Arrange the following Cobalt complexes in the order of increasing Crystal Field Stabilization Energy (CFSE) value.
Complexes:

Choose the correct option:

The Crystal Field Stabilization Energy (CFSE) of a coordination complex depends primarily on two factors:

• the oxidation state of the central metal ion, and
• the strength of the ligands as given by the spectrochemical series.

For Effect of the oxidation state of the central metal ion:

The magnitude of crystal field splitting $$\Delta_o$$ increases as the oxidation state of the central metal ion increases. A higher positive charge attracts the ligands more strongly, resulting in greater splitting of the $$d$$-orbitals and hence a larger CFSE.

The oxidation state of cobalt in each complex is:

• (A) $$[CoF_6]^{3-}$$

  $$x+6(-1)=-3$$

  $$x=+3$$

• (B) $$[Co(H_2O)_6]^{2+}$$

  $$x+6(0)=+2$$

  $$x=+2$$

• (C) $$[Co(NH_3)_6]^{3+}$$

  $$x+6(0)=+3$$

  $$x=+3$$

• (D) $$[Co(en)_3]^{3+}$$

  $$x+3(0)=+3$$

  $$x=+3$$

Since complex (B) contains $$Co^{2+}$$ whereas the remaining complexes contain $$Co^{3+}$$, complex (B) has the smallest crystal field splitting and therefore the lowest CFSE.

Thus,

$$B<(A,C,D).$$

For Effect of ligand field strength:

Among complexes (A), (C), and (D), the metal ion is the same $$\left(Co^{3+}\right)$$. Hence, the CFSE depends only on ligand strength.

According to the spectrochemical series,

$$F^-<H_2O<NH_3<en.$$

Therefore,

• (A) $$[CoF_6]^{3-}$$ contains the weak field ligand $$F^-$$ and has the smallest splitting among the $$Co^{3+}$$ complexes.
• (C) $$[Co(NH_3)_6]^{3+}$$ contains the stronger ligand $$NH_3$$ and has a larger splitting.
• (D) $$[Co(en)_3]^{3+}$$ contains ethylenediamine, a stronger field ligand than $$NH_3$$, and therefore exhibits the greatest splitting.

Hence, for the $$Co^{3+}$$ complexes,

$$A<C<D.$$

Combining both observations gives the overall order of CFSE as

$$B<A<C<D.$$

Therefore, the correct order is

$$\boxed{B<A<C<D}.$$