Question

The number of geomatrical isomers exhibited by \(\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\) is

Short answer

The compound exhibits 2 geometrical isomers: cis and trans.

Step-by-step solution

Identify the Coordination Complex

The compound given is \(\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\), which is a coordination compound with Chromium as the central metal ion surrounded by ligands: three ammonia \((\mathrm{NH}_{3})\) molecules and three chloride \((\mathrm{Cl}^{-})\) ions.

Determine the Coordination Number

The coordination number of Chromium in this complex is 6, as there are six ligands surrounding the central metal atom (three \(\mathrm{NH}_{3}\) and three \(\mathrm{Cl^-}\) ions).

Determine the Geometry of the Coordination Compound

For a coordination number of 6, the common geometry is octahedral. Therefore, \(\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\) forms an octahedral geometry around the Chromium ion.

Determine Possible Arrangements of Ligands

In an octahedral complex, the ligands can arrange themselves in different ways. With three ammonia molecules and three chloride ions, we can have the ligands arranged such that there are cis and trans isomers.

Identify the Geometrical Isomers

For \(\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\), the possible geometrical isomers are distinguished by the position of the \(\mathrm{Cl^-}\) ions relative to each other in the octahedron. There are two arrangements:1. **cis isomer**: Two \(\mathrm{Cl^-}\) ions are adjacent to each other, and the third \(\mathrm{Cl^-}\) is opposite one of them.2. **trans isomer**: The three \(\mathrm{Cl^-}\) ions are positioned such that each \(\mathrm{Cl^-}\) is opposite another \(\mathrm{Cl^-}\) across the central metal ion.

Count the Isomers

Since we have identified the above two distinct geometrical arrangements (cis and trans), there are 2 geometrical isomers possible for \(\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\).

Key concepts

Octahedral Geometry

In the fascinating world of coordination compounds, octahedral geometry is a common and significant form. This type of geometry consists of a central metal ion surrounded by six ligands forming a shape akin to two pyramids that share a square base. These ligands are positioned symmetrically around the central ion, much like the points of a three-dimensional star.

A quintessential example of octahedral geometry is witnessed in the compound \( \mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3} \). Here, the central metal ion is chromium, and it is encircled by three ammonia molecules and three chloride ions. This arrangement is inherently stable, allowing for symmetrical ligand distribution, which is a crucial aspect of octahedral compounds. The even distribution helps minimize repulsion between the electrons of adjacent ligands, providing stability to the complex.

The octahedral shape plays a vital role in determining the types and numbers of isomers that a coordination compound can form. Utilizing its symmetry, octahedral compounds can exhibit various configurational isomers, paving the way for an exciting exploration of geometrical isomerism.

Coordination Number

The coordination number of a coordination compound is an essential concept in understanding its geometric structure and potential isomers. Coordination number refers to the number of ligand bonds formed directly with the central metal ion.

For example, in the compound \( \mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3} \), the coordination number of chromium is 6. This result is because chromium bonds with six ligands directly: three ammonia molecules \( (\mathrm{NH}_{3}) \) and three chloride ions \( (\mathrm{Cl}^{-}) \). This specific coordination number leads to the octahedral geometry by default when dealing with transition metals like chromium.

The significance of the coordination number extends beyond just the shape, as it influences the physical and chemical properties of the compound, including color, magnetism, and reactivity. It also plays a fundamental role in the formation of isomers. With a coordination number of 6, compounds are more likely to exhibit symmetrical configurations, which can lead to multiple types of geometrical isomers.

Cis and Trans Isomers

Cis and trans isomerism is a specific form of geometrical isomerism that occurs in octahedral coordination complexes, among others. This type of isomerism arises due to the different spatial arrangements of ligands around the central atom. It is particularly evident in compounds with the formula \( \mathrm{Ma}_2b_4 \) like \( \mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3} \), where two types of ligands are present.

• Cis Isomer: Here, two identical ligands are adjacent to each other in the octahedral arrangement. In \( \mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3} \), this means two \( \mathrm{Cl}^{-} \) ions are side-by-side.
• Trans Isomer: In this configuration, identical ligands are positioned opposite each other. Again, for \( \mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3} \), this translates to each \( \mathrm{Cl}^{-} \) being directly opposite another \( \mathrm{Cl}^{-} \).

These configurations lead to distinct physical and chemical properties. Such differences arise because of the varying spatial distribution of the ligands, which can affect how light interacts with the compound, its solubility, reactivity, and even its biological activity. This binary isomer distinction in octahedral coordination compounds makes studying them both practical and fascinating.