Problem 24 - Chemistry The Central Science In Si Units

Question

Crystals of hydrated chromium(III) chloride are green, have an empirical formula of \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O},\) and are highly soluble, (a) Write the complex ion that exists in this compound. (b) If the complex is treated with excess \(\mathrm{AgNO}_{3}(a q)\), how many moles of \(\mathrm{AgCl}\) will precipitate per mole of \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) dissolved in solution? (c) Crystals of anhydrous chromium(III) chloride are violet and insoluble in aqueous solution. The coordination geometry of chromium in these crystals is octahedral, as is almost always the case for \(\mathrm{Cr}^{3+}\). How can this be the case if the ratio of \(\mathrm{Cr}\) to Cl is not \(1: 6 ?\)

Step-by-Step Solution

Answer

(a) \([\mathrm{Cr(H}_2\mathrm{O})_6]^{3+}\). (b) 3 moles of \(\mathrm{AgCl}\) per mole of complex. (c) Coordination geometry maintained with different chloride arrangement.

Step 1: Determine the Complex Ion

The empirical formula of the hydrated compound is \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\). In this coordination complex, Chromium (III) acts as the central metal ion. Typically, \(\mathrm{Cr}^{3+}\) forms octahedral complexes which means there could be six ligands around the \(\mathrm{Cr}^{3+}\), most probably the water molecules. This makes the complex ion \([\mathrm{Cr(H}_2\mathrm{O})_6]^{3+}\).

Step 2: Reaction with Excess AgNO3

In solution, the chloride ions that are not directly bound to the chromium in the coordination sphere can react with \(\mathrm{AgNO}_{3}\) to form \(\mathrm{AgCl}\) precipitate. Since the empirical formula shown is \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\), and if all chloride ions were outside the coordination sphere, treating with excess \(\mathrm{AgNO}_3\) would result in 3 moles of \(\mathrm{AgCl}\) per mole of the complex dissolved.

Step 3: Account for the Oxidation State and Geometry

In coordination chemistry, \(\mathrm{Cr}^{3+}\) typically forms hexa-coordinate complexes. In anhydrous \(\mathrm{CrCl}_3\), where the compound is insoluble, chromium is likely bonded directly to the chloride ions and the structure deviates from the hydrated complex. Here, the chloride ions are likely inside the coordination sphere and satisfy the octahedral geometry alongside some bridging or internal coordination between chloride ions.

Key Concepts

Complex Ion

In the realm of coordination chemistry, a complex ion consists of a central metal ion surrounded by molecules or ions known as ligands. In our case, the compound under discussion is the hydrated chromium(III) chloride, \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\). Chromium(III), or \(\mathrm{Cr}^{3+}\), is the metal ion, serving as the core of the complex. Usually, \(\mathrm{Cr}^{3+}\) forms octahedral complexes, implying six ligands are coordinated around the metal ion.

• The six water molecules in the molecular formula act as ligands.
• These water ligands surround the chromium ion, creating a stable complex structure.

This coordination leads to the formation of the complex ion \([\mathrm{Cr(H}_2\mathrm{O})_6]^{3+}\). This intricate structure contributes to the compound's solubility and specific properties observed in aqueous environments.

Precipitation Reaction

A precipitation reaction involves the formation of a solid, or precipitate, from a solution through a chemical reaction. In the exercise context, consider the interaction of the green, soluble chromium chloride complex with \(\mathrm{AgNO}_{3}\) in solution.

• When \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) is dissolved, chloride ions dissociate in the solution.
• Excess \(\mathrm{AgNO}_{3}\) added to this solution reacts with free chloride ions to form \(\mathrm{AgCl}\), a white, insoluble precipitate.

Each mole of \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) theoretically releases three moles of chloride ions, suggesting up to 3 moles of \(\mathrm{AgCl}\) can be precipitated, depending on the chloride ions available from the dissociation of the complex.

Coordination Geometry

Coordination geometry describes the spatial arrangement of ligands around a central atom. In the context of coordination complexes, it is crucial for understanding molecular structures. For \(\mathrm{Cr}^{3+}\), the typical coordination geometry is octahedral.

• In the hydrated form, \(\mathrm{CrCl}_3 \cdot 6 \mathrm{H}_{2} \mathrm{O}\), water molecules occupy the octahedral positions as ligands.
• This configuration helps stabilize the complex ion, contributing to its solubility.

In the anhydrous \(\mathrm{CrCl}_3\), chlorine ions occupy the coordination positions. Despite the lack of water, the chromium still forms an octahedral geometry. This structure is key in its insolubility and the violet color it exhibits in its solid form. The octahedral arrangement fulfills the preferred geometry for \(\mathrm{Cr}^{3+}\), even in different chemical environments.