Problem 26 - 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) \(\mathrm{K}_{3}\left[\mathrm{Co}(\mathrm{CN})_{6}\right]\) (b) \(\mathrm{Na}_{2}\left[\mathrm{CdBr}_{4}\right]\) (c) \(\left[\mathrm{Pt}(\mathrm{en})_{3}\right]\left(\mathrm{ClO}_{4}\right)_{4}\) (d) \(\left[\mathrm{Co}(\mathrm{en})_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)\right]^{+}\) (e) \(\mathrm{NH}_{4}\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{2}(\mathrm{NCS})_{4}\right]\) (f) \(\left[\mathrm{Cu}(\text { bipy })_{2} \mathrm{I}\right] \mathrm{I}\)

Step-by-Step Solution

Answer

\(a) \mathrm{Coordination\:number}=6, \: \mathrm{Oxidation\:number\:of\:Co}=+3, \: \mathrm{Number\:of\:CN\:ligands}=6 \\ b) \mathrm{Coordination\:number}=4, \: \mathrm{Oxidation\:number\:of\:Cd}=+2, \: \mathrm{Number\:of\:Br\:ligands}=4 \\ c) \mathrm{Coordination\:number}=6, \: \mathrm{Oxidation\:number\:of\:Pt}=+4, \: \mathrm{Number\:of\:en\:ligands}=3 \\ d) \mathrm{Coordination\:number}=6, \: \mathrm{Oxidation\:number\:of\:Co}=+3, \: \mathrm{Number\:of\:en\:ligands}=2, \: \mathrm{Number\:of\:C2O4\:ligands}=1 \\ e) \mathrm{Coordination\:number}=6, \: \mathrm{Oxidation\:number\:of\:Cr}=+3, \: \mathrm{Number\:of\:NH3\:ligands}=2, \: \mathrm{Number\:of\:NCS\:ligands}=4 \\ f) \mathrm{Coordination\:number}=5, \: \mathrm{Oxidation\:number\:of\:Cu}=+2, \: \mathrm{Number\:of\:bipy\:ligands}=2, \: \mathrm{Number\:of\:I\:ligands}=1\)

Step 1: Identify Central Metal Atom and Ligands

In this complex, the central metal atom is Cobalt (Co) and the ligands are six cyanide (CN) groups.

Step 2: Determine Coordination Number

There are six cyanide (CN) groups connected to the central metal atom, so the coordination number is 6.

Step 3: Identify Ionic Charge

The complex has a negative charge of 3-, as indicated by the three potassium (K) ions.

Step 4: Calculate Oxidation Number

The cyanide ligand has a charge of -1. To determine the oxidation number of Co, we can use the formula: \[\text{charge of complex} = \text{oxidation number of metal} + (\text{charge of ligands} \times \text{coordination number})\] Thus, the oxidation number of Co is: \[(-3)=\text{oxidation number of Co} +((-1) \times 6)\] The oxidation number of Co is +3. For this complex: Coordination number: 6 Oxidation number of Co: +3 Number of CN ligands: 6 &___ b) \(\mathrm{Na}_{2}\left[\mathrm{CdBr}_{4}\right]\)

Step 1: Identify Central Metal Atom and Ligands

In this complex, the central metal atom is Cadmium (Cd) and the ligands are four bromide (Br) ions.

Step 2: Determine Coordination Number

There are four bromide (Br) ions connected to the central metal atom, so the coordination number is 4.

Step 3: Identify Ionic Charge

The complex has a negative charge of 2-, as indicated by the two sodium (Na) ions.

Step 4: Calculate Oxidation Number

The bromide ligand has a charge of -1. To determine the oxidation number of Cd, we can use the formula: \[\text{charge of complex} = \text{oxidation number of metal} + (\text{charge of ligands} \times \text{coordination number})\] Thus, the oxidation number of Cd is: \[(-2)=\text{oxidation number of Cd} +((-1) \times 4)\] The oxidation number of Cd is +2. For this complex: Coordination number: 4 Oxidation number of Cd: +2 Number of Br ligands: 4 (c) \(\left[\mathrm{Pt}(\mathrm{en})_{3}\right]\left(\mathrm{ClO}_{4}\right)_{4}\)

Step 1: Identify Central Metal Atom and Ligands

In this complex, the central metal atom is Platinum (Pt) and the ligands are three ethylenediamine (en) groups.

Step 2: Determine Coordination Number

Each ethylenediamine (en) ligand forms two connections to the central metal atom. Hence, there are a total of 6 connections, making the coordination number 6.

Step 3: Identify Ionic Charge

The complex has a positive charge of 4+, as indicated by the four perchlorate (ClO4) anions.

Step 4: Calculate Oxidation Number

The ethylenediamine ligand is neutral, meaning it has no inherent charge. Thus, the oxidation number of Pt is equal to the overall charge of the complex, which is +4. For this complex: Coordination number: 6 Oxidation number of Pt: +4 Number of en ligands: 3 (d) \(\left[\mathrm{Co}(\mathrm{en})_{2}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)\right]^{+}\)

Step 1: Identify Central Metal Atom and Ligands

In this complex, the central metal atom is Cobalt (Co) and the ligands are two ethylenediamine (en) groups and an oxalate (C2O4) ion.

