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

Step 1: State Kohlrausch's Law of Independent Migration of Ions.
At infinite dilution, the molar conductivity of an electrolyte equals the sum of the individual limiting molar conductivities of its constituent ions. Each ion contributes independently to the total molar conductivity, regardless of what other ions are present. \[ \Lambda_m^\circ = x\lambda_+^\circ + y\lambda_-^\circ \] for an electrolyte $A_xB_y$, where $\lambda_+^\circ$ and $\lambda_-^\circ$ are limiting ionic conductivities.
Step 2: Why extrapolation works for strong electrolytes.
Strong electrolytes are fully dissociated at all concentrations. Their molar conductivity $\Lambda_m$ follows the Debye-Huckel-Onsager equation: \[ \Lambda_m = \Lambda_m^\circ - A\sqrt{C} \] The plot of $\Lambda_m$ vs. $\sqrt{C}$ is a straight line. This straight line can be reliably extrapolated to $C = 0$ to obtain $\Lambda_m^\circ$.
Step 3: Behaviour of weak electrolytes at low concentration.
Weak electrolytes (e.g., acetic acid) have a very small degree of ionisation at moderate concentrations. As the concentration decreases towards zero, the degree of ionisation increases sharply towards 1, and $\Lambda_m$ rises very steeply and non-linearly.
Step 4: Why extrapolation fails for weak electrolytes.
The plot of $\Lambda_m$ vs. $\sqrt{C}$ for a weak electrolyte rises very steeply and non-linearly near $C = 0$. There is no reliable straight-line region from which to extrapolate. Any extrapolation would be highly inaccurate, with a small measurement error leading to a huge error in the estimated $\Lambda_m^\circ$.
Step 5: Alternative method for weak electrolytes.
For weak electrolytes, $\Lambda_m^\circ$ is calculated indirectly using Kohlrausch's law from the limiting ionic conductivities of strong electrolytes. For acetic acid: \[ \Lambda_m^\circ(CH_3COOH) = \lambda^\circ(H^+) + \lambda^\circ(CH_3COO^-) \] These values come from strong electrolyte data (HCl and $CH_3COONa$).
Step 6: Summarise the key contrast.
Strong electrolytes: linear $\Lambda_m$ vs. $\sqrt{C}$, easy reliable extrapolation to $\Lambda_m^\circ$. Weak electrolytes: steeply rising non-linear curve near $C = 0$; extrapolation is unreliable; use Kohlrausch's law indirectly instead. \[ \boxed{\text{Weak electrolyte curve is steep and non-linear near } C=0 \Rightarrow \text{extrapolation unreliable}} \]