Problem 71 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one is the most likely structure of \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) is \(1 / 3\) of total chlorine of the compound is precipitated by adding \(\mathrm{AgNO}_{3}\) to its aqueous solution? (a) \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3} \mathrm{Cl}_{3}\right] \cdot\left(\mathrm{H}_{2} \mathrm{O}\right)_{3}\) (b) \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) (c) \(\left[\mathrm{CrCl}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}\right] \mathrm{Cl}_{2} . \mathrm{H}_{2} \mathrm{O}\) (d) \(\left[\mathrm{CrCl}_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right] . \mathrm{Cl}_{2} \mathrm{H}_{2} \mathrm{O}\)

Step-by-Step Solution

Answer

The most likely structure is (c): \([\mathrm{CrCl}(\mathrm{H}_2\mathrm{O})_5] \mathrm{Cl}_2 \cdot \mathrm{H}_2\mathrm{O}\).

Step 1: Determine the Formula Type

We know the compound is of the form \( \text{CrCl}_3 \cdot 6 \text{H}_2\text{O} \), so we need to consider how chlorine atoms can exist in the complex and coordinate water molecules.

Step 2: Analyze Chlorine Precipitation

When \( \mathrm{AgNO}_3 \) is added to the aqueous solution, only \( \frac{1}{3} \) of the total chlorine in the compound is precipitated, indicating that only 1 chlorine ion is free in the solution, while the others are coordinated in the complex.

Step 3: Evaluate the Complex Structures

(a) \([\mathrm{Cr} (\mathrm{H}_2\mathrm{O})_3 \mathrm{Cl}_3]\cdot(\mathrm{H}_2\mathrm{O})_3\) has all chlorines bonded, allowing none to precipitate.
(b) \(\mathrm{CrCl}_3 \cdot 6 \mathrm{H}_2 \mathrm{O}\) describes how the chemicals simply mix, indicating no structure fitting the behavior described.
(c) \([\mathrm{CrCl}(\mathrm{H}_2\mathrm{O})_5]\mathrm{Cl}_2 \cdot \mathrm{H}_2\mathrm{O}\) suggests only 1 chloride is part of the complex, allowing 2 free chlorines for precipitation, aligning with the problem structure.
(d) \([\mathrm{CrCl}_2(\mathrm{H}_2\mathrm{O})_4]\cdot \mathrm{Cl}_{2} \cdot \mathrm{H}_2\mathrm{O}\) allows too many free chlorines to precipitate, which is inconsistent.

Step 4: Select Most Likely Structure

Given the constraints, option (c) \([\mathrm{CrCl}(\mathrm{H}_2\mathrm{O})_5] \mathrm{Cl}_2 \cdot \mathrm{H}_2\mathrm{O}\) fits as 1 chlorine is part of the complex and 2 are outside, explaining why \( \frac{1}{3} \) precipitate.

Key Concepts

Complex Formation

In coordination chemistry, complex formation is a process where a central metal atom or ion forms bonds with surrounding molecules or ions, called ligands. These complexes have specific geometrical arrangements, significantly affecting the properties of the compound. In the exercise, chromium forms a complex with chloride ions and water molecules.

• Chromium (Cr) acts as the central metal ion, around which the structure is built.
• Water molecules (\( \text{H}_2\text{O} \)) and chloride ions (\( \text{Cl}^- \)) serve as ligands, attaching to the central chromium ion.
• The interaction leads to a formation of coordination bonds that are usually more stable than regular ionic or covalent bonds.

Understanding the number of ligands and their arrangement is crucial in predicting how the compound interacts in solutions, such as when reacting with\( \text{AgNO}_3 \).

Chloride Ion Precipitation

Chloride ion precipitation is an important indicator of the nature of a coordination compound. When certain anions or cations are free in a solution, they can react with other added reagents to produce a precipitate.

• In this case, adding silver nitrate (\( \text{AgNO}_3 \)) to the solution leads to the precipitation of silver chloride (\( \text{AgCl} \)).
• The amount of chloride ion precipitated demonstrates how many chloride ions are not coordinated in the complex. If only \( \frac{1}{3} \) of the chlorine content precipitates, it shows that 1 chloride ion is free while others are bound within the complex.

This exercise helps us identify how chloride ions coordinate in complexes, aiding in understanding the structure and bonding of the compound.

Coordination Compounds

Coordination compounds feature a central metal atom or ion surrounded by molecules or ions that form coordinate bonds. These compounds have distinctive characteristics that influence reactions and chemical behavior in solutions.

• The primary feature of these compounds is the central metal ion, which often dictates the geometry and coordination number (the number of ligand attachments).
• These compounds can exhibit unique reactivity, such as in the exercise where coordination limits the precipitation of chloride ions.
• Studying the structure and behavior of coordination compounds allows us to predict and understand various chemical behaviors, such as selective precipitation reactions. Understanding coordination numbers is important; in this exercise, chromium might typically coordinate with 6 ligands.

This discussion underscores coordination chemistry's role in enhancing the understanding of chemical structures and their complex reactions.