LEVELJEE Advanced
Visualized Solution
The Sigma Insight: Nomenclature, Isomerism and Werner's Theory
The Mystery of the Coordination Sphere
Imagine you are a chemical detective, and you are handed a mysterious blue-ish solution. You know its empirical formula is , but in the world of coordination chemistry, appearances are deceiving.
According to Werner's Theory, metals like Cobalt have two types of valencies. The primary valency is ionizable and satisfies the oxidation state, while the secondary valency is non-ionizable and dictates the coordination number (how many ligands are directly attached to the metal inside the square brackets).
Our mission is to figure out exactly how many of those chloride ions are trapped inside the coordination sphere, and how many are swimming freely in the solution. To do this, we will use a classic chemical interrogation technique: precipitation.
Decoding the Complex
Before we start interrogating the ions, we need to know exactly how much of the complex we are dealing with. We are given the mass of the complex as and its molar mass as .
Let's calculate the moles of our starting material.
So, we have exactly of the cobalt complex in our beaker. This is our baseline.
The Silver Nitrate Interrogation
Now, we introduce the interrogator: Silver Nitrate (). Silver ions () have an absolute affinity for free chloride ions (). When they meet, they instantly form a white precipitate of Silver Chloride ().
Crucially, silver ions can only react with the free chloride ions outside the coordination sphere. The chlorides trapped inside the square brackets are safe from precipitation.
The problem states that we obtain of precipitate. Let's find out how many moles this represents. The molar mass of is .
A quick note on exam realities: You might notice that isn't a perfect multiple of . This is a known slight numerical quirk in this specific AIEEE 2010 question. In chemistry, the number of counter ions must be a whole integer. Therefore, we can safely round this to for our stoichiometric ratio.
Unveiling the True Formula
Since one mole of contains exactly one mole of chloride ions, of precipitate means there were of free chloride ions in the solution.
Now, let's find the ratio of free chloride ions to the original complex:
This is the smoking gun! For every one molecule of the complex, exactly three chloride ions are released into the solution.
This means all three chloride ions must be outside the coordination sphere. To satisfy Cobalt's typical coordination number of 6, all six ammonia molecules must be inside the sphere acting as ligands.
Therefore, the true structural formula of our complex is . The mystery is solved!