Problem 26 - Chemistry: The Central Science

Question

Indicate the coordination number and the oxidation number of the metal 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) \(\mathrm{NH}_{4}\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{2}\left(\mathrm{NCS}_{4}\right]\right.\) (f) \(\left[\mathrm{Cu}(\mathrm{bipy})_{2} \mathrm{I}\right] \mathrm{I}\) common Ligands in Coordination Chemistry Section 23.3)

Step-by-Step Solution

Answer

(a) For \(K_3[Co(CN)_6]\), the coordination number is 6, and the oxidation number is +3. (b) For \(Na_2[CdBr_4]\), the coordination number is 4, and the oxidation number is +2. (c) For \([Pt(en)_3](ClO_4)_4\), the coordination number is 6, and the oxidation number is +4. (d) For \([Co(en)_2(C_2O_4)]^{+}\), the coordination number is 6, and the oxidation number is +3. (e) For NH\(_4\)[Cr(NH\(_3\))\(_2\)(NCS)\(_4\)], the coordination number is 6, and the oxidation number is +3. (f) For \(\left[\mathrm{Cu}(\mathrm{bipy})_{2} \mathrm{I}\right] \mathrm{I}\), the coordination number is 5, and the oxidation number is +1.

Step 1: (a) Coordination Number and Oxidation number for \(K_3[Co(CN)_6]\)

The complex is \([Co(CN)_6]^{3-}\). There are six \(\mathrm{CN}^{-}\) ligands attached to the metal \(\mathrm{Co}\), giving it a coordination number of 6. The overall charge of the complex is \(-3\). Considering the charges of the ligands, we have \(x - 6(-1) = -3\), where \(x\) is the oxidation number of Co. Solving for \(x\), we get an oxidation number of +3 for Co. The coordination number is 6, and the oxidation number is +3.

Step 2: (b) Coordination Number and Oxidation number for \(Na_2[CdBr_4]\)

The complex is \([CdBr_4]^{2-}\). There are four \(\mathrm{Br}^{-}\) ligands attached to the metal \(\mathrm{Cd}\), giving it a coordination number of 4. The overall charge of the complex is \(-2\). Considering the charges of the ligands, we have \(x - 4(-1) = -2\), where \(x\) is the oxidation number of Cd. Solving for \(x\), we get an oxidation number of +2 for Cd. The coordination number is 4, and the oxidation number is +2.

Step 3: (c) Coordination Number and Oxidation number for \([Pt(en)_3](ClO_4)_4\)

The complex is \([Pt(\mathrm{en})_3]^{4+}\). There are three \(\mathrm{en}\) ligands (each of which is a bi-dentate ligand) attached to the metal \(\mathrm{Pt}\), giving it a coordination number of 3 × 2 = 6. The overall charge of the complex is \(+4\). Considering the charges of the ligands and that en is neutral, we have \(x = 4\), where \(x\) is the oxidation number of Pt. So, the oxidation number of Pt is +4. The coordination number is 6, and the oxidation number is +4.

Step 4: (d) Coordination Number and Oxidation number for \([Co(en)_2(C_2O_4)]^{+}\)

The complex is \([Co(\mathrm{en})_2(\mathrm{C}_{2}\mathrm{O}_{4})]^{+}\). There are two \(\mathrm{en}\) ligands (each of which is a bi-dentate ligand) and one \(\mathrm{C}_{2}\mathrm{O}_{4}^{2-}\) ligand (bi-dentate as well) attached to the metal Co, giving it a coordination number of 2 × 2 + 2 × 1 = 6. The overall charge is \(+1\). Considering the charges of the ligands, we have \(x - 2(0) - 2(-1) = 1\), where \(x\) is the oxidation number of Co. Solving for \(x\), we get an oxidation number of +3 for Co. The coordination number is 6, and the oxidation number is +3.

Step 5: (e) Coordination Number and Oxidation number for NH\(_4\)[Cr(NH\(_3\))\(_2\)(NCS)\(_4\)]

The complex is \([Cr(\mathrm{NH}_{3})_2(\mathrm{NCS})_4]^{-}\). There are two \(\mathrm{NH}_3\) and four \(\mathrm{NCS}^{-}\) ligands attached to the metal \(\mathrm{Cr}\), giving it a coordination number of 2 + 4 = 6. The overall charge of the complex is \(-1\). Considering the charges of the ligands, we have \(x - 2(0) - 4(-1) = -1\), where \(x\) is the oxidation number of Cr. Solving for \(x\), we get an oxidation number of +3 for Cr. The coordination number is 6, and the oxidation number is +3.

