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 AgNO \(_{3}(a q)\) forms 2 mol of solid 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 \(\mathrm{RuCl}_{3}\) \(\cdot 5 \mathrm{H}_{2} \mathrm{O}\) has stood for about a year, addition of \(\mathrm{AgNO}_{3}(a q)\) precipitates 3 mol of AgCl per mole of complex. What has happened in the ensuing time?

Short answer

In summary, immediately after forming the solution, the complex has a formula of \(\mathrm{[RuCl}_{2}(\mathrm{H}_{2} \mathrm{O})_{4}] \cdot \mathrm{H}_{2} \mathrm{O} \cdot \mathrm{Cl\cdot} \mathrm{H}_{2} \mathrm{O}\) with a coordination sphere consisting of 4 water molecules and 2 chloride ions. After a year, the complex's formula changes to \(\mathrm{[RuCl}_{3}(\mathrm{H}_{2} \mathrm{O})_{3}] \cdot \mathrm{H}_{2} \mathrm{O} \cdot \mathrm{H}_{2} \mathrm{O}\), with a coordination sphere consisting of 3 water molecules and 3 chloride ions, indicating a substitution reaction where a water ligand has been replaced by a chloride ion over time.

Step-by-step solution

Determine the ligands in the coordination sphere immediately after the formation of the solution

In the first scenario, when the compound is immediately dissolved in water and forms a solution, the addition of excess AgNO\(_3\) forms 2 mol of solid AgCl per mole of complex. This implies that in the initial coordination sphere, there are 2 chloride ions. So, the complex immediately after formation in water should be: \(\mathrm{[RuCl}_{2}(\mathrm{H}_{2} \mathrm{O})_{4}] \cdot \mathrm{H}_{2} \mathrm{O} \cdot \mathrm{Cl\cdot} \mathrm{H}_{2} \mathrm{O}\) The coordination sphere consists of 4 water molecules and 2 chloride ions.

Determine the ligands in the coordination sphere after a year

In the second scenario, after a solution of \(\mathrm{RuCl}_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) has stood for about a year, the addition of \(\mathrm{AgNO}_{3}(a q)\) precipitates 3 mol of AgCl per mole of the complex. This change implies that over time, one of the water ligands has been replaced by a chloride ion, forming a complex part as \(\mathrm{[RuCl}_{3}(\mathrm{H}_{2} \mathrm{O})_{3}]\cdot\mathrm{H}_{2}\mathrm{O}\cdot \mathrm{H}_{2}\mathrm{O}\). In this case, the coordination sphere consists of 3 water molecules and 3 chloride ions.

Summarize the results

In summary, the complex immediately after the formation of the solution has a coordination sphere consisting of 4 water molecules and 2 chloride ions, with a formula: \(\mathrm{[RuCl}_{2}(\mathrm{H}_{2} \mathrm{O})_{4}] \cdot \mathrm{H}_{2} \mathrm{O} \cdot \mathrm{Cl\cdot} \mathrm{H}_{2} \mathrm{O}\). After a year, the complex's coordination sphere changes to include 3 water molecules and 3 chloride ions, with a formula: \(\mathrm{[RuCl}_{3}(\mathrm{H}_{2} \mathrm{O})_{3}] \cdot \mathrm{H}_{2} \mathrm{O} \cdot \mathrm{H}_{2} \mathrm{O}\). This change indicates that, over time, a substitution reaction has occurred where a water ligand has been replaced by a chloride ion.

Key concepts

Ligands

In coordination chemistry, ligands are ions or molecules that bind to a central metal atom to form a coordination complex. These ligands donate at least one pair of electrons to the metal center, creating a bond. Ligands can be monodentate, binding through a single atom, or polydentate, attaching through multiple atoms. In our example, water (\(\mathrm{H}_2\mathrm{O}\)) and chloride ions (\(\mathrm{Cl}^-\)) act as ligands.

• Water (\(\mathrm{H}_2\mathrm{O}\)) is a neutral molecule and acts as a common ligand due to its lone pairs on the oxygen atom.
• Chloride ions (\(\mathrm{Cl}^-\)) are negatively charged and can easily donate electrons to the metal center, forming stable complexes.

In the given example, the complex undergoes changes over time, impacting which ligands are found in the coordination sphere. Initially, the coordination sphere comprises water and chloride ligands, but this can evolve due to chemical reactions or changes in the environment.

Coordination Sphere

The coordination sphere is the part of a coordination complex consisting of the central metal ion and its directly bonded ligands. Typically, it is enclosed in square brackets. Factors influencing the composition of the coordination sphere include the size, charge, and electronic properties of the metal ion and ligands.

• In the initial solution, the compound's formula is \([\mathrm{RuCl}_2(\mathrm{H}_2\mathrm{O})_4]\). The coordination sphere consists of 4 \(\mathrm{H}_2\mathrm{O}\) and 2 \(\mathrm{Cl}^-\).
• Over time, a chloride ion replaces one water molecule, altering the coordination sphere to \([\mathrm{RuCl}_3(\mathrm{H}_2\mathrm{O})_3]\).

The coordination sphere determines the properties and reactivity of the complex. Changes in the coordination sphere can affect the physical and chemical characteristics of the compound, such as color shifts or changes in solubility.

Substitution Reaction

Substitution reactions in coordination chemistry involve the replacement of one ligand by another within the coordination sphere. These reactions are pivotal in determining the structure and reactivity of metal complexes. In the original exercise, a substitution reaction occurs over time.Initially, the solution contains \([\mathrm{RuCl}_2(\mathrm{H}_2\mathrm{O})_4]\) where 2 chloride ions are inside the coordination sphere. Over a year, chloride ions replace one of the water molecules, resulting in \([\mathrm{RuCl}_3(\mathrm{H}_2\mathrm{O})_3]\).

• Mechanism: Ligand exchange often involves breaking and forming bonds at the metal center, which can be influenced by the ligand's electronic characteristics and steric effects.
• Reactivity: The rate of substitution can vary widely. Slow changes might indicate stable complexes, while faster changes may suggest weaker bonding or higher reactivity.

These reactions can be reversible or irreversible, depending on the system's thermodynamics and kinetics. Understanding substitution reactions helps predict how coordination complexes behave in different environments.