Question

Determine the oxidation state and coordination number of the metal ion in each complex ion. $$\begin{array}{ll}{\text { a. }\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}} & {\text { b. }\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right]^{-}} \\\ {\text { c. }\left[\mathrm{Cu}(\mathrm{CN})_{4}\right]^{2-}} & {\text { d. }\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}}\end{array}$$

Short answer

a) Oxidation state of Cr: +3, Coordination number: 6; b) Oxidation state of Co: +2, Coordination number: 6; c) Oxidation state of Cu: +2, Coordination number: 4; d) Oxidation state of Ag: +1, Coordination number: 2.

Step-by-step solution

Identifying Oxidation State and Coordination Number for \( [Cr(H_2O)_6]^{3+} \)

The oxidation state of chromium can be determined by knowing that water is a neutral ligand, so it does not contribute to the charge. Since the overall charge of the complex is +3, the oxidation state of Cr must be +3. The coordination number is the number of ligands attached to the metal ion, which is 6 for this complex.

Determining Oxidation State and Coordination Number for \( [Co(NH_3)_3Cl_3]^{-} \)

In this case, ammonia is a neutral ligand, but chloride has a charge of -1. Since there are three chlorides, they contribute -3 to the charge. The overall charge of the complex is -1, so the oxidation state of Co must be +2 (+2 - 3 = -1). The coordination number is the total number of ligands bonded to the metal ion, which is 6 (3 ammines and 3 chlorides).

Calculating Oxidation State and Coordination Number for \( [Cu(CN)_4]^{2-} \)

Cyanide is a ligand with a charge of -1. With four cyanides, the total contribution is -4 to the charge. For the complex to have an overall charge of -2, the oxidation state of Cu must be +2 (+2 - 4 = -2). The coordination number is simply the count of ligands attached to copper, which is 4.

Figuring Out Oxidation State and Coordination Number for \( [Ag(NH_3)_2]^{+} \)

Again, ammonia is neutral and does not contribute to the overall charge. Since the overall charge is +1, and there are no negatively charged ligands, the oxidation state of Ag is +1. The coordination number is 2, corresponding to the two ammonia ligands.

Key concepts

Complex Ions

Complex ions are entities formed by a central metal ion bonded to one or more molecules or ions, often referred to as ligands. These ligands can donate pairs of electrons to the metal ion, creating a stable array called a coordination complex. The number of ligands attached to the central metal ion is known as the coordination number, and it can vary depending on the size, charge, and electron configuration of the metal ion.

For example, in \[\mathrm{[Cr(H_{2}O)_{6}]^{3+}}\], the chromium ion is surrounded by six water molecules, each a neutral ligand, leading to a coordination number of six. Understanding the arrangement and connectivity within complex ions is a fundamental aspect of coordination chemistry and is crucial for predicting the properties and reactivity of these species.

Metal Ion Oxidation States

The oxidation state of a metal ion in a complex, often denoted by a Roman numeral, represents the charge of the metal ion if all its bonded ligands were removed along with the electron pairs they shared with the metal. Figuring out the oxidation state is crucial for naming the complex, understanding its reactivity, and predicting the formation of chemical bonds.

For instance, in \[\mathrm{[Co(NH_{3})_{3}Cl_{3}]^{-}}\], cobalt has an oxidation state of +2. Determining this involves recognizing that ammonia (\(NH_{3}\)) is a neutral ligand whereas chloride (\(Cl^{-}\)) carries a -1 charge. Calculating the oxidation state requires a careful balance of the charges to match the overall charge of the complex ion.

Coordination Chemistry

Coordination chemistry is the field that explores the myriad of ways that metal ions interact with ligands to form coordination complexes. This aspect of inorganic chemistry is vital for synthesizing new compounds, understanding how enzymes work in biochemistry, and even developing new medications. The properties of coordination complexes - such as color, magnetism, and reactivity - depend heavily on the nature of the metal ion, its oxidation state, and its ligands. For example, the azure blue of \[\mathrm{[Cu(CN)_{4}]^{2-}}\] comes from the specific arrangement of copper ion with a +2 oxidation state coordinated by four cyanide ligands.

Understanding the principles of coordination chemistry allows scientists to predict and control the outcome of reactions involving complex ions. This foundational knowledge is also taught to students to prepare them for more advanced studies in chemistry and related fields.