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CUET · CHEMISTRY · PYQ PAPER 2025

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Molar conductivity \(\left(\Lambda_m\right)\) of a solution at a given concentration (c) is the conductance of volume, V of solution, containing one mole of electrolyte kept between the two electrodes with area of cross-section A and at a distance of unit length. It increases with the decrease in concentration and when the concentration approaches zero, the molar conductivity is called limiting molar
conductivity \(\left(\Lambda_m^0\right)\). For a strong electrolyte, \(\Lambda_m\) increases linearly with dilution and is given by \(\Lambda_m=\Lambda_m^0-A c^{1 / 2}\). The value of the constant A for a given solvent depends on the type of electrolyte along with temperature. According to Kohlrausch law, the value of \(\Lambda_m^0\) for an electrolyte is \(\Lambda_m^0=\nu_{+} \lambda_{+}^0+\nu_{-} \lambda_{-}^0\), where \(\nu_{+}\)and \(\nu_{-}\) are the number of cations and anions, respectively, per molecule of the electrolyte and \(\lambda_{+}^0\) and \(\lambda_{-}^0\) are limiting molar conductivities of cation and anion, respectively. Kohlrausch law finds many applications, like determining the solubility of a sparingly soluble salt, determining the degree of dissociation \(\left(\Lambda_m / \Lambda_m^0\right)\), and the dissociation constant of a weak electrolyte.
The plot between \(\Lambda_m\) and \(c^{1 / 2}\) is a straight line with

  1. A Slope = \(\Lambda_m^0\) and intercept = A
  2. B Slope = \(\Lambda_m^0\) and intercept = -A
  3. C Slope = A and intercept = \(\Lambda_m^0\)
  4. D Slope = -A and intercept = \(\Lambda_m^0\)
Verified Solution

Answer & Solution

Correct Answer

(C) Slope = A and intercept = \(\Lambda_m^0\)

Step-by-step Solution

Detailed explanation

Given equation: \(\Lambda_m = \Lambda_m^0 - A c^{1/2}\) Rewrite in \(y = mx + b\) form: \(\Lambda_m = (-A)c^{1/2} + \Lambda_m^0\) Comparing with \(y = mx + b\), where \(y = \Lambda_m\) and \(x = c^{1/2}\): Slope = \(-A\) Intercept = \(\Lambda_m^0\)
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