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 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 Clis not 1:6 ?

Short answer

The complex ion in hydrated chromium(III) chloride is \([\mathrm{Cr}(\mathrm{H}_2\mathrm{O})_6]^{3+}\). When treated with excess AgNO3, 3 moles of AgCl will precipitate per mole of \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) dissolved. The coordination geometry of chromium in anhydrous chromium(III) chloride is octahedral due to each chloride ion acting as a bidentate ligand, allowing the six-coordinate positions around chromium to be occupied in an octahedral fashion.

Step-by-step solution

(a) Identify the complex ion in hydrated chromium(III) chloride

To identify the complex ion, we first look at the empirical formula of hydrated chromium(III) chloride: \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\). Since the compound is soluble, the complex ion would be formed by the Cr and the H2O molecules. Hence, the complex ion would be \([{\mathrm{Cr}(\mathrm{H}_2\mathrm{O})_6}]^{3+}\).

(b) Calculate the moles of AgCl formed with excess AgNO3

When hydrated chromium(III) chloride is treated with excess silver nitrate (AgNO3), silver chloride (AgCl) will precipitate. To determine the number of moles of AgCl formed, we need to consider the number of moles of chloride ions, Cl-, in the solution. In the given empirical formula, \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\), we have 3 moles of chloride ions for every 1 mole of hydrated chromium(III) chloride. Thus, for every 1 mole of hydrated chromium(III) chloride that dissolves, 3 moles of AgCl will precipitate when treated with excess AgNO3.

(c) Explain the coordination geometry of chromium in anhydrous chromium(III) chloride

According to the information given, anhydrous chromium(III) chloride, CrCl3, has a violet color and is insoluble in water. The coordination geometry of chromium in this compound is octahedral. This means that there are 6 ligands surrounding the chromium ion. It is important to note that the ratio of chromium to chloride in the compound is not 1:6 but 1:3 as given by the formula CrCl3. However, the coordination geometry indicates that there are 6 ligands surrounding chromium. This can be explained by the fact that each chloride ion in the anhydrous chromium(III) chloride can act as a bidentate ligand, binding to the chromium ion in two different places. This way, the six-coordinate positions around the chromium can be occupied by the three chloride ions in an octahedral fashion.

Key concepts

Complex Ion Formation

In chemistry, a complex ion forms when a central metal ion bonds with surrounding molecules or ions, often called ligands. In the case of hydrated chromium(III) chloride with the formula \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\), the complex ion is created when \(\mathrm{Cr}^{3+}\) ions coordinate with water molecules (\(\mathrm{H}_2\mathrm{O}\)).
For this compound, the complex ion is represented as \([\mathrm{Cr} (\mathrm{H}_2\mathrm{O})_6]^{3+}\). Each water molecule donates a pair of electrons to the chromium ion, forming a stable hydrated complex.
This process is key in forming soluble compounds where the metal ion binds tightly to its surrounding ligands. Such formation helps in dissolving the entire compound in water.

Hydrated Chromium Compounds

Hydrated compounds include water molecules in their structure. For chromium(III) chloride, this hydration results in a green crystalline appearance. Specifically, the presence of 6 \(\mathrm{H}_2\mathrm{O}\) molecules in \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) helps form the complex ion \([\mathrm{Cr} (\mathrm{H}_2\mathrm{O})_6]^{3+}\).
Hydration not only impacts the physical properties, like color and solubility, but also affects how the compound behaves in reactions. This crystalline form dissolves well, as the complex ions are able to interact fully with water, facilitating various chemical reactions.

Precipitation Reactions

Precipitation occurs when two soluble salts react to form an insoluble solid, called a precipitate. In the context of chromium coordination compounds, treating \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) with excess \(\mathrm{AgNO}_3\) leads to precipitation.
Here, the chloride ions \((\mathrm{Cl}^-\)) from the chromium compound react with silver ions \((\mathrm{Ag}^+)\) from silver nitrate. This reaction forms silver chloride \((\mathrm{AgCl})\), a white insoluble substance.

• For every mole of \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\), three moles of \(\mathrm{Cl}^-\) produce three moles of \(\mathrm{AgCl}\).

This characteristic reaction is commonly used to identify and quantify chloride ions in a compound.

Coordination Geometry

Coordination geometry describes the arrangement of ligands around a central atom. In anhydrous chromium(III) chloride \(\mathrm{CrCl}_3\), even though it's violet and insoluble, chromium exhibits octahedral geometry.
Octahedral implies six ligands symmetrically arranged about the chromium ion. Here, the geometry results because each chloride ion functions as a bidentate ligand, coordinating in two different sites.

• Despite only three chloride ions, this bidentate nature allows full occupation of an octahedral coordination sphere.
• This geometry is typical for \(\mathrm{Cr}^{3+}\) due to its electronic configuration and stability needs.

Understanding coordination geometry helps predict chemical behavior and bonding in these compounds.