Engineering & Science
Kohlrausch's Square-Root Law of Molar Conductivity & Weak-Acid Dissociation (alpha)
Calculate strong-electrolyte molar conductivity Lambda_m = Lambda_m^0 - K * SQRT(c) and weak-electrolyte degree of dissociation alpha = Lambda_m / Lambda_m^0 in electrochemistry.
Model ionic drag in strong electrolytes vs partial ionization in weak acids!
Strong electrolytes (like KCl with limiting molar conductivity Lambda_m^0 = 149.86 S*cm^2/mol at 25 °C) are 100% dissociated in water, yet their molar conductivity drops linearly with the SQUARE ROOT of concentration c due to Debye-Huckel-Onsager inter-ionic relaxation and electrophoretic drag: Lambda_m = Lambda_m^0 - K * SQRT(c)! At c = 0.01 mol/L with K = 95.0 S*cm^2*mol^-3/2*L^1/2, KCl molar conductivity is 149.86 - 95*0.1 = 140.36 S*cm^2/mol, dropping to 130.86 S*cm^2/mol at c = 0.04 mol/L.
Weak electrolytes (like 0.01 M acetic acid with measured Lambda_m = 16.3 S*cm^2/mol) cannot be extrapolated linearly because Lambda_m spikes hyperbolically near c -> 0! Instead, Kohlrausch's law of independent migration of ions gives Lambda_m^0(CH3COOH) = lambda^0(H+) + lambda^0(CH3COO-) = 349.8 + 40.9 = 390.7 S*cm^2/mol, yielding degree of dissociation alpha = Lambda_m / Lambda_m^0 = 16.3 / 390.7 = 0.0417 (4.17% ionized)!
| Electrolyte Calculation | Inputs (25 °C) | Formula | Result |
|---|---|---|---|
| KCl at c = 0.01 M (Strong) | L0 = 149.86, K = 95.0 | L0 - K * SQRT(0.01) | 140.36 S*cm^2/mol |
| KCl at c = 0.04 M (Strong) | L0 = 149.86, K = 95.0 | L0 - K * SQRT(0.04) | 130.86 S*cm^2/mol |
| Acetic Acid 0.01 M (Weak alpha) | Lm = 16.3, L0 = 390.7 | Lm / L0 | alpha = 0.0417 (4.17%) |
Strong Electrolyte Molar Conductivity Lambda_m = Lambda_m^0 - K * SQRT(c)
Evaluates Kohlrausch's square-root law for dilute strong electrolytes.
=IF(OR(B2 <= 0, B3 < 0, B4 < 0), "Invalid Conductivity Inputs", ROUND(B2 - (B3 * SQRT(B4)), 2))Weak Electrolyte Degree of Dissociation alpha = Lambda_m / Lambda_m^0
Computes the ionized fraction alpha from measured weak-acid molar conductivity B5 and Kohlrausch limiting sum B6.
=IF(OR(B5 < 0, B6 <= 0, B5 > B6), "Invalid Conductivity Inputs", ROUND(B5 / B6, 4))Try the example
Use the original values or change them to test your understanding.