Question

A transition metal (M) among Mn, Cr, Co and Fe has the highest standard electrode potential (M$^{3+}$/M$^{2+}$). It forms a metal complex of the type [M(CN)$_6$]$^{4-}$. The number of electrons present in the e$_g$ orbital of the complex is _______

Answer 1

1

Answer 2

Solution Overview:

1. Choosing the Metal:
   Out of Mn, Cr, Co, and Fe, the highest standard electrode potential for the M³⁺/M²⁺ couple is observed for cobalt.

2. Determining Oxidation State in the Complex:
   For the complex $[M(CN)_6]^{4-}$, using the charge balance:

   $$x + 6(-1) = -4 \implies x = +2.$$

   Thus, for Co, it is Co(II) which corresponds to a $d^7$ configuration.

3. Crystal Field Considerations:
   The cyanide ligand ($\text{CN}^-$) is a strong field ligand, which forces a low-spin configuration for Co(II).
   In an octahedral crystal field, a low-spin $d^7$ complex has the electron configuration:

   $$t_{2g}^6 e_{g}^1.$$

   Hence, there is 1 electron in the $e_g$ orbital.