Problem 112 - A Complete Resource Book in Chemistry for JEE Main

Question

The number of moles of \(\mathrm{AgCl}\) precipitated when excess \(\mathrm{AgNO}_{3}\) is mixed with one mole of \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4}\right.\) \(\left.\mathrm{Cl}_{2}\right] \mathrm{Cl}\) is (a) 4 (b) 3 (c) 2 (d) 1

Step-by-Step Solution

Answer

The number of moles of \(\mathrm{AgCl}\) precipitated is 3.

Step 1: Understanding the Compound Structure

The given compound is a coordination complex: \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4}\right. \left.\mathrm{Cl}_{2}\right] \mathrm{Cl}\). It consists of a complex ion \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2}\right]^+\) and one \(\mathrm{Cl}^-\) ion outside the coordination sphere.

Step 2: Identifying Chloride Ions

Within the complex \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2}\right]^+\) sphere, 2 chloride ions (\(\mathrm{Cl}^-\)) are part of the coordination bonds. Additionally, there is 1 chloride ion outside the complex sphere due to the formula \(\mathrm{Cl}\). Thus, in total, there are \(2 + 1 = 3\) chloride ions available to form \(\mathrm{AgCl}\).

Step 3: Reaction with Silver Nitrate

When silver nitrate \(\mathrm{AgNO}_3\) is added, it reacts with chloride ions \(\mathrm{Cl}^-\) to form a precipitate of silver chloride \(\mathrm{AgCl}\). The reaction is \(\mathrm{Ag}^+ + \mathrm{Cl}^- \rightarrow \mathrm{AgCl}\).

Step 4: Calculating Moles of \(\mathrm{AgCl}\) Formed

Given 3 chloride ions (one from outside the complex and two from the coordinated complex), each chloride ion will form 1 mole of \(\mathrm{AgCl}\) with \(\mathrm{Ag}^+\). Therefore, 3 moles of \(\mathrm{AgCl}\) will precipitate.

Key Concepts

Coordination Complex

A coordination complex is a structure where a central metal atom is bonded to a group of molecules or ions, typically referred to as ligands. In this context, the compound is \([\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2}] \mathrm{Cl}\), with chromium (Cr) as the central metal. Ligands like ammonia (\(\mathrm{NH}_3\)) and chloride ions (\(\mathrm{Cl}^-\)) bond with the chromium atom. This type of structure allows the metal to fulfill its coordination number — the total number of bonds the metal forms with ligands. Coordination complexes often have unique properties that make them suitable for various applications in chemistry and industry.

Precipitation Reactions

Precipitation reactions occur when two soluble salts in aqueous solution react to form an insoluble solid, known as the precipitate. In this exercise, when silver nitrate \(\mathrm{AgNO}_3\) is added to the coordination complex containing excess chloride ions, a precipitation reaction occurs. The silver ions \(\mathrm{Ag}^+\) from \(\mathrm{AgNO}_3\) combine with chloride ions \(\mathrm{Cl}^-\) to form silver chloride \(\mathrm{AgCl}\). Silver chloride is insoluble in water, thus it precipitates as a solid. Precipitation reactions are essential in various analytical techniques, such as gravimetric analysis.

Chloride Ions

Chloride ions \(\mathrm{Cl}^-\) play a crucial role in this exercise. Within the coordination sphere of \([\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2}]^+\), there are two chloride ions bonded directly to the metal. Additionally, there is one more chloride ion present outside the sphere. It is this arrangement that determines how many chloride ions are available to react with silver ions. The chloride ions, being negatively charged, often serve to stabilize the central metal ion in a coordination complex by forming ionic bonds. Recognizing how chloride ions are distributed in complexes is key to predicting outcomes of reactions, such as precipitation.

Complex Ion

The term "complex ion" refers to the central metal atom or ion, together with its bonded ligands, which has an overall charge. In the given exercise, the complex ion is \([\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2}]^+\). The ligands, ammonia and chloride, donate electron pairs to bond with the chromium ion. This results in a net positive charge due to the number of ligands relative to the charge of the metal. Understanding complex ions is fundamental for predicting how they behave in reactions, such as how they engage in precipitation reactions.

Chemistry Problem Solving

Approaching chemistry problems, like this one involving a coordination complex, requires breaking the problem down into manageable steps. Each step should address a specific aspect of the question. Start by understanding the compound's structure, identifying all ions, and how they interact in solutions.

• First, analyze the coordination complex to determine the number of ions inside and outside the complex sphere.
• Second, recognize which ions will participate in reactions when reagents, such as \(\mathrm{AgNO}_3\), are added.
• Third, follow through with a balanced chemical reaction to determine the products.

Practicing systematic problem-solving approaches can improve efficiency and accuracy in chemistry calculations, aiding in understanding intricate reactions like those involving coordination complexes and precipitations.