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 (by volume) of air that would be displaced if all of the liquid nitrogen evaporated, we need to find the volume of the liquid nitrogen, and then calculate the percentage it represents compared to the total volume of the closet.
First, we need to find the volume of the liquid nitrogen by multiplying its density by its volume:
Volume of liquid nitrogen = density × volume
= (0.807 g/mL) × 1.5 L
= 1.2115 g
Next, we need to convert this mass of liquid nitrogen into its volume using its density:
Volume of liquid nitrogen = mass / density
= 1.2115 g / (0.807 g/mL)
= 1.502 L
Now that we have the volume of the liquid nitrogen, we can calculate the percentage it represents compared to the total volume of the closet.
Volume of closet = length × width × height
= 1.3 m × 1.3 m × 1.8 m
= 3.654 m³
To convert the volume of the closet into liters, we multiply by 1000 (since 1 m³ = 1000 L):
Volume of closet = 3.654 m³ × 1000 L/m³
= 3654 L
Finally, we can calculate the percentage of air that would be displaced by dividing the volume of the liquid nitrogen by the total volume of the closet, and then multiplying by 100:
Percentage of air displaced = (Volume of liquid nitrogen / Volume of closet) × 100
= (1.502 L / 3654 L) × 100
≈ 0.0411 × 100
≈ 4.11%
Therefore, if all of the liquid nitrogen evaporated, approximately 4.11% of the air in the closet would be displaced.