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

Step 1: Kohlrausch's law of independent migration of ions.
At infinite dilution, each ion migrates independently and contributes a fixed molar conductivity regardless of the co-ion present: \[ \Lambda_m^\circ = \nu_+\lambda_+^\circ + \nu_-\lambda_-^\circ \] where $\lambda^\circ$ values are limiting molar conductivities of individual ions.
Step 2: Strong electrolytes give a linear plot, enabling extrapolation.
For strong electrolytes: $\Lambda_m = \Lambda_m^\circ - A\sqrt{c}$. The plot of $\Lambda_m$ vs $\sqrt{c}$ is nearly linear, so $\Lambda_m^\circ$ can be obtained reliably by extrapolating the straight line to $c = 0$.
Step 3: Weak electrolytes give a steep curve that cannot be extrapolated accurately.
Weak electrolytes ionize more and more as dilution increases, causing $\Lambda_m$ to rise very sharply near zero concentration. The resulting curve becomes nearly vertical as $c \rightarrow 0$, making accurate extrapolation impossible. Therefore $\Lambda_m^\circ$ for weak electrolytes is calculated indirectly using Kohlrausch's law from tabulated ionic conductivities. \[ \boxed{\Lambda_m^\circ \text{ for weak electrolytes cannot be determined by extrapolation; it is calculated using Kohlrausch's law}} \]