Animated Solution for Chemistry - Coordination Compounds: 3 moles of metal complex with formula ${\text{Co(en)}}_2{\text{Cl}}_3$ gives 3 moles of silver chloride on treatment with excess of silver nitrate. The secondary valency of Co in the complex is ............. . (Round off to the nearest integer)

Imagine you are a chemist in the late 19th century. You mix two stable, independent compounds together, and suddenly, a completely new substance forms with entirely different properties. This was the profound mystery of coordination compounds before Alfred Werner came along. Werner revolutionized chemistry by proposing that metal atoms possess two distinct types of valencies: primary valency and secondary valency.

In this problem, we are acting as chemical detectives. We are given a cobalt complex with the empirical formula ${\text{Co(en)}}_2{\text{Cl}}_3$. Our mission is to deduce its true structure and find the secondary valency of the central cobalt atom.

Silver Nitrate

To uncover the true structure of the complex, we use a classic chemical test: the reaction with silver nitrate (${\text{AgNO}}_3$). Silver nitrate is an excellent reagent for detecting free, ionizable chloride ions in a solution because it reacts with them to form a white precipitate of silver chloride ($\text{AgCl}$).

The problem states that 3 moles of the complex yield 3 moles of silver chloride.

Let's simplify this ratio. If 3 moles of the complex give 3 moles of $\text{AgCl}$, then exactly 1 mole of the complex produces 1 mole of $\text{AgCl}$.

Why is this piece of information the key to the entire puzzle? According to Werner's theory, only the ions located outside the coordination sphere (the square brackets) are loosely bound by ionic forces and can ionize in water. The ligands inside the coordination sphere are tightly bound to the metal via coordinate covalent bonds and do not ionize.

Since 1 mole of $\text{AgCl}$ is formed per mole of the complex, there must be exactly 1 ionizable chloride ion outside the coordination sphere.

Now, let's look back at our empirical formula: ${\text{Co(en)}}_2{\text{Cl}}_3$.

We have a total of 3 chlorine atoms. We just discovered that 1 of these chlorine atoms is outside the coordination sphere acting as a counter ion.

This means the remaining $3-1=2$ chlorine atoms must be trapped inside the coordination sphere, acting as ligands directly bonded to the cobalt atom. The ethylenediamine ($\text{en}$) molecules are neutral organic ligands, so they are also safely tucked inside the sphere.

Putting it all together, the true structural formula of our complex is:

Werner defined the secondary valency as the total number of coordinate bonds formed between the central metal atom and the ligands inside the coordination sphere. In modern terms, this is simply the coordination number.

Let's count the bonds inside our square bracket $[{\text{Co(en)}}_2{\text{Cl}}_2{]}^{+}$.

1. Ethylenediamine ($\text{en}$): This is a famous bidentate ligand. It has two nitrogen atoms, each capable of donating a lone pair of electrons to the metal. Therefore, each 'en' molecule forms 2 coordinate bonds. Since we have 2 'en' molecules, they contribute $2\times 2=4$ bonds.

2. Chloride (${\text{Cl}}^{-}$): The chloride ion is a monodentate ligand, meaning it forms only 1 coordinate bond. We have 2 chloride ligands inside the sphere, contributing $2\times 1=2$ bonds.

Adding them up, the total coordination number (secondary valency) is:

With a secondary valency of 6, the complex adopts a beautiful octahedral geometry. The primary valency, which corresponds to the oxidation state of the metal, is satisfied by the total negative charge. Here, the cobalt is in a $+3$ oxidation state, balanced by the three chloride ions (two inside, one outside).

By simply measuring the amount of precipitate formed, we were able to peer into the microscopic world and deduce the exact 3D architecture of a complex molecule. This is the true power and elegance of chemistry!