To calculate the number of moles of air in the given volume, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atmospheres)
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 dimensions from meters to liters:
Volume = 10 m × 10 m × 60 m = 6000 m³ = 6000000 liters
Next, we convert the temperature from 0°C to Kelvin:
T = 0°C + 273.15 = 273.15 K
Assuming the pressure is at one atmosphere (1 atm), we can substitute the values into the equation and solve for n:
1 atm × 6000000 L = n × 0.0821 L·atm/(mol·K) × 273.15 K
6000000 = 22.41415n
n = 6000000 / 22.41415
n ≈ 267987.12 moles
Therefore, approximately 267987.12 moles of air fill the given volume at one atmosphere and 0°C.