Problem 56 - Chemistry and Chemical Reactivity

Question

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

Step-by-Step Solution

Answer

3.0 moles of AgCl will precipitate.

Step 1: Determine the Structure of the Compound

The compound given is \( \left| \mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right| \mathrm{Cl} \). The structure consists of a complex ion \( \left[ \mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2} \right]^{+} \) and an outer chloride ion \( \mathrm{Cl}^- \). Therefore, the coordination number of cobalt is 6 due to the presence of 4 ammonia ligands and 2 chloride ions within the coordination sphere.

Step 2: Identify the Number of Chloride Ions

Within the coordination sphere of the complex \( \left[ \mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2} \right]^{+} \), there are 2 chloride ions. Additionally, there is 1 chloride ion outside the coordination sphere contributing to the compound's neutrality, making a total of 3 chloride ions per formula unit.

Step 3: Calculate the Total Moles of Chloride Ions

Since the compound contains 3 chloride ions per unit, and there is 1 mole of the compound, the total moles of chloride ions is \( 3 \times 1.0 = 3.0 \) moles.

Step 4: Determine the Reaction with Silver Nitrate

Each chloride ion reacts with one silver ion to form silver chloride: \( \mathrm{Ag}^{+} (aq) + \mathrm{Cl}^- (aq) \rightarrow \mathrm{AgCl} (s) \). Since there are 3.0 moles of chloride ions, 3.0 moles of silver chloride will precipitate.

Key Concepts

Coordination Chemistry

Coordination chemistry revolves around the study of complex compounds where central metal atoms are bonded to surrounding molecules or ions, known as ligands. In our given compound, cobalt serves as the central metal ion, surrounded by ammonia and chloride ions. This setup forms a complex structure where cobalt is the hub of the coordination sphere. Understanding how these central ions connect with ligands is crucial, as it determines properties like geometric arrangement and optical activity. Coordination compounds are significant in various fields such as catalysis and pharmaceuticals.

Complex Ions

Complex ions are charged entities consisting of a central metal ion bonded to surrounding ligands. In the compound \( \left[ \mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2} \right]^{+} \), cobalt is bound to four ammonia molecules and two chloride ions within the coordination sphere, resulting in a charged complex. These ions are essential for determining how coordination compounds interact with other substances. The arrangement within a complex ion contributes to its stability and reactivity. Complex ions play critical roles in biological systems, including enzyme functions and electron transport.

Precipitation Reactions

Precipitation reactions occur when two soluble ions mix to form an insoluble solid, known as a precipitate. In our exercise, excess silver nitrate reacts with chloride ions from the complex compound to create silver chloride (\( \mathrm{AgCl} \)). Here’s how it works:

• Silver ions (\( \mathrm{Ag}^{+} \)) combine with chloride ions (\( \mathrm{Cl}^{-} \)) present in the solution.
• This reaction produces solid silver chloride, a visible precipitate.

Precipitation reactions are crucial in various industrial and laboratory processes, including water treatment and synthesis of pure compounds.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It helps us understand the quantitative relationships between compounds in a reaction. In the given exercise, we calculated the moles of chloride ions to predict the amount of silver chloride precipitate formed. Here, each mole of chloride ion reacts with one mole of silver ion to yield one mole of silver chloride. This one-to-one ratio highlights the stoichiometric balance, essential for predicting reaction outcomes accurately. Mastery of stoichiometry is vital for chemical manufacturing and environmental science, ensuring precise chemical applications.