Question

State Kohlrausch's law of independent migration of ions. With the help of a curve, explain why it is not easy to determine \(\Lambda_m^\circ\) for weak electrolytes by extrapolating the concentration--molar conductivity curve, as it is for strong electrolytes.

Hint:

For weak electrolytes, use Kohlrausch's law to calculate \(\Lambda_m^\circ\); do not use direct extrapolation.

Answer 1

Concept:
Kohlrausch's law states that at infinite dilution, each ion contributes independently to the total molar conductivity of the electrolyte. For an electrolyte \(A_xB_y\): \[ \Lambda_m^\circ=x\lambda_+^\circ+y\lambda_-^\circ \] where \(\lambda_+^\circ\) and \(\lambda_-^\circ\) are limiting ionic conductivities of cation and anion.

Step 1: State Kohlrausch's law.
At infinite dilution, the ions are far apart and there is no interionic attraction. Therefore, each ion migrates independently. So the limiting molar conductivity is the sum of the limiting ionic conductivities. \[ \boxed{\Lambda_m^\circ=\lambda_+^\circ+\lambda_-^\circ} \]

Step 2: Strong electrolyte curve.
For strong electrolytes, dissociation is almost complete even at higher concentration. Their molar conductivity increases gradually with dilution. The plot of \(\Lambda_m\) against \(\sqrt{C}\) is almost linear. So \(\Lambda_m^\circ\) can be obtained by extrapolation to: \[ \sqrt{C}=0 \]

Step 3: Weak electrolyte curve.
Weak electrolytes are only partially dissociated. On dilution, their degree of dissociation increases sharply. So molar conductivity increases steeply and non-linearly. Therefore, the curve is not a straight line near zero concentration. \[ \Lambda_m \text{ increases sharply for weak electrolytes} \] Hence, extrapolation is not reliable.

Step 4: Conclusion.
For weak electrolytes, \(\Lambda_m^\circ\) is determined indirectly using Kohlrausch's law from strong electrolytes. Hence: \[ \boxed{\text{Weak electrolytes cannot be reliably extrapolated because their }\Lambda_m\text{ changes sharply with dilution.}} \]