A person takes a breath as deep as possible by exhaling as far as possible (leaving a volume of 1.170 L in their lungs), and then slowly inhaling to increase their lung volume by 4.580 L. His body temperature is also 37.64 ¡ãC.
(i)How many particles of air do their lungs contain after inhaling?
To calculate the number of particles of air in the person's lungs after inhaling, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atm
V = volume in liters
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature in Kelvin
First, let's convert the given temperature from Celsius to Kelvin:
T = 37.64 °C + 273.15 = 310.79 K
Now, let's calculate the number of moles of air in the person's lungs before inhaling:
Using PV = nRT, we have:
(1 atm) * (1.170 L) = n * (0.0821 L.atm/mol.K) * (310.79 K)
Simplifying the equation:
1.170 = n * 25.516759
Now, solve for n:
n = 1.170 / 25.516759
n ≈ 0.045815 mol
Therefore, the person's lungs initially contain approximately 0.045815 moles of air.
Now, let's calculate the number of moles of air in the person's lungs after inhaling:
(1 atm) * (1.170 L + 4.580 L) = n' * (0.0821 L.atm/mol.K) * (310.79 K)
Simplifying the equation:
5.750 = n' * 25.516759
Now, solve for n':
n' = 5.750 / 25.516759
n' ≈ 0.225593 mol
Therefore, the person's lungs contain approximately 0.225593 moles of air after inhaling.
To convert moles to the number of particles, we can use Avogadro's number, which is 6.02214 x 10^23 particles/mol.
Number of particles = n' * (6.02214 x 10^23)
Plugging in the value of n' we calculated:
Number of particles ≈ 0.225593 mol * (6.02214 x 10^23)
Number of particles ≈ 1.35803 x 10^23 particles
Thus, the person's lungs contain approximately 1.35803 x 10^23 particles of air after inhaling.