A 1.5-L container of liquid nitrogen is kept in a closet measuring 1.3 m by 1.3 m by 1.8 m.
Assuming that the container is completely full, that the temperature is 22.3 C, and that the atmospheric pressure is 1.2 atm , calculate the percent (by volume) of air that would be displaced if all of the liquid nitrogen evaporated. (Liquid nitrogen has a density of 0.807 g/mL.)
To calculate the percent volume of air that would be displaced if all of the liquid nitrogen evaporated, we first need to calculate the volume of liquid nitrogen and the volume of the closet.
Step 1: Calculate the volume of liquid nitrogen:
Given that the container has a volume of 1.5 L and a density of 0.807 g/mL, we can convert the volume to milliliters and then multiply by the density to get the mass of the liquid nitrogen.
Volume of liquid nitrogen = 1.5 L = 1500 mL
Mass of liquid nitrogen = Volume × Density = 1500 mL × 0.807 g/mL = 1210.5 g
Step 2: Calculate the volume of the closet:
The closet is in the shape of a rectangular prism with dimensions 1.3 m by 1.3 m by 1.8 m.
Volume of the closet = Length × Width × Height = 1.3 m × 1.3 m × 1.8 m = 3.0144 m^3
Step 3: Calculate the percentage of air displacement:
To calculate the percentage of air displacement, we need to compare the volume of the liquid nitrogen to the volume of the closet and then calculate the percentage as a fraction of the total volume.
Percentage of air displacement = (Volume of liquid nitrogen / Volume of the closet) × 100%
= (1210.5 g / 0.807 g/mL) / 3.0144 m^3 × 100%
= 1500 mL / (807 g/L × 1000 L/m^3) / 3.0144 m^3 × 100%
= 0.001861 L / 3.0144 m^3 × 100%
= 0.6149% (approximately)
Therefore, approximately 0.6149% of the air would be displaced if all of the liquid nitrogen evaporated.