Problem 25 - Chemistry The Central Science

Question

Indicate the coordination number of the metal and the oxidation number of the metal as well as the number and type of each donor atom of the ligands for each of the following complexes: (a) \(\mathrm{Na}_{2}\left[\mathrm{CdCl}_{4}\right]\) (b) \(\mathrm{K}_{2}\left[\mathrm{MoOCl}_{4}\right]\) (c) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) (d) \(\left[\mathrm{Ni}(\mathrm{CN})_{5}\right]^{3-}\) (e) \(\mathrm{K}_{3}\left[\mathrm{~V}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]\) (f) \(\left[\mathrm{Zn}(\mathrm{en})_{2}\right] \mathrm{Br}_{2}\)

Step-by-Step Solution

Answer

(a) Coordination number: 4, Oxidation number of Cd: +2, 4 Cl donor atoms (b) Coordination number: 5, Oxidation number of Mo: +4, 1 O and 4 Cl donor atoms (c) Coordination number: 6, Oxidation number of Co: +3, 4 N (from NH3) and 2 Cl donor atoms (d) Coordination number: 5, Oxidation number of Ni: +2, 5 C (from CN) donor atoms (e) Coordination number: 6, Oxidation number of V: +3, 6 O (from C2O4) donor atoms (f) Coordination number: 4, Oxidation number of Zn: +2, 4 N (from en) donor atoms

Step 1: Coordination number

The coordination number is the number of ligands (atoms or molecules) directly bonded to the central metal ion. In this complex, Cd is the central metal ion and is surrounded by 4 Cl ligands. So, the coordination number is 4.

Step 2: Oxidation number of the metal

To calculate the oxidation number of the metal (Cd in this case), we can use the equation: oxidation number of metal = charge on the ligands x number of ligands. The charge on each Cl ligand is -1, so the oxidation number of Cd is (-1)(4) = -4. Since the overall complex has a charge of -2, and there are 2 Na ions with a charge of +1 each to balance the charge, the oxidation number of Cd is +2.

Step 3: Number and type of donor atoms

There is only one type of donor atom in this complex, with 4 chlorine atoms (Cl) as ligands. So, there are 4 donor atoms, all of which are Cl. (b) \(\text{K}_{2}\left[\text{MoOCl}_{4}\right]\)

Step 4: Coordination number

In this complex, Mo is the central metal ion and is surrounded by a total of 5 ligands: 1 O and 4 Cl. So, the coordination number is 5.

Step 5: Oxidation number of the metal

The charge on each Cl ligand is -1, and the charge on the O ligand is -2. The oxidation number of Mo is (-1)(4) + (-2)(1) = -6. Since the overall complex has a charge of -2, and there are 2 K ions with a charge of +1 each to balance the charge, the oxidation number of Mo is +4.

Step 6: Number and type of donor atoms

There are two types of donor atoms in this complex: 1 oxygen atom (O) and 4 chlorine atoms (Cl). So, there are 5 donor atoms in total. (c) \(\left[\text{Co}\left(\text{NH}_{3}\right)_{4} \text{Cl}_{2}\right]\text{Cl}\)

Step 7: Coordination number

In this complex, Co is the central metal ion and is surrounded by 6 ligands: 4 NH3 and 2 Cl. So, the coordination number is 6.

Step 8: Oxidation number of the metal

The NH3 ligands are neutral with no charge, and the charge on each Cl ligand is -1. The oxidation number of Co is (-1)(2) = -2. Since the overall complex has a charge of +1, the oxidation number of Co is +3.

Step 9: Number and type of donor atoms

There are two types of donor atoms in this complex: 4 nitrogen atoms (from the NH3 ligands) and 2 chlorine atoms (Cl). So, there are 6 donor atoms in total. (d) \(\left[\text{Ni}(\text{CN})_{5}\right]^{3-}\)

Step 10: Coordination number

In this complex, Ni is the central metal ion and is surrounded by 5 CN ligands. So, the coordination number is 5.

Step 11: Oxidation number of the metal

The charge on each CN ligand is -1. The oxidation number of Ni is (-1)(5) = -5. Since the overall complex has a charge of -3, the oxidation number of Ni is +2.

