Problem 70 - Chemistry: The Central Science in SI Units, Global Edition

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 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 mol of AgCl per mole of complex. What has happened in the ensuing time?

Step-by-Step Solution

Answer

The initial complex formula is \([\mathrm{RuCl}_{2}(\mathrm{H}_{2}\mathrm{O})_{2}]Cl\cdot 3\mathrm{H}_{2}\mathrm{O}\) after the immediate reaction with \(\mathrm{AgNO}_{3}\). After standing for about a year, the complex formula changes to \([\mathrm{RuCl}_{3}(\mathrm{H}_{2}\mathrm{O})]Cl_{2}\cdot 4\mathrm{H}_{2}\mathrm{O}\) due to the replacement of a water ligand by a Cl atom in the coordination sphere.

Step 1: Analyze the immediate reaction with AgNO3

The initial compound has the formula \(\mathrm{RuCl}_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O}\). When the compound is dissolved in water and reacts with an excess of AgNO3, it forms 2 moles of solid \(\mathrm{AgCl}\) per mole of complex. Based on this information, we can infer that there are 2 Cl atoms in the coordination sphere of the Ru complex.

Step 2: Propose the complex formula after initial reaction with AgNO3

Since two of the Cl atoms in the original compound \(\mathrm{RuCl}_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) are coordinated to the Ru atom, we can propose the complex formula to be: \([\mathrm{RuCl}_{2}(\mathrm{H}_{2}\mathrm{O})_{2}]Cl\cdot 3\mathrm{H}_{2}\mathrm{O}\).

Step 3: Analyze the reaction after a year of standing

After the solution has stood for about a year, we are informed that the addition of \(\mathrm{AgNO}_{3}(a q)\) precipitates 3 moles of \(\mathrm{AgCl}\) per mole of complex. This information suggests that an additional Cl atom in the coordination sphere of the Ru complex has been replaced.

Step 4: Determine the change in the coordination sphere

We infer that a water ligand in the coordination sphere has been replaced by a Cl atom, as the number of moles of \(\mathrm{AgCl}\) precipitated has increased. The coordination sphere of the complex after this change will contain 3 Cl atoms instead of 2.

Step 5: Propose the final complex formula

Accounting for the change in the coordination sphere of the Ru complex, we can now propose the complex formula to be: \([\mathrm{RuCl}_{3}(\mathrm{H}_{2}\mathrm{O})]Cl_{2}\cdot 4\mathrm{H}_{2}\mathrm{O}\). This is the formula of the complex after it has stood for about a year and then reacted with \(\mathrm{AgNO}_{3}(a q)\).

Key Concepts

Complex Ions

In coordination chemistry, a complex ion consists of a central metal atom or ion that is bonded to surrounding molecules or ions—these are known as ligands. The central metal and the ligands together form a coordination entity, which can carry a charge, thus forming a complex ion. This charge can be positive, negative, or neutral, depending on the charge of the central metal and the nature of the ligands present.
Moreover, the metal and ligands are bonded via coordinate covalent bonds, where the ligands donate electron pairs to the metal ion.
Understanding these complex ions is crucial, as they are found in many biological systems, such as hemoglobin in blood, and play significant roles in various chemical reactions.

Ligand Exchange

Ligand exchange is the process where one or more ligands in a coordination complex are replaced by different ligands. This exchange can occur for various reasons, such as changes in the concentration of the surrounding solution or over time due to thermodynamic stability.

• In our example, initially, the coordination sphere of the complex had two chloride ligands with two water molecules.
• As time progressed, one water ligand was replaced by a chloride ion, increasing the number of replaceable chloride ions in the solution.

This is an important reaction mechanism in coordination chemistry, as it affects the color, reactivity, and solubility of the complex ion.

Coordination Sphere

The coordination sphere consists of the central metal ion and the surrounding attached ligands. In a chemical formula, the coordination sphere is indicated using square brackets, such as in \( [\text{RuCl}_2(\text{H}_2\text{O})_2] \).
This represents the part of the complex where direct bonding interactions occur. The coordination sphere defines the geometry and coordination number (the number of direct bonds to the metal center) of the complex.

• In the original exercise, the coordination sphere contained two chloride ions and two water molecules.
• With time, changes in the coordination sphere were observed, featuring a transition to three chloride ions and one water molecule.

These changes dramatically impact the properties of the compound, illustrating the dynamic nature of coordination chemistry.