Animated Solution for Chemistry - Redox Reactions: The oxidation state of Cr in $[\text{Cr}({\text{NH}}_3{)}_4{\text{Cl}}_2{]}^{+}$ is

Imagine a coordination complex as a microscopic solar system. At the center, acting like the sun, is a transition metal atom—in this case, Chromium ($\text{Cr}$). Orbiting around it are various molecules or ions called ligands. In our specific complex, $[\text{Cr}({\text{NH}}_3{)}_4{\text{Cl}}_2{]}^{+}$, we have a bustling neighborhood: four ammonia (${\text{NH}}_3$) molecules and two chloride (${\text{Cl}}^{-}$) ions all bonded to the central chromium atom.

But here is the catch: the entire system isn't electrically neutral. The square brackets indicate that this entire cluster acts as a single entity, and the little $+$ sign outside tells us that the whole complex has a net charge of $+1$. Our mission is to play chemical detective and figure out the exact oxidation state (or charge) of the central chromium atom that makes this math work.

To find the oxidation state of the central metal, we use a fundamental principle of charge conservation. Think of it like a financial ledger. The sum of the individual charges (oxidation states) of every single atom and ligand inside the brackets must perfectly balance out to equal the net charge written on the outside.

Mathematically, we can write this as:

Let's assign our variables. We don't know the oxidation state of Chromium, so we will call it $x$.

Next, we look at our ligands. Ammonia (${\text{NH}}_3$) is a stable, happy molecule all on its own. It doesn't carry an extra electron, nor is it missing one. Therefore, it is a neutral ligand, and its oxidation state is exactly $0$.

On the other hand, we have Chloride ($\text{Cl}$). Halogens in coordination complexes typically exist as halide ions, meaning they have gained one electron to complete their octet. Thus, each chloride ligand carries an oxidation state of $-1$.

Now, we simply plug these values into our master equation. We have one Chromium ($x$), four neutral Ammonia molecules ($4\times 0$), and two Chloride ions ($2\times -1$). All of this must add up to the net charge of the complex, which is $+1$.

This simplifies beautifully. The ammonia term vanishes entirely, leaving us with:

By moving the $-2$ to the other side of the equation, we find our answer:

And there we have it! The oxidation state of the central Chromium atom is $+3$. Physically, this means that the chromium atom has lost three of its valence electrons to form this specific coordination geometry. It's a simple, elegant piece of chemical accounting that reveals the hidden electronic structure of the molecule.