Different hydrated isomers of CrCl₃.6H₂O can not be differentiated by:

Magnetic moment

The correct answer is option 4. Magnetic moment

Let us delve deeper into the reasoning behind why the magnetic moment cannot be used to differentiate the hydrated isomers of \(CrCl_3·6H_2O\).

Hydrated Isomers of \(CrCl_3·6H_2O\)

Chromium(III) chloride hexahydrate can exist in several hydrated forms, depending on how the water molecules and chloride ions are arranged around the central chromium ion. These isomers can be:

\([Cr(H_2O)_6]Cl_3\): All six water molecules are coordinated to the chromium ion, and the three chloride ions are free in the solution.

\([Cr(H_2O)_5Cl]Cl_2·H_2O\): Five water molecules and one chloride ion are coordinated to the chromium ion, with two chloride ions and one water molecule outside the coordination sphere.

\([Cr(H_2O)_4Cl_2]Cl·2H_2O\): Four water molecules and two chloride ions are coordinated to the chromium ion, with one chloride ion and two water molecules outside the coordination sphere.

Differentiation Methods

Conductivity Measurements: Different isomers release different numbers of chloride ions when dissolved in water, affecting the conductivity.

\([Cr(H_2O)_6]Cl_3\) releases 3 \(Cl^-\) ions.

\([Cr(H_2O)_5Cl]Cl_2·H_2O\) releases 2 \(Cl^-\) ions.

\([Cr(H_2O)_4Cl_2]Cl·2H_2O\) releases 1 \(Cl^-\) ion.

This means conductivity measurements can distinguish between the isomers based on the number of free ions in solution.

Precipitation by \(AgNO_3\): When \(AgNO_3\) is added, it precipitates free \(Cl^-\) ions as \(AgCl\). The amount of \(AgCl\) precipitate will vary with the number of free chloride ions. Thus, the amount of precipitate formed can be used to identify the different isomers.

Dipole Moment: The arrangement of water and chloride ligands around the central chromium ion affects the overall dipole moment of the complex. Different isomers will have different spatial arrangements and, therefore, different dipole moments. Measuring the dipole moment can help distinguish between the isomers.

Magnetic Moment: The magnetic moment is determined by the number of unpaired electrons in the central metal ion. Chromium in the \(+3\) oxidation state (\(Cr^{3+}\)) has an electronic configuration of \([Ar] 3d^3\). Regardless of the arrangement of water and chloride ligands (the isomers), the number of unpaired electrons in \(Cr^{3+}\) remains the same. Therefore, the magnetic moment, which depends on the number of unpaired electrons, will be the same for all isomers.

Conclusion: The magnetic moment cannot be used to differentiate the hydrated isomers of \(CrCl_3·6H_2O\) because the number of unpaired electrons in \(Cr^{3+}\) does not change with different isomers. The magnetic moment is a property intrinsic to the \(Cr^{3+}\) ion itself, which remains the same across all isomers. Thus, the property that cannot differentiate the hydrated isomers of CrCl₃·6H₂O is the magnetic moment.