Question

For the process $$ \mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}^{2+}+\mathrm{Cl}^{-} \longrightarrow \mathrm{Co}\left(\mathrm{NH}_{3}\right){ }_{4} \mathrm{Cl}_{2}^{+}+\mathrm{NH}_{3} $$ what would be the expected ratio of cis to trans isomers in the product?

Short answer

The expected ratio of cis to trans isomers in the product of the given reaction is 1:1. This means that there will be an equal number of cis and trans isomers of Co(NH3)4Cl2^+ formed in the reaction.

Step-by-step solution

Determine the structure of the product

The product of the reaction is a cobalt complex with the formula Co(NH3)4Cl2^+. This complex contains a central cobalt cation (Co^3+) surrounded by four ammonia (NH3) ligands and two chloride (Cl-) ligands. All the ligands are bound to the central ion via coordinate covalent bonds.

Identify the possible isomers of the product

To determine the cis and trans isomers, we look at the geometry and arrangement of the ligands around the cobalt cation in the product. The coordination number of the complex is 6, which typically leads to an octahedral geometry around the central ion. There are two possible isomers for the Co(NH3)4Cl2^+ complex, depending on the arrangement of the chloride ligands: 1. Cis-isomer: The two chloride ligands are adjacent to each other on the octahedral complex. In other words, they are in the same plane and share a 90° angle with the central cobalt ion. 2. Trans-isomer: The two chloride ligands are opposite to each other on the octahedral complex. This configuration results in a 180° angle between the chloride ligands and the central cobalt ion.

Determine the expected ratio of cis and trans isomers

According to the reaction, one chloride ligand replaces an ammonia ligand in the Co(NH3)5Cl2^+ complex. Since the incoming chloride ligand can replace any of the five ammonia ligands in the reactant, there is an equal probability of forming either the cis or trans isomer of the product. Thus, we can expect a 1:1 ratio of cis to trans isomers in the product. This means that there will be an equal number of cis and trans isomers of Co(NH3)4Cl2^+ formed in the reaction.

Key concepts

Coordination Chemistry

Coordination chemistry involves the study of compounds that feature a central metal atom or ion with a set of surrounding molecules or anions, known as ligands. These ligands can donate electron pairs to the metal, creating coordinate covalent bonds. These compounds, referred to as coordination complexes, have distinctive structures, properties, and reactivity patterns that make them fascinating subjects for research and applications ranging from catalysis to materials science.

Key to understanding coordination compounds is the idea of coordination number—the number of ligands that are bonded to the central metal. The geometry of these ligands around the central metal can vary, leading to different shapes such as octahedral, tetrahedral, or square planar, to name a few. The coordination chemistry of a compound dictates its color, magnetic properties, and overall reactivity, making this field a cornerstone in both theoretical and applied chemistry.

Octahedral Complex

When a central metal ion is surrounded by six ligands in a symmetric fashion, the resulting structure is known as an octahedral complex. This arrangement can be visualized as two pyramids with a common base, such that the metal ion resides at the intersection of the six coordination sites or vertices. In this geometry, the ligands are equidistant from the central ion, and the angles between any two adjacent ligand-metal-ligand vectors are 90 degrees, while those across the metal are 180 degrees.

An octahedral complex can exhibit various isomers depending on the spatial arrangement of its ligands, particularly when two or more types of ligands are involved. The significant isomers are 'cis' and 'trans'. In a 'cis' isomer, similar ligands are adjacent to each other; in a 'trans' isomer, they are opposite. These isomeric forms have different physical and chemical properties, which is critical in the field of stereochemistry and has practical implications in the synthesis and application of these compounds.

Ligand Substitution Reactions

Ligand substitution reactions are a type of chemical reaction where one ligand in a coordination complex is replaced by another ligand. These reactions occur through various mechanisms, including associative (where a ligand adds before another leaves), dissociative (where a ligand leaves before another adds), and interchange (a combination of the first two mechanisms).

The ease of ligand substitution is influenced by factors such as the charge and electron configuration of the metal center, the nature of the ligands involved, and the overall stability of the complex. For example, in octahedral complexes, ligands in the axial positions may be replaced more easily than those in the equatorial positions due to the spatial arrangement and electronic dynamics within the complex.

Understanding ligand substitution is crucial for catalysis and industrial applications; it also provides insights into biological processes like oxygen transport by hemoglobin. The fundamental characteristics of ligand substitution reactions enable chemists to manipulate coordination complexes for desired outcomes, including synthesizing compounds with specific configurations, like 'cis' and 'trans' isomers.