Step-by-step explanation:
To find the number of oxygen molecules in a normal breath, we can use the ideal gas law equation, which relates the pressure, volume, temperature, and number of molecules of a gas:
PV = nRT
Where:
P = Pressure (in Pa)
V = Volume (in m³)
n = Number of moles
R = Ideal gas constant (8.314 J/(mol·K))
T = Temperature (in K)
First, let's calculate the number of moles of air inhaled during a normal breath:
V = 5.16 x 10^4 m³ (Volume of air inhaled)
P = 0.967 x 10^5 Pa (Pressure in the lungs)
R = 8.314 J/(mol·K) (Ideal gas constant)
T = 310 K (Temperature)
Rearranging the equation, we get:
n = PV / RT
n = (0.967 x 10^5 Pa) * (5.16 x 10^4 m³) / (8.314 J/(mol·K) * 310 K)
n ≈ 16.84 mol
Next, let's find the number of oxygen molecules inhaled. Since fresh air contains approximately 21% oxygen, we can multiply the number of moles by the fraction of oxygen in the air:
Number of oxygen molecules = n * (0.21)
Number of oxygen molecules ≈ 16.84 mol * 0.21
Number of oxygen molecules ≈ 3.54 mol
Finally, we'll convert the number of moles of oxygen molecules to the actual number of molecules by using Avogadro's number, which is approximately 6.022 x 10^23 molecules/mol:
Number of oxygen molecules = 3.54 mol * (6.022 x 10^23 molecules/mol)
Number of oxygen molecules ≈ 2.13 x 10^24 molecules
Therefore, in a normal breath, there are approximately 2.13 x 10^24 oxygen molecules.