Question

The oxidation number of \(\mathrm{Fe}\) in \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4^{-}}, \mathrm{Cr}\) in \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{3}\left(\mathrm{NO}_{2}\right)_{3}\right]\) and \(\mathrm{Ni}\) in \(\left[\mathrm{Ni}(\mathrm{CO})_{4}\right]\) are respectively (a) \(0,+3,+2\) (b) \(+3,+3,0\) (c) \(+3,0,+3\) (d) \(+2,+3,0\)

Short answer

The oxidation states are respectively +2, +3, 0. Thus, the answer is (d).

Step-by-step solution

Identify the charge of the complex

First, for each complex ion, determine if it is charged or neutral based on the provided formula. This will help in balancing the oxidation states.

Determine the charge of ligands for each complex

Identify the charge for each ligand in the complexes: - CN (cyanide) has a charge of -1. - NH3 (ammonia) is a neutral ligand with a charge of 0. - NO2 (nitrito) has a charge of -1. - CO (carbonyl) is a neutral ligand with a charge of 0.

Calculate oxidation state of Fe in \\([\mathrm{Fe}(\mathrm{CN})_{6}]^{4^{-}}\\)

Set up the equation considering the ligand charges and the given charge on the complex:\[ x + 6(-1) = -4 \]Solve for \( x \):\[ x - 6 = -4 \]\[ x = +2 \]Hence, the oxidation state of \( \mathrm{Fe} \) is +2.

Calculate oxidation state of Cr in \\([\mathrm{Cr}(\mathrm{NH}_{3})_{3}(\mathrm{NO}_{2})_{3}]\\)

Set up the equation with the charges of the ligands:\[ x + 3(0) + 3(-1) = 0 \]Solve for \( x \):\[ x - 3 = 0 \]\[ x = +3 \]Thus, the oxidation state of \( \mathrm{Cr} \) is +3.

Calculate oxidation state of Ni in \\([\mathrm{Ni}(\mathrm{CO})_{4}]\\)

All ligands are neutral, thus:\[ x + 4(0) = 0 \]\[ x = 0 \]Therefore, the oxidation state of \( \mathrm{Ni} \) is 0.

Key concepts

Transition Metal Complexes

Transition metal complexes are fascinating structures formed when transition metals coordinate with ligands. These complexes are compounds where the metal is bonded to several ligands, which can either donate or share electrons with the metal. Transition metals have unique properties due to their d-orbitals, which allow them to form varied oxidation states and bond strengths.
The core of a transition metal complex is the central metal ion, which can exist in various oxidation states. This versatility makes these metals excellent at forming complex structures. By understanding the oxidation state of the metal, we gain insight into the type and number of electrons shared between the metal and the surrounding ligands, revealing crucial information about the chemical nature and reactivity of the complex.
In the exercise,

• the iron (Fe) in the complex \([ \mathrm{Fe} ( \mathrm{CN}) _{6} ] ^{4^{-}} \) is examined, along with chromium (Cr) in \([ \mathrm{Cr} ( \mathrm{NH}_3) _{3}( \mathrm{NO}_2) _{3} ] \) and nickel (Ni) in \([ \mathrm{Ni} ( \mathrm{CO}) _{4} ] \).

These structures examine different metals in coordination with ligands, showcasing how transition metals can stabilize varied coordination numbers and geometries.

Ligand Charge

Ligands are molecules or ions that attach to a central transition metal in a complex, playing a crucial role in defining the properties of that complex. The nature of a ligand can impact the metal's oxidation state and overall charge of the complex. Understanding the charge of ligands helps to determine the oxidation state of the central metal atom.
Ligands are classified based on their charge:

• charged ligands like CN− (cyanide) and NO2− (nitrito) carry a negative charge and tend to donate electron density to the metal, affecting its oxidation state.
• neutral ligands such as NH3 (ammonia) and CO (carbonyl) do not change the metal's oxidation state by charge. Instead, they donate electron pairs to the metal, influencing bonding geometry and properties.

In the exercise:

• Fe in the complex \([ \mathrm{Fe} ( \mathrm{CN}) _{6} ] ^{4^{-}}\), involves cyanide ligands which are negatively charged.


• Cr in \([ \mathrm{Cr} ( \mathrm{NH}_3) _{3}( \mathrm{NO}_2) _{3} ]\), uses both neutral (ammonia) and negatively charged (nitrito) ligands.


• Ni in \([ \mathrm{Ni} ( \mathrm{CO}) _{4} ]\) features neutral carbonyl ligands, leaving the metal's oxidation state balanced at zero.

Determining the ligand charge allows for the accurate calculation of the metal's oxidation state, which is essential in understanding the chemistry of these complexes.

Coordination Chemistry

Coordination chemistry involves the study of compounds that consist of a central metal atom or ion attached to surrounding molecules or anions, known as ligands. This branch of chemistry encompasses the principles governing the formation, stability, and reactions of metal complexes. It is essential in describing structures like \([ \mathrm{Fe} ( \mathrm{CN}) _{6} ] ^{4^{-}} \), \([ \mathrm{Cr} ( \mathrm{NH}_3) _{3}( \mathrm{NO}_2) _{3} ] \), and \([ \mathrm{Ni} ( \mathrm{CO}) _{4} ] \).
In coordination chemistry, understanding the concept of coordination number is integral. This number represents how many ligand bonds are formed around the central metal ion. It helps in predicting the geometry and electronic properties of the complex:

• The coordination number is often 4, 6, or higher, depending on the number of sites available for ligand attachment on the metal.
• For instance, in the complex \([ \mathrm{Fe} ( \mathrm{CN}) _{6} ] ^{4^{-}} \) the coordination number is 6 as there are six cyanide ligands surrounding the iron ion.

Coordination chemistry also delves into the types of ligands, coordination geometry, and the nature of metal-ligand interactions. Understanding these aspects allows chemists to manipulate complexes for desired properties and functions, which is vital in catalysis, materials science, and biological systems.