Step 2: Determine Coordination Number

Each ethylenediamine (en) ligand forms two connections to the central metal atom, while the oxalate also forms two connections. In total, we have 2 + 2 + 2 = 6 connections, making the coordination number 6.

Step 3: Identify Ionic Charge

The complex has an overall charge of +1, as seen in the formula.

Step 4: Calculate Oxidation Number

The ethylenediamine ligands are neutral and the oxalate ion has a charge of -2. Using the formula, we can determine the oxidation number of Co: \[(+1)=\text{oxidation number of Co} +(2\times0 + (-2)\times1)\] The oxidation number of Co is +3. For this complex: Coordination number: 6 Oxidation number of Co: +3 Number of en ligands: 2 Number of C2O4 ligands: 1 (e) \(\mathrm{NH}_{4}\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{2}(\mathrm{NCS})_{4}\right]\)

Step 1: Identify Central Metal Atom and Ligands

In this complex, the central metal atom is Chromium (Cr) and the ligands are two ammonia (NH3) molecules and four thiocyanate (NCS) ions.

Step 2: Determine Coordination Number

There are two ammonia and four thiocyanate ions connected to the central metal atom, giving a total coordination number of 6.

Step 3: Identify Ionic Charge

The complex has a negative charge of 1-, as indicated by the ammonium (NH4) cation.

Step 4: Calculate Oxidation Number

The ammonia ligands are neutral, and the thiocyanate ions have a charge of -1. Using the formula, we determine the oxidation number of Cr: \[(-1)=\text{oxidation number of Cr} +(2\times0 + (-1)\times4)\] The oxidation number of Cr is +3. For this complex: Coordination number: 6 Oxidation number of Cr: +3 Number of NH3 ligands: 2 Number of NCS ligands: 4 (f) \(\left[\mathrm{Cu}(\text { bipy })_{2} \mathrm{I}\right] \mathrm{I}\)

Step 1: Identify Central Metal Atom and Ligands

In this complex, the central metal atom is Copper (Cu) and the ligands are two 2,2'-bipyridine (bipy) molecules and an iodide (I) ion.

Step 2: Determine Coordination Number

Each 2,2'-bipyridine(bipy) ligand forms two connections to the central metal atom and there is one iodide ion. In total, we have 2 + 2 + 1 = 5 connections, making the coordination number 5.

Step 3: Identify Ionic Charge

The complex has an overall charge of +1, as indicated by the separate iodide (I) ion.

Step 4: Calculate Oxidation Number

The 2,2'-bipyridine ligands are neutral and the iodide ion has a charge of -1. Using the formula, we can determine the oxidation number of Cu: \[(+1)=\text{oxidation number of Cu} +(2\times0 + (-1)\times1)\] The oxidation number of Cu is +2. For this complex: Coordination number: 5 Oxidation number of Cu: +2 Number of bipy ligands: 2 Number of I ligands: 1

Key Concepts

Coordination Number

In coordination chemistry, the coordination number is a fundamental concept that refers to the number of ligand (donor atom) connections a central metal atom has in a coordination complex. It indicates the total number of bonds formed between the metal and the ligand molecules or ions. For instance, in the complex ewline ewline (\(\mathrm{Co}(\mathrm{en})_{2}\left(\mathrm{C}_{2}\mathrm{O}_{4}\right)\right)^{+}\), the coordination number is 6 because Cobalt (Co) forms a total of six bonds – four with two ethylenediamine (en) molecules (each offers two donor atoms) and two with an oxalate ion. It's essential for students to comprehend how to identify and count each ligand's donor atoms, as this can affect the structure and properties of the complex.

Oxidation State

The oxidation state, or oxidation number, is a critical piece of information that reflects the electron count associated with a metal in a compound, relative to the elemental form of the metal. To determine the oxidation number of a metal in a coordination complex, we can use the formula ewline ewline \[\text{charge of complex} = \text{oxidation number of metal} + (\text{charge of ligands} \times \text{coordination number})\].ewline ewline Through this formula, we can see that the oxidation state is effectively the charge that the metal would have if all ligands were removed along with the electrons they shared with the metal. For example, in ewline ewline \(\mathrm{K}_{3}\left[\mathrm{Co}(\mathrm{CN})_{6}\right]\), the oxidation number for Cobalt (Co) is calculated to be +3. Teachers often recommend writing out the individual charges of ligands and metals explicitly as a concrete step towards understanding the complex's overall charge distribution.

Ligand Field Theory

Ligand field theory is an advanced concept in coordination chemistry that provides insight into the electronic structure of coordination complexes. It builds upon crystal field theory by considering the covalent, as well as the ionic aspects of the metal-ligand bond. Ligand field theory explains the splitting of metal d-orbitals in the presence of ligands, which leads to the unique color and magnetic properties of coordination compounds. Students can visualize this through the crystal field splitting diagram, helping them understand the absorption of light and the color observed for a given complex.ewline ewline An example from ligand field theory can be applied to ewline ewline \(\left[\mathrm{Cu}(\text { bipy })_{2} \mathrm{I}\right] \mathrm{I}\), where the distinctive electronic arrangement around the Copper (Cu) atom due to the bipyridine ligands influences properties like the color and magnetic moment of the complex. Such concepts might require an in-depth look at the transitions between d-orbital levels and the factors that influence d-orbital splitting, such as the geometric arrangement of ligands around the central metal atom and the nature of the ligands themselves.