Question

Excess silver nitrate is added to a solution containing \(1.0 \mathrm{mol}\) of \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl} .\) What amount of \(\mathrm{AgCl}\) (in moles) will precipitate?

Short answer

1.0 mol of AgCl will precipitate.

Step-by-step solution

Identify the coordination complex

The given coordination complex is \[\text{\([\mathrm{Co}(\mathrm{NH}_3)_4 \mathrm{Cl}_2] \mathrm{Cl}\)}\] This complex consists of a central cobalt ion, four ammonia ligands, two chlorido ligands within the coordination sphere, and one chloride ion outside the coordination sphere.

Determine chloride ions available for precipitation

The complex contains two types of chloride ions: those inside the coordination sphere and those outside. Only the chloride ion outside the sphere can be precipitated by silver nitrate. Hence, the chloride ion available for reaction is the one situated outside the complex, equal to \(1.0 \text{ mol}\) of chloride ions.

Write the balanced equation for the precipitation

The reaction between chloride ions and silver nitrate can be represented as follows:\[\text{Cl}^{-} + \text{AgNO}_3 \rightarrow \text{AgCl} + \text{NO}_3^-\]This balanced equation shows that each chloride ion will react with one silver ion to produce one mole of \(\text{AgCl}\).

Calculate moles of AgCl precipitated

From the balanced chemical equation, each chloride ion reacts with one silver ion, resulting in one mole of \(\text{AgCl}\). Since there is \(1.0 \text{ mol}\) of chloride ion available, \(1.0 \text{ mol}\) of \(\text{AgCl}\) will be precipitated.

Key concepts

Understanding Coordination Complexes

A coordination complex is a structure composed of a central metal atom or ion surrounded by molecules or ions, known as ligands. The metal ion, such as cobalt in our problem, is central to forming these complexes. It serves as the core that attaches to ligands through coordinate covalent bonds. In the given complex [\text{Co}(\text{NH}_3)_4 \text{Cl}_2] \text{Cl}, cobalt is the center.
Ligands, which could be neutral or charged, donate a pair of electrons to the metal. Here, ammonia (\(\text{NH}_3\)) acts as a neutral ligand, while chloride ions (\(\text{Cl}^-\)) serve as charged ligands. These components form a structured arrangement, impacting the properties and reactions of the complex.

• Example: Complexes with different ligands can show varied colors and reactivity.
• Importance: Coordination complexes are significant in fields such as catalysis and bioinorganic chemistry.

Exploring Ligands

Ligands are atoms or molecules that bind to the central metal within a coordination complex. They donate lone pairs of electrons to the metal, forming stable coordinate covalent bonds. In our example, ammonia and chloride ions are the ligands binding to the cobalt center.
Ligands are key because they not only stabilize the metal but also influence the properties of the complex, such as its shape, charge, and reactivity. The variety of ligands and their arrangements lead to diverse chemical behaviors and potential applications in catalysis and medicine.

• Mono-dentate ligands bind through one donor atom, like \(\text{NH}_3\).
• Poly-dentate ligands can attach through multiple donor sites, offering greater stability.

Precipitation Reaction Basics

A precipitation reaction occurs when soluble ions in separate solutions combine to form an insoluble compound. In the reaction between chloride ions and silver nitrate, silver chloride (\(\text{AgCl}\)) is formed as a precipitate.
The process involves mixing a clear solution of silver nitrate with another solution containing chloride ions. As they react, \(\text{AgCl}\) solidifies and separates out from the solution. This reaction is a classical example of a precipitation reaction, driven by the low solubility of silver chloride in water.

• The equation is: \(\text{Cl}^- + \text{AgNO}_3 \rightarrow \text{AgCl} + \text{NO}_3^-\).
• Precipitation reactions are often used in qualitative analysis to identify ions.

Stoichiometry of the Reaction

Stoichiometry involves calculating the quantities of reactants and products in a chemical reaction. It’s a vital concept in predicting how much product will form from given substances.
In our problem, the stoichiometry is straightforward. One mole of chloride ion reacts with one mole of silver nitrate to produce one mole of silver chloride. The balanced equation confirms this 1:1:1 ratio, indicating that if you start with \(1.0\, \text{mol}\) of chloride ions, \(1.0\, \text{mol}\) of silver chloride will precipitate.

• This principle allows chemists to predict product amounts.
• Key to understanding reactions, it helps balance equations and conserve mass.