Question

Polluted air can have carbon monoxide (CO) levels of 15.0 ppm. An average human inhales about 0.50 L of air per breath and takes about 20 breaths per minute. How many milligrams of carbon monoxide dees the average person inhale in an 8 -hour period in this level of carbon monoxide pollution? Assume that the carbon monoxide has a density of 1.2 \(\mathrm{g} / \mathrm{L}\) .(Hint: 15.0 ppm CO means 15.0 \(\mathrm{L}\) \(\mathrm{CO} \operatorname{per} 10^{6} \mathrm{L}\) air. \()\)

Short answer

An average person inhales 86400 mg of carbon monoxide in an 8-hour period at 15.0 ppm CO level.

Step-by-step solution

Convert ppm to milligrams per breath

Since 15.0 ppm means 15.0 L of CO per 10^6 L of air and density of CO is 1.2 g/L, convert the volume of CO inhaled per breath into a mass. First, determine how much CO is inhaled per breath: 15.0 L CO / 10^6 L air * 0.50 L air/breath = 7.5 x 10^-3 L CO/breath. Then convert to grams using the density (1.2 g/L): 7.5 x 10^-3 L/breath * 1.2 g/L = 9.0 x 10^-3 g/breath. Finally, convert grams to milligrams: 9.0 x 10^-3 g/breath * 1000 mg/g = 9.0 mg/breath.

Calculate the total breaths in 8 hours

Calculate the total number of breaths taken in an 8-hour period. Since there are 60 minutes in an hour and 20 breaths per minute, the total breaths in 8 hours is: 8 hours * 60 minutes/hour * 20 breaths/minute = 9600 breaths.

Determine total milligrams of CO inhaled

Multiply the mass of CO inhaled per breath by the total number of breaths in 8 hours: 9.0 mg/breath * 9600 breaths = 86400 mg CO.

Key concepts

Parts Per Million (ppm)

When dealing with trace elements like pollutants in the air, we often use the measure 'parts per million' (ppm). This unit represents the ratio of the number of parts of a substance to a million parts of the total mixture or solution. In context, saying the air has 15.0 ppm of carbon monoxide (CO) means that for every million parts (units) of air, there are 15 parts of CO.

For example, if we imagine a container filled with a million tiny blocks, representing air, and we color 15 of those blocks red to represent CO, that coloring visually represents what 15.0 ppm means. This scale is commonly used because it can effectively communicate extremely low concentrations, which is essential when dealing with substances that are dangerous even in very small amounts.

Understanding ppm is crucial when we calculate the actual amount of a substance, like CO, someone might inhale, as demonstrated in the carbon monoxide inhalation calculation. Knowing how to convert ppm into a measurable quantity (milligrams, in our exercise) is an important skill in environmental health, chemistry, and various scientific analyses.

Chemical Density

Chemical density refers to the mass of a chemical per unit volume, typically expressed as grams per liter (g/L) in the metric system. For gases, density can vary with temperature and pressure, but standard conditions are often used for simplicity. In the case of carbon monoxide, the density is given as 1.2 g/L.

The knowledge of chemical density is essential when converting between volume and mass. It is an intrinsic property of a substance that can be used to identify compounds, compare their masses at a given volume, and calculate the amounts present in a mixture.

In our textbook solution, we used the given density of CO to convert the volume of CO that one would inhale per breath (in liters) to the mass of CO inhaled per breath (in grams). This is the crux of the calculation that leads to determining the total mass of CO inhaled over a set period, such as an 8-hour workday. Understanding how to apply density in stoichiometry and mixture problems is fundamental in chemistry and in applications concerning health and safety.

Stoichiometry

Stoichiometry is the section of chemistry that pertains to the calculation of the quantities of reactants and products in chemical reactions. However, stoichiometry is not limited to reactions; it also involves the quantitative relationships between substances in mixtures, as seen in our exercise.

In stoichiometry, we use balanced chemical equations to determine the amount of needed reactants or the quantity of expected products. However, in environmental applications like our exercise, we do not always have a chemical reaction. Instead, we might be dealing with the distribution of a chemical, such as CO, in the air. In such cases, we use stoichiometric principles to calculate the quantities involved—not through reaction balancing, but through unit conversions and proportional reasoning based on physical data (like ppm and density).

Inhale-exhale calculations, like the carbon monoxide inhalation calculation we explored, often rely on simple stoichiometry to estimate intake of a chemical based on its concentration (ppm) and other given conditions, such as breath volume, frequency of breaths, and time span. Guiding students through each conversion step, ensuring they understand the connections between units and the real-world implications, helps them master these calculations beyond merely following a formula.