The correct increasing order of stability of the complexes based on \(\Delta_{\mathrm{o}}\) value is : I.…

The correct increasing order of stability of the complexes based on \(\Delta_{\mathrm{o}}\) value is :
I. \(\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-}\)
II. \(\left[\mathrm{Co}(\mathrm{CN})_6\right]^{4-}\)
III. \(\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{4-}\)
IV. \(\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}\)
  1. \(\mathrm{IV} \lt \mathrm{III} \lt \mathrm{II} \lt \mathrm{I}\)
  2. \(\mathrm{I} \lt \mathrm{II} \lt \mathrm{IV} \lt \) III
  3. III \( \lt \) II \( \lt \) IV \( \lt \) I
  4. II \( \lt \) III \( \lt \) I \( \lt \) IV

Solution

Neglecting pairing energy
I. $[\mathrm{Mn}(\mathrm{CN}) \mathrm{B}]^{3-} \Rightarrow \mathrm{Mn}^{3+}, \mathrm{t}_2 \mathrm{~g}^4, \mathrm{CFSE}=-0.4 \times 4 \Delta \mathrm{o}$ $=-1.6 \Delta$ 。
II. $[\mathrm{Co}(\mathrm{CN}) 8]^{4-} \Rightarrow \mathrm{Co}^{2+}, \mathrm{t}_2{ }^6 \mathrm{eg}^1, \mathrm{CFSE}=-0.4 \times 6+$ $0.6 \times 1=-1.8 \Delta_{\circ}$
III. $\left[\mathrm{Fe}(\mathrm{CN})_8\right]^{4-} \Rightarrow \mathrm{Fe}^{2+}, \mathrm{t}_{2 g}{ }^6 \mathrm{e}^0, \mathrm{CFSE}=-0.4 \times 6=$ $-2.4 \Delta_0$
IV. $\left[\mathrm{Fe}(\mathrm{CN})_8\right]^{3-} \Rightarrow \mathrm{Fe}^{3+}, \mathrm{t}_{2 g}{ }^5 \mathrm{e}^0, \mathrm{CFSE}=-0.4 \times 5=$ $-2 \Delta_0$
Order of stability III $>$ IV $>$ II $>$ I

Asked in: JEE Main 2025 (29 Jan Shift 1)

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