Step-by-step explanation:
To find the number of oxygen molecules in one alveoli, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in Pascal)
V = Volume (in cubic meters)
n = Number of moles
R = Ideal gas constant (in J/mol·K)
T = Temperature (in Kelvin)
First, we need to convert the radius of the alveoli from millimeters to meters:
Radius (m) = 0.125 mm = 0.125 × 10^(-3) m
Next, we need to find the volume of the alveoli using the formula for the volume of a sphere:
V = (4/3) * π * r^3
V = (4/3) * π * (0.125 × 10^(-3))^3
Now we can calculate the volume in cubic meters.
The pressure is given as 1.00 × 10^5 Pa.
The percentage of oxygen in the air inside the alveoli is 14%. We can calculate the number of moles of oxygen using the percentage and the molar mass of oxygen.
The molar mass of oxygen (O2) is approximately 32 g/mol.
Now we can calculate the number of moles of oxygen using the following formula:
n = (Percentage / 100) * (Mass of Air / Molar Mass of Oxygen)
First, we need to calculate the mass of air using the ideal gas law equation:
PV = nRT
Rearranging the equation, we find:
n = PV / RT
Here, we assume that the total pressure of the air inside the alveoli is due to oxygen only since it is the primary and most significant component.
Now let's plug in the values into the equations to calculate the number of oxygen molecules in one alveoli.
V = (4/3) * π * (0.125 × 10^(-3))^3
P = 1.00 × 10^5 Pa
R = 8.314 J/mol·K
T = 310 K
Percentage of oxygen = 14%
Molar mass of oxygen = 32 g/mol
1. Calculate the volume (V):
V = (4/3) * π * (0.125 × 10^(-3))^3
2. Calculate the mass of air (m):
m = (P * V) / (R * T)
3. Calculate the number of moles of oxygen (n):
n = (Percentage / 100) * (m / Molar mass of oxygen)
4. Calculate the number of oxygen molecules (N):
N = n * Avogadro's number (6.022 × 10^23)
Plug in the values and calculate N.