Related Formula
Spin-only magnetic moment expression:
μ = √(n(n+2)) B.M.$$\mu = \sqrt{n(n+2)}\mathrm{\ B.M.}$$
Core Logic
Evaluating the oxidation states and stability profiles:
- In TiO$TiO$: Ti²⁺$Ti^{2+}$
- In VO$VO$: V²⁺$V^{2+}$
- In Mn₂O₃$Mn_2O_3$: Mn³⁺$Mn^{3+}$
Mn³⁺$Mn^{3+}$ possesses a very high reduction potential (E^°Mn³⁺/Mn²⁺ = +1.57 V$E^\circ_{Mn^{3+}/Mn^{2+}} = +1.57\mathrm{\ V}$), making it an exceptionally strong oxidizing agent because it easily gains an electron to form stable Mn²⁺$Mn^{2+}$ (d⁵$d^5$ configuration).
Step 1: Calculate the Magnetic Moment of Mn(III)
Electronic configuration of Mn³⁺$Mn^{3+}$:
Mn³⁺ = [Ar]3d⁴ n = 4 unpaired electrons$$Mn^{3+} = [Ar]3d^4 \implies n = 4\text{ unpaired electrons}$$
Calculating the spin-only magnetic moment:
μ = √(4(4+2)) = √(24) ≈ 4.89 B.M.$$\mu = \sqrt{4(4+2)} = \sqrt{24} \approx 4.89\mathrm{\ B.M.}$$
Step 2: Rounding to Nearest Integer
Rounding 4.89 B.M.$4.89\mathrm{\ B.M.}$ to the nearest integer gives 5$5$.
Pattern Recognition
High reduction potentials are strongly tied to manganese in its +3$+3$ oxidation state. To quickly estimate magnetic moments, remember that a system with n$n$ unpaired electrons always results in a value of 'n.something$n.\text{something}$' B.M. Thus, 4$4$ unpaired electrons arrow 4.89 B.M.$\rightarrow 4.89\mathrm{\ B.M.}$, which rounds up to 5$5$.
Chapter Mix
Class 12 Chemistry: d- and f-Block Elements