# Kohlrausch Law Calculator Λ°m = ν₊λ°₊ + ν₋λ°₋ from the limiting ionic conductivity table, with ion shares as transport numbers. > Canonical page: https://elysiatools.com/en/tools/kohlrausch-law - **Category:** Science & Education - **Keywords:** kohlrausch law, independent migration of ions, limiting molar conductivity, ionic conductivity, transport number ## 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. ## Inputs - **Cation** (select) - **Cations per formula unit (ν₊)** (number): e.g. 2 for Na₂SO₄ - **Anion** (select) - **Anions per formula unit (ν₋)** (number): e.g. 2 for CaCl₂ - **Custom cation λ° (S·cm²/mol, overrides preset)** (number): e.g. 63 for a 0.5 M survey value - **Custom anion λ° (S·cm²/mol, overrides preset)** (number): e.g. 154.8 ## 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 - Select a cation and anion from the preset list containing standard limiting ionic conductivities (λ° in S·cm²/mol), or enter custom λ° values. - Input the stoichiometric coefficients (ν₊ and ν₋) representing the number of cations and anions per formula unit. - The 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. - The 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. ## Frequently asked questions ### 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? 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