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Kohlrausch Law Calculator
Λ°m = ν₊λ°₊ + ν₋λ°₋ from the limiting ionic conductivity table, with ion shares as transport numbers.
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Tool usage guide
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Key facts
Category
Science & Education
Input types
select, number
Output type
text
Sample coverage
4
API ready
Yes
Overview
The Kohlrausch Law Calculator computes the limiting molar conductivity (Λ°m) of electrolytes using Kohlrausch's law of independent ionic migration (Λ°m = ν₊λ°₊ + ν₋λ°₋). By selecting standard ions or entering custom limiting ionic conductivities, the tool also calculates the stoichiometric ionic contributions and resulting transport numbers (t₊ and t₋) at infinite dilution.
When to use
Determining the limiting molar conductivity of strong and weak electrolyte solutions at infinite dilution.
Calculating the ionic transport numbers (t₊ and t₋) to identify current fraction distribution between ions.
Solving physical chemistry stoichiometry problems involving multi-valent salts like CaCl₂ or Na₂SO₄.
How it works
1Select a cation and anion from the preset list containing standard limiting ionic conductivities (λ° in S·cm²/mol), or enter custom λ° values.
2Input the stoichiometric coefficients (ν₊ and ν₋) representing the number of cations and anions per formula unit.
3The tool computes total limiting molar conductivity via Λ°m = ν₊λ°₊ + ν₋λ°₋ in S·cm²/mol and converts the result to S·m²/mol.
4The calculator determines the individual transport numbers by taking the ratio of each ionic component against the total molar conductivity (t₊ = ν₊λ°₊/Λ°m and t₋ = ν₋λ°₋/Λ°m).
Use cases
Verifying theoretical conductivities for physical chemistry lab reports and coursework.
Evaluating current-carrying capacity and ionic mobility in electrochemical cell design.
Determining limiting conductivities of weak electrolytes from known salt and acid components.
Examples
1. Hydrochloric Acid (HCl) Analysis
Chemistry Student
Background
Studying electrolyte conductivities and testing proton mobility in acid-base solutions.
Problem
Calculate the limiting molar conductivity and proton transport number for 1:1 HCl.
How to use
Select H⁺ for the cation with stoichiometric coefficient 1, and Cl⁻ for the anion with stoichiometric coefficient 1.
Cation: H⁺ (ν₊ = 1), Anion: Cl⁻ (ν₋ = 1)
Outcome
Yields Λ°m = 426.1 S·cm²/mol (0.04261 S·m²/mol) with a proton transport fraction t₊ = 0.8209 (82.1%).
Preparing an electrochemistry experiment using a divalent metal chloride salt.
Problem
Determine the total limiting molar conductivity and the share carried by chloride ions in CaCl₂.
How to use
Select Ca²⁺ with ν₊ = 1 and Cl⁻ with ν₋ = 2.
FAQ
What is Kohlrausch's law of independent migration?
It states that at infinite dilution, each ion migrates independently of its co-ion and contributes a distinct amount to the total molar conductivity of the electrolyte.
What units are used for limiting molar conductivity in this tool?
Conductivity inputs and outputs are primarily in Siemens square centimeters per mole (S·cm²/mol), with a conversion to Siemens square meters per mole (S·m²/mol).
How are transport numbers calculated?
Transport numbers are calculated as the fraction of total conductivity carried by each ion: t₊ = ν₊λ°₊ / Λ°m and t₋ = ν₋λ°₋ / Λ°m.
Can I use custom ions not listed in the preset dropdowns?
Yes, select 'Custom' from the dropdown menu and manually input the specific limiting ionic conductivity (λ°) in S·cm²/mol.
Why do stoichiometric coefficients matter in this calculation?
Salts dissociate into multiple ions per formula unit (e.g., CaCl₂ yields 2 Cl⁻ ions), so the ionic conductivity must be multiplied by its stoichiometric index (ν).