Kohlrausch law is useful in calculating ­\(\Lambda ^0\) for any electrolyte from the ­\(\lambda ^0\) of individual ions. The molar conductivities of H⁺ and OH⁻ ions are very high because these ions are passed from one molecule to another and released at the electrodes without travelling. Equivalent conductance of weak electrolytes can be calculated from the conductances of completely dissociated strong electrolytes e.g.,

\(\Lambda^0_{CH_3COOH} = \Lambda^0_{CH_3COONa} + \Lambda^0_{HCl} - \Lambda^0{NaCl}\)

Or,\(\Lambda^0_{CH_3COOH} = \Lambda^0_{Na^+} + \Lambda^0_{CH_3COO^-} + \Lambda^0_{H^+} + \Lambda^0_{Cl^-} - \Lambda^0_{Na^+} - \Lambda^0_{Cl^-}\)

Or,\(\Lambda^0_{CH_3COOH} = \Lambda^0_{CH_3COO^-} + \Lambda^0_{H^+} \)

Solubility of sparingly soluble salts can be calculated from the specific conductance of its saturated solution and from the equivalent conductivity at infinite dilution obtained from ­ ­

\[\Lambda ^0_e = \frac{1000 K_{salt}}{C}\]

\[\text{Absolute ionic mobility =} \frac{\text{Ionic conductance}}{96500} \]

\[\text{Absolute ionic mobility =} \frac{\Lambda _0}{96500} \]

Using ionic conductance measurements, the ionic product of water can be determined as 1 × 10⁻¹⁴ at 25°C.

According to Kohlrausch law, the limiting value of equivalent conductivity of an electrolyte A₂B is given by

\(\lambda^{\infty}_{A^+} + \frac{1}{2}\lambda^{\infty}_{B^{2-}}\)

The correct answer is option 3. \(\lambda^{\infty}_{A^+} + \frac{1}{2}\lambda^{\infty}_{B^{2-}}\).

Kohlrausch law states that the limiting value of equivalent conductivity of an electrolyte is equal to the sum of the limiting conductivities of the cations and anions that make up the electrolyte, with each ion weighted according to its valency. In the case of \(A_2B\), the electrolyte dissociates into \(A^+\) and \(B^{2-}\) ions. Therefore, the limiting value of equivalent conductivity of \(A_2B\) is given by \(\lambda^{\infty}_{A^+} + \frac{1}{2}\lambda^{\infty}_{B^{2-}}\).

The other options are incorrect. Option (1) is incorrect because it does not take into account the valency of the ions. Option (2) is incorrect because it only considers the limiting conductivity of the anion. Option (4) is incorrect because it adds the limiting conductivity of the cation twice.