Problem 83 - Chemistry: The Central Science in SI Units, Global Edition

Question

Oxyhemoglobin, with an \(\mathrm{O}_{2}\) bound to iron, is a low-spin Fe(II) complex; deoxyhemoglobin, without the \(\mathrm{O}_{2}\) molecule, is a high- spin complex. (a) Assuming that the coordination environment about the metal is octahedral, how many unpaired electrons are centered on the metal ion in each case? (b) What ligand is coordinated to the iron in place of \(\mathrm{O}_{2}\) in deoxyhemoglobin? (c) Explain in a general way why the two forms of hemoglobin have different colors (hemoglobin is red, whereas deoxyhemoglobin has a bluish cast). (d) A 15-minute exposure to air containing 400 ppm of CO causes about \(10 \%\) of the hemoglobin in the blood to be converted into the carbon monoxide complex, called carboxyhemoglobin. What does this suggest about the relative equilibrium constants for binding of carbon monoxide and \(\mathrm{O}_{2}\) to hemoglobin? (e) CO is a strong-field ligand. What color might you expect carboxyhemoglobin to be?

Step-by-Step Solution

Answer

(a) Oxyhemoglobin has 0 unpaired electrons and deoxyhemoglobin has 4 unpaired electrons. (b) In deoxyhemoglobin, a water molecule (H\(_2\)O) is coordinated to the iron. (c) Different colors are due to their different electronic structures and ligand coordination, which affect the absorption of specific wavelengths of light. (d) CO has a higher affinity for hemoglobin compared to \(\mathrm{O}_2\), thus K\(_\text{CO}\) is higher than K\(_\text{O2}\). (e) Carboxyhemoglobin is likely to be red, possibly more intensely red than oxyhemoglobin due to the stronger ligand field induced by CO.

Step 1: (a) Number of unpaired electrons

Oxyhemoglobin is a low-spin Fe(II) complex with an \(\mathrm{O}_2\) molecule bound to the iron, while deoxyhemoglobin is a high-spin complex without the \(\mathrm{O}_2\) molecule. In both cases, we can assume the environment around the metal ion is octahedral. The Fe(II) ion has a d6 configuration. For a low-spin complex in an octahedral environment like oxyhemoglobin, electrons will occupy the lowest energy orbitals without any unpaired electrons due to strong ligand fields. Therefore, oxyhemoglobin has 0 unpaired electrons. In contrast, a high-spin complex like deoxyhemoglobin would have the electrons distributed across the orbitals with a larger number of unpaired electrons due to lower energy differences between the orbitals. In deoxyhemoglobin, there would be 4 unpaired electrons.

Step 2: (b) Ligand in deoxyhemoglobin

In deoxyhemoglobin, the oxygen molecule is absent, and instead, a water molecule (H\(_2\)O) is coordinated to the iron.

Step 3: (c) Different colors of hemoglobin and deoxyhemoglobin

The different colors of hemoglobin and deoxyhemoglobin can be explained by their different electronic structures and ligand coordination. The number of unpaired electrons and ligand identity can affect the energy levels and transitions between d-orbitals, which in turn influences the absorption of specific wavelengths of light that contributes to the color of the compounds. Oxyhemoglobin has a red color due to the low-spin configuration, which absorbs light more readily in the blue region of the visible spectrum. Deoxyhemoglobin, with its high-spin configuration and different ligand coordination, absorbs light in a different region of the spectrum, giving it a bluish cast.

Step 4: (d) Equilibrium constants for CO and \(\mathrm{O}_2\) binding to hemoglobin

The fact that a 15-minute exposure to air containing 400 ppm of CO causes about \(10\%\) of the hemoglobin to convert into carboxyhemoglobin suggests that CO has a higher affinity for hemoglobin compared to \(\mathrm{O}_2\). Therefore, the equilibrium constant for binding CO (K\(_\text{CO}\)) is higher than the equilibrium constant for binding \(\mathrm{O}_2\) (K\(_\text{O2}\)). This means that hemoglobin has a higher tendency to bind to CO than \(\mathrm{O}_2\), causing the displacement of \(\mathrm{O}_2\) and formation of carboxyhemoglobin.

