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Question #44764

Difficulty: 8/10 | 🟢 Free

The Question

A 0.01 M0.01\text{ M} aqueous solution of the violet hydrate isomer of chromium(III) chloride (\ceCrCl3⋅6H2O\ce{CrCl3 \cdot 6H2O}) is heated from 298 K298\text{ K} to 348 K348\text{ K}. At 348 K348\text{ K}, the complex completely isomerizes to its dark green hydrate isomer. The temperature coefficient of equivalent conductivity for all ions is α=0.02 K−1\alpha = 0.02\text{ K}^{-1}, such that λeq,T=λeq,298[1+α(T−298)]\lambda_{eq, T} = \lambda_{eq, 298}[1 + \alpha(T - 298)]. Assuming the equivalent ionic conductivities (λeq\lambda_{eq}) of all cationic and anionic species present are identical at any given temperature, what is the net percentage change in the molar conductivity (Λm\Lambda_m) of the solution?

Options

  • A.

    -33.3%

  • B.

    +33.3%

  • C.

    -66.7%

  • D.

    +100.0%

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Exception_Exposure

Learn to identify edge cases and boundary exceptions that JEE examiners hide in math problems.

Concepts Behind This Question

Molar Conductivity Trend|Temperature Coefficient (Q10)

Why This Question Is Tricky

Common Mistakes

This problem tests the interplay between kinetic and thermodynamic factors in electrolytic conductance.

Students typically apply the general rule that heating decreases solvent viscosity, thereby increasing ionic mobility and conductivity (leading to the +100% trap).

However, they must recognize the 'Chemical Exception': the thermal activation triggers an endothermic anation (isomerization from the violet to the dark green hydrate), which drastically reduces the van't Hoff factor and the total charge (n-factor) of the electrolyte.

This speciation change overrides the kinetic mobility increase, resulting in a net decrease in molar conductivity.

Quick Facts About This Question

Question Information

SubjectChemistry
ChapterElectrochemistry - Class 12
ConceptMolar Conductivity Trend
Difficulty8
Cognitive Load7
Target Solve Time160 sec
AccessFree