JEE Main 2025 Apr 4 Shift 1, Chemistry Q6: Colour, Magnetism And Stability Of Co-ordination Compounds

JEE Main2025Apr 4, Shift 1Chemistry

Which one of the following complexes will have $Δ_{0} = 0$ and $μ = 5.96$ B.M.?

A
$[F e (C N)_{6}]^{4 -}$
B
$[C o (N H_{3})_{6}]^{3 +}$
C
$[F e F_{6}]^{4 -}$
D
$[M n (S C N)_{6}]^{4 -}$

Solution

The spin-only magnetic moment is $μ = n (n + 2)$ B.M., where $n$ is the number of unpaired electrons. A value of $μ = 5.96$ B.M. corresponds to $n = 5$ (since $35 \approx 5.92$ ).

A $d^{5}$ high-spin configuration with $n = 5$ unpaired electrons has its $t_{2 g}$ orbitals singly filled with 3 electrons and $e_{g}$ singly filled with 2 electrons, giving CFSE $= (- 0.4 \times 3 + 0.6 \times 2) Δ_{0} = 0$ . So $Δ_{0}$ effectively does not stabilize the complex, matching the condition $Δ_{0} = 0$ in the question.

Checking each option:

Complex	$d^{n}$ config	$n$ unpaired	$μ$ (B.M.)
$[F e (C N)_{6}]^{4 -}$ (Fe $^{2 +}$ , $d^{6}$ , SFL)	$t_{2 g}^{6}$	0	0
$[C o (N H_{3})_{6}]^{3 +}$ (Co $^{3 +}$ , $d^{6}$ , SFL)	$t_{2 g}^{6}$	0	0
$[F e F_{6}]^{4 -}$ (Fe $^{2 +}$ , $d^{6}$ , WFL)	$t_{2 g}^{4} e_{g}^{2}$	4	$24 \approx 4.89$
$[M n (S C N)_{6}]^{4 -}$ (Mn $^{2 +}$ , $d^{5}$ , WFL)	$t_{2 g}^{3} e_{g}^{2}$	5	$35 \approx 5.96$

Only $[M n (S C N)_{6}]^{4 -}$ matches both $μ = 5.96$ B.M. and CFSE $= 0$ (the $d^{5}$ high-spin case).

$∴$ Correct option: (4).

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JEE Main 2025 Apr 4 Shift 1, Chemistry Q6: Colour, Magnetism And Stability Of Co-ordination Compounds

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