Step 12: Number and type of donor atoms

There is only one type of donor atom in this complex, with 5 carbon atoms (from the CN ligands) acting as donor atoms. So, there are 5 donor atoms. (e) \(\text{K}_{3}\left[\text{V}\left(\text{C}_{2}\text{O}_{4}\right)_{3}\right]\)

Step 13: Coordination number

In this complex, V is the central metal ion and is surrounded by 3 C2O4 ligands. So, the coordination number is 6 (as each C2O4 ligand has two donor atoms).

Step 14: Oxidation number of the metal

The charge on each C2O4 ligand is -2. The oxidation number of V is (-2)(3) = -6. Since the overall complex has a charge of -3, and there are 3 K ions with a charge of +1 each to balance the charge, the oxidation number of V is +3.

Step 15: Number and type of donor atoms

There is only one type of donor atom in this complex: 6 oxygen atoms (from the C2O4 ligands). So, there are 6 donor atoms in total. (f) \(\left[\text{Zn}(\text{en})_{2}\right] \text{Br}_{2}\)

Step 16: Coordination number

In this complex, Zn is the central metal ion and is surrounded by 2 en ligands. So, the coordination number is 4 (as each en ligand has two donor atoms).

Step 17: Oxidation number of the metal

The en ligands are neutral with no charge. The oxidation number of Zn is 0. Since the overall complex has a neutral charge, the oxidation number of Zn is +2.

Step 18: Number and type of donor atoms

There is only one type of donor atom in this complex: 4 nitrogen atoms (from the en ligands). So, there are 4 donor atoms in total.

Key Concepts

Coordination Number

The coordination number in a metal complex is an important concept that refers to the number of ligand donor atoms bonded to the central metal atom. It is determined by counting how many coordination sites are occupied by ligands. For example, in the complex \([\mathrm{Zn}(\mathrm{en})_{2}] \mathrm{Br}_{2}\), the central metal ion Zn is bonded to 2 en ligands, each contributing two donor atoms (nitrogen atoms), making the total coordination number 4.
Coordination numbers can vary widely depending on the metal ion and the available coordination sites. Common coordination numbers include 4, 6, and sometimes 5. Knowing the coordination number helps in understanding the geometry and chemical properties of the metal complex.

Oxidation Number

The oxidation number of a metal in a coordination complex indicates the charge of the metal after all ligands have been removed along with their associated electron pairs. It helps in determining the degree of oxidation of the metal ion and its potential chemical reactivity. For instance, in \([\mathrm{Co}(\mathrm{NH}_{3})_{4} \mathrm{Cl}_{2}]\mathrm{Cl}\), ammonia contributes no charge, while each chlorine ligand contributes a -1 charge. The overall complex charges must balance, leading to an oxidation number of +3 for Co.
The calculation of the oxidation number requires knowledge of the charge of each ligand. For negatively charged ligands, the sum of these charges will help to ascertain the metal's valence state. This value is critical for chemical reactions and bonding analyses involving metal complexes.

Ligand Donor Atoms

Ligand donor atoms are the atoms within a ligand that donate an electron pair to form a coordinate covalent bond with the central metal ion. These atoms play a crucial role in determining the nature of the complex, as they directly participate in the bonding mechanism. For example, in the complex \([\mathrm{Ni}(\mathrm{CN})_{5}]^{3-}\), the carbon atoms in each cyanide ion act as the donor atoms, adding up to 5 donor atoms in total.
Different ligands have varying types and numbers of donor atoms. For instance, ethylenediamine (en) acts as a bidentate ligand, offering two nitrogen donor atoms for bonding. Recognizing the donor atoms is crucial for identifying the structure and stability of coordination compounds.

Metal Complexes

Metal complexes, or coordination compounds, are formed when ligands bond to a central metal atom through donor atoms. These complexes are characterized by specific geometries and configurations that depend on the coordination number and the nature of the ligands. An example is \([\mathrm{V}(\mathrm{C}_{2}\mathrm{O}_{4})_{3}]^{3-}\), which includes a central vanadium ion surrounded by three oxalate ions acting as bidentate ligands.
Metal complexes are prevalent in biological systems, industrial processes, and as catalysts. They can exhibit properties such as magnetic behavior, color changes, and variable oxidation states, making them integral to many fields of chemistry. Understanding their formation and characteristics helps in leveraging their versatile applications.