Molar Conductivity Calculator

Calculate molar conductivity, equivalent conductivity, and degree of dissociation from solution conductance.

Measured conductance G (S or mS) (S)

Cell constant κ_cell (cm⁻¹) (cm⁻¹)

Concentration c (mol/L) (M)

Limiting molar conductivity Λ° (S·cm²/mol) (S·cm²/mol)

NaCl: 126, HCl: 426, NaOH: 248

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Why Molar Conductivity Changes with Concentration

Conductivity κ measures how well a solution carries current. Dividing by concentration gives molar conductivity Λ_m — conductivity per mole of electrolyte — which reveals how efficiently each mole contributes. The way that quantity varies with dilution distinguishes strong from weak electrolytes sharply.

κ = G × cell constant Λ_m = 1000κ/c

Electrolyte type	Behaviour on dilution	Why	Example
Strong	Λ_m rises slightly, levels off	Already fully dissociated; only ion crowding relaxes	NaCl, HCl, KNO₃
Weak	Λ_m rises steeply	Degree of dissociation itself increases	Acetic acid, NH₃

For strong electrolytes, Kohlrausch found that Λ_m falls linearly with the square root of concentration, so extrapolating to zero gives Λ°. That extrapolation fails completely for weak electrolytes, because their Λ_m is still climbing steeply at the lowest measurable concentrations.

Kohlrausch’s Law of Independent Migration

At infinite dilution ions move independently, so Λ° is simply the sum of individual ionic contributions. This lets Λ° for a weak electrolyte be assembled from strong electrolyte measurements:

Λ°(CH₃COOH) = Λ°(CH₃COONa) + Λ°(HCl) − Λ°(NaCl)

Ion	λ° (S·cm²/mol, 25°C)	Note
H⁺	349.8	Exceptionally high — Grotthuss hopping
OH⁻	198.0	Also anomalous, same mechanism
Na⁺	50.1	Typical cation
Cl⁻	76.3	Typical anion
CH₃COO⁻	40.9	Large ion, low mobility

Hydrogen ion conductivity is roughly seven times that of sodium despite being far smaller. The reason is that protons do not physically travel — they hop along hydrogen-bonded water chains, each water molecule passing a proton to the next. This Grotthuss mechanism moves charge much faster than any ion could diffuse.

For a weak acid, the ratio α = Λ_m/Λ° gives the degree of dissociation directly. At 0.01 M, acetic acid gives α ≈ 0.042 — about 4.2% dissociated, consistent with K_a = 1.8 × 10⁻⁵ via α ≈ √(K_a/c).

Worked Examples

Example 1: 0.01M acetic acid: G=0.0015S, kc=1.5, Λ°=390

κ=0.000163 S/cm, Λ_m=16.3 S·cm²/mol

Result: α=16.3/390.7=0.042=4.2% dissociated

Matches the Ka cross-check: sqrt(1.8e-5/0.01) = 0.042

Example 2: 0.01M NaCl: G=0.00842S, kc=1.5

κ=0.01263, Λ_m=1263

Result: Strong electrolyte — fully dissociated

Verifies cell calibration

Example 3: Degree of dissociation

0.01 M acetic acid, Λ_m = 16.3, Λ° = 390.7 S·cm²/mol

Result: α = 0.0417, about 4.2% dissociated

Cross-check with α ≈ √(K_a/c) = √(1.8×10⁻⁵/0.01) = 0.042. The two methods agree closely.

Example 4: Kohlrausch assembly

Λ°: sodium acetate 91.0, HCl 426.1, NaCl 126.4

Result: Λ°(acetic acid) = 390.7 S·cm²/mol

Weak acid Λ° cannot be measured directly, but assembling it from three strong electrolytes gives the value needed for dissociation calculations.

Example 5: Why H⁺ conducts so well

λ°(H⁺) = 349.8 versus Na⁺ at 50.1

Result: Seven times higher despite smaller size

Protons hop between hydrogen-bonded water molecules rather than migrating physically. The same mechanism explains hydroxide’s elevated value.

Common Mistakes

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Extrapolating weak electrolyte data to find Λ°

Kohlrausch’s square root extrapolation works only for strong electrolytes. For weak ones, assemble Λ° from ionic contributions using the law of independent migration instead.

⚠️

Forgetting the cell constant

Measured conductance depends on electrode geometry. Conductivity requires multiplying by the cell constant, determined by calibrating with a standard KCl solution.

⚠️

Confusing conductivity with molar conductivity

κ is per unit volume and increases with concentration. Λ_m is per mole and generally increases on dilution — they move in opposite directions.

⚠️

Ignoring temperature

Conductivity rises roughly 2% per degree because viscosity falls and ions move more freely. Measurements must be temperature controlled or corrected.

Frequently Asked Questions

Kohlrausch's law?

Λ_m = Λ° - K√c for strong electrolytes. Plot Λ_m vs √c: extrapolate to c=0 for Λ°. For weak electrolytes, Ostwald dilution law: Ka = α²c/(1-α) where α=Λ_m/Λ°.

pH from conductivity?

Very pure water: κ=5.5×10⁻⁸ S/cm. Any contamination raises κ dramatically. Conductivity monitors water purity in pharma, semiconductor, and power plant applications.

What is the difference between conductivity and molar conductivity?

Conductivity is per unit volume and rises with concentration. Molar conductivity is conductivity per mole of electrolyte and generally rises on dilution.

Why does molar conductivity increase on dilution?

For strong electrolytes, reduced ion crowding lets ions move more freely. For weak electrolytes, the degree of dissociation itself increases — a much larger effect.

What is Kohlrausch’s law?

At infinite dilution each ion contributes independently, so Λ° is the sum of individual ionic conductivities. This allows Λ° for weak electrolytes to be calculated indirectly.

Why does H⁺ have such high conductivity?

Protons move by hopping along hydrogen-bonded water chains rather than physically migrating. This Grotthuss mechanism transports charge far faster than ordinary diffusion.

How do I find degree of dissociation from conductivity?

Divide the measured molar conductivity by the limiting value: α = Λ_m/Λ°. For 0.01 M acetic acid this gives about 4.2%.

Formula Explorer connections

Interpretation: This formula links electron transfer, charge, potential, current or ionic transport in an electrochemical system. Assumption: Balance electron count and half-reactions, preserve sign conventions, and use consistent concentration, temperature and electrical units. Real cells include losses and overpotential.

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