What is the spin only magnetic moment of the tetrahedral complex ion [NiCl4]2 minus, assuming that Ni2 plus is a high spin d8 metal ion?

Introduction / Context:
This coordination chemistry question tests understanding of crystal field theory, electron configuration of transition metal ions, and the calculation of spin only magnetic moments. The complex [NiCl4]2 minus contains Ni2 plus in a tetrahedral environment. Learners must determine the number of unpaired electrons in the d orbitals and then apply the spin only formula for magnetic moment. Such problems are common in inorganic chemistry examinations and require careful reasoning through several steps.

Given Data / Assumptions:
- The complex ion is [NiCl4]2 minus, where nickel is in the plus two oxidation state.
- Chloride ligands are weak field ligands and usually form high spin complexes.
- The geometry is tetrahedral, which leads to a particular pattern of d orbital splitting.
- The magnetic moment is to be calculated using the spin only formula mu equals square root of n multiplied by n plus 2 Bohr magneton, where n is the number of unpaired electrons.

Concept / Approach:
First, we determine the electron configuration of Ni2 plus. Neutral nickel has atomic number 28, which corresponds to [Ar]3d8 4s2. The Ni2 plus ion loses two 4s electrons, giving [Ar]3d8. In a tetrahedral crystal field, the d orbitals split into two sets, but the splitting is relatively small and the complex is almost always high spin with maximum number of unpaired electrons. For a d8 high spin tetrahedral complex, there are two unpaired electrons. Substituting n equals 2 into the spin only formula mu equals square root of n multiplied by n plus 2 gives the magnetic moment, which evaluates to approximately 2.83 Bohr magneton, rounded in the options to 2.82 Bohr magneton.

Step-by-Step Solution:
Step 1: Write the electron configuration of neutral nickel. Atomic number 28 gives [Ar]3d8 4s2.
Step 2: For Ni2 plus, remove two electrons from the 4s orbital, giving [Ar]3d8 as the electronic configuration.
Step 3: Recognise that chloride ligands are weak field and that tetrahedral complexes generally experience smaller splitting than octahedral ones, so pairing of electrons is not favoured and the complex is high spin.
Step 4: For a d8 configuration in a high spin tetrahedral field, the electrons occupy the split d orbitals in such a way that there are two unpaired electrons.
Step 5: Use the spin only formula for magnetic moment: mu equals square root of n multiplied by n plus 2 Bohr magneton. Here n equals 2.
Step 6: Substitute n equals 2. Then mu equals square root of 2 multiplied by 4, which is square root of 8, approximately 2.828 Bohr magneton.
Step 7: Match this value to the closest option, which is 2.82 Bohr magneton.

Verification / Alternative check:
You can cross check by recalling common patterns. For d8 octahedral complexes that are low spin, such as some strong field ligands, there can be zero unpaired electrons. However, high spin d8 complexes, especially in tetrahedral fields with weak ligands like chloride, typically have two unpaired electrons. Reference tables for magnetic moments list mu values around 2.8 Bohr magneton for complexes with two unpaired electrons. This independent check confirms that 2.82 Bohr magneton is the correct approximate spin only magnetic moment.

Why Other Options Are Wrong:
- 1.41 Bohr magneton: This would correspond to a system with one unpaired electron using the spin only formula, which does not match the high spin d8 tetrahedral arrangement of Ni2 plus.

Why Other Options Are Wrong (continued):
- 1.82 Bohr magneton: This does not correspond neatly to a standard integer number of unpaired electrons under the spin only approximation for this complex.
- 5.46 Bohr magneton: This value is roughly twice 2.73 and would correspond to a system with four or five unpaired electrons, which is not possible for a d8 high spin tetrahedral Ni2 plus complex.

Common Pitfalls:
A common error is to assume octahedral geometry for every complex and forget that [NiCl4]2 minus is tetrahedral. Another mistake is to miscount the electrons when forming Ni2 plus, sometimes incorrectly writing d6 or d7 instead of d8. Students can also confuse low spin and high spin situations and think that chloride might cause pairing, which it does not. Finally, some learners misuse the spin only formula by substituting the wrong value of n or by performing the calculation incorrectly. Careful attention to geometry, ligand field strength, and correct electron counting avoids these mistakes.

Final Answer:
2.82 BM is the spin only magnetic moment of the tetrahedral complex [NiCl4]2 minus, corresponding to two unpaired electrons in high spin Ni2 plus.