Problem 68 - Chemistry The Central Science

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 \(\mathrm{RuCl}_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) 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?

Step-by-Step Solution

Answer

The initial complex is \(\mathrm{[RuCl_{2}(H_{2}O)_{4}]^{+}}\mathrm{Cl^{-}}\). After about a year, the complex changes to \(\mathrm{[RuCl_{3}(H_{2}O)_{3}]^{2-}}\) due to a replacement of a water ligand by a chloride ligand in the coordination sphere.

Step 1: (a) Identify Ligands and Write Compound Formula

To determine the formula of the complex, we need to consider the given coordination compound RuCl3·5H2O, dissolved in water. The compound forms 2 moles of AgCl per mole of complex when excess AgNO3 is added. Since one mole of RuCl3·5H2O reacts with 2 moles of silver ions to form 2 moles of AgCl, and considering that there are 3 chloride ions in the complex, one of the chloride ions must be involved in this reaction. That means, only two chlorine atoms remain as part of the coordination sphere of the complex. Thus, the complex can be written as \(\mathrm{[RuCl_{2}(H_{2}O)_{4}]^{+}}\mathrm{Cl^{-}}\).

Step 2: (b) Determine Changes Over Time

After about a year, the addition of AgNO3 precipitates 3 moles of AgCl per mole of complex. This indicates that an additional chloride ion has become available outside the coordination sphere during this time. It's likely that one of the water molecules in the coordination sphere is replaced by a chloride ion over time. As a result, the new complex can be written as \(\mathrm{[RuCl_{3}(H_{2}O)_{3}]^{2-}}\). So, when AgNO3 is added, 3 moles of AgCl are formed instead of 2 moles. In conclusion, the initial complex is \(\mathrm{[RuCl_{2}(H_{2}O)_{4}]^{+}}\mathrm{Cl^{-}}\). After about a year, the complex changes to \(\mathrm{[RuCl_{3}(H_{2}O)_{3}]^{2-}}\) due to a replacement of a water ligand by a chloride ligand in the coordination sphere.

Key Concepts

Ligand Substitution

The concept of ligand substitution is a fundamental aspect of coordination chemistry. In the context of coordination compounds, it involves the replacement of one ligand (a molecule, ion, or atom that can donate a pair of electrons to the central metal atom) in a complex with another ligand. This can occur through different mechanisms, depending on factors such as the nature of the metal, the leaving ligand, and the incoming ligand.

In the exercise provided, over time, a ligand substitution occurs when one of the water molecules in the coordination sphere is replaced by a chloride ion. This process often takes place when the incoming ligand is present in higher concentration or is a stronger field ligand, which has a stronger ability to bond with the central metal ion compared to the one it replaces. Ligand substitution is a dynamic process and can significantly change the properties and reactivity of the complex ion.

Complex Ions

Complex ions are species formed from a central metal ion surrounded by ligands bonded to it through coordinate covalent bonds. The central metal ion typically has a positive charge, and the ligands are either neutral molecules or anions, which donate electron pairs to the metal ion, forming a coordination complex.

The number of ligands attached to the metal ion is known as the coordination number, which can vary based on the size, charge, and electron configuration of the metal ion and the ligands involved. Complex ions exhibit various geometries, like octahedral, tetrahedral, or square planar, amongst others. They are represented by a formula that includes the metal ion and its surrounding ligands within square brackets, reflecting the entirety of the complex ion. For example, in the exercise, the complex ion after ligand substitution is denoted as \[\mathrm{[RuCl_{3}(H_{2}O)_{3}]^{2-}}\].

Precipitation Reaction

A precipitation reaction is a type of chemical reaction that occurs when two soluble reactants produce an insoluble solid known as the precipitate. This change is often visible as a cloudiness or formation of a solid in the solution.

Precipitation reactions are key in the study of ionic compounds and are often used to deduce the presence of specific ions in a solution. When \(\mathrm{AgNO}_{3}(aq)\) is added to a solution containing chloride ions, as in the original exercise, a white precipitate of silver chloride (\mathrm{AgCl}) forms, which is an indicator of chloride ions. The stoichiometry of the reaction reveals the number of chloride ions that were present, which further assists in determining the composition of the original coordination compound. It's a vital step in understanding the chemistry behind coordination compounds and their interactions in a solution.