Question

As stated in the chapter, carbon monoxide has a much higher affinity for hemoglobin than oxygen does. (a) Write the equilibrium constant expression \(\left(K_{\mathrm{c}}\right)\) for the following process: $$ \mathrm{CO}(g)+\mathrm{HbO}_{2}(a q) \rightleftarrows \mathrm{O}_{2}(g)+\mathrm{HbCO}(a q) $$ where \(\mathrm{HbO}_{2}\) and \(\mathrm{HbCO}\) are oxygenated hemoglobin and carboxyhemoglobin, respectively. (b) The composition of a breath of air inhaled by a person smoking a cigarette is \(1.9 \times 10^{-6} \mathrm{~mol} / \mathrm{L} \mathrm{CO}\) and \(8.6 \times 10^{-3} \mathrm{~mol} / \mathrm{L}\) \(\mathrm{O}_{2} .\) Calculate the ratio of \([\mathrm{HbCO}]\) to \(\left[\mathrm{HbO}_{2}\right]\), given that $$ K_{\mathrm{c}} \text { is } 212 \text { at } 37^{\circ} \mathrm{C} $$

Short answer

The ratio of \([\mathrm{HbCO}]") to \([\mathrm{HbO}_2]\) is approximately 0.0468.

Step-by-step solution

Write the Equilibrium Constant Expression

For the given reaction: \( \mathrm{CO}(g) + \mathrm{HbO}_2(aq) \rightleftharpoons \mathrm{O}_2(g) + \mathrm{HbCO}(aq) \), the equilibrium constant expression \( K_c \) is written in terms of the concentrations of the products over the reactants.\[ K_c = \frac{[\mathrm{O}_2][\mathrm{HbCO}]}{[\mathrm{CO}][\mathrm{HbO}_2]} \]

Rearrange the Equilibrium Expression

Rearrange the equilibrium expression to find the ratio \( \frac{[\mathrm{HbCO}]}{[\mathrm{HbO}_2]} \).Firstly, \[ \frac{[\mathrm{HbCO}]}{[\mathrm{HbO}_2]} = \frac{K_c \cdot [\mathrm{CO}]}{[\mathrm{O}_2]} \]

Substitute the Given Values

Substitute the values provided into the rearranged expression:- \( K_c = 212 \)- \([\mathrm{CO}] = 1.9 \times 10^{-6} \) mol/L- \([\mathrm{O}_2] = 8.6 \times 10^{-3} \) mol/LThis gives:\[ \frac{[\mathrm{HbCO}]}{[\mathrm{HbO}_2]} = \frac{212 \cdot 1.9 \times 10^{-6}}{8.6 \times 10^{-3}} \]

Perform the Calculation

Calculate the final ratio:\[ \frac{[\mathrm{HbCO}]}{[\mathrm{HbO}_2]} = \frac{212 \times 1.9 \times 10^{-6}}{8.6 \times 10^{-3}} \approx 0.0468 \]

Key concepts

Carbon Monoxide

Carbon monoxide (CO) is a colorless, odorless gas that is highly toxic. It is produced by the incomplete combustion of carbon-containing fuels, such as gasoline, natural gas, oil, coal, and wood. CO is notorious for its ability to bind with hemoglobin in the blood, a protein responsible for carrying oxygen throughout the body. This binding is significantly stronger than oxygen's, which makes CO particularly dangerous. When CO is inhaled, it enters the bloodstream, where it can prevent oxygen from being delivered to vital tissues and organs, leading to effects like dizziness, headaches, and even death in severe cases.

Due to carbon monoxide's high affinity for hemoglobin, even low levels of exposure can lead to significant health risks. Therefore, it's crucial to ensure that areas where combustion can occur, like kitchens and garages, are properly ventilated and equipped with CO detectors.

Hemoglobin

Hemoglobin is a vital protein found in red blood cells. Its primary function is to transport oxygen from the lungs to the rest of the body. Hemoglobin is composed of four subunits, each containing an iron atom that binds to oxygen molecules. This ability to bind oxygen is what allows hemoglobin to carry it through the bloodstream and release it where it's needed in the body.

Interestingly, hemoglobin can bind to other molecules aside from oxygen, such as carbon monoxide. This binding occurs at the same site as oxygen, which can significantly disrupt the body's ability to distribute oxygen if CO is present in the environment.

• Structure: Four subunits with iron
• Primary function: Oxygen transport
• Can bind to other molecules: Like CO

Understanding hemoglobin's role is crucial because its interactions with both oxygen and carbon monoxide can have significant impacts on health.

Chemical Equilibrium

Chemical equilibrium occurs in a reversible chemical reaction when the rate of the forward reaction (reactants to products) equals the rate of the reverse reaction (products to reactants). At this point, the concentrations of the different substances involved remain constant over time. Equilibrium is a dynamic process, with reactants continually being converted to products and vice versa.

In the context of the given exercise, the equilibrium constant expression for the reaction involving carbon monoxide and hemoglobin is a way to quantify the balance of products (oxygen and carboxyhemoglobin) to reactants (carbon monoxide and oxygenated hemoglobin) in the bloodstream.

• Equilibrium state: No net change in concentration
• Proportion of products and reactants: Constant

The equilibrium condition in a chemical reaction like this is described by the equilibrium constant, which helps predict how a change in conditions can affect the concentrations of different components.

Oxygenated Hemoglobin

Oxygenated hemoglobin, often represented as \( ext{HbO}_2\), is hemoglobin that has bound with oxygen. This form of hemoglobin is responsible for the bright red color of oxygen-rich blood found in arteries. Hemoglobin's affinity for oxygen allows it to bind oxygen in the lungs, where oxygen concentration is high, and release it in tissues, where it's needed for cellular respiration.

Oxygenated hemoglobin is essential for life because it carries the oxygen necessary for producing energy in cells. The efficiency of this process can be compromised by factors that affect hemoglobin's ability to bind oxygen, such as the presence of carbon monoxide. In understanding disorders related to oxygen transportation, the role of oxygenated hemoglobin provides critical insight.

• Bound to oxygen: Bright red color
• Functions: Carrying oxygen from lungs to tissues

Carboxyhemoglobin

Carboxyhemoglobin (HbCO) is formed when carbon monoxide binds to the hemoglobin in the blood. This complex is stable and reduces the hemoglobin's ability to carry oxygen, effectively reducing the amount of oxygen that reaches tissues and organs.

The formation of carboxyhemoglobin is dangerous because CO binding with hemoglobin is over 200 times stronger than oxygen's binding. This strong affinity means even low concentrations of CO can lead to significant levels of carboxyhemoglobin, impairing the body's ability to transport oxygen efficiently.

In conditions of high exposure to carbon monoxide, such as during smoking or in poorly ventilated spaces, carboxyhemoglobin formation can lead to symptoms ranging from mild headaches to life-threatening conditions.

• Formation: CO binding to hemoglobin
• Result: Decreased oxygen transport capacity
• Health effects: Impaired oxygen delivery