Which of the following will be having maximum magnetic moment?

1. \([Fe(H_2O)_6]Cl_2\)

2. \([Mn(CN)_6]SO_4\)

3. \(Na_3[FeCl_6]\)

4. \([Co(NH_3)_6]Cl_3\)

\(Na_3[FeCl_6]\)

The correct answer is option 3. \(Na_3[FeCl_6]\).

To determine which complex has the maximum magnetic moment, we need to evaluate the number of unpaired electrons in the central metal ion for each complex. Magnetic moment is directly related to the number of unpaired electrons and can be calculated using the formula:

\(\mu = \sqrt{n(n+2)} \, \text{BM} \)

where \(n\) is the number of unpaired electrons.

Let us evaluate each option:

1. \([Fe(H_2O)_6]Cl_2\):

Oxidation state of Fe: \(+2\) (since \(H_2O\) is neutral, and \(Cl^-\) provides a -2 charge).

Electronic configuration of \(Fe^{2+}\): \(3d^6\).

With water as a weak field ligand, pairing of electrons does not occur. So, there are 4 unpaired electrons.

Magnetic moment: \(\mu = \sqrt{4(4+2)} = \sqrt{24} \approx 4.90 \, \text{BM}\).

2. \([Mn(CN)_6]SO_4\):

Oxidation state of Mn: \(+4\) (since CN⁻ provides -1).

Electronic configuration of \(Mn^{4+}\): \(3d^3\).

\(CN^-\) is a strong field ligand and causes pairing of electrons, leaving one unpaired electron.

Magnetic moment: \(\mu = \sqrt{1(1+2)} = \sqrt{3} \approx 1.73 \, \text{BM}\).

3. \(Na_3[FeCl_6]\):

Oxidation state of Fe: \(+3\) (since 3 \(Na^+\) neutralize the -3 charge of the complex).

Electronic configuration of \(Fe^{3+}\): \(3d^5\).

With \(Cl^-\) as a weak field ligand, pairing does not occur. So, there are 5 unpaired electrons.

Magnetic moment: \(\mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \, \text{BM}\).

4. \([Co(NH_3)_6]Cl_3\):

Oxidation state of Co: \(+3\) (since \(NH_3\) is neutral and Cl⁻ gives a -3 charge).

Electronic configuration of \(Co^{3+}\): \(3d^6\).

\(NH_3\) is a strong field ligand and causes pairing of electrons, leaving no unpaired electrons.

Magnetic moment: \(\mu = 0 \, \text{BM}\).

Conclusion:

The complex with the maximum magnetic moment is \(Na_3[FeCl_6]\) with 5 unpaired electrons, giving a magnetic moment of approximately 5.92 BM.

Thus, the correct answer is option 3: \(Na_3[FeCl_6]\).