Question

Carbon monoxide and the cyanide ion are both toxic because they bind more strongly than oxygen to the iron in hemoglobin (Hb). $$\begin{array}{ll}\mathrm{Hb}+\mathrm{O}_{2} \rightleftharpoons \mathrm{HbO}_{2} & K=2 \times 10^{12} \\\\\mathrm{Hb}+\mathrm{CO} \rightleftharpoons \mathrm{HbCO} & K=1 \times 10^{14}\end{array}$$Calculate the equilibrium constant value for this reaction: $$\mathrm{HbO}_{2}+\mathrm{CO} \rightleftharpoons \mathrm{HbCO}+\mathrm{O}_{2} $$Does the equilibrium favor reactants or products?

Short answer

The equilibrium constant for the reaction HbO2 + CO ⇌ HbCO + O2 is 50, favoring the formation of HbCO (products) over the reactants.

Step-by-step solution

Write the equilibrium reactions involved

Identify the two separate equilibrium reactions and their equilibrium constants.Reaction 1: Hb + O2 ⇌ HbO2 with K1 = 2 x 10^12.Reaction 2: Hb + CO ⇌ HbCO with K2 = 1 x 10^14.

Deduce the equilibrium reaction for which the constant is sought

Write the reaction where the oxyhemoglobin reacts with carbon monoxide to form carboxyhemoglobin and release oxygen:HbO2 + CO ⇌ HbCO + O2.

Derive the equilibrium constant for the target reaction

Use the equilibrium constants of the given reactions. For the target reaction, the equilibrium constant K3 can be found using the relationship K3 = K2 / K1, because the target reaction is the result of reaction 2 going forward and reaction 1 going in reverse. Calculate K3.

Calculate the equilibrium constant K3

K3 = K2 / K1 = (1 x 10^14) / (2 x 10^12) = 50.

Determine the direction of the equilibrium

Since K3 is significantly greater than 1, this means the equilibrium of the reaction HbO2 + CO ⇌ HbCO + O2 heavily favors the formation of HbCO and O2, the products.

Key concepts

Chemical Equilibrium

Chemical equilibrium represents a state in which chemical reactions occur at equal rates in both forward and reverse directions, so there is no net change in the amounts of reactants and products. It's essential in understanding how reactions proceed and how changes in conditions can affect the outcome. For a balanced reaction, say \( A + B \leftrightarrow C + D \), the equilibrium constant \( K \) quantifies the ratio of products to reactants at equilibrium, expressed as \( K = \frac{[C][D]}{[A][B]} \), where \( [x] \) denotes the concentration of substance \( x \). A high \( K \) indicates a reaction that tends to complete to form products, as in the reaction \( \mathrm{Hb} + \mathrm{CO} \rightleftharpoons \mathrm{HbCO} \) with \( K = 10^{14} \), showing a strong penchant for product formation.

Le Chatelier's Principle

Le Chatelier's principle is a critical tool for predicting the effect of changes in concentration, temperature, or pressure on a system at equilibrium. If a system at equilibrium is disturbed, it reacts in such a way as to counteract the disturbance and return to a state of equilibrium.

For instance, if the concentration of a reactant in a balanced reaction is increased, the equilibrium shifts toward the products to reduce the disturbance. Conversely, increasing a product's concentration shifts the equilibrium toward reactants. In the exercise problem, the introduction of \( \mathrm{CO} \) shifts the equilibrium in favor of \( \mathrm{HbCO} \) formation. Understanding this principle helps explain why carbon monoxide is so effective at outcompeting oxygen for binding to hemoglobin.

Hemoglobin Binding Affinity

The binding affinity of hemoglobin for different molecules is a measure of how readily hemoglobin attracts and attaches to these molecules. Hemoglobin's affinity for oxygen is crucial for transporting oxygen from the lungs to tissues. However, affinities can vary—for example, hemoglobin has a higher affinity for carbon monoxide than for oxygen.

The equilibrium constants provided in the exercise, \( K = 2 \times 10^{12} \) for \( \mathrm{HbO}_2 \) and \( K = 1 \times 10^{14} \) for \( \mathrm{HbCO} \) demonstrate this difference in affinity quantitatively. A higher \( K \) for \( \mathrm{HbCO} \) indicates a stronger tendency to form this complex, vastly outpacing the affinity for oxygen. This concept allows us to understand the biological implications and potential dangers when competing substances, like carbon monoxide, are present.

Toxicity of Carbon Monoxide

Carbon monoxide's toxicity arises from its high affinity for the iron in hemoglobin, which is more than 200 times greater than that of oxygen. This prevents oxygen from binding effectively, leading to diminished oxygen transport in the bloodstream and potentially serious health consequences.

The calculations from our exercise illustrate this toxicity quantitatively. Because the equilibrium constant for \( \mathrm{HbCO} \) formation is so high, exposure to carbon monoxide leads to the rapid formation of \( \mathrm{HbCO} \) and a corresponding decrease in oxygen transport. Understanding the dangers of carbon monoxide exposure and the importance of preventive measures, such as carbon monoxide detectors, is essential for health and safety.