Question

(a) Carbon monoxide (CO) is a poisonous gas because it binds very strongly to the oxygen carrier hemoglobin in blood. A concentration of \(8.00 \times 10^{2}\) ppm by volume of carbon monoxide is considered lethal to humans. Calculate the volume in liters occupied by carbon monoxide in a room that measures \(17.6 \mathrm{~m}\) long, \(8.80 \mathrm{~m}\) wide, and \(2.64 \mathrm{~m}\) high at this concentration.

Short answer

The volume occupied by carbon monoxide is 327.72 liters.

Step-by-step solution

Calculate the Volume of the Room

To find the volume of the room, use the formula for the volume of a rectangular prism: \( V = ext{length} \times ext{width} \times ext{height} \). Here, \( V = 17.6 \text{ m} \times 8.80 \text{ m} \times 2.64 \text{ m} \). This calculates to \( V = 409.6512 \text{ cubic meters} \).

Convert Room Volume to Liters

Since 1 cubic meter equals 1,000 liters, convert the room's volume from cubic meters to liters: \( 409.6512 \text{ m}^3 \times 1,000 \text{ L/m}^3 = 409,651.2 \text{ L} \).

Calculate the Volume of Carbon Monoxide

Use the ppm concentration to find the volume of CO. A concentration of 800 ppm means 800 liters of CO in every 1,000,000 liters of air. Therefore, calculate the CO volume using the proportion: \( \frac{800}{1,000,000} \times 409,651.2 \text{ L} \). This results in \( 327.72 \text{ L} \) of CO.

Key concepts

Carbon Monoxide

Carbon monoxide (CO) is a colorless and odorless gas, making it difficult to detect without proper sensors. It is a byproduct of the incomplete combustion of carbon-based fuels. Due to its properties, it can be especially dangerous in enclosed spaces. Despite its simple molecular structure, CO is a potent poison.

The main reason for its toxicity is its ability to readily bind with hemoglobin in the blood, which is the protein responsible for carrying oxygen throughout the body. When CO binds to hemoglobin, it forms a stable compound known as carboxyhemoglobin. This prevents hemoglobin from effectively releasing oxygen to body tissues, which can quickly lead to serious health complications and even death if exposure is high enough.

Volume Calculation

Volume calculation is crucial in understanding the distribution and potential impact of gases like carbon monoxide in a particular space. In the exercise you've seen, the volume of a room was calculated to determine how much carbon monoxide would accumulate at a hazardous concentration.

The calculation begins with finding the volume of the room using the formula: \[ V = ext{length} \times ext{width} \times ext{height} \]Given the dimensions of the room, this formula results in the total volume of the room in cubic meters. Once you have the room volume in cubic meters, it is typically converted to liters, as standard atmospheric gas concentrations, such as ppm, are often referenced in terms of liters. Since 1 cubic meter equals 1,000 liters, this conversion is straightforward.

Poisonous Gases

Poisonous gases like carbon monoxide pose significant risks due to their physical and chemical properties that cause harm at cellular levels. These gases can lead to severe outcomes when inhaled, primarily because they interfere with essential biological processes.

For carbon monoxide, the key danger is its hindrance of oxygen delivery in humans. It does so by binding to hemoglobin more strongly than oxygen does. Other poisonous gases may harm by damaging respiratory tissues, affecting neurological functions or disturbing other critical bodily functions.

• Effects can be subtle, like dizziness or headaches, which might be misdiagnosed or overlooked.
• More severe exposure can lead to unconsciousness and death, particularly in enclosed spaces where gas concentrations can rise quickly.
• Proper ventilation and the use of detectors can help mitigate these risks.

Hemoglobin Binding

Hemoglobin is a protein found in red blood cells responsible for transporting oxygen from the lungs to the rest of the body and returning carbon dioxide back to the lungs for exhalation. Its efficient function is critical to life.

When carbon monoxide is present, it competes with oxygen for binding sites on the hemoglobin molecule. CO binds to hemoglobin at the same site as oxygen, but with about 240 times greater affinity. This means if carbon monoxide is in the bloodstream, it will preferentially bind, reducing the capacity of hemoglobin to carry oxygen.

Understanding this mechanism is crucial in comprehending the danger posed by carbon monoxide. It not only explains the symptoms of poisoning but also highlights the need for immediate medical intervention in cases of suspected CO exposure. Treatments often involve providing high levels of oxygen to displace CO from hemoglobin, thereby restoring its ability to carry and supply oxygen to the body's cells.