Problem 55 - Chemistry and Chemical Reactivity

Question

Hemoglobin (Hb) can form a complex with both \(\mathrm{O}_{2}\) and CO. For the reaction $$ \mathrm{HbO}_{2}(\mathrm{aq})+\mathrm{CO}(\mathrm{g}) \rightleftarrows \mathrm{HbCO}(\mathrm{aq})+\mathrm{O}_{2}(\mathrm{g}) $$ at body temperature, \(K\) is about \(200 .\) If the ratio \([\mathrm{HbCO}] /\left[\mathrm{HbO}_{2}\right]\) comes close to \(1,\) death is probable. What partial pressure of CO in the air is likely to be fatal? Assume the partial pressure of \(\mathrm{O}_{2}\) is \(0.20 \mathrm{atm}\).

Step-by-Step Solution

Answer

A partial pressure of CO around 0.001 atm is likely to be fatal.

Step 1: Understand the Chemical Equilibrium

The equilibrium reaction given is: \( \mathrm{HbO}_{2}(\mathrm{aq})+\mathrm{CO}(\mathrm{g}) \rightleftarrows \mathrm{HbCO}(\mathrm{aq})+\mathrm{O}_{2}(\mathrm{g}) \). The equilibrium constant \( K \) is defined as \( K = \frac{[\mathrm{HbCO}][\mathrm{O}_{2}]}{[\mathrm{HbO}_{2}][\mathrm{CO}]} \). Here, \( K = 200 \) at body temperature.

Step 2: Set Up the Expression for the Ratio

We are interested in the situation where the ratio \( \frac{[\mathrm{HbCO}]}{[\mathrm{HbO}_{2}]} \) approaches 1, which implies \([\mathrm{HbCO}] = [\mathrm{HbO}_{2}]\). Substitute this into our equilibrium constant expression: \( K = \frac{[\mathrm{HbO}_{2}][\mathrm{O}_{2}]}{[\mathrm{HbO}_{2}][\mathrm{CO}]} = \frac{[\mathrm{O}_{2}]}{[\mathrm{CO}]} \).

Step 3: Solve for the Partial Pressure of CO

Rearrange the equilibrium constant expression to solve for the partial pressure of CO: \( K = \frac{[\mathrm{O}_{2}]}{P_{\mathrm{CO}}} \rightarrow P_{\mathrm{CO}} = \frac{[\mathrm{O}_{2}]}{K} \). Substitute the known values: \( [\mathrm{O}_{2}] = 0.20 \text{ atm} \) and \( K = 200 \). Calculate to find \( P_{\mathrm{CO}} = \frac{0.20}{200} = 0.001 \text{ atm} \).

Step 4: Interpret the Result

The calculation indicates that a partial pressure of CO in the air of 0.001 atm can be fatal, assuming the critical condition where \( [\mathrm{HbCO}] = [\mathrm{HbO}_{2}] \) is met.

Key Concepts

Hemoglobin

Hemoglobin (Hb) is a crucial protein in your red blood cells. It helps transport oxygen from your lungs to other parts of your body. Hemoglobin can bind with different gases, including oxygen ( O_2 ) and carbon monoxide (CO).

Its ability to bind with these gases allows it to pick up oxygen in the lungs and deliver it to tissues. Conversely, it can also inadvertently bind with carbon monoxide. When hemoglobin combines with CO, a stable compound called carboxyhemoglobin (HbCO) forms, preventing oxygen transport.

• This binding is harmful because CO binds more tightly than oxygen.
• Even small amounts of CO can displace large amounts of oxygen, causing harmful effects.

Understanding how hemoglobin interacts with these gases helps us know the dangers of CO exposure.

Equilibrium Constant

The equilibrium constant (K) is a number that expresses the balance between products and reactants in a reversible chemical reaction. For hemoglobin's binding with CO and oxygen, the equation is:

\[K = \frac{[\text{HbCO}][\text{O}_{2}]}{[\text{HbO}_{2}][\text{CO}]}\]

Here, K gives us insight into the position of equilibrium:

• A high K value (like 200, as shown) indicates a strong tendency to form more products, in this case, HbCO and O_2.
• It tells us how favored one side of the reaction is compared to the other.

A clear understanding of the equilibrium constant helps predict the behavior under specific conditions.

Partial Pressure

Partial pressure refers to the pressure that a single gas in a mixture contributes to the total pressure. In our hemoglobin scenario, we are concerned with the partial pressure of CO and O_2 .

Partial pressures are crucial in determining how much of each gas will react or dissolve:

• The partial pressure of oxygen in the air is 0.20 atm, a standard condition for adequate oxygen transport.
• When the partial pressure of CO rises to 0.001 atm, it can severely impact oxygen binding with hemoglobin.

By understanding partial pressures, we can evaluate potential risks of gas exposure.

Oxygen

Oxygen ( O_2 ) is essential for metabolic processes in living organisms. In the context of hemoglobin, it binds with this protein to form oxyhemoglobin (HbO_2), carrying oxygen throughout the body.

However, competition with other gases like CO can hinder this process:

• Oxygen must maintain adequate partial pressure for effective transport.
• Lower levels of oxygen relative to CO in the bloodstream can be life-threatening.

Recognizing the role of oxygen in these reactions underlines the importance of maintaining clean air environments.