Question
For strong electrolyte $\Lambda_{\text{m}}$ increases slowly with dilution and can be represented by the equation $\Lambda_{\text{m}} = \Lambda_{\text{m}}^{\circ} - \text{A}\text{c}^{1/2}$
Molar conductivity values of the solutions of strong electrolyte AB at $18^{\circ}\text{C}$ are given below :$\text{c } [\text{mol L}^{-1}]$ $0.04$ $0.09$ $0.16$ $0.25$ $\Lambda_{\text{m}} \ [\text{S cm}^{2}\text{ mol}^{-1}]$ $96.1$ $95.7$ $95.3$ $94.9$
The value of constant A based on the above data $[\text{in S cm}^{2}\text{ mol}^{-1} / (\text{mol}/\text{L})^{1/2}]$ unit is _________.
Calculating Electrolyte Constant A
The molar conductivity ($\Lambda_{\text{m}}$) of a strong electrolyte is related to its concentration ($c$) by the Debye-Hückel-Onsager equation: $ \Lambda_{\text{m}} = \Lambda_{\text{m}}^{\circ} - \text{A}c^{1/2} $ Here, $\Lambda_{\text{m}}^{\circ}$ is the molar conductivity at infinite dilution, and $\text{A}$ is a constant specific to the electrolyte, solvent, and temperature ($18^{\circ}\text{C}$ in this case).
This equation indicates a linear relationship between $\Lambda_{\text{m}}$ and $c^{1/2}$. Rearranging the equation, we get: $ \Lambda_{\text{m}} = -\text{A}c^{1/2} + \Lambda_{\text{m}}^{\circ} $ This represents the equation of a straight line ($y = mx + b$), where $y = \Lambda_{\text{m}}$, $x = c^{1/2}$, the slope $m = -\text{A}$, and the y-intercept $b = \Lambda_{\text{m}}^{\circ}$.
Data Table and Calculations
| Concentration, $c$ [mol L-1] | $\sqrt{c}$ [(mol L-1)1/2] | Molar Conductivity, $\Lambda_{\text{m}}$ [S cm2 mol-1] |
|---|---|---|
| 0.04 | $\sqrt{0.04} = 0.2$ | 96.1 |
| 0.09 | $\sqrt{0.09} = 0.3$ | 95.7 |
| 0.16 | $\sqrt{0.16} = 0.4$ | 95.3 |
| 0.25 | $\sqrt{0.25} = 0.5$ | 94.9 |
Determining Constant A
The constant $\text{A}$ can be found from the slope of the $\Lambda_{\text{m}}$ versus $c^{1/2}$ plot. The slope ($m$) is equal to $-\text{A}$. We calculate the slope using pairs of points from the table:
- Using points (0.2, 96.1) and (0.3, 95.7):
Since the slope $m = -\text{A}$:
$ -\text{A} = -4 $ $ \text{A} = 4 \text{ S cm}^2 \text{ mol}^{-1} / (\text{mol L}^{-1})^{1/2} $The value of constant A calculated from the data is 4.
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