Problem 13 - Chemistry: The Central Science

Question

Indicate the coordination number of the metal and the oxidation number of the metal in 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) The coordination number in Na2[CdCl4] is 4, and the oxidation number is +2. (b) The coordination number in K2[MoOCl4] is 5, and the oxidation number is +4. (c) The coordination number in [Co(NH3)4Cl2]Cl is 6, and the oxidation number is +3. (d) The coordination number in [Ni(CN)5]3- is 5, and the oxidation number is +2. (e) The coordination number in K3[V(C2O4)3] is 6, and the oxidation number is +3. (f) The coordination number in [Zn(en)2]Br2 is 4, and the oxidation number is +2.

Step 1: (a) Coordination number in Na2[CdCl4]

In \(\mathrm{Na}_{2}\left[\mathrm{CdCl}_{4}\right]\), the central metal atom is Cd (Cadmium). There are 4 Chloride ions (Cl) surrounding the central atom, hence the coordination number of Cd is 4.

Step 2: (a) Oxidation number in Na2[CdCl4]

To find the oxidation number of Cd in \(\mathrm{Na}_{2}\left[\mathrm{CdCl}_{4}\right]\), consider the charges of the individual ions. The overall charge on the complex is 0, and there are 2 sodium ions (2x +1), therefore the charge on the complex ion [CdCl4]^2- must be -2. There are 4 Chloride ions (4x -1), so the oxidation number of Cd must be +2 to balance the charges.

Step 3: (b) Coordination number in K2[MoOCl4]

In \(\mathrm{K}_{2}\left[\mathrm{MoOCl}_{4}\right]\), the central metal atom is Mo (Molybdenum). There are 1 Oxygen atom and 4 Chloride ions surrounding the central atom, hence the coordination number of Mo is 5.

Step 4: (b) Oxidation number in K2[MoOCl4]

In \(\mathrm{K}_{2}\left[\mathrm{MoOCl}_{4}\right]\), there are 2 potassium ions (2x +1), so the charge on the complex ion [MoOCl4]^2- must be -2. Considering the Oxygen atom (-2) and 4 Chloride ions (4x -1), the oxidation number of Mo must be +4 to balance the charges.

Step 5: (c) Coordination number in [Co(NH3)4Cl2]Cl

In $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl}$, the central metal atom is Co (Cobalt). There are 4 Ammonia molecules and 2 Chloride ions surrounding the central atom, hence the coordination number of Co is 6.

Step 6: (c) Oxidation number in [Co(NH3)4Cl2]Cl

The overall charge on the complex is 0, and there is 1 Chloride ion (-1), therefore the charge on the complex ion [Co(NH3)4Cl2]^+ must be +1. The oxidation number of Co must be +3 to balance the charges as the 2 Chloride ions and 4 Ammonia molecules (-1 each) contribute -2.

Step 7: (d) Coordination number in [Ni(CN)5]3-

In \(\left[\mathrm{Ni}(\mathrm{CN})_{5}\right]^{3-}\), the central metal atom is Ni (Nickel). There are 5 Cyanide ions surrounding the central atom, hence the coordination number of Ni is 5.

Step 8: (d) Oxidation number in [Ni(CN)5]3-

The charge on the complex ion [Ni(CN)5]^3- is -3. Considering the 5 Cyanide ions (-1 each), the oxidation number of Ni must be +2 to balance the charges.

Step 9: (e) Coordination number in K3[V(C2O4)3]

In \(\mathrm{K}_{3}\left[\mathrm{~V}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{3}\right]\), the central metal atom is V (Vanadium). There are 3 Oxalate ions surrounding the central atom, hence the coordination number of V is 6 (since each oxalate has two binding points).

Step 10: (e) Oxidation number in K3[V(C2O4)3]

In \(\mathrm{K}_{3}\left[\mathrm{~V}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)_{3}\right]\), there are 3 potassium ions (3x +1), so the charge on the complex ion [V(C2O4)3]^3- must be -3. Considering the 3 Oxalate ions (-2 each), the oxidation number of V must be +3 to balance the charges.

