Question

The relation between molar conductivity and concentration is given by \[ \Lambda_m = \Lambda_m^{0} - A\sqrt{c} \] For various solution concentrations of \(0.04\,\text{M},\ 0.09\,\text{M},\ 0.01\,\text{M}\) and \(0.16\,\text{M}\), the corresponding molar conductivities are \(95.7,\ 95.3,\ 94.9\) and \(94.5\ \text{S cm}^2\text{ mol}^{-1}\), respectively. Using the given data, determine the value of \(A\).

Hint:

When given \(\Lambda_m = \Lambda_m^{0} - A\sqrt{c}\), use any two data points to eliminate \(\Lambda_m^{0}\) quickly and find \(A\).

Answer 1

Correct Answer: 4

Concept:
For strong electrolytes, molar conductivity decreases linearly with \(\sqrt{c}\) according to: \[ \Lambda_m = \Lambda_m^{0} - A\sqrt{c} \] Here, \(A\) is a constant characteristic of the electrolyte.
Step 1: Use Two Sets of Given Data
For \(c = 0.04\,\text{M}\): \[ \sqrt{c} = \sqrt{0.04} = 0.2 \] \[ 95.7 = \Lambda_m^{0} - 0.2A \quad \cdots (1) \] For \(c = 0.09\,\text{M}\): \[ \sqrt{c} = \sqrt{0.09} = 0.3 \] \[ 95.3 = \Lambda_m^{0} - 0.3A \quad \cdots (2) \]
Step 2: Subtract Equation (2) from (1)
\[ (95.7 - 95.3) = ( -0.2A + 0.3A ) \] \[ 0.4 = 0.1A \] \[ A = 4 \] \[ \boxed{A = 4} \]