Question

The U. S. Environmental Protection Agency (EPA) sets limits on healthful levels of air pollutants. The maximum level that the EPA considers safe for lead air pollution is 1.5 μg/m³. If your lungs were filled with air containing this level of lead, how many lead atoms would be in your lungs? (Assume a total lung volume of 5.40 L .)

Answer 1

The number of lead atoms in the lungs at the EPA's maximum safe level of lead air pollution, convert the lung volume to cubic meters, find the mass of lead, convert to grams, convert mass to moles, and then use Avogadro's number to find the number of atoms, resulting in approximately 2.35 × 10^13 atoms.

Step-by-step explanation:

The student has asked about calculating the number of lead atoms in the lungs at the maximum safe level of lead air pollution set by the U.S. Environmental Protection Agency (EPA), which is 1.5 µg/m³. To solve this, we need to use the given lung volume of 5.40 L and convert that volume to cubic meters.


Next, we calculate the mass of lead in the total lung volume and then convert this mass to moles. Finally, we use Avogadro's number to find the number of atoms:

1. Convert lung volume from liters to cubic meters: 5.40 L × (1 m³ / 1000 L) = 0.0054 m³
   
2. Calculate the mass of lead in the lungs: 1.5 µg/m³ × 0.0054 m³ = 8.1 × 10-3 µg
   
3. Convert the mass of lead to grams: 8.1 × 10-3 µg × (1 g / 106 µg) = 8.1 × 10-9 g
   
4. Calculate moles of lead: 8.1 × 10-9 g / (207.2 g/mol) = 3.91 × 10-11 mol (using the atomic mass of lead)
   
5. Calculate the number of lead atoms: 3.91 × 10-11 mol × (6.022 × 1023 atoms/mol) = 2.35 × 1013 atoms

Therefore, if your lungs were filled with air at the EPA's maximum safe level for lead air pollution, there would be approximately 2.35 × 1013 lead atoms in your lungs.