Animated Solution for Chemistry - Redox Reactions: The oxidation states of iron atoms in compounds (A), (B) and (C), respectively, are $x,y$ and $z$. The sum of $x,y$ and $z$ is ${\text{Na}}_4[\text{Fe}(\text{CN}{)}_5(\text{NOS})]$, (A) ${\text{Na}}_4[{\text{FeO}}_4]$, (B) $[{\text{Fe}}_2(\text{CO}{)}_9]$ (C)

The journey to mastering coordination chemistry often involves deciphering the hidden charges within complex molecules. In this thrilling problem, we are tasked with uncovering the oxidation states of iron in three distinct and fascinating complexes. Let's embark on this chemical detective work!

We are given three compounds, each harboring iron in a potentially different oxidation state: 1. Compound (A): ${\text{Na}}_4[\text{Fe}(\text{CN}{)}_5(\text{NOS})]$ 2. Compound (B): ${\text{Na}}_4[{\text{FeO}}_4]$ 3. Compound (C): $[{\text{Fe}}_2(\text{CO}{)}_9]$

Our mission is to find the oxidation states $x$, $y$, and $z$ for iron in these respective compounds, and finally, compute their sum. The golden rule here is that the sum of the oxidation states of all atoms in a neutral molecule must equal zero.

Let's start with the most intimidating of the trio: ${\text{Na}}_4[\text{Fe}(\text{CN}{)}_5(\text{NOS})]$.

We know a few things for sure. Sodium ($\text{Na}$) is an alkali metal, so it proudly carries a $+1$ charge. Cyanide (${\text{CN}}^{-}$) is a classic ligand with a $-1$ charge. But what about the $\text{NOS}$ ligand? This is a classic JEE trap!

The $\text{NOS}$ ligand can be visualized as a combination of a nitrosonium ion (${\text{NO}}^{+}$) and a sulfide ion (${\text{S}}^{2-}$). When you combine these, the net charge becomes:

Now, let's set up our master equation for the entire complex. Let the oxidation state of iron be $x$:

Simplifying this, we get:

Iron is in a $+2$ oxidation state here!

Moving on to the second compound, ${\text{Na}}_4[{\text{FeO}}_4]$, things look a bit more familiar. This is sodium ferrate.

Again, sodium contributes $+1$. Oxygen, in the vast majority of its complexes, acts as an oxide ion with a $-2$ charge. Let the oxidation state of iron be $y$. Setting up the equation:

Let's do the math:

Here, iron is flexing a higher oxidation state of $+4$.

Finally, we arrive at $[{\text{Fe}}_2(\text{CO}{)}_9]$, diiron nonacarbonyl. This is a metal carbonyl complex.

The beauty of metal carbonyls lies in the carbon monoxide ($\text{CO}$) ligand. It is a completely neutral molecule, meaning its charge is exactly $0$. Let the oxidation state of iron be $z$. Since there are two iron atoms, our equation is:

This simplifies beautifully to:

Yes, you read that right! Iron can exist in a zero oxidation state when bonded to neutral ligands like $\text{CO}$.

We have successfully unmasked all three oxidation states: - $x=+2$ - $y=+4$ - $z=0$

The question asks for the sum of these values. Let's bring it all together:

And there we have it! The final answer is 6. This problem beautifully illustrates the incredible versatility of transition metals like iron, capable of adopting oxidation states ranging from $0$ all the way to $+4$ and beyond. Always keep an eye out for those tricky ligands!