Step 11: (f) Coordination number in [Zn(en)2]Br2

In \(\left[\mathrm{Zn}(\mathrm{en})_{2}\right] \mathrm{Br}_{2}\), the central metal atom is Zn (Zinc). There are 2 Ethylenediamine (en) molecules surrounding the central atom, hence the coordination number of Zn is 4 (since each en has two binding points).

Step 12: (f) Oxidation number in [Zn(en)2]Br2

The overall charge on the complex is 0, and there are 2 Bromide ions (2x -1), therefore the charge on the complex ion [Zn(en)2]^2+ must be +2. The oxidation number of Zn must be +2, as it matches the charges in the complex ion.

Key Concepts

Coordination Number

In coordination chemistry, the coordination number is very important. It refers to how many atoms or molecules are directly attached to the central metal ion. Consider it like counting the friends standing next to someone at a party. This number gives us insight into the geometry of the complex, which tells us the shape and structure.

Coordination numbers often range from 2 to 9, but numbers 4 and 6 are the most common. For example, in the complex \(\text{[CdCl}\_4\text{]}\), the coordination number of cadmium (Cd) is 4 because there are four chloride ions directly attached to it. This usually results in a coordination geometry that looks like a tetrahedral shape.

• In \(\text{[MoOCl}_4\text{]}\), the coordination number is 5, often resulting in a square pyramidal or trigonal bipyramidal geometry.
• In \(\text{[Co(NH}_3\text{)}_4\text{Cl}_2\text{]}\), the coordination number is 6, resulting in an octahedral structure.

Oxidation Number

The oxidation number is crucial for understanding the electron transfer of the metal center in a complex. It is like a bookkeeper maintaining an account of electrons for the central metal. Calculating the oxidation number involves considering the charges on the ligands and the overall charge on the complex.

Take, for example, \(\text{[CdCl}_4\text{]}\): we determine the oxidation number of cadmium (Cd) by balancing the charges. The chloride ions each have a charge of -1, making the total -4. Since the complex itself is neutral, cadmium must contribute +4 in charge. However, with \(\text{Na}_2\text{[CdCl}_4\text{]}\), two sodium ions provide a +2 charge, meaning Cd carries a +2 oxidation state, neutralizing the anions.

• For \(\text{[MoOCl}_4\text{]}\), Mo must be +4 as it balances the -2 from oxygen and -4 from chloride ions.
• Co in \(\text{[Co(NH}_3\text{)}_4\text{Cl}_2\text{]}\) has an oxidation state of +3, balancing two Cl ions’ charge.

Transition Metals

Transition metals form a crucial part of coordination chemistry. They are located in the d-block of the periodic table and are known for their variety of oxidation states and rich colors in compounds. Transition metals often serve as the central metal in coordination complexes, giving these complexes unique magnetic and optical properties.

Such metals can form multiple bonds with a set of ligands, which is due to their partially filled d orbitals. This electron configuration allows them to form stable complexes with a wide range of ligands. For instance:

• Cobalt in \(\text{[Co(NH}_3\text{)}_4\text{Cl}_2\text{]}\), where it can adopt multiple oxidation states, showing varied coordination preferences.
• Nickel in \(\text{[Ni(CN}_5\text{]}^3-\), where the multiple cyanide ions showcase Ni's flexibility in bonding.

Understanding transition metals' chemistry helps predict the properties and reactivity of the formed complex ions.

Complex Ions

Complex ions form when a central metal ion forms coordinate covalent bonds with surrounding ligands—atoms, ions, or molecules that donate a pair of electrons to the metal ion. These complex ions have a central metal atom or ion at their core, surrounded by molecules or anions acting as ligands.

The study of complex ions involves understanding their formulas, charges, and structures. For instance, a complex like \(\text{[Zn(en)}_2\text{]} \text{Br}_2\) consists of a central zinc ion bonded to two bidentate ethylenediamine ligands. Each ethylenediamine ligand can form two bonds with zinc, stabilizing the complex.

• The complex \(\text{[V(C}_2\text{O}_4\text{)}_3\text{]}\) forms with oxalate ions, each contributing two oxygen atoms as binding sites.
• Understanding the role and behavior of such ions aids in grasping how different metal centers interact with diverse ligands, impacting their resultant properties.