Conductance of electrolytic solutions

What is electrolytic conductance?

Conditions used below: compare solutions at the same temperature and in NCERT’s dilute range. Subtract the solvent background when defining the electrolyte’s limiting molar conductivity; otherwise dividing water’s finite conductivity by a concentration tending to zero would diverge. At very high concentrations, viscosity and ion association can make conductivity non-monotonic. The usual weak-acid formulas assume a monoprotic electrolyte, negligible water autoionisation and ion mobilities close to their limiting values.

In plain words: a salt solution conducts because its ions drift towards the electrodes. Add water and each cubic centimetre holds fewer ions, so it conducts less. But each mole of salt is now spread through more solution, its ions drag on one another less, and a weak electrolyte splits into more ions, so one mole’s worth conducts better. Molar conductivity tracks that one mole, and Kohlrausch’s law splits its limiting value into a share for each ion.

Resistance, resistivity and conductivity

• Resistance, R, is measured in ohm (Ω), and it can be measured with a Wheatstone bridge (NCERT page 41). In SI base units, Ω = kg m² s⁻³ A⁻².
• NCERT slip (page 41): NCERT writes the ohm as (kg m²)/(S³ A²). The unit there is the second, s; S is the siemens.
• R is proportional to the length l and inversely proportional to the area of cross-section A: R = ρl/A (NCERT Eq. (2.17), page 41). The constant ρ is the resistivity, in Ω m or Ω cm, with 1 Ω m = 100 Ω cm. IUPAC prefers “resistivity” to “specific resistance” (NCERT page 41).
• Conductance, G = 1/R = κA/l, is measured in siemens, S = Ω⁻¹, once called mho (NCERT Eq. (2.18), page 41).
• Conductivity, κ = 1/ρ, once called specific conductance, is measured in S m⁻¹ or S cm⁻¹, with 1 S cm⁻¹ = 100 S m⁻¹ (NCERT page 41).

• Conductivity varies enormously with the nature of the material, and also with temperature and pressure. By conductivity, materials are conductors (metals and alloys; also graphite, carbon-black and some organic polymers), insulators (glass, ceramics) or semiconductors (silicon, doped silicon, gallium arsenide). Superconductors have zero resistivity; some ceramics and mixed oxides are superconducting at up to 150 K (NCERT page 42).
• NCERT Table 2.2 (page 42), at 298.15 K, for some aqueous solutions and others:

• NCERT slip (Table 2.2, page 42): the metals’ values (copper 5.9 × 10³ S m⁻¹, for example) and graphite’s 1.2 × 10 S m⁻¹ are about 10⁴ times too small. NCERT’s own Physics book gives metals resistivities of 10⁻⁸ to 10⁻⁶ Ω m, that is, conductivities of 10⁶ to 10⁸ S m⁻¹ (NCERT Physics Part I (Class 12), page 90; resistivity of materials). Copper’s is 5.96 × 10⁷ S m⁻¹, and graphite’s along its layers 2 × 10⁵ to 3 × 10⁵ S m⁻¹ (Wikipedia, “Electrical resistivity and conductivity”).

Electronic and electrolytic conductance

• Metallic or electronic conductance is due to the movement of electrons. It depends on the nature and structure of the metal, the number of valence electrons per atom, and the temperature: it usually decreases as the temperature rises for ordinary metals near room temperature. The metal’s composition does not change (NCERT pages 42–43).
• Electrolytic or ionic conductance is due to ions. It depends on (NCERT page 43):
  • the nature of the electrolyte;
  • the size of its ions and their solvation;
  • the nature of the solvent and its viscosity;
  • the concentration of the electrolyte;
  • the temperature: it usually increases as the temperature rises, as ionic mobility increases.
• At 298 K, very pure water has about 10⁻⁷ M each of H⁺ and OH⁻ ions, which give it a very low conductivity. An electrolyte dissolved in water adds its own ions and raises the conductivity (NCERT page 43).
• NCERT slip (pages 42–43): NCERT gives pure water’s conductivity as 3.5 × 10⁻⁵ S m⁻¹. Its own figures give far less: c = 1.0 × 10⁻⁴ mol m⁻³ and Λ°_m = 349.6 + 199.1 = 548.7 × 10⁻⁴ S m² mol⁻¹, so κ = cΛ°_m = 5.5 × 10⁻⁶ S m⁻¹ (reasoned from NCERT Table 2.4). The Xylem/WTW Conductivity Handbook gives 0.055 μS cm⁻¹ at 25 °C, equivalent to 5.5 × 10⁻⁶ S m⁻¹. NCERT’s value is about six times too high; in a problem, use the value the question gives.
• Passing direct current through an ionic solution for a long time changes its composition, by electrochemical reactions at the electrodes (NCERT page 43).
• NCERT’s footnote (page 42): in 1977 MacDiarmid, Heeger and Shirakawa found that polyacetylene exposed to iodine vapour acquires metallic lustre and conductivity; they shared the 2000 Nobel Prize in Chemistry for the discovery of conducting polymers, which are light and flexible.

