Question

\[ \text{The conductivity of }0.001M\text{ solution of acetic acid is }3.905\times10^{-5}\;S\,cm^{-1}.\text{ Calculate its molar conductivity and degree of dissociation }(\alpha). \]
\[ \lambda^\circ_{CH_3COO^-}=40.9\;S\,cm^2mol^{-1} \]
\[ \lambda^\circ_{H^+}=349.6\;S\,cm^2mol^{-1} \]

Hint:

For weak electrolytes, \(\alpha=\frac{\Lambda_m}{\Lambda_m^\circ}\). Salt bridge prevents charge build-up in half-cells.

Answer 1

Concept:
Molar conductivity is related to conductivity by: \[ \Lambda_m=\frac{\kappa\times1000}{C} \] For a weak electrolyte: \[ \alpha=\frac{\Lambda_m}{\Lambda_m^\circ} \] where: \[ \Lambda_m^\circ=\lambda_+^\circ+\lambda_-^\circ \]

Step 1: Write given values.
\[ \kappa=3.905\times10^{-5}\;S\,cm^{-1} \] \[ C=0.001M \]

Step 2: Calculate molar conductivity.
\[ \Lambda_m=\frac{\kappa\times1000}{C} \] \[ \Lambda_m= \frac{3.905\times10^{-5}\times1000}{0.001} \] \[ \Lambda_m=39.05\;S\,cm^2mol^{-1} \]

Step 3: Calculate limiting molar conductivity.
\[ \Lambda_m^\circ = \lambda^\circ_{CH_3COO^-} + \lambda^\circ_{H^+} \] \[ \Lambda_m^\circ=40.9+349.6 \] \[ \Lambda_m^\circ=390.5\;S\,cm^2mol^{-1} \]

Step 4: Calculate degree of dissociation.
\[ \alpha=\frac{\Lambda_m}{\Lambda_m^\circ} \] \[ \alpha=\frac{39.05}{390.5} \] \[ \alpha=0.10 \] or \[ \alpha=10\% \]

Step 5: Reason for constant voltage of mercury cell.
In mercury cell, the overall reaction is: \[ Zn(Hg)+HgO\rightarrow ZnO+Hg \] The electrolyte concentration does not change appreciably during the cell reaction. Therefore, cell potential remains almost constant throughout its life.

Step 6: Need of salt bridge in galvanic cell.
Salt bridge has two important functions:

• It maintains electrical neutrality in both half-cells.

• It completes the internal circuit by allowing migration of ions.
Without salt bridge, charge accumulation would stop the flow of current. Hence: \[ \Lambda_m=39.05\;S\,cm^2mol^{-1} \] \[ \alpha=0.10=10\% \] Mercury cell delivers constant voltage because electrolyte concentration remains almost unchanged. Salt bridge maintains electrical neutrality and completes the circuit.