# Conductance and Kohlrausch's Law > Conductance and Kohlrausch's law for JEE Chemistry: molar conductivity variation with dilution, limiting values, degree of dissociation and Ka of weak acids. - Canonical URL: https://prepelephant.com/topics/jee/chemistry/conductance-and-kohlrausch-law - Exam / course: JEE · Subject: Chemistry - Publisher: PrepElephant (https://prepelephant.com) — Prepared and reviewed by the PrepElephant Academic Review Team - First published: 2026-10-02 - Last updated: 2026-10-02 - How to cite: "Conductance and Kohlrausch's Law", PrepElephant, https://prepelephant.com/topics/jee/chemistry/conductance-and-kohlrausch-law ## Direct answer Molar conductivity of a strong electrolyte climbs gently on dilution toward a limiting value, while that of a weak electrolyte rises steeply and never levels off on a plot against concentration — because dilution of a weak acid creates more ions, not just faster ones. The working definitions are molar conductivity lambda_m = 1000 kappa / M (units S cm2 mol^-1) and the strong-electrolyte straight line lambda_m = lambda_m° - A sqrt(c). Kohlrausch's law then states that the limiting molar conductivity is the sum of independent ionic contributions: lambda_m° = v+ lambda+° + v- lambda-°, which is how the unmeasurable lambda° of a weak acid is assembled from salts, and how alpha = lambda_m / lambda_m° feeds into Ka = c alpha^2 / (1 - alpha). ## What you must remember - **Unit chain:** conductivity kappa in S cm^-1; molar conductivity = 1000 kappa / M in S cm2 mol^-1 — forgetting the factor 1000 wrecks every numerical. - **Two dilution curves:** strong electrolytes flatten (interionic attractions ease as ions separate); weak electrolytes keep climbing (dissociation increases), so extrapolation to zero concentration fails for weak — Kohlrausch is the only route to their lambda°. - **The law itself:** lambda°(CH3COOH) = lambda°(CH3COONa) + lambda°(HCl) - lambda°(NaCl); assemble any weak electrolyte from three strong ones whose ions overlap. - **Square-root law:** lambda_m = lambda_m° - A sqrt(c) holds only for strong electrolytes; plot lambda_m against sqrt(c) and the intercept is lambda_m°. - **Mobility outliers:** lambda°(H+) is about 350 and lambda°(OH-) about 199 S cm2 mol^-1 — the Grotthuss proton-jump mechanism, not ordinary drift, makes them anomalously fast. - **Dissociation arithmetic:** alpha = lambda_m / lambda_m°, then Ka = c alpha^2/(1-alpha); this pair converts one conductivity reading into an equilibrium constant. - **Sparingly soluble salts:** measure kappa of the saturated solution, subtract kappa of water, then solubility s = 1000 kappa / lambda_m° — a standard route to Ksp. - **Temperature direction:** conductance of electrolytes rises with temperature as viscosity falls and ions move faster. ## From one conductivity reading to Ka Acetic acid at 0.01 M shows lambda_m = 16.4 S cm2 mol^-1; Kohlrausch assembly gives lambda° = 390.5 S cm2 mol^-1. The degree of dissociation is alpha = 16.4/390.5 = 0.042, about 4 per cent — the acid is mostly molecules even at this modest dilution. Feed it into Ka = c alpha^2/(1-alpha) = (0.01)(0.042)^2/0.958, which is 1.8 × 10^-5, the textbook value of acetic acid. Notice how the calculation needs no pH meter and no titration: one conductance cell, three strong-electrolyte constants and the Kohlrausch combination deliver the equilibrium constant. The same skeleton with a saturated silver chloride solution — kappa(solution) minus kappa(water), divided by lambda°(AgCl) — gives solubility near 1.3 × 10^-5 mol per litre, and squaring it gives Ksp about 1.8 × 10^-10. ## How the exam frames it Electrochemistry with its conductance block remains firmly in the JEE Main syllabus, and one conductance numerical is near-guaranteed territory; JEE Advanced prefers the construction questions — building lambda° of a weak electrolyte, or the alpha-to-Ka chain. The recurring errors: dropping the 1000 factor between kappa and lambda_m, applying the sqrt(c) straight line to a weak acid (it bends), and quoting H+ mobility as ordinary. A favourite Advanced nuance asks why lambda_m rises but kappa falls on dilution: total ions per cubic centimetres shrink even as each ion moves freer, so the specific conductivity drops while the molar quantity rises. ## Frequently asked questions ### Why does molar conductivity of weak electrolytes rise steeply with dilution? Dilution drives the dissociation equilibrium forward, producing more ions per mole of electrolyte — an effect absent in strong electrolytes that are already fully dissociated. ### How is the limiting molar conductivity of acetic acid determined? By Kohlrausch's law: add lambda° of CH3COONa and HCl and subtract lambda° of NaCl, since the ions contribute independently at infinite dilution. ### Why is the ionic conductivity of H+ so high? The Grotthuss mechanism lets a proton hop along hydrogen bonds between water molecules, so charge moves without any single hydronium ion travelling the distance. ### For which electrolytes does the sqrt(c) law hold? Only strong electrolytes, and only at low concentrations; weak electrolytes deviate because alpha itself changes with dilution. ### How is Ksp of a sparingly soluble salt found conductometrically? Measure the saturated solution's conductivity, subtract the solvent's, convert to molarity through s = 1000 kappa / lambda°, then compute Ksp from the ion concentrations.