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Question

(A) In $[Co(CN)_6]^{3-}$,the central metal ion is $Co^{3+}$. The electronic configuration of $Co^{3+}$ is $3d^6$.Since $CN^-$ is a strong field ligand

Vedclass · Accepted Answer

$-2.4\,\Delta_0 + 2p$

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(A) In $[Co(CN)_6]^{3-}$,the central metal ion is $Co^{3+}$. The electronic configuration of $Co^{3+}$ is $3d^6$.Since $CN^-$ is a strong field ligand,it causes pairing of electrons,resulting in a low-spin complex.All $6$ electrons occupy the $t_{2g}$ orbitals,and $0$ electrons occupy the $e_g$ orbitals.The formula for $CFSE$ is: $CFSE = (n_{t_{2g}} 	imes -0.4\Delta_0) + (n_{e_g} 	imes 0.6\Delta_0) + mP$,where $m$ is the number of extra electron pairs formed.For $d^6$ in a strong field,$CFSE = (6 	imes -0.4\Delta_0) + (0 	imes 0.6\Delta_0) = -2.4\Delta_0$.Including the pairing energy $2p$ (for the two extra pairs formed compared to the free ion),the total energy is $-2.4\Delta_0 + 2p$.

Calculate the crystal field stabilization energy $(CFSE)$ in $[Co(CN)_6]^{3-}$.

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