The molar conductivity of an electrolyte solution is defined as its conductivity divided by its molar concentration:
Λ m = κ c , {\displaystyle \Lambda _{\text{m}}={\frac {\kappa }{c}},}
where
κ is the measured conductivity (formerly known as specific conductance), c is the molar concentration of the electrolyte. The SI unit of molar conductivity is siemens metres squared per mole (S m2 mol−1). However, values are often quoted in S cm2 mol−1. In these last units, the value of Λm may be understood as the conductance of a volume of solution between parallel plate electrodes one centimeter apart and of sufficient area so that the solution contains exactly one mole of electrolyte.
Variation of molar conductivity with dilution There are two types of electrolytes: strong and weak. Strong electrolytes usually undergo complete ionization, and therefore they have higher conductivity than weak electrolytes, which undergo only partial ionization. For strong electrolytes, such as salts, strong acids and strong bases, the molar conductivity depends only weakly on concentration. On dilution there is a regular increase in the molar conductivity of strong electrolyte, due to the decrease in solute–solute interaction. Based on experimental data Friedrich Kohlrausch (around the year 1900) proposed the non-linear law for strong electrolytes:
Λ m = Λ m ∘ − K c = α f λ Λ m ∘ , {\displaystyle \Lambda _{\text{m}}=\Lambda _{\text{m}}^{\circ }-K{\sqrt {c}}=\alpha f_{\lambda }\Lambda _{\text{m}}^{\circ },}
where
Λ∘m is the molar conductivity at infinite dilution (or limiting molar conductivity), which can be determined by extrapolation of Λm as a function of √c, K is the Kohlrausch coefficient, which depends mainly on the stoichiometry of the specific salt in solution, α is the dissociation degree even for strong concentrated electrolytes, fλ is the lambda factor for concentrated solutions. This law is valid for low electrolyte concentrations only; it fits into the Debye–Hückel–Onsager equation. For weak electrolytes (i.e. incompletely dissociated electrolytes), however, the molar conductivity strongly depends on concentration: The more dilute a solution, the greater its molar conductivity, due to increased ionic dissociation. For example, acetic acid has a higher molar conductivity in dilute aqueous acetic acid than in concentrated acetic acid.
Kohlrausch's law of independent migration of ions Friedrich Kohlrausch in 1875–1879 established that to a high accuracy in dilute solutions, molar conductivity can be decomposed into contributions of the individual ions. This is known as Kohlrausch's law of independent ionic migration. For any electrolyte AxBy, the limiting molar conductivity is expressed as x times the limiting molar conductivity of Ay+ and y times the limiting molar conductivity of Bx−.
Λ m ∘ = ∑ i ν i λ i , {\displaystyle \Lambda _{\text{m}}^{\circ }=\sum _{i}\nu _{i}\lambda _{i},}
where:
λi is the limiting molar ionic conductivity of ion i, νi is the number of ions i in the formula unit of the electrolyte (e.g. 2 and 1 for Na+ and SO2−4 in Na2SO4). Kohlrausch's evidence for this law was that the limiting molar conductivities of two electrolytes with two different cations and a common anion differ by an amount which is independent of the nature of the anion. For example, Λ0(KX) − Λ0(NaX) = 23.4 S cm2 mol−1 for X = Cl−, I− and 1/2 SO2−4. This difference is ascribed to a difference in ionic conductivities between K+ and Na+. Similar regularities are found for two electrolytes with a common anion and two cations.
Molar ionic conductivity The molar ionic conductivity of each ionic species is proportional to its electrical mobility (μ), or drift velocity per unit electric field, according to the equation
λ = z μ F , {\displaystyle \lambda =z\mu F,}
where z is the ionic charge, and F is the Faraday constant. The limiting molar conductivity of a weak electrolyte cannot be determined reliably by extrapolation. Instead it can be expressed as a sum of ionic contributions, which can be evaluated from the limiting molar conductivities of strong electrolytes containing the same ions. For aqueous acetic acid as an example,
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