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Q. Which one of these statements about $\left[ Co ( CN )_{6}\right]^{3-}$ is true?

Coordination Compounds

Solution:

$\left[ Co ( CN )_{6}\right]^{3-}$
$Co ^{3+}=1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{6}, 3 d^{6}$
$CN ^{-}$is a strong field ligand and as it approaches the metal ion, the electron must pair up.
The splitting of the $d$-orbitals into two sets of orbitals in as octahedral complex $\left[ Co ( CN )_{6}\right]^{3-}$ may be represented as
image
Here, for $d^{6}$ ions, three electrons first inter orbitals with parallel spin out the remaining may pair up in $t_{2 g}$ orbital giving rise to low spin complex (strong ligand) field.
$\therefore\left[ Co ( CN )_{6}\right]^{3-}$ has no unpaired electrons and will be in low spin configuration.