Problem 34 - A Complete Resource Book in Chemistry for JEE Main

Question

The number of moles of \(\mathrm{AgCl}\) precipitated when excess \(\mathrm{AgNO}_{3}\) is added to one mole of \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]\) \(\mathrm{Cl}\) is (a) \(3.0\) (b) \(2.0\) (c) \(1.0\) (d) zero

Step-by-Step Solution

Answer

The number of moles of AgCl precipitated is 1.0.

Step 1: Identify the Complex Structure

The given compound is \( [\mathrm{Cr}(\mathrm{NH}_3)_4 \mathrm{Cl}_2] \mathrm{Cl} \). This structure indicates that there is one chlorine atom outside the coordination sphere and two chlorine atoms inside the coordination sphere.

Step 2: Determine Cl- Ions Involved in Precipitation

When \( \text{AgNO}_3 \) is added, it reacts with chloride ions to form \( \text{AgCl} \) precipitate. Only the chlorine ions outside the coordination sphere can react directly to form \( \text{AgCl} \) precipitate. Therefore, \( \mathrm{Cl}^- \) ions outside the coordination sphere participate in precipitation.

Step 3: Calculate Moles of AgCl Formed

In the compound \( [\mathrm{Cr}(\mathrm{NH}_3)_4 \mathrm{Cl}_2] \mathrm{Cl} \), there is one chloride ion (\( \mathrm{Cl}^- \)) outside the coordination sphere. Since one mole of compound is used, one mole of \( \text{AgCl} \) is precipitated.

Key Concepts

Complex Structure

When studying coordination compounds, understanding their complex structure is crucial. Coordination compounds, like the presented \[ [\mathrm{Cr}(\mathrm{NH}_3)_4 \mathrm{Cl}_2] \mathrm{Cl}\]compound, consist of a central metal atom or ion surrounded by molecules or ions known as ligands. In this case, chromium (Cr) is the central metal ion. The ligands are the four ammonia (\(\mathrm{NH}_3\)) molecules and two \(\mathrm{Cl}^-\) ions inside the brackets, indicating they are part of the coordination sphere. This sphere is a reversible association where the ligands form a complex with the metal ion, protected from external reactions unless the sphere is broken or opened.
Outside of the coordination sphere, we find a separate chloride ion (\(\mathrm{Cl}\)) which is not bound in the complex structure, thus participating differently in reactions.

Chloride Ions

Chloride ions play a significant role in determining the behavior of coordination compounds in chemical reactions. In the compound \( [\mathrm{Cr}(\mathrm{NH}_3)_4 \mathrm{Cl}_2] \mathrm{Cl} \), there are three chloride ions in total. However, only one is positioned outside the coordination sphere, which allows it to directly engage in reactions with other chemical species, like the addition of \(\mathrm{AgNO}_3.\)

Inside the coordination sphere, the chloride ions don't participate freely in external reactions like precipitation because they are tightly bound to the central metal ion. Conversely, the chloride ion outside is free to react because it's not bound. Therefore, when considering chemical reactions involving this compound, identify which chloride ions are free to participate based on their location relative to the coordination sphere.

Precipitation Reaction

A precipitation reaction involves the formation of a solid from a solution during a chemical reaction. This often occurs when two aqueous solutions are mixed, and an insoluble solid, called a precipitate, forms. In the context of the coordination compound we are studying, adding \(\mathrm{AgNO}_3\) leads to such a reaction.

The equation to consider is that AgNO₃ reacts with free chloride ions to form silver chloride (\(\mathrm{AgCl}\)), which precipitates out of the solution. This means that the unbound chloride ion in \( [\mathrm{Cr}(\mathrm{NH}_3)_4 \mathrm{Cl}_2] \mathrm{Cl}\)is free to react. Thus, when one mole of \(\mathrm{AgNO}_3\) is added, it will engage with the single free chloride ion to form one mole of \(\mathrm{AgCl}\) precipitate.

• Precipitation helps in isolating substances from a mixture.
• It is a useful process in both analytical and synthetic chemistry.
• The reaction helps to confirm the presence and quantity of chloride ions outside of the coordination sphere.