Question

Give the oxidation numbers of the metals in the following species: (a) \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right],(\mathrm{b}) \mathrm{K}_{3}\left[\mathrm{Cr}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right],\) (c) \(\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{2-}\).

Short answer

(a) Fe: +3, (b) Cr: +3, (c) Ni: +2.

Step-by-step solution

Determine Charge of Entire Complex

First, we need to identify the overall charges of the various complexes in the given compounds. This is determined by considering the given charges or any counter-ion present. For (a) \(\mathrm{K}_3[\mathrm{Fe}(\mathrm{CN})_6]\): The charge of \(\mathrm{K}_3\) is +3 since each \(\mathrm{K}^+\) has a +1 charge. Thus, the charge of the complex ion \([\mathrm{Fe}(\mathrm{CN})_6]\) is -3.For (b) \(\mathrm{K}_3[\mathrm{Cr}(\mathrm{C}_2 \mathrm{O}_4)_3]\): Similarly, the potassium ions contribute a +3 charge, indicating the complex \([\mathrm{Cr}(\mathrm{C}_2 \mathrm{O}_4)_3]\) has an overall charge of -3.For (c) \([\mathrm{Ni}(\mathrm{CN})_4]^{2-}\): The complex itself has an overall charge of -2, as indicated in the formula.

Assign Oxidation Numbers to Ligands

Next, assign the oxidation numbers for the ligands present in each complex.- In \([\mathrm{Fe}(\mathrm{CN})_6]^{3-}\) and \([\mathrm{Ni}(\mathrm{CN})_4]^{2-}\), the cyanide ion (\(\mathrm{CN}^-\)) has an oxidation number of -1 for each CN group.- In \([\mathrm{Cr}(\mathrm{C}_2 \mathrm{O}_4)_3]^{3-}\), the oxalate ion (\(\mathrm{C}_2\mathrm{O}_4^{2-}\)) has an overall charge of -2. Since there are three oxalates, they contribute a total of -6 to the charge of the complex.

Calculate Oxidation Number of Metal Center

With the ligand information, solve for the metal's oxidation number using the charge balance principle. The sum of the oxidation number of the central metal and the total oxidation numbers of the ligands must equal the charge on the complex ion.- For \([\mathrm{Fe}(\mathrm{CN})_6]^{3-}\): \[ x + 6(-1) = -3 \] Solving gives: \( x = +3 \). Thus, the oxidation number of Fe is +3.- For \([\mathrm{Cr}(\mathrm{C}_2 \mathrm{O}_4)_3]^{3-}\): \[ x + 3(-2) = -3 \] Solving gives: \( x = +3 \). Thus, the oxidation number of Cr is +3.- For \([\mathrm{Ni}(\mathrm{CN})_4]^{2-}\): \[ x + 4(-1) = -2 \] Solving gives: \( x = +2 \). Thus, the oxidation number of Ni is +2.

Key concepts

Chemical Complexes

A chemical complex is a fascinating assembly in coordination chemistry. It involves a central metal atom or ion bonded to surrounding molecules or ions, known as ligands. These complexes are often stable due to the interactions between the metal and its ligands.
For students just diving into this topic, it's helpful to visualize chemical complexes like planets and their orbiting moons.

• The central metal acts as the planet.
• The ligands are the moons in orbit.

The way these complexes form is pivotal in understanding many biological and industrial processes. As you study them, keep in mind that their stability comes from the electrostatic interactions and sometimes even covalent bonding between the central metal and its ligands.

Transition Metals

Transition metals, at the heart of chemical complexes, are elements found in the d-block of the periodic table. They are known for their ability to form various oxidation states.
This flexibility is due to their unique electron configurations, which allow them to lose different numbers of electrons.

• The d-orbitals in transition metals can hold versatile electronic arrangements.
• These metals often form colorful complexes.

Because of these characteristics, transition metals like iron (Fe), nickel (Ni), and chromium (Cr) are indispensable in introducing diversity to chemistry. They can form stable compounds with a wide range of oxidation states, making them crucial in both biological systems and technological applications.

Charge Balance

Charge balance is a vital concept in determining the oxidation numbers of metals in complexes. It ensures that the sum of the charges is consistent within a compound. Simply put, the overall charge of the complex ion is the combined total of the oxidation numbers of the metal and any ligands.
For example, when calculating the oxidation number of iron in \[\mathrm{Fe}(\mathrm{CN})_6\]^{3-}\, we focus on charge balance:

• The total charge from six cyanide ions (each with a charge of -1) is -6.
• This must combine with the oxidation state of the iron to equal the overall complex charge of -3.

By setting up the equation, we quickly solve for the unknown oxidation number of the metal, highlighting the importance of maintaining charge balance for accurate calculations.

Ligands

Ligands play a crucial role in coordination chemistry. They are the molecules or ions surrounding the central metal within a chemical complex. Ligands donate electron pairs to the metal, forming coordinate bonds which are essential for complex formation.
Here are some ligands you'll frequently encounter:

• Cyanide (CN^-), which often contributes a -1 charge per ligand.
• Oxalate (C₂O₄^2-), which contributes a -2 charge.

Understanding the role of ligands helps in determining the oxidation numbers of metals, as they significantly impact the overall charge and stability of a complex.

Coordination Chemistry

Coordination chemistry is focused on the study of complexes formed between transition metals and ligands. This field shines light on the intriguing connections within these complexes, exploring how metals and ligands interact.
Here are key points to help you understand coordination chemistry:

• Coordination number: Refers to the number of ligand atoms bound directly to the metal. For example, in \[\mathrm{Cr}(\mathrm{C_2O_4})_3\]^{3-}\, chromium has a coordination number of 6.
• Geometry: The spatial arrangement of ligands is important. Complexes can be octahedral, tetrahedral, or square planar, affecting their physical and chemical properties.

By diving into coordination chemistry, you uncover a world where metals and ligands create core structures used in everything from industrial catalysts to biological enzymes.