Question

Roughly \(4.00 \%\) of what you exhale is carbon dioxide. Assume that \(22.4 \mathrm{~L}\) is the volume of \(1 \mathrm{~mole}\left(6.02 \cdot 10^{23} \mathrm{~mole}-\right.\) cules) of carbon dioxide and that you exhale \(0.500 \mathrm{~L}\) per breath. a) Estimate how many carbon dioxide molecules you breathe out each day. b) If each mole of carbon dioxide has a mass of \(44.0 \mathrm{~g}\), how many kilograms of carbon dioxide do you exhale in a year?

Short answer

Answer a: To find the number of carbon dioxide molecules exhaled per day, follow steps 1-3 of the solution, and calculate CO2_molecules_per_day using the given information and formulas. Question b: What is the mass of carbon dioxide exhaled by an average adult in a year (in kg)? Answer b: To find the mass of CO2 exhaled per year in kg, follow steps 4-5 of the solution, and calculate mass_CO2_per_year_kg using the given information and formulas.

Step-by-step solution

Calculate the number of moles in 0.500 L of exhaled breath

We are given that 22.4 L of gas is 1 mole. To find the moles of gas in 0.500 L of exhaled breath, we can use the following formula: moles = (given volume) / (molar volume) moles = 0.500 L / 22.4 L/mol

Calculate the number of moles of CO2 in each breath

We know that 4% of the exhaled breath is carbon dioxide (CO2). So, multiply the total moles of exhaled breath by 4% to get the moles of CO2 in each breath. moles_CO2 = moles * 0.04

Calculate the number of CO2 molecules exhaled per day (Answer to question a)

We need to know how many breaths we take in a day. On average, an adult takes 12 to 20 breaths per minute. We'll take the average of 16 breaths per minute for this calculation. breaths_per_day = 16 breaths/minute * 60 minutes/hour * 24 hours/day Now, multiply the number of breaths per day by the moles of CO2 in each breath. Then, multiply it by Avogadro's number (6.02 x 10^23) to get the number of CO2 molecules exhaled per day. CO2_molecules_per_day = moles_CO2 * breaths_per_day * 6.02 x 10^23

Calculate the mass of CO2 exhaled per day

Given each mole of CO2 has a mass of 44.0 g, we can find the mass of CO2 exhaled per day by multiplying the moles of CO2 in each breath by the molar mass of CO2 (44.0 g/mol), and then the number of breaths per day. mass_CO2_per_day = moles_CO2 * 44.0 g/mol * breaths_per_day

Calculate the mass of CO2 exhaled per year (Answer to question b)

To find the mass of CO2 exhaled per year, multiply the mass of CO2 exhaled per day by the number of days in a year (365 days). mass_CO2_per_year = mass_CO2_per_day * 365 days/year Finally, convert the mass of CO2 per year to kilograms by dividing by 1000 g/kg: mass_CO2_per_year_kg = mass_CO2_per_year / 1000 g/kg

Key concepts

Mole Concept in Chemistry

The mole is a fundamental concept in chemistry that relates mass to the number of particles. It is defined as the amount of a substance containing the same number of entities (such as atoms, molecules, or ions) as there are atoms in 12 grams of carbon-12.

A mole is simply a unit of measurement used in chemistry to express amounts of a chemical substance, and it is one of the seven SI base units. When dealing with chemicals, it's not practical to count out individual atoms or molecules due to their miniscule size and large numbers. Therefore, the mole allows chemists to work with macroscopic amounts of substances while being able to relate it to the number of particles present.

For gaseous substances at standard temperature and pressure, one mole of any gas occupies 22.4 liters, known as the molar volume. This makes calculations involving gases more straightforward, as seen with the exhaled carbon dioxide calculation provided in the textbook exercise.

Avogadro's Number

Avogadro's number, approximately equal to \(6.02 \times 10^{23}\), is the number of units (atoms, molecules, ions, etc.) in one mole of a substance. Amadeo Avogadro, an Italian scientist, first proposed that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. This number is a dimensionless quantity and is used to convert between the number of atoms/molecules and moles.

When calculating the number of particles in a sample, you multiply the number of moles by Avogadro's number. This is a crucial step in problems like estimating the number of carbon dioxide molecules exhaled in a day, as shown in the exercise. Knowing Avogadro's number allows us to make sense of chemical reactions and quantities on a molecular level, linking the microscopic world to real-world, tangible quantities.

Stoichiometry in Respiratory Physiology

Stoichiometry is a section of chemistry that involves the calculation of relative quantities of reactants and products in chemical reactions. In respiratory physiology, this concept is used to measure the exchange of gases—such as oxygen intake and carbon dioxide expulsion—during breathing.

In the context of the exercise, we utilize stoichiometry to understand how much carbon dioxide is exhaled. Since only a certain percentage (4%) of our breath is carbon dioxide, stoichiometry helps us calculate the precise amount of CO2 being exhaled with each breath. This is relevant in medical and environmental studies, where the balance of oxygen and carbon dioxide is essential for health and is related to metabolic rates and respiratory health.

Gas Volume to Moles Conversion

Converting gas volume to moles is a common task in chemistry, particularly when dealing with gases at standard temperature and pressure (STP). As mentioned earlier, at STP, one mole of any gas occupies 22.4 liters. Using this knowledge, we can calculate the number of moles in a given volume of gas by dividing the volume of the gas by the molar volume (22.4 L/mol).

In the provided exercise, the calculation begins with the conversion of volume of exhaled breath to moles. This step is crucial because it allows us to work with moles, which can then be connected to the number of molecules using Avogadro's number, and ultimately to mass, which gives us a tangible understanding of the quantity of gas. This conversion underpins many calculations in various scientific fields, from chemistry and physics to environmental science and medicine.