Animated Solution for Chemistry - Coordination Compounds: The equivalents of ethylene diamine required to replace the neutral ligands from the coordination sphere of the trans-complex of ${\text{CoCl}}_3\cdot 4{\text{NH}}_3$ is ...... (Round off to the nearest integer).

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, build the structure around it. In this problem, we are tasked with modifying an existing structure—a cobalt complex—by swapping out some of its building blocks.

To do this correctly, we must first understand the blueprint of our starting material and the nature of the new blocks we are bringing in.

Decoding the Blueprint

We are given the empirical formula ${\text{CoCl}}_3\cdot 4{\text{NH}}_3$. At first glance, this just looks like a collection of atoms. However, thanks to Alfred Werner's coordination theory, we know that transition metals like Cobalt have two types of valencies: primary (oxidation state) and secondary (coordination number).

Cobalt in the $+3$ oxidation state almost exclusively exhibits a secondary valency, or coordination number, of $6$. This means the central ${\text{Co}}^{3+}$ ion must be directly bonded to exactly six ligands inside the square brackets, which represent the coordination sphere.

To satisfy this requirement of six, all four ammonia (${\text{NH}}_3$) molecules and two of the three chloride (${\text{Cl}}^{-}$) ions must move inside the coordination sphere. The remaining chloride ion stays outside as a counter ion.

Thus, our actual complex is $[\text{Co}({\text{NH}}_3{)}_4{\text{Cl}}_2]\text{Cl}$.

Identifying the Targets

The question specifically asks us to replace the neutral ligands from the coordination sphere.

Looking at our complex, $[\text{Co}({\text{NH}}_3{)}_4{\text{Cl}}_2{]}^{+}$, we have two types of ligands: 1. Chloride ions (${\text{Cl}}^{-}$): These are anionic (negatively charged). 2. Ammonia molecules (${\text{NH}}_3$): These are neutral.

Therefore, our targets for replacement are the four ammonia molecules. Ammonia is a monodentate ligand, meaning each molecule forms exactly one coordinate bond with the central cobalt atom.

Enter our replacing ligand: ethylene diamine, commonly abbreviated as en. Its chemical structure is ${\text{H}}_2\ddot{\text{N}}-{\text{CH}}_2-{\text{CH}}_2-\ddot{\text{N}}{\text{H}}_2$.

Unlike ammonia, ethylene diamine is a bidentate ligand. It possesses two nitrogen atoms, each equipped with a lone pair of electrons. This allows a single molecule of ethylene diamine to act like a pair of pincers, forming two coordinate bonds with the central metal atom simultaneously. This formation of ring structures is known as chelation, which adds immense thermodynamic stability to the complex.

Now, let's do the math for the substitution. We need to replace four coordinate bonds currently held by four monodentate ammonia molecules.

Since one molecule of ethylene diamine (en) can form two coordinate bonds, it is functionally equivalent to two ammonia molecules.

To find the total equivalents of ethylene diamine required to replace all four ammonia molecules, we simply divide the number of ammonia molecules by the denticity of ethylene diamine:

The reaction proceeds as follows:

The trans-geometry of the complex is maintained, with the two chloride ions remaining opposite each other, while the two ethylene diamine molecules wrap around the equatorial plane.

The exact number of equivalents of ethylene diamine required is 2.