Strong vs Weak Electrolytes: Λm vs √c Graph Explained

Chemistry · Electrochemistry · NEET

When you plot molar conductivity (Λm) against the square root of concentration (√c), a strong electrolyte like KCl or BaCl₂ gives an almost straight line that only dips a little as concentration rises. A weak electrolyte like acetic acid (CH₃COOH) gives a curve that shoots up very steeply near zero concentration and never becomes a straight line. Memory hook: "Strong = Straight, Weak = Whip-up curve."
√c (square root of concentration)ΛmStrong (KCl) — straightWeak (CH₃COOH) — steep curveΛ°mno straightextrapolate line → Λ°m (strong only)
Λm vs √c: the strong electrolyte (blue) is a near-straight line you can extend back to read Λ°m; the weak electrolyte (red) curves up steeply near zero concentration, so extrapolation fails and Λ°m needs Kohlrausch's law.

Your doubts, answered

Why does the Λm vs √c graph of a strong electrolyte come out almost straight?

In a strong electrolyte (like KCl, NaCl, BaCl₂) the substance is fully ionised at all concentrations. So the number of ions does not change much with dilution. The only reason Λm rises a little on dilution is that ions get farther apart, so they slow each other down less (less ion-ion attraction). This gives a small, steady increase, which is why the plot is a straight line that follows Λm = Λ°m − A√c. You can just extend (extrapolate) this straight line back to √c = 0 to read off Λ°m directly.

Why does a weak electrolyte's graph curve up so sharply near zero concentration?

A weak electrolyte (like acetic acid CH₃COOH, or NH₄OH) is only partly ionised. At normal concentration very few molecules break into ions, so Λm is low. As you dilute a lot, the degree of dissociation (α) jumps up a lot, so suddenly there are many more ions and Λm shoots up steeply. Because this rise is due to more ions forming (not just ions moving apart), the curve keeps climbing sharply near √c = 0 instead of flattening. That is why it is a curve, not a straight line.

Does the equation Λm = Λ°m − A√c work for weak electrolytes too?

No. This is the Debye-Hückel-Onsager equation and it only works for strong electrolytes, where the plot is linear. For weak electrolytes the plot is a steep curve, so a single straight-line equation cannot describe it. This is a very common NEET trap: the statement 'this equation applies to both strong and weak electrolytes' is FALSE.

Why can't we get Λ°m of a weak electrolyte by extrapolating the graph?

For a strong electrolyte the line is straight, so extending it back to √c = 0 gives Λ°m easily. For a weak electrolyte the curve rises almost vertically near √c = 0, so there is no straight part to extend — extrapolation gives a wrong answer. Instead, we find Λ°m of a weak electrolyte indirectly using Kohlrausch's law (adding up limiting values of strong electrolytes). This is exactly why the next topic, Kohlrausch's law, exists.

Does the slope A depend on the electrolyte or on the solvent?

Both. The slope A depends on the nature of the solvent (its viscosity and dielectric constant) AND on the charge type of the electrolyte. A 1:1 electrolyte (like KCl) has a different A than a 2:2 electrolyte (like MgSO₄). But two electrolytes of the SAME charge type have the same A — for example BaCl₂ (2:1) and Mg(OH)₂ (2:1) share the same slope, while BaCl₂ (2:1) and MgSO₄ (2:2) do not.

⚠️ The NEET trap
The equation Λm = Λ°m − A√c is valid for both strong and weak electrolytes, so both give a straight line.
The equation and the straight-line plot are valid ONLY for strong electrolytes. Weak electrolytes give a steep curve, and their Λ°m is found by Kohlrausch's law, not by extrapolation.
🧠 Straight line and √c equation = STRONG only. If you see 'applies to both' or 'weak gives straight line', it is a trap.

Real NEET questions

NEET 2023 Phase 2

Molar conductance of an electrolyte increases with dilution according to the equation: Λm = Λ°m − A√c. Which of the following statements are true? (A) This equation applies to both strong and weak electrolytes. (B) Value of the constant A depends upon the nature of the solvent. (C) Value of constant A is same for both BaCl₂ and MgSO₄. (D) Value of constant A is same for both BaCl₂ and Mg(OH)₂.

A · (B) and (C) only
B · (B) and (D) only
C · (A) and (B) only
D · (A), (B) and (C) only
Solution: The equation Λm = Λ°m − A√c is the Debye-Hückel-Onsager equation. It holds only for STRONG electrolytes (linear plot), so (A) is FALSE. The slope A depends on the nature of the solvent and the charge type, so (B) is TRUE. A is the same only for electrolytes of the same charge type: BaCl₂ is 2:1 while MgSO₄ is 2:2, so (C) is FALSE; BaCl₂ (2:1) and Mg(OH)₂ (2:1) are the same type, so (D) is TRUE. Correct: (B) and (D) only.
ReNEET 2026

For a strong electrolyte salt XY, the plot of Λm versus √c has slope −90.0 S cm² mol⁻³ᐟ² L¹ᐟ² at 298 K. At 0.01 M, Λm = 145.0 S cm² mol⁻¹. The limiting molar conductivity of Y⁻ ion, λ°(Y⁻) (in S cm² mol⁻¹), is: [Given λ°(X⁺) = 74.0 S cm² mol⁻¹]

A · 80.0
B · 100.0
C · 90.0
D · 76.0
Solution: Because XY is a strong electrolyte, use Λm = Λ°m − A√c with A = 90. At c = 0.01 M, √c = 0.1, so 145 = Λ°m − 90(0.1) = Λ°m − 9, giving Λ°m = 154. By Kohlrausch's law Λ°m(XY) = λ°(X⁺) + λ°(Y⁻), so 154 = 74 + λ°(Y⁻), giving λ°(Y⁻) = 80.0 S cm² mol⁻¹.

Solved Electrochemistry NEET PYQs

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Frequently asked

What is the shape of the Λm vs √c graph for strong and weak electrolytes?

Strong electrolytes give a nearly straight line with a small downward slope. Weak electrolytes give a curve that rises steeply near √c = 0 (very low concentration) and does not become linear.

Give one example each of a strong and a weak electrolyte for this graph.

Strong electrolyte: KCl, NaCl, HCl, BaCl₂. Weak electrolyte: acetic acid (CH₃COOH), NH₄OH. Strong ones are fully ionised; weak ones are only partly ionised.

Why is Λm of a weak electrolyte so low at high concentration?

Because at high concentration a weak electrolyte is only slightly dissociated (small α), so there are very few ions to carry current. On dilution α increases, more ions form, and Λm rises sharply.

How do we find Λ°m of a weak electrolyte if extrapolation fails?

We use Kohlrausch's law of independent migration of ions. We add and subtract the limiting molar conductivities of suitable strong electrolytes to build up the value for the weak electrolyte, for example Λ°m(CH₃COOH) = Λ°m(CH₃COONa) + Λ°m(HCl) − Λ°m(NaCl).

Is the slope A the same for all electrolytes?

No. A is the same only for electrolytes of the same charge type and the same solvent. A 1:1 salt and a 2:2 salt have different slopes; a 2:1 salt like BaCl₂ has the same slope as another 2:1 salt like Mg(OH)₂.