To determine the mass of nitrogen in a tank, we need to apply the ideal gas law. The ideal gas law equation is as follows:
PV = nRT
Where: P = Pressure V = Volume n = Number of moles R = Ideal gas constant T = Temperature
First, we need to convert the given temperature from Celsius to Kelvin: T = 21°C + 273.15 = 294.15 K
Next, we need to determine the number of moles of nitrogen. To do that, we need to rearrange the ideal gas law equation and solve for n:
n = PV / RT
P = 1 ATM V = 57 m³ R = 0.0821 L·atm/(mol·K) (ideal gas constant)
Converting the volume to liters: V = 57 m³ * 1000 L/m³ = 57000 L
Now, we can calculate the number of moles: n = (1 ATM) * (57000 L) / (0.0821 L·atm/(mol·K)) * (294.15 K)
n ≈ 2340.21 mol
Finally, to determine the mass of nitrogen, we need to multiply the number of moles by the molar mass of nitrogen. The molar mass of nitrogen is approximately 28.0134 g/mol.
Mass = n * molar mass Mass = 2340.21 mol * 28.0134 g/mol
Mass ≈ 65,463.19 g or 65.46 kg
Therefore, the mass of nitrogen contained in the 57 m³ tank, at a pressure of 1 ATM and a temperature of 21°C, is approximately 65.46 kg.