Question

What can be inferred from the magnetic moment values of the following complex species? 
Example Magnetic Moment (BM)
K₄[Mn(CN)₆] 2.2 
[Fe(H₂O)₆]²⁺ 5.3 
K₂[MnCl₄] 5.9

Answer 1

Magnetic moment (\(\mu\)) is given as \(\mu\)=\(\sqrt{n(n+2)}\)
For value n = 1,\(\mu\)=\(\sqrt{1(1+2)}\)= \(\sqrt 3\)=1.732
For value n = 2, \(\mu\)=\(\sqrt{2(2+2)}=\sqrt 8\)=2.83
For value n = 3, \(\mu\)=\(\sqrt{3(3+2)}=\sqrt {15}\)=3.87
For value n = 4, \(\mu\)=\(\sqrt{4(4+2)}=\sqrt {24}\)=4.899
For value n = 5, \(\mu\)=√\(\sqrt{5(5+2)}=\sqrt {35}\)=5.92

---

(i) K₄[Mn(CN)₆] 
For in transition metals, the magnetic moment is calculated from the spin-only formula. Therefore, \(\sqrt{n(n+2)}\)=2.2
We can see from the above calculation that the given value is closest to n=1 . Also, in this complex, Mn is in the +2 oxidation state. This means that Mn has 5 electrons in the d-orbital. 
Hence, we can say that CN^- is a strong field ligand that causes the pairing of electrons.

---

(ii) [Fe(H₂O)₆]²⁺
\(\sqrt{n(n+2)}\)=5.3
We can see from the above calculation that the given value is closest to n=4. Also, in this complex, Fe is in the +2 oxidation state. This means that Fe has 6 electrons in the d-orbital. 
Hence, we can say that H₂O is a weak field ligand and does not cause the pairing of electrons.

---

(iii) K₂[MnCl₄]
\(\sqrt{n(n+2)}\)=5.9
We can see from the above calculation that the given value is closest to n=5. Also, in this complex, Mn is in the +2 oxidation state. This means that Mn has 5 electrons in the d-orbital. 
Hence, we can say that Cl^- is a weak field ligand and does not cause the pairing of electrons.