Problem 60 - Chemistry and Chemical Reactivity

Question

Three different compounds of chromium(III) with water and chloride ion have the same composition: \(19.51 \%\) Cr, \(39.92 \%\) Cl, and \(40.57 \%\) H \(_{2}\) O. One of the compounds is violet and dissolves in water to give a complex ion with a 3+ charge and three chloride ions. All three chloride ions precipitate immediately as AgCl on adding AgNO \(_{3} .\) Draw the structure of the complex ion and name the compound. Write a net ionic equation for the reaction of this compound with silver nitrate.

Step-by-Step Solution

Answer

The complex is [Cr(H₂O)₆]Cl₃, named hexaaquachromium(III) chloride. The net ionic equation is 3Cl⁻ + 3Ag⁺ → 3AgCl (s).

Step 1: Identify the Empirical Formula

Use the given percentages to find the empirical formula of the compound. Assuming a 100 g sample, convert the percentages into grams: 19.51 g Cr, 39.92 g Cl, and 40.57 g H\(_2\)O. Convert these to moles: \(\text{mol Cr} = \frac{19.51}{51.996} = 0.375\), \(\text{mol Cl} = \frac{39.92}{35.453} = 1.125\), \(\text{mol H}_2\text{O} = \frac{40.57}{18.015} = 2.25\). Simplify the mole ratios to get the empirical formula as CrCl\(_3\)·6H\(_2\)O.

Step 2: Interpret the Compound's Structure

Since the complex is violet and forms a complex ion with a 3+ charge, the chromium must be part of the coordination shell forming [Cr(H\(_2\)O)\(_6\)]\(^{3+}\). The structure of the compound in solution would show the complex ion surrounded by the excess chloride ions.

Step 3: Write the Net Ionic Equation

The violet complex, [Cr(H\(_2\)O)\(_6\)]Cl\(_3\) dissolves in water. When silver nitrate is added, the chloride ions that are not part of the coordination sphere of the chromium precipitate as AgCl. The net ionic equation for the reaction is: \[\text{3Cl}^- + \text{3Ag}^+ \rightarrow \text{3AgCl (s)}\].

Step 4: Draw and Name the Complex

The compound can be named as hexaaquachromium(III) chloride, represented as [Cr(H\(_2\)O)\(_6\)]Cl\(_3\). The structure consists of a central chromium ion coordinated by six water molecules forming an octahedral complex, with three chloride ions providing counterions.

Key Concepts

Coordination Chemistry

Coordination chemistry is a fascinating area of chemistry that explores how metal ions bind with surrounding molecules or ions, often called ligands, to form complex structures. In these complexes, the metal ion is referred to as the central atom, while the ligands are the surrounding bound entities. This bonding is crucial as it affects the properties and function of the whole complex. In the case of chromium(III) complexes, chromium, with a 3+ oxidation state, frequently forms coordination compounds where it is closely surrounded by water molecules or other ligands in an octahedral shape.
Chromium(III) complexes often display vibrant colors due to d-d transitions, which are typical in transition metal complexes. These colors are useful in distinguishing between different coordination environments.

• The number of ligands attached to the central metal ion usually corresponds to the coordination number. For instance, the [Cr(H _2O)_6]^{3+} complex includes six water molecules as ligands, indicating a coordination number of six.
• Due to their charge and stability, coordination complexes often participate in a variety of chemical reactions, like precipitation reactions.

Empirical Formula

An empirical formula represents the simplest whole-number ratio of elements in a compound. This is key in understanding the composition and basic structure of a chemical compound. For chromium(III) complexes, knowing the percentages by mass of elements—like chromium, chlorine, and water—can help deduce the empirical formula.
To determine an empirical formula, convert the mass percentage to moles, considering a hypothetical 100g sample. The relative number of moles helps find the simplest ratio:

• Given 19.51% Cr, calculating moles gives approximately 0.375 moles of Cr.
• For 39.92% Cl, around 1.125 moles of Cl is found.
• For 40.57% H_2O, approximately 2.25 moles are calculated.

By simplifying these mole ratios, one adjusts to the nearest whole number to find the empirical formula: CrCl_3·6H_2O. This tells us that every chromium atom coordinates with three chloride ions and six water molecules.

Net Ionic Equation

Net ionic equations are used to focus on the species involved directly in a chemical reaction, removing spectator ions to simplify understanding. These equations are particularly useful in identifying the ions that actually participate in a meaningful way during reactions.
In the reaction involving a chromium(III) complex with silver nitrate, we focus on the role of chloride ions and silver ions. The chromium complex, [Cr(H_2O)_6]Cl_3, contains chloride ions that can precipitate when reacted with silver ions. The reaction goes as follows:

• The chloride ions ( Cl^-) from the compound interact with the silver ions (Ag^+) to form solid silver chloride (AgCl).
• The net ionic equation simplifies this by eliminating ions that do not change during the reaction, such as the water molecules surrounding chromium.

The result of this specific reaction is represented by:\[ 3Cl^- + 3Ag^+ \rightarrow 3AgCl(s) \]Emphasizing that only the actual change—formation of solid AgCl—is included.

Silver Nitrate Reaction

The interaction of silver nitrate with other chemicals often results in precipitation reactions, making it a valuable tool in understanding reactions like those with chromium(III) complexes. Silver nitrate (AgNO_3) in aqueous solutions is a source of silver ions (Ag^+), which can form insoluble precipitates with various anions.
When silver nitrate is added to a solution of [Cr(H_2O)_6]Cl_3, the present chloride ions ( Cl^-) react with silver ions, forming silver chloride (AgCl), a typical white precipitate.

• This reaction occurs because silver chloride is insoluble in water, prompting the formation of a solid, easily observable in lab settings.
• The formation of AgCl helps identify the presence of chloride ions indirectly, aiding in substance identification and analysis.

This type of reaction showcases a practical application of chemistry principles in identifying ions and studying solubility rules.