Problem 174 - A Complete Resource Book in Chemistry for JEE Main

Question

A solution containing \(2.675 \mathrm{~g}\) of \(\mathrm{CoCl}_{3} \cdot 6 \mathrm{NH}_{3}\) (molar mass \(=267.5 \mathrm{~g} \mathrm{~mol}^{-1}\) ) is passed through a cation exchanger. The chloride ions obtained in solution were treated with excess of \(\mathrm{AgNO}_{3}\) to give \(4.78 \mathrm{~g}\) of \(\mathrm{AgCl}\) (molar mass \(\left.=143.5 \mathrm{~g} \mathrm{~mol}^{-1}\right) .\) The formula of the complex is (Atomic mass of \(\mathrm{Ag}=108 \mathrm{u}\) ) [2010] (a) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3}\) (b) \(\left[\mathrm{CoCl}_{2}\left(\mathrm{NH}_{3}\right)_{4}\right] \mathrm{Cl}\) (c) \(\left[\mathrm{CoCl}_{3}\left(\mathrm{NH}_{3}\right)_{3}\right]\) (d) \(\left[\mathrm{CoCl}\left(\mathrm{NH}_{3}\right)_{5}\right] \mathrm{Cl}_{2}\)

Step-by-Step Solution

Answer

Formula of the complex is \([\mathrm{Co(NH}_3)_6]\mathrm{Cl}_3\).

Step 1: Determine the moles of AgCl formed

Calculate the number of moles of AgCl using its given mass and molar mass. \[\text{Moles of AgCl} = \frac{4.78 \text{ g}}{143.5 \text{ g/mol}} = 0.0333 \text{ mol}\]

Step 2: Determine the moles of Cl- ions

Since each mole of AgCl formed corresponds to a mole of Cl- ions, the moles of Cl- ions are the same as the moles of AgCl. Thus, there are 0.0333 moles of Cl- ions.

Step 3: Determine moles of Co complex

Calculate moles of the CoCl3·6NH3 complex using its mass and molar mass. \[\text{Moles of Co complex} = \frac{2.675 \text{ g}}{267.5 \text{ g/mol}} = 0.01 \text{ mol}\]

Step 4: Calculate the ratio of Cl- to Co complex

Use the ratio of moles of Cl- ions to moles of Co complex to determine the number of chloride ions outside the coordination sphere. \[\text{Ratio} = \frac{0.0333 \text{ mol Cl}^-}{0.01 \text{ mol Co complex}} = 3.33 \text{ Cl}^-\]This implies there are approximately 3 chloride ions.

Step 5: Write the chemical formulas

Based on the number of chloride ions found, deduce that the complex must be of the form where 3 Cl- ions are outside the coordination sphere. This corresponds to the formula \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]\mathrm{Cl}_{3}\).

Step 6: Verify the solution

Check if the determined formula satisfies the given conditions by considering the expected stoichiometry. In this case, \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]\mathrm{Cl}_{3}\) is consistent with 3 chloride ions available to react with AgNO3 to form 3 moles of AgCl.

Key Concepts

Cation Exchange Process

Cation exchange is a fascinating technique often used to analyze or separate ionic compounds into their constituent parts. In this process, a cation exchanger, usually a resin, is used to trap positively charged ions from a solution while replacing them with another cation, commonly hydrogen ions or sodium ions.
For instance, in the given exercise involving the compound \[\text{CoCl}_{3} \cdot 6\text{NH}_{3}\], when it passes through a cation exchanger, the cobalt ions from the compound are exchanged on the resin surface. This allows the chloride ions to enter the solution, making them accessible for further chemical treatment.
The importance of cation exchange lies in its ability to selectively remove or concentrate specific ions from a solution, making it invaluable in various industrial and laboratory applications. This selective ion removal can help determine the composition of complex ionic compounds and verify molecular formulas.

Stoichiometry

Stoichiometry is the quantitative heart of chemistry, ensuring that the atoms balance out during chemical reactions. It involves using balanced chemical equations to calculate the amounts of reactants and products in a reaction.
In the context of our exercise, stoichiometry helps determine the formula of the cobalt complex: - Firstly, the moles of \[\text{AgCl}\] formed are calculated, indicating how many moles of chloride ions were present.- Then, the stoichiometric relationship between the chloride ions and the cobalt complex is analyzed.
This exercise demonstrates stoichiometry by calculating the precise ratio of chloride ions to the cobalt complex. Here, you have 0.0333 moles of chloride ions per 0.01 mole of the cobalt amine complex, resulting in a ratio of approximately 3:1.Such calculations highlight not just the chemical balance involved but also provide proof for the determined molecular structure. Stoichiometry is essential for anyone wanting to predict the outcomes of chemical reactions, ensuring no atoms are unaccounted for.

Complex Ions

Complex ions are a cornerstone of coordination chemistry, involving central metal ions bound to surrounding molecules or ions. These surrounding participants, called ligands, attach to the metal through coordinate covalent bonds.The cobalt complex in this exercise is a prime example:- Ammonia (\[\text{NH}_3\]) acts as a ligand, offering its lone pair of electrons to bond with the cobalt ion.- The entire assembly yields a charged entity capable of forming further ionic interactions with other species, such as chloride ions in this example.
Complex ions can exhibit fascinating properties, including varied solubilities, colors, and reactivities, depending on factors like the metal's oxidation state and the nature of the ligands.
The ability to form these complex structures allows for sophisticated chemistry, enabling the creation of materials with tailored properties. Understanding the formation and stability of complex ions is crucial for applications ranging from medicinal chemistry to catalysis and beyond.