Problem 24 - Chemistry: The Central Science in SI Units, Global Edition

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 Cl is not \(1: 6 ?\)

Step-by-Step Solution

Answer

(a) The complex ion in hydrated chromium(III) chloride is \([\mathrm{Cr}(\mathrm{H}_{2}\mathrm{O})_{6}]^{3+}\). (b) 3 moles of AgCl will precipitate per mole of \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) dissolved in the solution. (c) In anhydrous \(\mathrm{CrCl}_{3}\), the octahedral geometry of \(\mathrm{Cr}^{3+}\) is possible due to the presence of non-chloride ligands in addition to chloride ions, which complete the coordination.

Step 1: (a) Identify the complex ion

The given empirical formula of the crystals is \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\). Since it is stated as a highly soluble compound, the complex ion can be assumed to be hydrated. Therefore, the complex ion that exists is \([\mathrm{Cr}(\mathrm{H}_{2}\mathrm{O})_{6}]^{3+}\).

Step 2: (b) Calculate moles of AgCl precipitated

When the complex \([\mathrm{Cr}(\mathrm{H}_{2}\mathrm{O})_{6}]^{3+}\) is treated with excess \(\mathrm{AgNO}_{3}(a q)\), the reaction between \(\mathrm{Cl}^{-}\) and \(\mathrm{Ag}^{+}\) ions leads to the precipitation of AgCl. The reaction can be represented as: \[3\mathrm{Ag}^{+} + 3\mathrm{Cl}^{-} \rightarrow 3\mathrm{AgCl}\] For each mole of \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) dissolved in the solution, there are 3 moles of \(\mathrm{Cl}^{-}\) ions. Therefore, 3 moles of AgCl will precipitate per mole of \(\mathrm{CrCl}_{3} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) dissolved in the solution.

Step 3: (c) Explanation of octahedral structure in CrCl3

In the anhydrous \(\mathrm{CrCl}_{3}\), the ratio of Cr to Cl is 1:3. Despite this ratio, the coordination geometry of chromium is found to be octahedral. This is possible because in addition to the chloride ions, there are other non-chloride ligands that complete the octahedral coordination for the chromium ion. For the chromium(III) ion, three chloride ions can be coordinated directly to Cr3+, and the remaining three positions of the octahedral geometry can be occupied by other non-chloride ligands such as water molecules or other counter ions. This explains the octahedral geometry for \(\mathrm{Cr}^{3+}\) in anhydrous chromium(III) chloride even though the ratio of Cr to Cl is not 1:6.

Key Concepts

Complex Ion

A complex ion is a type of molecule consisting of a central metal atom or ion, surrounded by molecules or ions called ligands, which are bound to it. This configuration forms a coordination complex. In coordination chemistry, a metal ion like chromium in this exercise can bind to several ligands. This forms a distinct entity with a net charge.

In the context of hydrated chromium(III) chloride,

• the empirical formula is CrCl₃ · 6 H₂O,
• the metal ion involved is chromium ( Cr³⁺).

When this compound dissolves in water, it forms hexaaquachromium(III) ion, [Cr(H₂O)₆]³⁺. This suggests that the chromium ion is surrounded by six water molecules as ligands. The complex ion maintains the integrity of the solution's charge, with a net charge of +3 in this example. Always remember that the identity of the ligands and the charge contribute significantly to the properties and reactivity of the complex ion.

Octahedral Geometry

Octahedral geometry is a common shape for complex ions, particularly those formed with transition metals like chromium. This geometry involves a central atom, around which six atoms, groups, or ligands are symmetrically arranged at the corners of an octahedron. Generally, it implies a specific arrangement and bonding, which affects the compound's stability and reactivity.

In the given chromium compounds,

• the hydrated complex has six water molecules around the Cr³⁺ ion,
• forming a classic octahedral shape.

Even for anhydrous CrCl₃, the octahedral geometry is maintained through additional ligands. Although the Cr:Cl ratio is 1:3, additional ligands (like water or other ions) can coordinate to the central chromium ion. This maintains the typical six-coordinate (⁶ coordination) environment. Understanding this geometry is crucial because it affects properties like magnetic behavior and color.

Precipitation Reaction

A precipitation reaction occurs when two soluble salts react in solution to form an insoluble solid, called a precipitate. This solid separates from the liquid. Such reactions are essential to understand how compounds interact in solution, often revealing information about ion interactions and product stability.

In our example, chromium complex ions and silver nitrate interact:

• The chloride ions from the dissolved complex ( CrCl₃ · 6 H₂O) meet silver ions ( Ag⁺) from AgNO₃,
• leading to the formation of silver chloride ( AgCl),
• an insoluble product that precipitates out of solution.

Each mole of CrCl₃ · 6 H₂O yields three moles of Cl^- ions, hence producing three moles of AgCl.

Recognizing these precipitation patterns helps in predicting the outcome of mixing solutions and designing qualitative analysis experiments. These reactions are crucial in detecting specific ions in a solution by the patterns they form.