Question

Hemoglobin (Hb) transports oxygen in the blood: $$ \mathrm{HbH}^{+}(a q)+\mathrm{O}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{HbO}_{2}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q) $$ In blood, \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) is held nearly constant at \(4 \times 10^{-8} \mathrm{M}\) (a) How does the equilibrium position change in the lungs? (b) How does it change in \(\mathrm{O}_{2}\) -deficient cells? (c) Excessive vomiting may lead to metabolic alkalosis, in which \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) in blood decreases. How does this condition affect the ability of Hb to transport \(\mathrm{O}_{2} ?\) (d) Diabetes mellitus may lead to metabolic acidosis, in which \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) in blood increases. How does this condition affect the ability of Hb to transport \(\mathrm{O}_{2} ?\)

Short answer

(a) Equilibrium shifts right. (b) Equilibrium shifts left. (c) Increases Hb's ability to transport O_2. (d) Decreases Hb’s ability to transport O_2.

Step-by-step solution

- Understand the basic equilibrium equation

The given reaction shows hemoglobin (Hb) reacting with oxygen (O_2) and water (H_2O) to form oxyhemoglobin (HbO_2) and hydronium ion (H_3O^+): \[\mathrm{HbH}^{+}(a q)+\mathrm{O}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\longrightarrow \mathrm{HbO}_{2}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q) \]

- Analyze how equilibrium shifts in the lungs

In the lungs, the concentration of oxygen is high. According to Le Chatelier's Principle, if we increase the concentration of one of the reactants (O_2), the equilibrium will shift to the right to produce more HbO_2. This is because the system tries to minimize the change by using up the added O_2.

- Analyze how equilibrium shifts in O_2-deficient cells

In O_2-deficient cells, the concentration of oxygen is low. Again, by Le Chatelier's Principle, the equilibrium will shift to the left to produce more reactants (HbH^+ and O_2) in an attempt to reduce the impact of the decreased O_2 concentration.

- Effect of decreased H_3O^+ due to metabolic alkalosis

In the case of metabolic alkalosis, the concentration of H_3O^+ in blood decreases. According to Le Chatelier's Principle, a decrease in the product (H_3O^+) will shift the equilibrium to the right, producing more HbO_2. Thus, the ability of Hb to transport O_2 would increase.

- Effect of increased H_3O^+ due to metabolic acidosis

In the case of metabolic acidosis, the concentration of H_3O^+ in blood increases. According to Le Chatelier's Principle, an increase in the product (H_3O^+) will shift the equilibrium to the left, reducing the production of HbO_2. Thus, the ability of Hb to transport O_2 would decrease.

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle helps us understand how a system at equilibrium responds to changes in concentration, pressure, or temperature. If a change is applied to a system, the system will adjust itself to counteract that change and restore a new equilibrium. For instance, in the equilibrium reaction involving hemoglobin and oxygen, if more oxygen is added, the system will shift to consume the additional oxygen and form more oxyhemoglobin. This fundamental principle is essential for predicting the behavior of biochemical reactions under different conditions.

Equilibrium Shift

Equilibrium shift refers to the movement of the equilibrium position in response to changes in external conditions. In the context of hemoglobin oxygen transport:

• In the lungs, where oxygen concentration is high, the equilibrium shifts to the right to form more oxyhemoglobin.
• In oxygen-deficient cells, where oxygen concentration is low, the equilibrium shifts to the left to release oxygen from oxyhemoglobin.

Understanding equilibrium shifts helps in predicting how hemoglobin will behave in varying environments within the body.

Metabolic Alkalosis

Metabolic alkalosis is a condition where the blood becomes too alkaline, often from excessive vomiting which reduces \(\text{[H}_3\text{O}^+]\theta\). According to Le Chatelier's Principle, a decrease in \(\text{[H}_3\text{O}^+]\theta\) shifts the equilibrium of the hemoglobin reaction to the right, promoting the formation of oxyhemoglobin. This means hemoglobin can bind and transport more oxygen during metabolic alkalosis. While this might seem beneficial, it can also interfere with oxygen delivery to tissues since hemoglobin might hold onto oxygen more tightly.

Metabolic Acidosis

Metabolic acidosis occurs when the blood becomes too acidic, such as in diabetes mellitus, increasing \(\text{[H}_3\text{O}^+]\theta\). This increase shifts the equilibrium to the left, reducing the formation of oxyhemoglobin and thus decreasing hemoglobin's ability to transport oxygen. This condition can worsen oxygen delivery to tissues, contributing to symptoms such as fatigue and difficulty breathing. It's a critical consideration in managing diseases that alter blood pH.

Oxyhemoglobin Formation

Oxyhemoglobin is formed when hemoglobin binds with oxygen in the lungs. This process is crucial for oxygen transport in the blood. The formation reaction can be represented as:
\[ \text{HbH}^{+}+ \text{O}_2+ \text{H}_2\text{O} \rightarrow \text{HbO}_2+ \text{H}_3 \text{O}^{+} \]. This reaction demonstrates the dynamic nature of hemoglobin, which can bind and release oxygen based on the body's needs. Factors such as partial pressure of oxygen and blood pH greatly influence this equilibrium, dictating how efficiently oxygen is picked up in the lungs and released to tissues.

Oxygen Deficiency in Cells

Oxygen deficiency in cells, or hypoxia, happens when tissues don't get enough oxygen.
When cells are in an oxygen-deficient state, the concentration of \(\text{O}_2\) is low. According to Le Chatelier's Principle, the equilibrium shifts to the left, leading to the release of oxygen from oxyhemoglobin (HbO_2) to form free hemoglobin (HbH^{+}) and \(\text{O}_2\). This adjustment helps to counteract the low oxygen levels by increasing the amount available for cellular processes. Managing oxygen levels effectively is essential for maintaining cellular function and overall health.