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 complete name of this salt. (c) What is the oxidation state of Fe in this complex? How many d electrons are associated with the \(\mathrm{Fe}\) in this complex? (d) Would you expect this complex to be high spin or low spin? Explain.

Short answer

(a) The complex has an octahedral structure with Fe at the center, surrounded by four CN ligands and two CO ligands in trans positions. (b) The sodium salt of the complex is Sodium trans-Tetracyanododicarbonylferrate(II). (c) The oxidation state of Fe is +2, and there are 4 d electrons associated with the Fe in this complex. (d) We expect this complex to be low spin because both CN and CO ligands are strong field ligands.

Step-by-step solution

(a) Sketch the structure of the complex

In order to sketch the structure of the complex trans-[Fe(CN)\(_{4}\)(CO)\(_{2}\)]\(^{2-}\), first, let us understand its composition. The complex consists of one Fe atom bonded to four cyanide ions (CN\(^{-}\)) and two carbonyl ligands (CO). The term "trans" indicates that the two carbonyl ligands are opposite to each other. We would draw a Fe atom at the center, surrounded by four CN ligands and two CO ligands. CN ligands will occupy four coordinate positions around the Fe atom while the CO ligands will occupy the remaining two positions opposite to each other. The resulting structure will be in octahedral geometry. The two negative charges will be distributed on two of the CN ligands.

(b) Name the sodium salt of the complex

Since the complex has a charge of -2, it will be isolated as a sodium salt with two sodium ions (Na\(^{+}\)). The complete name of the sodium salt of the complex will be Sodium trans-Tetracyanododicarbonylferrate(II).

(c) Determine the oxidation state of Fe and the number of d electrons associated with Fe

To find the oxidation state of Fe, let's look at the charges of the ligands. Each CN ligand has -1 charge and each CO ligand has neutral charge. The overall charge of the complex is -2. Let the oxidation state of Fe be x. x - 4(1) + 0 = -2 x - 4 = -2 x = +2 So, the oxidation state of Fe is +2. Since Fe belongs to the 3d transition series (atomic number 26), it has 6 3d electrons in the neutral state. In the oxidation state of +2, the Fe atom will lose 2 electrons. Number of d electrons = 6 - 2 = 4 Therefore, there are 4 d electrons associated with the Fe in this complex.

(d) Determine if the complex is high spin or low spin

To determine if the complex is high spin or low spin, we need to evaluate the ligands' strength. Cyanide (CN) and carbonyl (CO) ligands are both strong field ligands, which means they lead to a large crystal field splitting, causing electron pairs to avoid occupying the same orbital if possible. When a complex has strong field ligands, it is likely to be low spin. Therefore, we would expect this complex to be low spin.

Key concepts

Oxidation State

Understanding the oxidation state of a metal in a complex is crucial for grasping its chemical properties. Oxidation state denotes the charge on a central metal atom if all ligands are removed along with the electron pairs that are shared with the central atom. In our exercise with the complex trans-[Fe(CN){4}(CO){2}]^{2-}, we determine the oxidation state of iron (Fe) by considering the charges of the surrounding ligands.
Cyanide (CN-) is a monodentate ligand with a charge of -1, and there are four of them, contributing a total charge of -4. Carbonyl (CO) ligands are neutral. The complex itself has an overall charge of -2, which helps us establish the oxidation state of Fe. By setting up the equation, without the ligands:\[x - 4(1) = -2\]\[x = 2\]we find that the oxidation state of Fe is +2. This means that in this complex, the iron atom essentially 'loses' two electrons, leading to four d electrons remaining in its d-orbital, crucial in determining magnetic properties and the reactivity of the complex.

Crystal Field Theory

Crystal field theory (CFT) is a model that describes the electronic structure of metal complexes. It assumes that the ligands are point charges interacting with the d orbitals of the central metal ion. The approach is to split the degenerate d orbitals into different energy levels due to the electrostatic repulsion between the d electrons of the metal and the negative charge of the ligands.
In an octahedral complex like trans-[Fe(CN){4}(CO){2}]^{2-}, CFT suggests the d orbitals split into two sets: the lower-lying {t}{2g} and the higher-lying e{g} orbitals. The splitting of the orbitals depends on the strength of the ligands’ field. As both CN- and CO are strong field ligands, a larger crystal field splitting occurs. This larger splitting affects the spin pairing of electrons and is the basis for determining whether a complex is high spin or low spin.

Ligand Field Strength

Ligand field strength is an essential factor in predicting the properties of transition metal complexes. It refers to the ability of ligands to split the d orbital energies of a central metal ion. When we rank ligands according to their field strength, as in the spectrochemical series, we see that different ligands exert different amounts of crystal field splitting.
In our exercise, the cyanide and carbonyl ligands are considered strong field ligands. Strong field ligands, like CN- and CO, cause a significant crystal field splitting, which influences the distribution of d electrons across the orbitals and determines the magnetic nature of the complex. This concept helps us understand the reactivity and color of complexes.

Spin State of Complexes

The spin state of a complex determines its magnetic properties and is a direct consequence of ligand field strength and the resulting crystal field splitting. For a given central metal ion, a complex can either be 'high spin' or 'low spin' based on the arrangement of its d electrons.
A 'high spin' complex occurs when the splitting energy is small relative to the pairing energy, and as a result, electrons occupy higher energy orbitals before pairing up in the lower ones. Conversely, a 'low spin' complex arises when ligand field strength is strong, causing a large crystal field splitting where electrons pair in the lower orbitals to minimize energy before occupying higher ones. As deduced from the exercise, the trans-[Fe(CN){4}(CO){2}]^{2-} complex has strong field ligands and hence is expected to be low spin. Determining the spin state is critical for understanding the magnetic behavior and stability of transition metal complexes.