A conductivity cell with two electrodes (dark side) are half filled with infinitely dilute aqueous solution of a weak electrolyte. If volume is doubled by adding more water at constant temperature, the molar conductivity of the cell will -
The question involves understanding how the molar conductivity of a weak electrolyte changes when the volume of its solution is doubled by adding water.
Molar conductivity (\(Λ_m\)) is defined as:
\(Λ_m = \frac{κ}{C}\)
where \(κ\) is the conductivity of the solution and \(C\) is the concentration of the electrolyte.
When the volume of the solution is doubled, the concentration \((C)\) of the electrolyte is halved, as concentration is inversely proportional to volume.
However, since the solution is infinitely dilute, the impact on conductivity \((κ)\) is negligible. This is because at infinite dilution, the ions are completely dissociated and do not experience additional interactions.
Given this understanding, the molar conductivity for weak electrolytes does not change significantly with dilution at infinite dilution.
Therefore, the correct answer is: remain same or can not be measured accurately.
The measurement accuracy is also an issue due to the limitations of measuring extremely low conductance values at high dilutions.
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Approach Solution -2
The solution is already infinitely dilute, meaning the molar conductivity is at its maximum value. Adding more water will not dilute the solution further; therefore, there will be no change in molar conductivity. It will remain the same. \[\text{Molar conductivity } (\Lambda_m) \propto \frac{\kappa}{c}\] where $\kappa$ is the conductivity and $c$ is the concentration. For infinitely dilute solutions, $c$ is already approaching zero, and $\Lambda_m$ becomes constant.
