Animated Solution for Chemistry - Coordination Compounds: The coordination number and the oxidation state of the element 'E' in the complex $[E(\text{en}{)}_2(C_2{O}_4)]N{O}_2$ (where (en) is ethylene diamine) are, respectively

Coordination chemistry is like a grand architectural puzzle where a central metal atom acts as the foundation, and various molecules or ions, known as ligands, attach themselves to it like intricate scaffolding. In this problem, we are tasked with decoding the structural and electronic secrets of a specific coordination complex: $[E(\text{en}{)}_2(C_2{O}_4)]N{O}_2$.

Our mission is twofold: we need to determine the coordination number (how many direct bonds the central metal 'E' forms) and its oxidation state (the hypothetical charge it would carry if all ligands were removed along with the electron pairs they shared).

Before we dive into the math, let's look at the anatomy of our complex. The square brackets $[\dots ]$ enclose the coordination sphere. Everything inside this bracket is directly and tightly bound to the central metal 'E'.

Outside the bracket, we have $N{O}_2$. This is the counter ion, specifically the nitrite ion ($N{O}_2^{-}$). It is not directly attached to the metal; instead, it hovers nearby in the crystal lattice or solution to balance the overall charge of the complex cation.

To find the coordination number, we must understand the 'bite' of our ligands, formally known as denticity. Denticity refers to the number of donor atoms a single ligand molecule uses to attach to the central metal.

1. Ethylene diamine (en): The formula for 'en' is $H_2\ddot{N}-C{H}_2-C{H}_2-\ddot{N}{H}_2$. Notice the two nitrogen atoms? Each possesses a lone pair of electrons. Because it can attach to the metal at two distinct points simultaneously, it is classified as a bidentate ligand. 2. Oxalate ($C_2{O}_4^{2-}$): This ion features two negatively charged oxygen atoms, both eager to donate their electron pairs to the metal center. Like ethylene diamine, oxalate is also a bidentate ligand.

The coordination number is simply the total number of coordinate covalent bonds formed between the ligands and the central metal.

We have two molecules of 'en', and since each is bidentate, they contribute $2\times 2=4$ bonds. We also have one oxalate ion, which contributes $1\times 2=2$ bonds.

Adding these together:

This tells us that the central metal 'E' sits in an octahedral geometry, surrounded by six coordinate bonds.

Now, let's find the oxidation state. This requires a bit of algebraic charge balancing. First, we must determine the net charge on the coordination sphere itself.

Since the complex is electrically neutral overall, and the counter ion is $N{O}_2^{-}$, the coordination sphere must carry a $+1$ charge to perfectly balance the $-1$ charge of the nitrite ion.

Now, we set up an equation where the sum of the oxidation states of all components inside the bracket equals the net charge of the sphere ($+1$). Let the oxidation state of 'E' be $x$.

- Ethylene diamine ('en') is a neutral organic molecule, so its charge is $0$. - The oxalate ion ($C_2{O}_4^{2-}$) carries a standard charge of $-2$.

Plugging these values into our equation:

Through careful analysis of ligand denticity and charge conservation, we have successfully decoded the complex. The central element 'E' has a coordination number of 6 and an oxidation state of +3. This perfectly aligns with option (d), proving that a systematic approach makes even the most intimidating chemical formulas completely manageable.