Step 5: (e) Color of carboxyhemoglobin

CO is a strong-field ligand, causing the carboxyhemoglobin complex to have a low-spin configuration with fewer unpaired electrons. This would result in a different electronic structure compared to both hemoglobin and deoxyhemoglobin, causing the absorption of light at different wavelengths. Considering that oxyhemoglobin appears red due to its low-spin configuration, one might expect carboxyhemoglobin to also display a red color, possibly even more intensely red than oxyhemoglobin due to the stronger ligand field induced by CO.

Key Concepts

Hemoglobin

Hemoglobin is a fascinating and complex protein found in red blood cells. It serves a critical role, binding to oxygen to transport it throughout the body. At the heart of this molecule is an iron ion, which plays a fundamental part in its function.
Oxyhemoglobin, the form of hemoglobin carrying oxygen, is known as a low-spin complex. This means that its electrons are paired up in the lower energy orbitals, due to strong interaction with the ligand, which in this case is \(\mathrm{O}_2\). This results in oxyhemoglobin having no unpaired electrons, leading to its characteristic bright red color.
Contrastingly, deoxyhemoglobin—hemoglobin without bound oxygen—forms a high-spin complex. Here, the iron ion has unpaired electrons because of the weaker field generated by the remaining ligands, producing four unpaired electrons. Water \(\mathrm{H}_2\mathrm{O}\) takes the place of the oxygen molecule in deoxyhemoglobin, contributing to its bluish color. This difference in spin states between oxyhemoglobin and deoxyhemoglobin not only alters their electronic structures but also affects how they interact with light, resulting in their distinct color changes.

Ligand Field Theory

Ligand Field Theory is a concept used to describe the bonding and electronic structures of coordination complexes such as hemoglobin. It focuses on how ligands, which are atoms or molecules bound to the central metal, can influence the distribution of electrons among the metal's d-orbitals.
When ligands bond to a metal ion, they create an electric field that splits the degenerate d-orbitals into two higher energy (\(e_g\)) and three lower energy (\(t_{2g}\)) orbitals. The difference in energy between these split orbitals is called the 'ligand field splitting energy' (\(\Delta\)). The strength of the ligand field can vary significantly, dictated by the nature of the ligands involved.
Strong-field ligands, such as CO, cause greater splitting, often resulting in low-spin complexes where electrons pair in the lower energy orbitals. Weak-field ligands, like water, lead to high-spin complexes where electrons remain unpaired. In hemoglobin, \(\mathrm{O}_2\) acts as a strong-field ligand in oxyhemoglobin, leading to a low-spin state. In deoxyhemoglobin, the weaker ligand \(\mathrm{H}_2\mathrm{O}\) allows for a high-spin state, illustrating the principles of Ligand Field Theory.

High-spin and Low-spin Complexes

The concepts of high-spin and low-spin complexes are essential in understanding many coordination chemistry phenomena, particularly in metal complexes like hemoglobin.
In high-spin complexes, the crystal field splitting energy (\(\Delta\)) is small compared to the pairing energy. As a result, the electrons occupy the available orbitals singly before pairing occurs. With deoxyhemoglobin, the presence of water as a weak ligand results in a high-spin configuration—and hence—four unpaired electrons.
On the other hand, low-spin complexes occur when ligands create a larger splitting energy than the pairing energy. In this scenario, electrons pair up in the lower energy orbitals, resulting in fewer or no unpaired electrons. In oxyhemoglobin, the binding of the strong-field ligand \(\mathrm{O}_2\) induces a low-spin state, with all electrons paired.
The spin state influences not just the electronic configuration but also properties such as magnetism and color of the complexes. Understanding the spin state gives insight into the behavior and characteristics of complex molecules like hemoglobin in various physiological and chemical environments.