Question

The molar conductivities at infinite dilution of \(HCl\), \(CH_3COONa\) and \(CH_3COOH\) are \(426.0\), \(91.0\) and \(390.5\ \Omega^{-1}cm^2mol^{-1}\), respectively. If the molar conductivity of \(0.01\,M\) acetic acid solution is \(15.62\ \Omega^{-1}cm^2mol^{-1}\), the value of \(K_a\) is:

• A. \(1.8\times10^{-5}\)
• B. \(1.8\times10^{-4}\)
• C. \(1.8\times10^{-3}\)
• D. \(1.8\times10^{-6}\)

Hint:

For weak electrolytes, degree of dissociation can be directly obtained from conductivity measurements.

Answer 1

The Correct Option is A

Concept: For weak electrolytes, \[ \alpha=\frac{\Lambda_m}{\Lambda_m^\circ} \] and \[ K_a=\frac{C\alpha^2}{1-\alpha} \]

Step 1: \[ \alpha=\frac{15.62}{390.5} =0.04 \]

Step 2: \[ K_a=\frac{0.01(0.04)^2}{1-0.04} \] \[ =\frac{1.6\times10^{-5}}{0.96} \] \[ \approx1.7\times10^{-5} \] Closest value: \[ \boxed{1.8\times10^{-5}} \]