Question

(a) A compound with formula \(\mathrm{RuCl}_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) is dissolved in water, forming a solution that is approximately the same color as the solid. Immediately after forming the solution, the addition of excess \(\mathrm{AgNO}_{3}(a q)\) forms \(2 \mathrm{~mol}\) of solid \(\mathrm{AgCl}\) per mole of complex. Write the formula for the compound, showing which ligands are likely to be present in the coordination sphere. (b) After a solution of \(\mathrm{RuCl}_{3}+5 \mathrm{H}_{2} \mathrm{O}\) has stood for about a year, addition of \(\mathrm{AgNO}_{3}(a q)\) precipitates \(3 \mathrm{~mol}\) of \(\mathrm{AgCl}\) per mole of complex. What has happened in the ensuing time?

Short answer

The formula for the compound after reacting with excess \(\mathrm{AgNO}_{3}(a q)\) is \(\mathrm{[RuCl(\mathrm{H}_{2}\mathrm{O})_{5}]} \mathrm{Cl}_{2}\). After the solution has stood for about a year, its composition changes, with water molecules replacing some chloride ions in the coordination sphere, resulting in \(\mathrm{[Ru(\mathrm{H}_{2}\mathrm{O})_{6}]}_{3}\mathrm{Cl}\).

Step-by-step solution

Part (a): Determine the complex formula and ligands

First, the given compound is reacted with excess \(\mathrm{AgNO}_{3}(a q)\). Since 2 moles of \(\mathrm{AgCl}\) are formed per mole of complex, we can write the balanced reaction as follows: \[\mathrm{RuCl}_{3} \cdot 5\mathrm{H}_{2}\mathrm{O} + 2\mathrm{AgNO}_{3}(aq) \rightarrow \mathrm{RuCl}_{2}\mathrm{H}_{2}\mathrm{O} + 2 \mathrm{AgCl}(s)\] The reaction indicates that one Chloride ion has been removed from the complex. Now, we need to determine the ligands that are present in the coordination sphere of \(\mathrm{Ru}\). Based on the reaction, the ligands that are most likely to be present in the coordination sphere are \(\mathrm{H}_{2}\mathrm{O}\) and \(\mathrm{Cl}\). Hence, the formula for the compound is \(\mathrm{[RuCl(\mathrm{H}_{2}\mathrm{O})_{5}]} \mathrm{Cl}_{2}\).

Part (b): Explanation of change in the compound

After the solution of \(\mathrm{RuCl}_{3} \cdot 5 \mathrm{H}_{2}\mathrm{O}\) has stood for about a year, the addition of \(\mathrm{AgNO}_{3}(aq)\) precipitates 3 moles of \(\mathrm{AgCl}\) per mole of complex. This indicates the oxidation state of the metal (Ru) and the ligands present have changed over time. To determine what happened during this time, we can write the reaction with the updated number of moles of \(\mathrm{AgCl}\). \[\mathrm{RuCl}_{3} \cdot 5\mathrm{H}_{2}\mathrm{O} + 3\mathrm{AgNO}_{3}(aq) \rightarrow \mathrm{Ru}\mathrm{H}_{2}\mathrm{O} + 3 \mathrm{AgCl}(s)\] The reaction now indicates that two Chloride ions have been removed from the complex. During this change, water molecules from the outside solution may have replaced the chloride ions, and one of the \(\mathrm{H}_{2}\mathrm{O}\) molecules in the coordination sphere could be more likely to act as a ligand. Considering this information, we can propose that over time, the following process occurred: 1. One of the \(\mathrm{H}_{2}\mathrm{O}\) molecules in the coordination sphere dissociated from the metal center. 2. Two more Chloride ions were removed from the complex, which could have happened through ligand substitution or via redox reactions (either of the metal center or ligands). Overall, the compound formula evolution over time can be shown as: \[\mathrm{[RuCl(\mathrm{H}_{2}\mathrm{O})_{5}]} \mathrm{Cl}_{2} \xrightarrow{\text{~1 year~}} \mathrm{[Ru(\mathrm{H}_{2}\mathrm{O})_{6}]}_{3}\mathrm{Cl}\]

Key concepts

Ligands

Ligands are ions or molecules that bind to a central metal atom to form a coordination complex.
These entities provide electrons to the metal through coordinate bonds.
In coordination chemistry, ligands play a crucial role in determining the structure and reactivity of the complex.
Ligands can be:

• Mono-dentate: Bind to the metal through a single donor site (e.g., Cl^-).
• Bi-dentate and Poly-dentate: Bind through two or more donor sites (e.g., ethylenediamine).

In the given exercise, we identify that the chloride (Cl^-) and water (H₂O) molecules act as ligands.
The original compound, \([\text{RuCl}\_3\cdot5 \text{H}_2\text{O}]\), suggests that chloride and water surround the ruthenium center, forming the complex [RuCl(H₂O)₅]Cl₂.

Oxidation State

The oxidation state of a metal in a complex provides insight into the electron count and reactivity.
It is defined as the hypothetical charge that the metal would carry if all ligands were removed, along with the associated electron pairs.
Determining the oxidation state helps in understanding:

• The electronic configuration.
• The possible redox reactions.
• The stability of the metal complex.

For ruthenium (Ru) in the complexes mentioned, initially, it exists as a +3 oxidation state in \([\text{RuCl}\_3\cdot5 \text{H}_2\text{O}]\).
However, when the compound stands over time, leading to the formation of [Ru(H₂O)₆]Cl₃, it suggests that ligand substitution and potential changes in oxidation have occurred.
Therefore, the analysis over time might imply a reorganization of the coordination sphere and the oxidation state assessment ensures these changes are accurately interpreted.

Ligand Substitution

Ligand substitution involves swapping one ligand in the coordination sphere of a metal complex with a different ligand.
This process can greatly affect the properties, including the color and reactivity of the complex.
The exchange may happen due to:

• Reaction conditions (such as temperature, concentration).
• Kinetics and thermodynamics (some ligands can form stronger or weaker bonds).

In the given exercise, after leaving the Ru complex standing for a year, more chloride ions are precipitated, allowing us to postulate a substitution.
Specifically, water molecules may have replaced some chloride ions in the coordination sphere, transforming [RuCl(H₂O)₅]Cl₂ to [Ru(H₂O)₆]Cl₃.
This change showcases the dynamic nature of metal complexes, where environmental conditions and time can drive ligand substitution.

Redox Reactions

Redox reactions in coordination chemistry involve the transfer of electrons between the metal center and its ligands or the surrounding environment.
These reactions can result in oxidation (loss of electrons) or reduction (gain of electrons) of the central metal.
The implications of redox reactions include:

• Altered oxidation states.
• Affected ligand stability or type.
• Observed changes in color or solubility of the complex.

For the ruthenium complex described, aging resulted in more chloride being removed, suggesting a change in electronic arrangement without direct redox involving Ru.
While the direct redox event isn't described, understanding redox concepts aids in comprehending how oxidative-stressors or ligands could catalyze similar reactions.
The evolved ligand substitution might also suggest an indirect influence, necessitating consideration of potential redox-active conditions.