Question

Oxyhemoglobin, with an \(\mathrm{O}_{2}\) bound to iron, is a low-spin \(\mathrm{Fe}(\mathrm{II})\) 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?

Short answer

In summary, oxyhemoglobin has no unpaired electrons, while deoxyhemoglobin has 4 unpaired electrons. The ligand replacing O₂ in deoxyhemoglobin is a water molecule (H₂O). The colors of oxyhemoglobin (red) and deoxyhemoglobin (bluish) are based on their electronic configurations and transitions. The fact that exposure to CO results in the formation of carboxyhemoglobin suggests that the equilibrium constant for CO binding to hemoglobin is larger than that of O₂, indicating a higher affinity of CO for the iron in hemoglobin.

Step-by-step solution

a) Unpaired Electrons in Oxyhemoglobin and Deoxyhemoglobin

To determine the number of unpaired electrons, we need to know the electronic configurations of low-spin and high-spin Fe(II) complexes. In an octahedral environment, Fe(II) has the electron configuration [Ar] 3d6. For low-spin Fe(II) in oxyhemoglobin: The electrons fill the lower energy levels and pair up due to strong ligand field, resulting in the electron configuration: \(t_{2g}^{6} e_{g}^{0}\). There are no unpaired electrons in the low-spin complex. For high-spin Fe(II) in deoxyhemoglobin: The electrons do not pair up due to a weak ligand field, giving the electron configuration: \(t_{2g}^{4} e_{g}^{2}\). There are 4 unpaired electrons in the high-spin complex.

b) Ligand Replacing O₂ in Deoxyhemoglobin

In deoxyhemoglobin, the ligand replacing O₂ is a water molecule (H₂O). When hemoglobin loses the oxygen molecule, the iron ion can form a bond with a water molecule, creating a high-spin complex.

c) Difference in Color Between Hemoglobin and Deoxyhemoglobin

The difference in color between oxyhemoglobin (red) and deoxyhemoglobin (bluish) can be attributed to the differences in their electronic configurations and transitions. The low-spin Fe(II) complex in oxyhemoglobin has a smaller energy gap between the \(t_{2g}\) and \(e_{g}\) orbitals compared to the high-spin complex in deoxyhemoglobin. As a result, the absorbed light wavelength for oxyhemoglobin will be longer, which corresponds to the red color, while the absorbed light wavelength for deoxyhemoglobin will be shorter, giving it a bluish cast.

d) Relative Equilibrium Constants for Binding of CO and O₂

The formation of carboxyhemoglobin upon exposure to 400 ppm of CO suggests that the equilibrium constant for binding of carbon monoxide (CO) to hemoglobin is significantly larger than the equilibrium constant for binding of O₂. This means that CO has a higher affinity for the iron in hemoglobin compared to O₂, making it more likely to form a bond with the iron ion which in turn forms carboxyhemoglobin, leaving less hemoglobin available for oxygen transport.

Key concepts

Spin States in Hemoglobin

Spin states in coordination chemistry refer to the arrangement of electrons in the d-orbitals of a metal ion when it is bound to ligands in a complex. In hemoglobin, these spin states are significant due to their impact on electron configuration and magnetic properties.

• In oxyhemoglobin, the presence of an oxygen molecule results in a low-spin state for the Fe(II) ion. This means the electrons are paired in lower energy orbitals, resulting in no unpaired electrons.
• Conversely, deoxyhemoglobin exhibits a high-spin state. Here, the electrons are unpaired due to a weaker ligand field influence, with four unpaired electrons in the \( t_{2g}^{4} e_{g}^{2} \) configuration.

The distinction between high-spin and low-spin states is pivotal for understanding the magnetic properties and the color differences in hemoglobin.

Ligand Field Theory and Color Differences

Ligand field theory is a vital framework in coordination chemistry, explaining how ligand interactions affect the properties of metal complexes. It provides insights into color changes based on alterations in the electronic structure.

• The field strength of ligands in oxyhemoglobin is substantial, creating a low-spin state with a small energy gap between the \( t_{2g} \) and \( e_{g} \) orbitals. This results in the red color seen in oxygenated blood.
• In deoxyhemoglobin, water molecules serve as ligands. The weaker field from water molecules results in a high-spin state, with a larger energy gap in the electronic orbitals. This results in a bluish cast.

Understanding how ligand field theory explains these differences enriches our knowledge of hemoglobin's behavior under varying conditions.

Role of Hemoglobin in Oxygen Transport

Hemoglobin is a crucial protein in red blood cells, responsible for the transport of oxygen from the lungs to body tissues and facilitating the return transport of carbon dioxide. Its ability to transition between different states based on its ligand environment is key.

• When hemoglobin binds to oxygen, forming oxyhemoglobin, iron is in a low-spin state, promoting efficient oxygen transport.
• In the absence of oxygen, deoxyhemoglobin forms, and iron takes on a high-spin state, ready to bind either oxygen again or other small molecules like carbon dioxide.

These transitions are essential for maintaining the balance of oxygen and carbon dioxide in the blood, contributing to the overall metabolic processes in the body.

Equilibrium Constants in Hemoglobin Binding

Equilibrium constants play a critical role in chemical reactions, indicating the affinity of hemoglobin for different ligands, such as oxygen and carbon monoxide.

• The larger the equilibrium constant, the greater the affinity of hemoglobin for that specific ligand.
• The formation of carboxyhemoglobin is indicative of a higher equilibrium constant for carbon monoxide than oxygen. This means carbon monoxide binds more tightly to hemoglobin, limiting oxygen transport and posing a health risk.
• This information highlights the competitive binding scenario observed in hemoglobin, crucial for understanding the dangerous impact of carbon monoxide exposure.

Learning about equilibrium constants helps illustrate challenges and innovations in treating exposure to toxic gases like carbon monoxide.