Question

The ion $C{r^{ + 2}}$ is reducing in nature while the same d-orbital configuration $\left( {{d^4}} \right)$ , $M{n^{ + 3}}$ is an oxidizing agent.

Answer 1

Chromium is the chemical element that can lose electrons and forms an ion $C{r^{ + 2}}$ , Manganese is a chemical element that can lose two electrons and forms an ion $M{n^{ + 3}}$ . Both of these ions have the same configuration, but one tries to attain half-filled ${t_{2g}}$ orbitals and the other tries to attain half-filled d-orbital configuration.

Complete answer:
Chromium is an element with atomic number $24$ , it has $4{s^1}3{d^5}$ valence configuration. It can lose two electrons and turn into an ion $C{r^{ + 2}}$ with the valence configuration of $3{d^4}$ .
This chromium ion $C{r^{ + 2}}$ is reducing in nature, which means itself undergoes oxidation and forms ion with $3{d^3}$ configuration, which has half-filled ${t_{2g}}$ orbital.
Manganese is an element with atomic number $25$ , it has $4{s^2}3{d^5}$ valence configuration. It can lose electrons and forms $M{n^{ + 3}}$ with the valence configuration of $3{d^4}$ . This ion can act as an oxidizing agent which means it undergoes reduction to form an ion with half-filled d-orbital $\left( {3{d^5}} \right)$ .
Thus, the ion $C{r^{ + 2}}$ is reducing in nature while the same d-orbital configuration $\left( {{d^4}} \right)$ , $M{n^{ + 3}}$ is an oxidizing agent due to attain half-filled ${t_{2g}}$ and half-filled d-orbital configuration.

Note:
Orbitals are classified into s, p, d, and f orbitals. d-orbital has the degeneracy of five, namely ${d_{xy}},{d_{yz}},{d_{zx}},{d_{{x^2} - {y^2}}},{d_{{z^2}}}$ these five degenerate orbitals are divided into ${t_{2g}}$ and ${e_g}$ orbitals. The degenerate orbitals that come under ${t_{2g}}$ are ${d_{xy}},{d_{yz}},{d_{zx}}$ and the degenerate orbitals that comes under ${e_g}$ are ${d_{{x^2} - {y^2}}},{d_{{z^2}}}$ . Ions try to attain completely filled, half filled, or half-filled ${t_{2g}}$ electronic configuration.