Question

Carbon monoxide competes with oxygen for binding sites on the transport protein hemoglobin. CO can be poisonous if inhaled in large quantities. A safe level of CO in air is \(50 .\) parts per million (ppm). When the CO level increases to \(800 .\) ppm, dizziness, nausea, and unconsciousness occur, followed by death. Assuming the partial pressure of oxygen in air at sea level is 0.20 at \(m\), what proportion of \(\mathrm{CO}\) to \(\mathrm{O}_{2}\) is fatal?

Short answer

The fatal proportion of CO to O2 is 4 parts of CO to 1,000 parts of O2.

Step-by-step solution

Find the partial pressure of CO at safe and fatal levels

First, we will determine the partial pressure of CO at both the safe level (50 ppm) and the fatal level (800 ppm). Since there are 1,000,000 parts per million, the safe level of CO in air is 50 parts per million (ppm) and the fatal level is 800 ppm. Let's calculate the partial pressures for these levels: Safe level: \(\frac{50}{1,000,000}\) Fatal level: \(\frac{800}{1,000,000}\) Now, let's find the partial pressures for safe and fatal levels.

Calculate partial pressures for safe and fatal levels

To calculate the partial pressures for the safe and fatal levels, we can use the following formula: Partial pressure = (total pressure) * (mole fraction) In this problem, the total pressure is not given, but as we are only interested in the ratio of partial pressures, the total pressure in the calculation ultimately cancels out, thus we can leave it out from our calculation. Safe level partial pressure of CO: \(\frac{50}{1,000,000}\) Fatal level partial pressure of CO: \(\frac{800}{1,000,000}\) Now we know the partial pressures of CO at safe and fatal levels.

Calculate the ratio of CO to O2 at fatal level

Now we should calculate the ratio of CO to O2 at the fatal level: Fatal ratio of CO to O2 = \(\frac{\text{Fatal level partial pressure of CO}}{\text{Partial pressure of O2}}\)

Calculate the proportion of CO to O2 that is fatal

Now, we have the information we need to calculate the fatal proportion of CO to O2: Fatal proportion of CO to O2 = \(\frac{800}{1,000,000}\) / \(0.2\)

Simplify the proportion

Lastly, we simplify the proportion: Fatal proportion of CO to O2 = \(\frac{800}{1,000,000*0.2}\) = \(\frac{800}{200,000}\) = \(\frac{4}{1,000}\) Therefore, the fatal proportion of CO to O2 is 4 parts of CO to 1,000 parts of O2.

Key concepts

Hemoglobin Oxygen Binding

Hemoglobin is a crucial protein in red blood cells responsible for carrying oxygen from the lungs to the rest of the body and returning carbon dioxide to the lungs for exhalation. Each hemoglobin molecule can bind to four oxygen molecules. However, carbon monoxide (CO) competes with oxygen for the same binding sites on hemoglobin. CO has a much greater affinity for hemoglobin than oxygen does – about 200 to 250 times greater. This means that even small amounts of CO can significantly reduce the ability of hemoglobin to deliver oxygen to where it's needed. This is why CO is such a dangerous gas; it deprives body tissues and organs of oxygen, leading to serious health effects or even death.

When studying the impact of CO on hemoglobin, one must understand that hemoglobin's affinity for CO can dramatically alter oxygen transportation. In cases of CO poisoning, the binding of CO to hemoglobin forms carboxyhemoglobin, which not only reduces oxygen supply but can also lead to a change in the shape of the hemoglobin molecule, further diminishing its oxygen-carrying capacity.

Partial Pressure Calculation

In the context of gases, the term 'partial pressure' refers to the pressure that a single gas component in a mixture of gases would exert if it alone occupied the entire volume. Partial pressure is an important concept in gas exchange because it helps predict the movement of gases. Gases tend to move from areas of higher partial pressure to areas of lower partial pressure. The partial pressure of a gas can be calculated by multiplying the total pressure of the gas mixture by the mole fraction of the gas in question.

For the fatal level of CO in our original problem, we calculated the partial pressure based on its concentration in parts per million, and then compared this to the known partial pressure of oxygen in air at sea level. Understanding these calculations is crucial when assessing the risks posed by different levels of gases like CO and determining the safe exposure limits.

Mole Fraction

The mole fraction is a way to express the concentration of a component in a mixture, and it is defined as the number of moles of a component divided by the total number of moles of all components in the mixture. It is a dimensionless number that provides a ratio of one substance's presence compared to the entirety of the mixture. This measurement is particularly useful when dealing with gas mixtures because it directly relates to partial pressures.

The mole fraction is critical when calculating the partial pressure, as seen in our exercise, where the mole fraction of CO at a fatal level is used to calculate its partial pressure. By understanding the mole fraction, students and scientists can predict how gases will behave under different conditions, such as when they are mixed or when the pressure changes.

Toxicity Levels

Toxicity levels of substances like carbon monoxide are measures of the concentration at which a substance can cause harm or death. These levels are determined by various factors, including the substance's potency, the route of exposure, the duration of exposure, and individual susceptibility. In the case of CO, toxicity is related to its ability to bind with hemoglobin and reduce oxygen transport, which can lead to tissue hypoxia and potentially fatal outcomes.

Different toxicity levels can be expressed as safe, tolerable, dangerous, and lethal concentrations. For CO, a safe level for indoor air is generally accepted to be below 50 parts per million (ppm). As levels increase, adverse health effects become more severe. At around 800 ppm, symptoms like dizziness and nausea can escalate to unconsciousness and death. It is essential to understand these toxicity levels for safety and health regulations, as well as for medical diagnostics and treatment in cases of suspected poisoning.