Step 6: (f) Coordination Number and Oxidation number for \(\left[\mathrm{Cu}(\mathrm{bipy})_{2} \mathrm{I}\right] \mathrm{I}\)

The complex is \([\mathrm{Cu}(\mathrm{bipy})_{2}\mathrm{I}]^{+}\). There are two \(\mathrm{bipy}\) ligands (each of which is a bi-dentate ligand) and one \(\mathrm{I}^{-}\) ligand attached to the metal \(\mathrm{Cu}\), giving it a coordination number of 2 × 2 + 1 = 5. The overall charge of the complex is \(+1\). Considering the charges of the ligands, we have \(x - 2(0) - 1(-1) = 1\), where \(x\) is the oxidation number of Cu. Solving for \(x\), we get an oxidation number of +1 for Cu. The coordination number is 5, and the oxidation number is +1.

Key Concepts

Coordination Number

Coordination number is a fundamental concept in coordination chemistry and refers to the total number of points of attachment a central atom, usually a metal ion, has to its surrounding ligands. Ligands are ions or molecules that can donate a pair of electrons to the metal to form coordinate covalent bonds. For example, in the complex \( K_3[Co(CN)_6] \), the cobalt metal ion is surrounded by six cyanide ligands, which means its coordination number is six. Coordination numbers can vary typically from 2 to 12, with 4 (tetrahedral, square planar) and 6 (octahedral) being the most common.

To further understand the coordination number, let's consider another example from the exercise: \( [Pt(en)_3](ClO_4)_4 \). In this complex, 'en' stands for ethylenediamine, a bi-dentate ligand, meaning it forms two bonds to the platinum ion. Since there are three 'en' ligands, each forming two bonds, the coordination number for Pt is 6, calculated by 3 bi-dentate ligands times 2 points of attachment each.

When determining the coordination number, it is crucial to identify the nature of the ligands and their binding sites to the central metal ion accurately. This will ensure a correct count and understanding of the metal's geometrical arrangement in the complex.

Oxidation Number

The oxidation number, also referred to as oxidation state, in coordination chemistry, represents the charge on a central atom if all ligands and electron pairs that are shared with the atom were removed. It's a hypothetical charge that assumes ionic character of bonds, even though the actual bonding often has significant covalent character. Considering our previous example of \( K_3[Co(CN)_6] \), to determine the oxidation number of Co, one begins by considering the overall charge of the complex \( [Co(CN)_6]^{3-} \), the charge on each cyanide ligand \( CN^{-} \), and then solving for the cobalt's oxidation state. In this case, the oxidation number of Co is found to be +3.

The process involves a simple algebraic calculation: if we represent the oxidation number of cobalt as 'x' and know that each cyanide ligand has a charge of -1, we have the equation \( x - 6(-1) = -3 \). Solving for 'x', we find that \( x = +3 \), signifying the oxidation number of cobalt. This step is vital as it tells us about the electron distribution between the metal and ligands, which affects the properties of the complex, such as color, magnetic behavior, and reactivity.

Metal Complexes

Metal complexes, also known as coordination compounds, consist of a central metal atom or ion bonded to one or more ligands, which can be ions, molecules, or even anions. These complexes are unique due to their structural and chemical versatility, which leads to a wide range of applications in chemistry, such as catalysis, materials science, and medication development.

A characteristic feature of metal complexes is that they have a certain geometry defining the spatial arrangement of the ligands around the central atom. The geometry depends largely on the coordination number; for instance, complexes with a coordination number of four can be tetrahedral or square planar, while those with six are typically octahedral. The exercise solutions provide multiple examples of metal complexes with varying coordination numbers and arrangements, such as the linear \( [Cu(bipy)_2 I]I \) complex, with a coordination number of five, which is relatively less common and often dictates a trigonal bipyramidal or square pyramidal geometry.

Ligands in Coordination Chemistry

In coordination chemistry, ligands are atoms, ions, or molecules that can donate one or more pairs of electrons to the central metal atom to form a coordination compound. Ligands come in many varieties, such as monodentate, which bind through a single atom, bi-dentate, which attach at two points, and polydentate ligands, which can attach at multiple points.

Common ligands include water (\( H_2O \)), ammonia (\( NH_3 \)), chloride (\( Cl^- \) ), and cyanide (\( CN^- \) ). Some ligands, like ethylenediamine (\( en \)) and oxalate (\( C_2O_4^{2-} \)), are bi-dentate, creating a chelate complex when they bond to the metal. This 'chelating effect' can stabilize the complex and enhance its properties. For example, in \( [Co(en)_2(C_2O_4)]^+ \), both 'en' and oxalate ligands form multiple bonds with the cobalt ion, resulting in a robust octahedral structure.

Ligands are crucial for the function and stability of metal complexes, as shown by the various examples in the solutions provided. Their electronic and steric properties dictate the geometry, reactivity, and electronic structure of the coordination compound, making the choice of ligand essential for the desired outcome in chemical synthesis and industrial applications.