Question

In 2001 , chemists at SUNY-Stony Brook succeeded in synthesizing the complex trans-[Fe(CN) \(\left._{4 (\mathrm{CO})_{2}\right]^{2-},\) which could be a model of complexes that may have played a role in the origin of life. (a) Sketch the structure of the complex. (b) The complex is isolated as a sodium salt. Write the com- (c) What is the oxidation state of Fe plete name of this salt. in this complex? How many \(d\) electrons are associated with the Fe in this complex? (d) Would you expect this complex to be high spin or low spin? Explain.

Short answer

The complex trans-[Fe(CN)\(_4\)(CO)\(_2\)]\(^{2-}\) has an octahedral geometry, with Iron (Fe) as the central atom and Cyanide (CN\(^{-}\)) and Carbon Monoxide (CO) as ligands. The complete name of the sodium salt is Sodium trans-tetracyanodihydroxoiron(II). The oxidation state of Fe is +2, and there are 6 d electrons associated with it in this complex. The strong-field ligands and octahedral geometry result in a low-spin complex.

Step-by-step solution

(a) Sketching the structure of the complex.

First, we have to identify the ligands, central atom, and the overall charge in the complex compound trans-[Fe(CN)\(_4\)(CO)\(_2\)]\(^{2-}\). 1. Central atom: Iron (Fe) 2. Ligands: Cyanide (CN\(^{-}\)) and Carbon Monoxide (CO) 3. Charge: 2- The complex has the prefix "trans," which indicates that the ligands are located across from each other in an octahedral geometry. Draw an octahedron with Fe in the center. There are four CN ligands and two CO ligands. Place the CN ligands on four of the vertices of the octahedron, with the C of the CN ligand bonded to Fe. Place the CO ligands on the two opposite vacant vertices of the octahedron, with their carbon atoms bonded to Fe.

(b) Writing the complete name of the sodium salt.

Since the complex ion has an overall charge of 2-, we need two sodium ions (each with a 1+ charge) to balance the charge of the compound. The complete name of this salt is Sodium trans-tetracyanodihydroxoiron(II).

(c) Oxidation state of Fe and the number of d electrons.

To determine the oxidation state of Fe, we must consider the charges of the ligands and the overall charge of the complex: Fe + 4(-1) + x = -2, where x is the charge from CO ligands, which is neutral (0). Therefore, Fe = +2. As Fe has an oxidation state of +2, the electron configuration for Fe\(^{2+}\) is [Ar] 3d\(^6\), meaning that there are 6 d electrons associated with Fe in this complex.

(d) Predicting high-spin or low-spin complex.

To predict the high-spin or low-spin nature of the complex, first, we need to know the nature of ligands and the coordination complex's geometry. The complex has an octahedral geometry, and both CN\(^{-}\) and CO are strong-field ligands and lead to a strong crystal field splitting. In an octahedral geometry, when the ligands are strong-field, they force the electrons to pair up in the lower energy d orbitals, resulting in a low-spin complex. Therefore, this complex is expected to be low-spin due to the strong-field ligands.

Key concepts

Ligand Field Theory

Ligand Field Theory is an essential concept in coordination chemistry that explains how the metal and ligands interact in a complex. It provides insight into the splitting of d orbitals when ligands approach the central metal ion. This theory builds on the Crystal Field Theory, considering covalent interactions in addition to ionic. When ligands surrounding a metal ion are significantly strong, like in the case of our exercise with CN\(^{-}\) and CO ligands, they cause a larger splitting of the metal's d orbitals.

The d orbitals are split into two groups in an octahedral complex: the lower-energy t\(_{2g}\) orbitals and the higher-energy e\(_g\) orbitals. The degree of splitting, also referred to as the crystal field splitting energy \(\Delta\), depends on the nature of the ligands and plays a crucial role in determining the high-spin or low-spin state of the complex.

Understanding how different ligands affect these energy levels is crucial because it impacts the electronic configuration and, consequently, the properties of the metal complex. Strong field ligands like CN\(^{-}\) will lead to a larger \(\Delta\), often resulting in electron pairing in the lower t\(_{2g}\) orbitals, indicative of a low-spin configuration.

Oxidation States

Oxidation state, a concept central to understanding redox reactions, describes the degree of oxidation (loss of electrons) of an element within a compound. In coordination complexes, it is essential to determine the oxidation state to predict the number of d electrons and the possible magnetic properties of the compound.

In our example, trans-[Fe(CN)\(_{4}\)(CO)\(_{2}\)]\(^{2-}\), we find that iron (Fe) has an oxidation state of +2. This calculation involves summing the known charges of the ligands and balancing it with the overall charge of the complex. Here, four cyanide ions (CN\(^{-}\)) contribute a -4 charge collectively. Since the carbon monoxide ligands are neutral (0 charge), the total negative charge from the ligands is subtracted from the complex's overall -2 charge, leaving Fe with an oxidation state of +2.

This +2 state of iron corresponds to the electron configuration [Ar] 3d\(^6\), meaning it has six d electrons. Knowing the number of d electrons helps determine whether the electrons will remain unpaired or pair up due to ligand effects, which leads us to explore the spin states of the complex.

High-spin and Low-spin Complexes

High-spin and low-spin complexes are defined by how electrons are distributed among the d orbitals when ligands coordinate with a central metal ion. The nature of ligands in a complex will decide whether the electrons will occupy higher energy orbitals (high-spin) or pair up in lower energy orbitals (low-spin).

In an octahedral complex like the one in our exercise with strong-field ligands, you typically observe low-spin behavior. Both CN\(^{-}\) and CO are strong-field ligands that cause large crystal field splitting \((\Delta)\). This strong splitting energy forces electron pairing in the lower energy t\(_{2g}\) orbitals, instead of them occupying the higher e\(_g\) orbitals.

This pairing results in a low-spin configuration, characterized by fewer unpaired electrons and, generally, lower magnetic properties. Understanding whether a complex is high-spin or low-spin is important for predicting its magnetic behavior, color, and even its reactivity.