Question

What is the coordination number of the metal in the following complexes? (a) \(\left[\mathrm{Mo}(\mathrm{CNS})_{2}(e n)_{2}\right]^{+}\) (b) \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)(\mathrm{OH})_{2} \mathrm{Br}\right]^{-}\) (c) \(\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}\) (d) \(\left[\mathrm{PtCl}_{2}\left(\mathrm{NO}_{2}\right)_{2}\right]^{2-}\)

Short answer

Answer: The coordination numbers of the metals in the given complexes are: (a) Mo: 4, (b) Co: 4, (c) Ag: 2, and (d) Pt: 4.

Step-by-step solution

(a) Coordination number of Mo in \([\mathrm{Mo}(\mathrm{CNS})_{2}(e n)_{2}]^{+}\)

To determine the coordination number for Mo in this complex, we need to count the total number of bonds between Mo and the ligands. We have two \((\mathrm{CNS})\) and two \((e n)\) ligands. Therefore, the coordination number for Mo is: \(2 (\mathrm{CNS}) + 2 (e n) = 2 + 2 = 4\)

(b) Coordination number of Co in \([\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)(\mathrm{OH})_{2}\mathrm{Br}]^{-}\)

To determine the coordination number for Co in this complex, we need to count the total number of bonds between Co and the ligands. We have \((\mathrm{H}_{2} \mathrm{O})\), two \((\mathrm{OH})\), and one \(\mathrm{Br}\) ligand. Therefore, the coordination number for Co is: \((\mathrm{H}_{2} \mathrm{O}) + 2 (\mathrm{OH}) + \mathrm{Br} = 1 + 2 + 1 = 4\)

(c) Coordination number of Ag in \([\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}]^{+}\)

To determine the coordination number for Ag in this complex, we need to count the total number of bonds between Ag and the ligands. We have two \((\mathrm{NH}_{3})\) ligands. Therefore, the coordination number for Ag is: \(2 (\mathrm{NH}_{3}) = 2\)

(d) Coordination number of Pt in \([\mathrm{PtCl}_{2}\left(\mathrm{NO}_{2}\right)_{2}]^{2-}\)

To determine the coordination number for Pt in this complex, we need to count the total number of bonds between Pt and the ligands. We have two \(\mathrm{Cl}\) and two \((\mathrm{NO}_{2})\) ligands. Therefore, the coordination number for Pt is: \(2 (\mathrm{Cl}) + 2 (\mathrm{NO}_{2}) = 2 + 2 = 4\)

Key concepts

Metal Complexes

Metal complexes play a crucial role in coordination chemistry. They are formed when a central metal atom or ion binds to surrounding molecules or ions known as ligands. This binding forms a coordinated structure often depicted with a complex's formula, like \([\mathrm{Mo}(\mathrm{CNS})_{2}(e n)_{2}]^{+}\). The central metal provides empty orbitals that interact with ligands, accepting electron pairs to form coordinate covalent bonds. This interaction is not just about physical connection but also involves the sharing or transfer of electrons between the metal and ligands, leading to a stable configuration.
Metal complexes are fascinating because they often determine the properties and reactivity of the metallic center. For example, the type of ligands attached can greatly influence catalytic activity, biological functions, or even oxidative states. The geometry around the metal, defined by the ligands, defines the type of the complex, such as tetrahedral, square planar, or octahedral, each impacting the overall behavior of the complex.

Ligands

Ligands are atoms, ions, or molecules that donate electron pairs to a metal to form metal complexes. They can be simple ions like Cl\(^{-}\), or complex molecules like ethylenediamine (en). The capacity of ligands to donate electrons defines their role in stabilizing the metal center. Some ligands, known as monodentate, bind through a single donor atom. Examples include water (H\(_{2}\)O) and ammonia (NH\(_{3}\)).
However, ligands can also be multidentate, binding through multiple atoms. Ethylenediamine, abbreviated as \((en)\), is a bidentate ligand, meaning it forms two bonds with the metal. This ability to provide multiple bonding sites increases the stability of complexes they form. The nature of the ligands—whether hard or soft, strong-field or weak-field—impacts the metal’s oxidation state, its electronic environment, and even its color in visible light.

• Monodentate: H\(_{2}\)O, NH\(_{3}\)
• Bidentate: Ethylenediamine (en)
• Polydentate: EDTA (ethylenediaminetetraacetate)

Coordination Chemistry

Coordination chemistry focuses on the study of metal complexes. Central to this field are the concepts of coordination number and geometry. The coordination number describes the number of ligand atoms directly bonded to the central metal ion. For instance, in the complex \([\mathrm{Ag}(\mathrm{NH}_{3})_{2}]^{+}\), the silver ion is surrounded by two ammonia ligands, giving it a coordination number of two.
This contrasts with a more complex species, such as \([\mathrm{PtCl}_{2}(\mathrm{NO}_{2})_{2}]^{2-}\), which exhibits a coordination number of four, owing to the two chloride and two nitrite ligands bound to platinum. The geometry of these complexes—linear, square planar, tetrahedral, or octahedral—determines many properties, including stereochemistry and reactivity.

• Low Coordination Numbers: Linear, Tetrahedral
• High Coordination Numbers: Square Planar, Octahedral

Understanding the interaction between metal ions and ligands helps in the design of catalysts, drug molecules, and various industrial processes.