Kohlrausch's law

How do we get Λ°_m for a weak electrolyte such as acetic acid, when its graph cannot be extended to zero concentration? Kohlrausch's law of independent migration of ions solves it.

Kohlrausch found that at infinite dilution, every ion makes its own fixed contribution to the molar conductivity, whatever the other ion is. So:

Λ°_m = ν₊λ°₊ + ν₋λ°₋

where λ° is each ion's limiting molar conductivity and ν is how many of that ion the formula gives.

Now the trick for acetic acid. We need the acetate ion and the hydrogen ion. Take three strong electrolytes whose Λ°_m values are known:

• Sodium acetate gives the acetate we need.
• HCl gives the H⁺ we need.
• Adding those two also brings in an extra Na⁺ and Cl⁻, which together are NaCl, so subtract NaCl.

Λ°(CH₃COOH) = Λ°(HCl) + Λ°(CH₃COONa) – Λ°(NaCl)

In short: add the two that hold the ions you want, then subtract the one made of the leftovers. The same method gives Λ° for water, from HCl, NaOH and NaCl.

Once Λ°_m is known, the degree of dissociation of the weak electrolyte at any concentration is:

α = Λ_m/Λ°_m

and its dissociation constant is K_a = cα²/(1 – α).