagine a room full of people (ions). If you spread them out into a larger room, each person can move more freely, but the number of people per square metre drops. The overall “crowd density” (conductivity) goes down, even though each individual moves faster.

Method: Kohlrausch's Law of Independent Migration of Ions

This method explains the why behind conductivity changes with dilution using the concept of molar conductivity ($\Lambda_m$).

Step 1: Define the key quantities

• Conductivity ($\kappa$) — the ability of a solution to conduct electricity. It depends on the number of ions per unit volume.
• Molar conductivity ($\Lambda_m$) — conductivity per mole of electrolyte:

where $c$ is the concentration in mol/L.

Step 2: Understand what happens on dilution

When you dilute a solution:

• The number of ions per unit volume decreases (because you add more solvent).
• Therefore, conductivity ($\kappa$) decreases — fewer charge carriers per cm³.

But — this is only part of the story.

Step 3: The key insight — Molar conductivity increases on dilution

Even though $\kappa$ falls, $\Lambda_m$ rises because:

When $c$ decreases (dilution), $\kappa$ also decreases — but not proportionally. The drop in $\kappa$ is slower than the drop in $c$, so the ratio $\kappa/c$ increases.

Why? Because at higher dilution, interionic attractions weaken. Ions move more freely, so each mole of electrolyte contributes more to conductivity.

Step 4: The final answer — why conductivity decreases

Conductivity ($\kappa$) decreases with dilution simply because:

• The number of ions per unit volume falls.
• Fewer charge carriers → lower ability to conduct electricity per cm³.

But the molar conductivity ($\Lambda_m$) increases because each ion moves more freely when the solution is dilute.

Summary Table

Final takeaway for exams:

Conductivity drops because ion concentration per cm³ falls. Molar conductivity rises because ions move more independently — this is explained by Kohlrausch’s law and the concept of interionic attraction.

Here are the common mistakes students make when explaining why conductivity decreases with dilution, along with the concept-first reasoning to avoid them.

✗ Mistake 1: Confusing Conductivity with Molar Conductivity

The error:

Students say “conductivity decreases because the number of ions decreases.”

This is partially true but misses the key distinction — they often blur the line between conductivity ($\kappa$) and molar conductivity ($\Lambda_m$).

Why it’s wrong:

• 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 drops → $\kappa$ decreases.
• But molar conductivity ($\Lambda_m$) actually increases on dilution because ions move more freely (less interionic attraction).

How to avoid:

• Always define both terms before answering.
• Remember the formula:

where $C$ is concentration. As $C$ drops, $\kappa$ drops less steeply, so $\Lambda_m$ rises.

Key takeaway: Conductivity falls because ion density per mL falls — not because ions disappear.

✗ Mistake 2: Saying “Ions are fewer” Without Explaining Why

The error:

Students write: “On dilution, the number of ions decreases, so conductivity decreases.”

This is vague and can be misinterpreted.

Why it’s wrong:

• The total number of ions in the whole solution actually remains the same (if the electrolyte is strong).
• What changes is concentration — ions per unit volume.

How to avoid:

• Use precise language:

  “On dilution, the concentration of ions (ions per cm³) decreases, so the conductivity (which depends on ion density) decreases.”

• Draw a mental picture:

  • Before dilution: many ions packed tightly → high conductivity.
  • After dilution: same ions spread over larger volume → fewer ions per cm³ → lower conductivity.

✗ Mistake 3: Forgetting the Role of Interionic Attractions

The error:

Students treat ions as independent particles and ignore electrostatic interactions.

Why it’s wrong:

• In concentrated solutions, ions are close together → strong attraction → ions move sluggishly.
• On dilution, ions move farther apart → weaker attraction → each ion moves faster.
• This is why molar conductivity increases with dilution — but conductivity still drops because the drop in ion density outweighs the increase in ion speed.

How to avoid:

• Mention Kohlrausch’s law and the concept of interionic attraction.
• For strong electrolytes:

As $C \to 0$, $\Lambda_m \to \Lambda_m^\infty$ (maximum molar conductivity).

Remember: Conductivity is number of charge carriers × speed of each carrier. Dilution reduces number drastically, even though speed increases slightly.

✗ Mistake 4: Ignoring the Difference Between Strong and Weak Electrolytes

The error:

Students give the same explanation for both strong and weak electrolytes.

Why it’s wrong:

• Strong electrolytes (e.g., NaCl): fully dissociated at all dilutions. Conductivity drops purely due to dilution of ions.
• Weak electrolytes (e.g., CH₃COOH): on dilution, degree of dissociation ($\alpha$) increases. So the number of ions per unit volume drops less sharply than for strong electrolytes.

How to avoid:

• For weak electrolytes, mention that dilution increases $\alpha$ (Ostwald’s dilution law):

As $C$ decreases, $\alpha$ increases → partially compensates the drop in conductivity.

• For strong electrolytes, $\alpha \approx 1$ always → no such compensation.

✗ Mistake 5: Writing the Wrong Graph Trend

The error:

Students draw a graph of $\kappa$ vs. dilution that increases with dilution, or they confuse it with the $\Lambda_m$ vs. $\sqrt{C}$ graph.

Why it’s wrong:

• $\kappa$ decreases steadily with dilution (approaches zero).
• $\Lambda_m$ increases with dilution (approaches $\Lambda_m^\infty$).

How to avoid:

• Memorise the two distinct graphs:

• Practice sketching both side-by-side.

✓ Quick Summary: How to Answer Correctly

1. Define conductivity ($\kappa$) — conductance per unit length and area.
2. State clearly: On dilution, concentration of ions decreases → fewer charge carriers per cm³ → $\kappa$ decreases.
3. Distinguish from molar conductivity: $\Lambda_m$ increases because ions move more freely.
4. Mention interionic attractions (for strong electrolytes) and degree of dissociation (for weak electrolytes).
5. End with the formula:

Final exam tip: If the question asks “Why does conductivity decrease?” — never say “because molar conductivity increases.” That’s a different concept. Stick to ion density per unit volume.