Final answer:
To determine the volume occupied by 88.2 lb of nitrogen (N₂) at 2464.6 psi and 324⁰R, we can use the ideal gas law equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Step-by-step explanation:
To determine the volume occupied by 88.2 lb of nitrogen (N₂) at 2464.6 psi and 324⁰R, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. First, we need to convert the pressure and temperature to the appropriate units. Since the given pressure is in psi, we need to convert it to atm by dividing it by 14.7. Similarly, we need to convert the temperature from Rankine to Kelvin by subtracting 459.67. Next, we need to calculate the number of moles of nitrogen in 88.2 lb. The molar mass of nitrogen is 28.0 g/mol, so we can convert the given mass to moles by dividing it by the molar mass. Finally, we can rearrange the ideal gas law equation to solve for the volume: V = (nRT) / P. Plugging in the converted values, the number of moles, and the gas constant (0.0821 L.atm.mol⁻¹K⁻¹), we can calculate the volume in m³.