Measurement of the conductivity of ionic solutions

• A Wheatstone bridge measures resistance accurately, but a solution raises two problems: direct current changes its composition, and a solution cannot be wired into the bridge like a metal wire (NCERT page 43).
• The first is solved with an alternating current source; the second with a conductivity cell: two platinum electrodes coated with platinum black (platinised), each of area A, a distance l apart. The solution between them is a column of length l and cross-section A (NCERT page 43).
• In the bridge (NCERT Fig. 2.5, page 44), R₃ and R₄ are fixed, R₁ is variable and the cell is the unknown R₂. An oscillator feeds a.c. in the audio range, 550 to 5000 cycles per second, and a detector, such as a headphone, shows balance when no current passes through it. Then R₂ = R₁R₄/R₃ (NCERT Eq. (2.19), page 44). Inexpensive conductivity meters now read the conductance or resistance directly (NCERT page 44).

Cell constant and molar conductivity

• Cell constant. The quantity l/A is the cell constant, G*, with the dimension length⁻¹. Measuring l and A is inconvenient and unreliable, so G* is found from the resistance of the cell filled with a solution of known conductivity, usually KCl (NCERT Table 2.3, page 44):

• Once G* is known, the conductivity of any solution follows from its resistance in the same cell (NCERT Eq. (2.20), page 44):

• NCERT Table 2.3 (page 44), KCl at 298.15 K:

• Molar conductivity. Solutions of different electrolytes differ in conductivity because their ions differ in charge, size, concentration and ease of movement, so a more meaningful quantity is defined (NCERT Eq. (2.21), page 45):

• Units. With κ in S m⁻¹ and c in mol m⁻³, Λ_m is in S m² mol⁻¹; 1 mol L⁻¹ = 1000 mol m⁻³. With κ in S cm⁻¹ and the molarity M in mol L⁻¹, Λ_m = 1000κ/M in S cm² mol⁻¹. And 1 S m² mol⁻¹ = 10⁴ S cm² mol⁻¹ (NCERT page 45).
• NCERT slip (page 45): NCERT’s first unit equation divides κ in S cm⁻¹ by the concentration in mol m⁻³ and calls the result S cm² mol⁻¹. Dividing by mol m⁻³ needs κ in S m⁻¹ and gives S m² mol⁻¹. For S cm² mol⁻¹, use NCERT’s next equation, with 1000 cm³ L⁻¹.

Variation of conductivity and molar conductivity with concentration

• Conductivity falls on dilution. In NCERT’s words:

Conductivity always decreases with decrease in concentration both, for weak and strong electrolytes.

NCERT Chemistry Part I (Class 12), Section 2.4.2, page 46

• This is the trend in the dilute solutions considered here: on dilution, fewer ions per unit volume carry the current. The word “always” in the NCERT quotation should not be extended to highly concentrated solutions. κ is the conductance of one unit volume of solution between electrodes of unit area a unit length apart (NCERT pages 46–47).
• Molar conductivity rises on dilution. Λ_m is the conductance of the volume V of solution that holds one mole of electrolyte, between electrodes a unit length apart, so Λ_m = κV (NCERT Eq. (2.22), page 47). On dilution V grows faster than κ falls (NCERT page 47).
• As the concentration approaches zero, Λ_m approaches the limiting molar conductivity, Λ°_m. How Λ_m varies is different for strong and weak electrolytes (NCERT Fig. 2.6, page 47).

