What is the CFSE (Crystal Field Stabilization Energy) in the compound [Cr(OH2)6]³⁺?

To determine the Crystal Field Stabilization Energy (CFSE) in the complex ion [Cr(OH2)6]³⁺, we first need to consider the oxidation state of chromium and the nature of its electronic configuration.

Chromium in this complex is in the +3 oxidation state. The electron configuration for Cr in its ground state is [Ar] 4s² 3d⁴. Upon losing three electrons to form Cr³⁺, the electron configuration becomes [Ar] 3d³ because the 4s electrons are removed before the 3d electrons.

In an octahedral field, which is the geometry of [Cr(OH2)6]³⁺, the five d orbitals split into two sets: the lower energy t₂g (dxy, dyz, dzx) and the higher energy e_g (dx²-y², dz²). The electrons will fill the lower energy t₂g orbitals first before occupying the higher energy e_g orbitals.

Since Cr³⁺ has three d electrons, all of these will occupy the t₂g orbitals. The CFSE is calculated by assigning a stabilizing energy to the t₂g electrons and a