Step 1: What molar conductivity measures.
Imagine one mole of an electrolyte fully dissolved and held between two parallel plates 1 cm apart. The total conducting power of that one-mole worth of ions is the molar conductivity, written \(\Lambda_m\). Numerically it is obtained from the measured conductivity \(\kappa\) by dividing out the concentration: \(\Lambda_m = \kappa \times 1000 / c\), giving units of \(S\ cm^2\ mol^{-1}\). On dilution more of the electrolyte is ionised and the ions move freely, so \(\Lambda_m\) rises and reaches a maximum limiting value \(\Lambda_m^0\) at infinite dilution.
Step 2: Kohlrausch's statement.
Kohlrausch observed that at infinite dilution the ions no longer interfere with each other, so every ion contributes a fixed share to the conductivity. Therefore the limiting molar conductivity of any electrolyte can be split into a cation part and an anion part: \(\Lambda_m^0 = \nu_+ \lambda_+^0 + \nu_- \lambda_-^0\).
Step 3: Why it is useful.
Because the ionic values are additive, we can build \(\Lambda_m^0\) of a weak electrolyte like acetic acid by combining the values of strong electrolytes (\(HCl\), \(CH_3COONa\), \(NaCl\)). Comparing the actual \(\Lambda_m\) at a concentration with \(\Lambda_m^0\) then gives the degree of dissociation \(\alpha = \Lambda_m / \Lambda_m^0\).
\(\boxed{\Lambda_m^0 = \nu_+ \lambda_+^0 + \nu_- \lambda_-^0}\)