Strong and weak electrolytes

• Strong electrolytes, fully ionised in solution, show Λ_m rising slowly on dilution (NCERT Eq. (2.23), page 47):

• A plot of Λ_m against c^1/2 is a straight line with intercept Λ°_m and slope −A; this A is a constant, not an area. The constant A depends on the solvent, the temperature and the type of electrolyte, set by the charges on its ions: NaCl, CaCl₂ and MgSO₄ are 1-1, 2-1 and 2-2 electrolytes, and NCERT groups slopes by electrolyte type (page 47). More precisely, the limiting-law slope also depends on limiting ionic mobilities, so it is not identical for every electrolyte with the same charge type.
• Beyond the NCERT text: A depends mainly, not only, on the type, and NCERT Eq. (2.23) holds only in dilute solution (Wikipedia, “Molar conductivity”). With KCl’s 150.0 and 87.46 it gives 141.3 at 0.010 M, near NCERT Table 2.3’s 141.0, but 62.5 at 1.000 M against 111.3 (reasoned from NCERT Example 2.6).
• Weak electrolytes, such as acetic acid, are less dissociated at higher concentration. On dilution their degree of dissociation, and so the number of ions per mole, rises, and Λ_m rises steeply, especially at low concentration. So a simple straight-line extrapolation of Λ_m against √c is unreliable; near zero the conductivity is too low to measure accurately. It comes from Kohlrausch’s law instead (NCERT page 49).
• For a weak electrolyte at concentration c, the degree of dissociation is approximately α = Λ_m/Λ°_m (NCERT Eq. (2.26), page 50), and the dissociation constant is K_a = cα²/(1 − α) (NCERT Eq. (2.27), page 50).

Kohlrausch’s law and its applications

• Kohlrausch noticed regularities in Λ°_m of strong electrolytes at 298 K (NCERT page 49):
  • Λ°_m(KX) − Λ°_m(NaX) ≈ 23.4 S cm² mol⁻¹ for X = Cl, Br and I;
  • Λ°_m(NaBr) − Λ°_m(NaCl) = Λ°_m(KBr) − Λ°_m(KCl) ≈ 1.8 S cm² mol⁻¹.
• These led him to the law of independent migration of ions. In NCERT’s words:

The law states that limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and cation of the electrolyte.

NCERT Chemistry Part I (Class 12), Section 2.4.2, page 49

• For an electrolyte that gives ν₊ cations and ν₋ anions (NCERT Eq. (2.25), page 49):

• NCERT Table 2.4 (page 49), limiting molar conductivities of ions in water at 298 K:

• The table explains both regularities: λ°(K⁺) − λ°(Na⁺) = 73.5 − 50.1 = 23.4 and λ°(Br⁻) − λ°(Cl⁻) = 78.1 − 76.3 = 1.8 (reasoned from NCERT Table 2.4). H⁺ and OH⁻ stand out as unusually fast.
• Applications (NCERT page 50):
  • Λ°_m of any electrolyte from the λ° of its ions;
  • Λ°_m of a weak electrolyte, for which straight-line extrapolation is unreliable, from the values of strong electrolytes;
  • the degree of dissociation and the dissociation constant of a weak electrolyte, from Λ_m at one concentration and Λ°_m.

Solved examples

Common mistakes to avoid

Quick revision summary

• R = ρl/A; conductance G = 1/R; conductivity κ = 1/ρ, in S m^⁻¹ or S cm^⁻¹.
• Cell constant G* = l/A, found with KCl of known conductivity; then κ = G*/R. Measure with a.c. and a platinised cell.
• Molar conductivity Λ_ₘ = κ/c; in S cm^² mol^⁻¹, Λ_ₘ = 1000κ/M.
• On dilution κ falls and Λ_ₘ rises. Strong electrolytes: Λ_ₘ = Λ°_ₘ − A√c, a straight line in √c for dilute solutions. Weak electrolytes: a steep curved rise; use Kohlrausch’s law instead of simple linear extrapolation.
• Kohlrausch’s law: Λ°_ₘ = ν_₊λ°_₊ + ν_₋λ°_₋, the sum of the ions’ shares.
• Dilute monoprotic weak electrolytes: α ≈ Λ_ₘ/Λ°_ₘ and concentration-based K_ₐ ≈ cα^²/(1 − α).

Questions students ask

Why does the molar conductivity of a strong electrolyte rise on dilution if it is already fully ionised?

The molar conductivity of a strong electrolyte rises on dilution, though its number of ions per mole stays the same, because the ions hold one another back less: beyond the NCERT text, each ion is surrounded by a cloud of oppositely charged ions, its ionic atmosphere, which the field distorts so that it drags on the ion, and on dilution the ions are farther apart and the drag weakens (Wikipedia, “Debye–Hückel theory”). So Λ_m of KCl rises only slowly, from 111.3 S cm^² mol^⁻¹ at 1.000 mol L^⁻¹ to 141.0 at 0.010 mol L^⁻¹ (NCERT Table 2.3, page 44); the same theory explains the A√c term of NCERT Eq. (2.23).

