The complex ion that will lose its crystal field stabilization energy upon oxidation of metal to +3 state is:

(Phen = phenanthroline, ignore pairing energy)

CFSE for Strong Field Complexes

Phenanthroline ($$\text{phen}$$) is a strong field bidentate ligand. In an octahedral crystal field, it forces electrons to pair up in the lower-energy $$t_{2g}$$ orbitals before filling the higher-energy $$e_g$$ orbitals (low-spin complexes). The CFSE formula for an octahedral complex (ignoring pairing energy) is:

$$\text{CFSE} = [(-0.4 \times n_{t2g}) + (0.6 \times n_{eg})]\Delta_o$$

Step-by-Step Analysis of Each Complex Ion:

• 1. $$\mathbf{[Ni(phen)_3]^{2+}}\rightarrow\mathbf{[Ni(phen)_3]^{3+}}$$

  • $$\text{Ni}^{2+}$$ ($$s^0 d^8$$) configuration: $$t_{2g}^6 e_g^2 \implies \text{CFSE} = [6(-0.4) + 2(0.6)]\Delta_o = -1.2\Delta_o$$
  • $$\text{Ni}^{3+}$$ ($$s^0 d^7$$) configuration: $$t_{2g}^6 e_g^1 \implies \text{CFSE} = [6(-0.4) + 1(0.6)]\Delta_o = -1.8\Delta_o$$
  • Result: CFSE increases in magnitude (gains stabilization energy).

  
  

• 2. $$\mathbf{[Fe(phen)_3]^{2+}}\rightarrow\mathbf{[Fe(phen)_3]^{3+}}$$

  • $$\text{Fe}^{2+}$$ is a $$d^6$$ system. In a strong field, its configuration is $$t_{2g}^6 e_g^0$$.
    $$\text{CFSE} = [6 \times (-0.4) + 0 \times 0.6]\Delta_o = -2.4\Delta_o$$
  • $$\text{Fe}^{3+}$$ is a $$d^5$$ system. In a strong field, its configuration is $$t_{2g}^5 e_g^0$$.
    $$\text{CFSE} = [5 \times (-0.4) + 0 \times 0.6]\Delta_o = -2.0\Delta_o$$
  • Result: The CFSE magnitude drops from $$-2.4\Delta_o$$ to $$-2.0\Delta_o$$ (it loses stabilization energy).

• 3. $$\mathbf{[Co(phen)_3]^{2+}} \rightarrow \mathbf{[Co(phen)_3]^{3+}}$$

  • $$\text{Co}^{2+}$$ ($$s^0 d^7$$) configuration: $$t_{2g}^6 e_g^1 \implies \text{CFSE} = [6(-0.4) + 1(0.6)]\Delta_o = -1.8\Delta_o$$
  • $$\text{Co}^{3+}$$ ($$s^0 d^6$$) configuration: $$t_{2g}^6 e_g^0 \implies \text{CFSE} = [6(-0.4) + 0(0.6)]\Delta_o = -2.4\Delta_o$$
  • Result: CFSE increases in magnitude (gains stabilization energy).



• 4. $$\mathbf{[Zn(phen)_3]^{2+}} \rightarrow \mathbf{[Zn(phen)_3]^{3+}}$$

  • $$\text{Zn}^{2+}$$ ($$s^0 d^{10}$$) configuration: $$t_{2g}^6 e_g^4 \implies \text{CFSE} = [6(-0.4) + 4(0.6)]\Delta_o = 0\Delta_o$$
  • $$\text{Zn}^{3+}$$ ($$s^0 d^9$$) configuration: $$t_{2g}^6 e_g^3 \implies \text{CFSE} = [6(-0.4) + 3(0.6)]\Delta_o = -0.6\Delta_o$$
  • Result: CFSE increases in magnitude (gains stabilization energy).

Conclusion:

Only the iron complex undergoes a decrease in its crystal field stabilization energy upon oxidation from $$+2$$ to $$+3$$.

Answer: Option B — [Fe(phen)₃]²⁺