Consider the following complexes : [ F e ( H 2 O ) 6 ] 2 + , [ C o F 6 ] 3 − , [ C o ( N H 3 ) 6 ] 3 + , [ F e F 6 ] 3 − , [ F e ( CN ) 6 ] 4 − If x = number of high-spin complexes y = n

Question

Consider the following complexes : [ F e ( H 2 ​ O ) 6 ​ ] 2 + , [ C o F 6 ​ ] 3 − , [ C o ( N H 3 ​ ) 6 ​ ] 3 + , [ F e F 6 ​ ] 3 − , [ F e ( CN ) 6 ​ ] 4 − If x = number of high-spin complexes y = number of complexes having an odd number of electrons in the e g ​ orbitals and an even number of electrons in ' t 2 g ​ '. find the value of ( x + y ) .

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Solution:

Let's analyze each complex:

1. $[F e (H_{2} O)_{6}]^{2 +}$ : Fe is in +2 oxidation state ( $d^{6}$ ). H₂O is a weak field ligand. This is a high-spin complex. Electron configuration: $t_{2 g}^{4} e_{g}^{2}$ . $e_{g}$ has an even number of electrons, $t_{2 g}$ has an even number of electrons.

2. $[C o F_{6}]^{3 -}$ : Co is in +3 oxidation state ( $d^{6}$ ). F⁻ is a weak field ligand. This is a high-spin complex. Electron configuration: $t_{2 g}^{4} e_{g}^{2}$ . $e_{g}$ has an even number of electrons, $t_{2 g}$ has an even number of electrons.

3. $[C o (N H_{3})_{6}]^{3 +}$ : Co is in +3 oxidation state ( $d^{6}$ ). NH₃ is a strong field ligand. This is a low-spin complex. Electron configuration: $t_{2 g}^{6} e_{g}^{0}$ . $e_{g}$ has an even number of electrons, $t_{2 g}$ has an even number of electrons.

4. $[F e F_{6}]^{3 -}$ : Fe is in +3 oxidation state ( $d^{5}$ ). F⁻ is a weak field ligand. This is a high-spin complex. Electron configuration: $t_{2 g}^{3} e_{g}^{2}$ . $e_{g}$ has an even number of electrons, $t_{2 g}$ has an odd number of electrons.

5. $[F e (CN)_{6}]^{4 -}$ : Fe is in +2 oxidation state ( $d^{6}$ ). CN⁻ is a strong field ligand. This is a low-spin complex. Electron configuration: $t_{2 g}^{6} e_{g}^{0}$ . $e_{g}$ has an even number of electrons, $t_{2 g}$ has an even number of electrons.

Number of high-spin complexes ( $x$ ): $[F e (H_{2} O)_{6}]^{2 +}$ , $[C o F_{6}]^{3 -}$ , $[F e F_{6}]^{3 -}$ . So, $x = 3$ .

Number of complexes with an odd number of electrons in $e_{g}$ and an even number in $t_{2 g}$ ( $y$ ): None of the complexes satisfy this condition. So, $y = 0$ .

Therefore, $x + y = 3 + 0 = 3$ .

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