The correct order of spin-only magnetic moments among the following is :
(Atomic number : Mn=25,Co=27,Ni=28,Zn=30)

Options

A. `[ZnCl_(4)]^(2-) gt [NiCl_(4)]^(2-) gt [CoCl_(4)]^(2-) gt [MnCl_(4)]^(2-)`
B. `[CoCl_(4)]^(2-) gt [MnCl_(4)]^(2-) gt [NiCl_(4)]^(2-) gt [ZnCl_(4)]^(2-)`
C. `[NiCl_(4)]^(2-) gt [CoCl_(4)]^(2-) gt [MnCl_(4)]^(2-) gt [ZnCl_(4)]^(2-)`
D. `[MnCl_(4)]^(2-) gt [CoCl_(4)]^(2-) gt[NiCl_(4)]^(2-) gt [ZnCl_(4)]^(2-)`

Answer

To determine the correct order of spin-only magnetic moments among the given coordination compounds (ZnCl4^2-, NiCl4^2-, CoCl4^2-, and MnCl4^2-), we will follow these steps:

### Step 1: Determine the oxidation states of the central metal atoms.
- For each complex, the oxidation state of the central metal can be calculated using the formula:
\[ \text{Oxidation state} = \text{Charge of the complex} - \text{Sum of the oxidation states of the ligands} \]
- In all cases, the charge of the complex is -2 and the oxidation state of Cl is -1. Since there are 4 Cl ligands:
\[ \text{Oxidation state} = -2 - (4 \times -1) = +2 \]
- Therefore, the oxidation states for all metal ions in the complexes are:
- Zn: +2
- Ni: +2
- Co: +2
- Mn: +2

### Step 2: Write the electronic configurations of the metal ions in their +2 oxidation states.
- The electronic configurations for the +2 oxidation states are:
- Zn^2+: [Ar] 3d^10
- Ni^2+: [Ar] 3d^8
- Co^2+: [Ar] 3d^7
- Mn^2+: [Ar] 3d^5

### Step 3: Determine the number of unpaired electrons.
- Since Cl^- is a weak field ligand, it does not cause pairing of electrons. Therefore, we can directly count the unpaired electrons:
- Zn^2+: 0 unpaired electrons (3d^10)
- Ni^2+: 2 unpaired electrons (3d^8)
- Co^2+: 3 unpaired electrons (3d^7)
- Mn^2+: 5 unpaired electrons (3d^5)

### Step 4: Calculate the spin-only magnetic moments using the formula.
The formula for calculating the spin-only magnetic moment (μ) is:
\[ \mu = \sqrt{n(n + 2)} \]
where \( n \) is the number of unpaired electrons.

- For Zn^2+:
\[ \mu = \sqrt{0(0 + 2)} = 0 \, \mu_B \]
- For Ni^2:
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{8} \approx 2.83 \, \mu_B \]
- For Co^2+:
\[ \mu = \sqrt{3(3 + 2)} = \sqrt{15} \approx 3.87 \, \mu_B \]
- For Mn^2+:
\[ \mu = \sqrt{5(5 + 2)} = \sqrt{35} \approx 5.92 \, \mu_B \]

### Step 5: Order the magnetic moments from highest to lowest.
Based on the calculated magnetic moments:
1. MnCl4^2-: 5.92 μ_B (5 unpaired electrons)
2. CoCl4^2-: 3.87 μ_B (3 unpaired electrons)
3. NiCl4^2-: 2.83 μ_B (2 unpaired electrons)
4. ZnCl4^2-: 0 μ_B (0 unpaired electrons)

### Final Answer:
The correct order of spin-only magnetic moments is:
**MnCl4^2- > CoCl4^2- > NiCl4^2- > ZnCl4^2-**

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