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, limiting molar conductivity is usually calculated using Kohlrausch's law rather than obtained graphically.

Answer 1

Concept: Molar conductivity increases with dilution because the ions present in solution become more mobile and interionic attractions decrease. The variation of molar conductivity with concentration is different for strong and weak electrolytes. This difference forms the basis for understanding Kohlrausch's law.

Kohlrausch's Law of Independent Migration of Ions The law states that: At infinite dilution, each ion contributes a definite value to the molar conductivity of an electrolyte irrespective of the nature of the other ion present with it. Mathematically, \[ \Lambda_m^\circ = \nu_+\lambda_+^\circ + \nu_-\lambda_-^\circ \] where \[ \lambda_+^\circ \] and \[ \lambda_-^\circ \] represent limiting ionic conductivities.

Strong Electrolytes Strong electrolytes are almost completely ionized in solution. For strong electrolytes: \[ \Lambda_m = \Lambda_m^\circ - A\sqrt{c} \] Thus a plot of \[ \Lambda_m \] versus \[ \sqrt{c} \] is nearly a straight line. Therefore the graph can easily be extrapolated to: \[ \sqrt{c}=0 \] to obtain \[ \Lambda_m^\circ \]

Weak Electrolytes Weak electrolytes are only partially ionized. As dilution increases, ionization also increases significantly. Consequently, the variation of molar conductivity with concentration becomes highly non-linear. The graph is strongly curved. Because of this curvature, extrapolation to zero concentration becomes unreliable and inaccurate. Hence direct determination of \[ \Lambda_m^\circ \] for weak electrolytes is difficult.

Schematic Curve Strong electrolytes give almost straight-line plots whereas weak electrolytes give curved plots. Therefore direct extrapolation is possible only for strong electrolytes.

Conclusion: Since weak electrolytes undergo progressive ionization on dilution, their conductivity-concentration plots are curved. Therefore \[ \Lambda_m^\circ \] cannot be obtained accurately by extrapolation and is instead calculated using Kohlrausch's law.