Question

The acetylacetonate ion (acac) forms a complex with \(\mathrm{Co}^{3+}\). Sketch the geometry of \(\left[\mathrm{Co}(\mathrm{acac})_{3}\right]\)

Short answer

The complex has an octahedral geometry.

Step-by-step solution

Understand the Components

The complex \([\text{Co}(\text{acac})_3]\) involves a cobalt ion \(\text{Co}^{3+}\) and three acetylacetonate ligands (acac). Each acac ligand is bidentate, meaning it can bind through two donor atoms.

Determine the Coordination Number

The coordination number for cobalt in \([\text{Co}(\text{acac})_3]\) is determined by the number of sites where ligands can attach. Since each acac ligand forms two coordinate bonds, the coordination number is 6.

Identify the Geometry

A coordination number of 6 typically results in an octahedral geometry. This is due to the spatial arrangement of ligands around the central metal ion minimizing repulsion and achieving a stable configuration.

Sketch the Octahedral Geometry

Visualize the central cobalt ion at the center of an octahedron. Draw six vertices representing the electron donor sites of the acetylacetonate ligands, with each pair forming the triangular base of one face of the octahedron.

Key concepts

Geometry of Complex Ions

The geometry of complex ions is crucial in understanding how these structures form and function. Complex ions are formed when central metal ions bind with ligands—molecules or ions that donate a pair of electrons to the metal. The spatial arrangement of these ligands around the central atom defines the geometry of the complex ion, which can significantly impact its chemical and physical properties.

When ligands are positioned around the central ion, they tend to arrange themselves to minimize repulsion and maximize stability. This naturally leads to specific geometric shapes. Some common geometries include linear, tetrahedral, square planar, and octahedral geometries. The choice of geometry largely depends on the coordination number as well as the electrostatic forces between the ligands and the central metal ion. For instance, five-coordinate complexes can display either square pyramidal or trigonal bipyramidal shapes. The geometry affects not only stability but also the reactivity and color of the complex ion.

Coordination Number

The coordination number in a complex ion refers to the number of ligand donor atoms that are bound directly to the central metal ion. It is one of the primary parameters defining the structure of the complex.

Understanding the coordination number helps predict the geometry of the complex. For mono-dentate ligands, the coordination number is equal to the number of ligands attached; however, with poly-dentate ligands (like acetylacetonate), each ligand can provide multiple bonds, influencing the coordination number accordingly.

• In our case, the acetylacetonate ligand is bidentate, forming two bonds per ligand. Therefore, three acac ligands in \([ ext{Co}( ext{acac})_3]\) result in a coordination number of 6 for the cobalt ion.
• This coordination number is quite common and generally leads to an octahedral geometry.

Coordination numbers can vary widely, ranging typically from 2 to 12, although values outside this range are also possible depending on the specific metal ion and ligands involved.

Octahedral Geometry

Octahedral geometry is one of the most prevalent forms for complex ions, particularly those with a coordination number of 6. This geometry forms when six ligand donor atoms arrange symmetrically around a central metal ion, providing a shape akin to two square pyramids base to base.

The preferred octahedral arrangement minimizes the electron-electron repulsions among the ligands through symmetrical distribution around the central ion. This geometric scheme yields not only a stable configuration but also distinct electronic and magnetic properties.

In visualizing the \([ ext{Co}( ext{acac})_3]\) complex, the cobalt ion is located at the center of the octahedron. Each acetylacetonate ligand forms a part of a triangular face by coordinating through two donor atoms. This spatial arrangement is crucial in fields like coordination chemistry and molecular spectroscopy, as octahedral complexes can exhibit characteristic splitting patterns in their electron energy levels when interacting with light or other electromagnetic radiation.