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CUET · CHEMISTRY · PYQ PAPER 2025

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Molar conductivity \(\Lambda_m^0\)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 \(\Lambda_m^0\) . 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, they 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.
If the molar conductance values of Ca2+ and Cl- at infinite dilution are, respectively, 118.8 × 10-4 ohm-1 m2 mol-1 and 77.33 × 10-4 ohm-1 m2 mol-1, then the molar conductance of CaCl2 at infinite dilution will be :

  1. A 273.46 ohm-1 m2 mol-1
  2. B 196.13 ohm-1 m2 mol-1
  3. C 41.47 ohm-1 m2 mol-1
  4. D -41.47 ohm-1 m2 mol-1
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Correct Answer

(A) 273.46 ohm-1 m2 mol-1

Step-by-step Solution

Detailed explanation

\( \Lambda_m^0(CaCl_2) = \nu_{Ca^{2+}} \lambda_{Ca^{2+}}^0 + \nu_{Cl^{-}} \lambda_{Cl^{-}}^0 \) \( \Lambda_m^0(CaCl_2) = (1 \times 118.8) + (2 \times 77.33) \) \( \Lambda_m^0(CaCl_2) = 118.8 + 154.66 \)…
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