Conductance and Kohlrausch's Law
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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.