Total spin only magnetic moment of the ion [Mn(SCN)6]x– is 5.92 B.M. Find out the value of x.
- 5
- 3
- 2
- 4
The Correct Option is D
Solution and Explanation
The magnetic moment (\( \mu \)) is related to the number of unpaired electrons (\( n \)) by the formula :
\( \mu = \sqrt{n(n+2)} \, \text{BM} \)
Step 1: Given Data:
\( \mu = 6.06 \, \text{BM} \)
Step 2: Solve for \( n \):
\( 6.06 = \sqrt{n(n+2)} \)
Squaring both sides :
\( 36.72 = n(n+2) \)
Step 3 : Solve the Equation:
\( n \approx 5 \) (nearest integer).
Step 4 : Oxidation State of Mn:
Since Mn has 5 unpaired electrons, its oxidation state must be +2, as follows :
\( \text{Mn}^{2+} \Rightarrow x = +2. \)
Conclusion:
The number of unpaired electrons is 5, and the oxidation state of Mn is +2.
So, Mn must be in +2 oxidation state (Mn+2)
\(⇒ 2 + (–6) = –x \)
\(⇒ –4 = –x \)
\(⇒ x = 4\)
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Concepts Used:
Coordination Compounds
A coordination compound holds a central metal atom or ion surrounded by various oppositely charged ions or neutral molecules. These molecules or ions are re-bonded to the metal atom or ion by a coordinate bond.
Coordination entity:
A coordination entity composes of a central metal atom or ion bonded to a fixed number of ions or molecules.
Ligands:
A molecule, ion, or group which is bonded to the metal atom or ion in a complex or coordination compound by a coordinate bond is commonly called a ligand. It may be either neutral, positively, or negatively charged.