Final answer:
To fill a 13.0×12.0×10.0 ft room with argon at 1 atm and 20°C, you would need approximately 1826 moles of argon, calculated using the ideal gas law and the conversion of room dimensions to liters.
Step-by-step explanation:
To determine the number of moles of argon needed to fill a room, we can use the ideal gas law, 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 temperature to Kelvin (20.0 °C = 293.15 K) and the dimensions of the room to cubic feet to liters, then calculate the volume of the room.
The room has dimensions of 13.0 × 12.0 × 10.0 ft, so its volume in cubic feet is 13.0 × 12.0 × 10.0 = 1560 cubic feet. Using the conversion factor 28.2 L/ft³, we can convert this to liters: 1560 ft³ × 28.2 L/ft³ = 44012 L.
Since the pressure is 1.00 atm and the temperature is 293.15 K, we can rearrange the ideal gas law to solve for the number of moles: n = PV / RT. Using the known values, including R = 0.0821 L·atm/mol·K, we calculate the number of moles of argon required:
n = (1.00 atm × 44012 L) / (0.0821 L·atm/mol·K × 293.15 K) ≈ 1826 moles of argon.
Therefore, to fill the room with argon at the given conditions, we would need approximately 1826 moles of argon.