Liquid nitrogen has a density of 0.808 g/mL and boils at 77 K. Researchers often purchase liquid nitrogen in insulated 175 L tanks. The liquid vaporizes quickly to gaseous nitrogen (which has a density of 1.15 g/L at room temperature and atmospheric pressure) when the liquid is removed from the tank. Suppose that all 175 L of liquid nitrogen in a tank accidentally vaporized in a lab that measured 10.00 m * 10.00 m * 2.50 m. What maximum fraction of the air in the room could be displaced by the gaseous nitrogen?

Verified step by step guidance

1. Calculate the mass of liquid nitrogen using its density and volume: \( \text{mass} = \text{density} \times \text{volume} = 0.808 \, \text{g/mL} \times 175,000 \, \text{mL} \).
2. Convert the mass of liquid nitrogen to moles using the molar mass of nitrogen (N2), which is approximately 28.02 g/mol: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \).
3. Determine the volume of gaseous nitrogen at room temperature and atmospheric pressure using the ideal gas law: \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is moles, \( R \) is the ideal gas constant, and \( T \) is temperature in Kelvin.
4. Calculate the volume of the room: \( \text{volume} = 10.00 \, \text{m} \times 10.00 \, \text{m} \times 2.50 \, \text{m} \).
5. Determine the fraction of the room's air displaced by dividing the volume of gaseous nitrogen by the volume of the room.