What is the difference between molar conductivity and equivalent conductivity?

Molar conductivity divides the conductivity by the concentration in moles, Λ_m = κ/c (NCERT Eq. (2.21), page 45), while the older equivalent conductivity divides it by the concentration in equivalents, an equivalent being the amount of ions with the charge of one mole of singly charged ions, such as ½ mol of Ca²⁺ (beyond the NCERT text; Wikipedia, “Molar conductivity”). For Na₂SO₄, two equivalents per mole, Λ°_m = 2(50.1) + 160.0 = 260.2 S cm^² mol^⁻¹ (NCERT Table 2.4) is twice the equivalent value, 130.1 S cm^² per equivalent. IUPAC has recommended dropping the term; NCERT uses only molar conductivity.

What is the unit of the cell constant, and what does it depend on?

The cell constant, G* = l/A, has the SI unit m^⁻¹ and is often quoted in cm^⁻¹, with 1 cm^⁻¹ = 100 m^⁻¹; it depends only on the cell, the distance between its electrodes and their area, not on the solution in it (NCERT page 44). It is calibrated with KCl solution of known conductivity and reused while geometry, immersion depth and measurement conditions remain suitable (NCERT page 44): in a cell with G* = 0.50 cm^⁻¹, a solution of resistance 250 Ω has κ = 0.50/250 = 2.0 × 10^⁻³ S cm^⁻¹ (NCERT Eq. (2.20)). A cell constant of 1 cm^⁻¹ means that the conductivity in S cm^⁻¹ equals the conductance in S (reasoned).

Why does Li⁺ conduct less than K⁺ in water though it is a smaller ion?

Li⁺ moves less readily than Na⁺ or K⁺ in water despite its smaller bare-ion radius: strong ion–water interactions increase the resistance to its motion (beyond NCERT’s list of solvation factors, page 43). Do not picture a permanent rigid Li(H₂O)₄⁺ ball: hydration shells exchange water, and coordination number is not the same as hydrodynamic size.

Why are the molar conductivities of H⁺ and OH⁻ ions so high?

H⁺ and OH⁻ ions have high limiting molar conductivities, 349.6 and 199.1 S cm^² mol^⁻¹ against 50.1 for Na⁺ and 76.3 for Cl⁻ (NCERT Table 2.4, page 49), because, beyond the NCERT text, they move by a relay of protons along the hydrogen bonds of water, the Grotthuss mechanism, in addition to ordinary molecular diffusion through the solvent (Wikipedia, “Grotthuss mechanism” and “Molar conductivity”). An H₃O⁺ ion passes a proton to the next water molecule, which passes one on, so the charge moves without any one ion travelling far (reasoned). OH⁻ moves the same way, by taking a proton from a neighbouring water molecule.

Is Kohlrausch’s law in the JEE Main and NEET syllabus?

Yes, Kohlrausch’s law is in both syllabuses: Unit 7, Redox Reactions and Electrochemistry, of the JEE Main syllabus and of the NEET (UG) 2026 syllabus lists “conductance in electrolytic solutions, molar conductivities and their variation with concentration” and “Kohlrausch’s law and its applications.” NCERT Class 12 Chemistry Part I covers the law in Section 2.4.2 (pages 49–50), with Examples 2.7–2.9 and Intext Questions 2.8–2.9; conductance as a whole is Section 2.4 (pages 41–51).

Practice questions

Try each question first, then open the answer to check your working.

1. Q1. Why does the conductivity of a solution decrease with dilution? (NCERT Intext Question 2.7)

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   For a uniform cell, conductivity is conductance multiplied by length divided by area; volume alone does not fix conductance. On dilution there are fewer ions in each unit volume to carry the current (NCERT page 46).

2. Q2. Suggest a way to find Λ°_m of water. (NCERT Intext Question 2.8)

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   By Kohlrausch’s law, Λ°_m(H₂O) = λ°(H⁺) + λ°(OH⁻) = 349.6 + 199.1 = 548.7 S cm² mol⁻¹ (NCERT Table 2.4). This is the limiting ionic sum per mole of dissociated water; it is not the measured conductivity of bulk liquid water divided by its roughly 55.5 M molecular concentration. Equivalently, Λ°_m(HCl) + Λ°_m(NaOH) − Λ°_m(NaCl) (reasoned from NCERT page 50).

3. Q3. Why is a conductivity cell measured with alternating current and not direct current?

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   Direct current would change the composition of the solution by electrochemical reactions at the electrodes (NCERT page 43).