Animated Solution for Chemistry - Coordination Compounds: In which of the following octahedral complexes of Co (At no. 27), will the magnitude of ${\Delta }_o$ be the highest?

Decoding Crystal Field Splitting

Have you ever wondered why some transition metal complexes are brilliantly colored while others are pale, or why some are strongly attracted to magnets while others couldn't care less? The secret lies in a fascinating phenomenon called Crystal Field Splitting. Let's dive into a classic problem that tests our understanding of this very concept.

A Tale of Five Orbitals

Imagine a free Cobalt ion floating in space. It has five $d$-orbitals, and they are all perfectly degenerate, meaning they sit at the exact same energy level. They are like five empty rooms on the same floor of a hotel, waiting for electrons to move in.

But things change drastically when ligands—molecules or ions with lone pairs of electrons—approach the metal ion to form an octahedral complex. These ligands are negatively charged (or have a partial negative charge), and the electrons in the metal's $d$-orbitals repel them. Because of the specific geometry of an octahedral complex, the ligands approach directly along the axes where the $d_{x^2-y^2}$ and $d_{z^2}$ orbitals lie.

This targeted approach causes a split. The orbitals pointing directly at the ligands experience massive repulsion and are pushed to a higher energy level. We call this the $e_g$ set. The other three orbitals ($d_{xy}$, $d_{yz}$, $d_{zx}$), which point between the axes, experience less repulsion and drop to a lower energy level. We call this the $t_{2g}$ set.

The energy gap between these two new levels is the Crystal Field Splitting Energy, denoted by ${\Delta }_o$ (the 'o' stands for octahedral).

Ranking the Contenders

Now, here is the crucial part: the size of this gap, ${\Delta }_o$, is not fixed. It depends entirely on the "strength" of the approaching ligands. Some ligands are gentle, causing a small split, while others are aggressive, causing a massive divide.

Chemists have ranked ligands based on their splitting power in what is known as the Spectrochemical Series. It looks something like this:

Our question asks which Cobalt complex will have the highest magnitude of ${\Delta }_o$. To answer this, we simply need to look at our options and find the strongest ligand.

We have four contenders: 1. Cyanide ($C{N}^{-}$) 2. Oxalate ($C_2{O}_4^{2-}$) 3. Water ($H_{2}O$) 4. Ammonia ($N{H}_3$)

Looking at our spectrochemical series, the order of strength is $C{N}^{-}>N{H}_3>H_{2}O>C_2{O}_4^{2-}$.

Cyanide is a notoriously strong field ligand. It forms incredibly strong bonds with the metal, pulling itself very close and causing immense repulsion with the $d$-orbitals. This results in a massive energy gap.

Therefore, the complex $[Co(CN{)}_6{]}^{3-}$ will exhibit the maximum crystal field splitting energy.

Why does this matter? Because ${\Delta }_o$ dictates the entire personality of the complex! A huge ${\Delta }_o$ means electrons won't have enough energy to jump to the higher $e_g$ orbitals. Instead, they will pair up in the lower $t_{2g}$ orbitals, creating a low-spin, diamagnetic complex. It also means the complex will absorb higher-energy light (like violet or blue) and reflect lower-energy light (like yellow or red).

So, the next time you see a coordination compound, don't just look at the formula. Look at the ligands, gauge their strength, and you'll be able to predict its secrets!