Kohlrausch Law Calculator
Find limiting molar conductivity from ion contributions, or extrapolate molar conductivity with Kohlrausch's law.
📈 What is the Kohlrausch Law Calculator?
This Kohlrausch law calculator works two ways. Independent Migration mode builds an electrolyte's limiting molar conductivity Λm° from its cation and anion's individual ionic conductivities, following Kohlrausch's law that each ion contributes independently. Extrapolation mode instead uses the empirical square-root law to estimate an electrolyte's molar conductivity at a specific finite concentration.
Kohlrausch's law is a foundational tool in electrochemistry for predicting properties of electrolytes that are hard to measure directly, especially weak acids and bases, by combining tabulated ionic conductivity data from easier-to-study strong electrolytes. It also underlies the standard graphical method for finding Λm° experimentally: plot measured Λm against √c and extrapolate the line back to zero concentration.
A common misconception is that the square-root extrapolation law applies universally. It only holds for strong electrolytes at low concentration; weak electrolytes follow a completely different, much steeper curve driven by changing degree of dissociation, which is why weak-electrolyte Λm° values are found via independent migration instead of direct extrapolation.
This calculator is useful for physical and analytical chemistry students, and for chemists who need a fast, correct limiting or concentration-dependent molar conductivity without manually applying either form of Kohlrausch's law by hand.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - CaCl2 limiting molar conductivity via independent migration
Example 2 - NaCl molar conductivity at 0.01 mol/L
Example 3 - NaCl molar conductivity at a more dilute concentration
❓ Frequently Asked Questions
🔗 Related Calculators
What is Kohlrausch's law?
Kohlrausch's law of independent migration of ions states that the limiting molar conductivity of an electrolyte equals the sum of the independent contributions of its cation and anion: Lambda_m° = nu_plus x lambda_plus° + nu_minus x lambda_minus°, where nu is the number of each ion in the formula unit.
How do you calculate limiting molar conductivity with Kohlrausch's law?
Multiply each ion's limiting ionic conductivity by how many of that ion appear in the electrolyte's formula, then add the two contributions together. For CaCl2, that is 1 x lambda(Ca2+) + 2 x lambda(Cl-), since each formula unit contains one Ca2+ and two Cl- ions.
What is the Kohlrausch square-root law?
For strong (fully dissociated) electrolytes, molar conductivity falls linearly with the square root of concentration at low concentration: Lambda_m = Lambda_m° - K*sqrt(c), where K is an empirical constant specific to that electrolyte. This is used to extrapolate Lambda_m° from measurements at finite concentration.
Why does molar conductivity depend on the square root of concentration, not concentration directly?
The square-root dependence comes from Debye-Huckel-Onsager theory: the ionic atmosphere surrounding each ion, which slows its mobility, has a thickness that scales with 1/sqrt(ionic strength), so the resulting conductivity correction naturally comes out proportional to sqrt(c).
Does the Kohlrausch square-root law work for weak electrolytes?
No. Weak electrolytes show a much steeper, curved rise in molar conductivity as concentration falls, driven mainly by increasing degree of dissociation rather than the ionic-atmosphere effect the square-root law describes. The Molar Conductivity Calculator's Ostwald dilution law approach is more appropriate for weak electrolytes.
Why is Kohlrausch's law useful for weak electrolytes even though the square-root law is not?
The independent migration law still applies to individual ion contributions regardless of electrolyte strength, so it can be used to calculate a weak electrolyte's Lambda_m° indirectly, by combining ionic conductivities measured from strong electrolytes that happen to share the same ions.
How is Lambda_m° for acetic acid found if it cannot be measured directly by extrapolation?
Because acetic acid is weak and never approaches full dissociation even at very low concentration, its Lambda_m° cannot be extrapolated directly. Instead, combine Lambda_m° values from strong electrolytes sharing its ions: Lambda_m°(CH3COOH) = Lambda_m°(CH3COONa) + Lambda_m°(HCl) - Lambda_m°(NaCl), using Kohlrausch's law of independent migration.
What are typical limiting ionic conductivity values?
At 25C in water, typical limiting ionic conductivities (S.cm2/mol) include H+ 349.6, OH- 198.0, K+ 73.5, Na+ 50.1, Cl- 76.3, and SO4^2- 160.0. H+ and OH- stand out as unusually high due to the Grotthuss proton-relay conduction mechanism.
What is the difference between the two modes in this calculator?
Independent Migration mode computes Lambda_m° purely from ion identity and stoichiometry, with no concentration dependence at all. Extrapolation mode instead estimates Lambda_m at a specific finite concentration for a strong electrolyte, given its Lambda_m° and Kohlrausch constant K.
Can the Kohlrausch square-root law be extrapolated to very high concentration?
No, the linear Lambda_m versus sqrt(c) relationship only holds at low concentration (typically below about 0.1-0.2 mol/L for common strong electrolytes). At higher concentration, the real relationship curves away from the straight-line prediction.