Question

The conductivity of \(0.001\ \mathrm{M}\) acetic acid is \(5\times10^{-5}\ \mathrm{S\,cm^{-1}}\). If the molar conductivity of acetic acid solution at infinite dilution is \(390.5\ \mathrm{S\,cm^2\,mol^{-1}}\), what is the degree of dissociation?

• A. 0.218
• B. 0.128
• C. 0.138
• D. 0.238 \bigskip

Hint:

For weak electrolytes, \[ \boxed{\Lambda_m=\frac{1000\kappa}{C}} \] and \[ \boxed{\alpha=\frac{\Lambda_m}{\Lambda_m^\circ}} \]

Answer 1

The Correct Option is B

Concept: For weak electrolytes, \[ \boxed{\alpha=\frac{\Lambda_m}{\Lambda_m^\circ}} \] where \[ \Lambda_m=\frac{1000\,\kappa}{C} \]

Step 1: Calculate molar conductivity. Given, \[ \kappa=5\times10^{-5}\ \mathrm{S\,cm^{-1}} \] \[ C=0.001\ \mathrm{M} \] \[ \Lambda_m = \frac{1000\times5\times10^{-5}}{0.001} = 50\ \mathrm{S\,cm^2\,mol^{-1}} \]

Step 2: Calculate degree of dissociation. \[ \alpha = \frac{50}{390.5} = 0.128 \]

Step 3: Final conclusion. \[ \boxed{\alpha=0.128} \] Hence, the correct option is \(\boxed{(B)}\).