calculate the mass of air inside a 500 liter container at a pressure of 200 kpaa and temperature is 30 degree celsuis
To calculate the mass of air inside a container, you can use the ideal gas law equation:
PV = nRT
where:
P = pressure (in Pascals, Pa)
V = volume (in cubic meters, m³)
n = number of moles
R = universal gas constant (8.314 J/(mol·K))
T = temperature (in Kelvin, K)
First, let's convert the given values to the respective units.
Pressure:
1 kilopascal (kPa) = 1000 Pascal (Pa)
200 kpaa = 200 * 1000 Pa = 200,000 Pa
Volume:
1 liter = 0.001 cubic meters (m³)
500 liters = 500 * 0.001 m³ = 0.5 m³
Temperature:
Temperature in Kelvin (K) = Temperature in Celsius (°C) + 273.15
30 °C = 30 + 273.15 = 303.15 K
Now, let's substitute the values into the ideal gas law equation:
PV = nRT
200,000 Pa * 0.5 m³ = n * 8.314 J/(mol·K) * 303.15 K
Simplifying the equation:
100,000 Pa * m³ = n * 2515.6471 J/mol
To calculate the number of moles (n), we can rearrange the equation:
n = (100,000 Pa * m³) / (2515.6471 J/mol)
Next, we utilize the molar mass of air, which is approximately 28.97 g/mol.
To convert moles to mass, we can multiply the number of moles by the molar mass of air:
Mass = n * molar mass
Mass = [(100,000 Pa * m³) / (2515.6471 J/mol)] * 28.97 g/mol
Calculating the value will give you the mass of air inside the container at the given conditions.