Question

The "Chemistry in Focus" segment Breath Fingerprinting discusses using breath analysis to diagnose diseases. The volume of the average human breath is approximately \(500 \mathrm{~mL}\), and carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) makes up \(4 \%\) of what we exhale. Determine the mass of carbon dioxide exhaled in an average human breath.

Short answer

The mass of CO2 exhaled in an average human breath can be calculated using the given information and the ideal gas law. The volume of CO2 in a breath is 500 mL × 0.04. Converting the volume and pressure to appropriate units and using the ideal gas law, we find the moles of CO2. Then, multiply the moles by the molar mass of CO2 (44.01 g/mol) to get the mass of CO2 in an average human breath.

Step-by-step solution

Calculate the volume of CO2 in a breath.

To calculate the volume of CO2 in a breath, we can simply use the given percentage and volume of the average human breath. Since CO2 makes up 4% of what we exhale, we can find the volume of CO2 by multiplying the volume of the breath (500 mL) by the percentage of CO2 (0.04). So, Volume of CO2 = 500 mL × 0.04

Convert the volume of CO2 to moles.

Now, we will use the ideal gas law to convert the volume of CO2 to moles. The ideal gas law is given as: PV = nRT where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (\(8.31 \mathrm{~J/(mol\cdot K)}\)), and T is the temperature in Kelvin. We will use standard atmospheric temperature and pressure conditions in this calculation. Assume that the pressure is 1 atm and the temperature is 298 K (approximately room temperature). First, we need to convert the pressure P from atm to Pa. Since 1 atm = 101325 Pa: P = 1 atm × 101325 Pa/atm ≈ 101325 Pa Next, we need to convert the volume V from mL to m³. Since 1 mL = 1 × 10⁻⁶ m³: V = 500 mL × 1 × 10⁻⁶ m³/mL = 5 × 10⁻⁴ m³ Now, we can solve the ideal gas law equation for n: \(n = \frac{PV}{RT}\) n = \(\frac{(101325 \mathrm{~Pa})(5 \times 10^{-4} \mathrm{~m^3})}{(8.31 \mathrm{~J/(mol\cdot K)})(298 \mathrm{~K})}\)

Convert moles of CO2 to mass.

To find the mass of the CO2 exhaled in a breath, we need to multiply the moles calculated in Step 2 by the molar mass of CO2. The molar mass of CO2 is approximately 44.01 g/mol. So, Mass of CO2 = n × molar mass of CO2 Mass of CO2 = n × 44.01 g/mol Now, plug in the value of n from Step 2 to get the mass of CO2 in an average human breath.

Key concepts

Breath Analysis

Breath analysis is a fascinating method used in medical diagnostics. It enables doctors to detect diseases simply by analyzing the composition of a person's breath. When you exhale, your breath contains various gases, including carbon dioxide, nitrogen, oxygen, and trace amounts of other compounds. Carbon dioxide is a significant player here, comprising about 4% of the exhaled air. This proportion is crucial since any deviation could indicate various respiratory or metabolic conditions. Researchers and scientists can understand your respiratory health by analyzing these gas levels.
Understanding the typical volume of human breath, which is approximately 500 mL, helps in calculating the concentration of different gases and diagnosing certain diseases. With breath analysis, non-invasive, quick assessments of a patient's health become possible, making it an invaluable tool in modern medicine.

Carbon Dioxide Chemistry

Carbon dioxide (CO$_2$) plays an essential role in both the respiratory process and Earth's ecological balance. It’s a gas that results from combustion in our bodies during cellular respiration—where cells convert glucose into energy. Every time we inhale and exhale, CO$_2$ that our cells produce is expelled from our lungs.
The chemistry of CO$_2$ within the atmosphere involves a delicate dance with other components. It's absorbed by plants during photosynthesis where it contributes to the life-supporting energy cycle. Importantly, it regulates Earth’s temperature through the greenhouse effect, retaining heat in our atmosphere. However, an excess of CO$_2$, due to human activities, has led to the critical challenge of climate change. Thus, understanding CO$_2$ chemistry is pivotal both in environmental science and in diagnostics using breath analysis.

Mole Calculation

Mole calculation involves using Avogadro’s law in chemistry, which relates the volume of a gas to the amount of substance in moles. In the context of the original exercise, to determine the number of moles of CO\(_2\) exhaled, we apply the ideal gas law: \( PV = nRT \). Here, each variable must be clearly defined:

• \(P\) is pressure, typically in Pascals (Pa).
• \(V\) is volume in cubic meters (m\(^3\)).
• \(n\) is the number of moles.
• \(R\) is the ideal gas constant, approximately \(8.31 \, \text{J/mol} \cdot \text{K}\).
• \(T\) is temperature, usually considered to be room temperature around 298 K.

Using this equation, we can find how many moles are present in a given volume of gas, providing a bridge between macroscopic gas volumes and microscopic particle quantities—allowing conversion from volume to moles simply and effectively.

Gas Volume Conversion

Gas volume conversion is a critical process when dealing with gases in different conditions, especially under varying pressures and temperatures. Standard conditions for temperature and pressure (STP) are often used, which are 273 K for temperature and 1 atm for pressure. However, room conditions (around 298 K and 1 atm) are more common in everyday situations.
To convert gas volumes from milliliters to cubic meters, you employ the conversion factor: 1 mL is equivalent to \(1 \times 10^{-6}\) m\(^3\). This conversion helps in the application of the ideal gas law, which operates in these units.
Understanding and accurately converting gas volumes allows precise calculations in chemistry, affecting everything from laboratory measurements to industrial applications. It ensures correct interpretations of chemical reactions and interactions, whether in a lab test or a real-world breath analysis scenario.