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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 \(\left(\Lambda_m^0\right)\) for an electrolyte is A\(\Lambda_m^0=\nu_{+} \lambda_{+}^0+\nu_{-} \lambda_{-}^0\), 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.
If the equivalent conductivity of 1 M Phthalic acid is \(12.8 S cm ^2 eq ^{-1}\) and the limiting equivalent conductivities of the
hydrogen and Phthalate ions are 42 and \(288.42 S cm ^2 eq ^{-1}\), respectively, the degree of dissociation of Phthalic acid will be :

  1. A 0.304
  2. B 0.044
  3. C 0.387
  4. D 0.0387
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Answer & Solution

Correct Answer

(D) 0.0387

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Detailed explanation

\(\Lambda_{eq}^0 = \lambda_{H^+}^0 + \lambda_{Phthalate^{2-}}^0 = 42 + 288.42 = 330.42 \,S\,cm^2\,eq^{-1}\) \(\alpha = \frac{\Lambda_{eq}}{\Lambda_{eq}^0} = \frac{12.8}{330.42} \approx 0.0387\)
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