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

Short answer

The number of moles of \(\mathrm{AgCl}\) precipitated is 1.0.

Step-by-step solution

Understanding the Coordination Compound

The compound given is \([\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}] \mathrm{Cl}\). This formula indicates that there are two \(\mathrm{Cl}^-\) ions inside the coordination sphere and one outside. The chloride ions inside the coordination sphere do not participate in precipitation, so we count only the chloride ions outside.

Determine Chloride Ions Available for Reaction

From the structure \([\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}] \mathrm{Cl}\), there is one \(\mathrm{Cl}^-\) ion outside the coordination sphere. Therefore, upon reaction with excess \(\mathrm{AgNO}_{3}\), only this \(\mathrm{Cl}^-\) will precipitate.

Calculate Moles of \(\mathrm{AgCl}\) Formed

Each mole of free \(\mathrm{Cl}^-\) ion will form a mole of \(\mathrm{AgCl}\) when reacted with \(\mathrm{AgNO}_{3}\). Since there is 1 mole of \(\mathrm{Cl}^-\) ion per formula unit, 1 mole of \(\mathrm{AgCl}\) will be precipitated.

Key concepts

Precipitation Reactions

Precipitation reactions occur when two solutions mix and an insoluble solid, known as a precipitate, forms in the solution. In these reactions, the exchange of ions between the reacting compounds results in the formation of a solid. The classic example often taught involves silver nitrate (\(\text{AgNO}_3\)) and a chloride source, which together form silver chloride (\(\text{AgCl}\)).
\[\text{Ag}^+_{(aq)} + \text{Cl}^-_{(aq)} \rightarrow \text{AgCl}_{(s)}\]
This equation shows that both silver ions from \(\text{AgNO}_3\) and chloride ions from a chloride salt come together to form the solid \(\text{AgCl}\). In our original exercise, by adding \(\text{AgNO}_3\) to a solution containing chloride ions, \(\text{AgCl}\) precipitates because it is not soluble in water. This simple exchange reaction wherein the ions swap partners leading to precipitation is a cornerstone of chemical practice, highlighting how selective ion pairing can lead to new product formations.

Coordination Sphere

A coordination sphere typically includes the central metal ion and the ligands directly bonded to it. In the coordination compound \([\text{Cr}(\text{NH}_3)_4 \text{Cl}_2]\text{Cl}\), the coordination sphere contains the chromium (Cr) ion surrounded by four ammonia (\(\text{NH}_3\)) molecules and two chloride ions.
These ligands are bound tightly to the metal ion, creating a stable complex inside the sphere. Anything outside the sphere, such as the free \(\text{Cl}^−\) ion in our example, is generally more reactive.
Coordination compounds are involved in a wide range of reactions, particularly in inorganic chemistry. This sphere often influences the reaction's specificity and overall behavior. Thus, understanding which ions are inside or outside this sphere helps predict the compound's behavior in different chemical environments.

Chloride Ions in Complexes

In coordination compounds such as \([\text{Cr}(\text{NH}_3)_4 \text{Cl}_2]\text{Cl}\), the location of chloride ions plays a vital role in the compound's reactivity. Not all chloride ions in a complex participate in reactions like precipitation.
Here, two chloride ions are coordinated to the central chromium ion. These ions are inside the coordination sphere, bound tightly and not free to react with other substances. There is an additional chloride ion located outside the coordination sphere, which is free and available for reaction with \(\text{AgNO}_3\) to form \(\text{AgCl}\).
Understanding which ions are available for chemical reactions is crucial, as it affects the outcome of reactions. In our exercise, only the chloride ion outside the sphere was available to form a solid \(\text{AgCl}\), demonstrating the importance of discerning the roles and places of ions in such complexes.