Among \(\mathrm{Sc^{3+}},\ \mathrm{Cr^{2+}},\ \mathrm{Mn^{3+}},\ \mathrm{Fe^{3+}},\ \mathrm{Co^{3+}}\),
\(n\) is the number of isoelectronic species.
\(n\) moles of \(\mathrm{AgNO_3}\) react with \(1\) mole of the complex \([\mathrm{Co(en)_3}]Cl_3\).
Find the number of electrons in the \(t_{2g}\) set of the complex.
Show Hint
Strong-field ligands like {en} cause electron pairing.
Low-spin octahedral complexes fill the \(t_{2g}\) orbitals completely first.
Part I: Find the number of isoelectronic species
Write electronic configurations:
Isoelectronic species have the same electronic configuration.
\[
\mathrm{Cr^{2+}} \text{ and } \mathrm{Mn^{3+}} \text{ both are } d^4
\]
Hence,
\[
n = 2
\]
Part II: Reaction with \(\mathrm{AgNO_3}\)
Complex given:
\[
[\mathrm{Co(en)_3}]Cl_3
\]
Here, all three chloride ions are outside the coordination sphere and ionizable.
Thus:
\[
1\ \text{mole of complex reacts with } 3\ \text{moles of } \mathrm{AgNO_3}
\]
Given:
\[
n = 2
\]
Part III: Find electrons in \(t_{2g}\) set
Oxidation state of Co:
\[
x + 0 = +3 \Rightarrow \mathrm{Co^{3+}}
\]
Electronic configuration of \(\mathrm{Co^{3+}}\):
\[
[\mathrm{Ar}]\,3d^6
\]
Ligand:
\[
\text{en (ethylenediamine)} \Rightarrow \text{strong field ligand}
\]
Thus, the complex is low spin octahedral .
Electron distribution:
\[
t_{2g}^6\ e_g^0
\]
\[
\boxed{\text{Number of electrons in } t_{2g} = 6}
\]
