A 1.5-L container of liquid nitrogen is kept in a closet measuring 1.2 m by 1.2 m by 1.8 m . Assume that the container is completely filled to the top with liquid nitrogen, that the temperature is 21.8 ∘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 into the closet. The closet is ventilated such that the temperature and pressure remain constant through this process. (Liquid nitrogen has a density of 0.807 g/mL.)
To find the percent (by volume) of air that would be displaced if all of the liquid nitrogen evaporated into the closet, we need to calculate the volume of liquid nitrogen and the volume of the closet.
First, let's find the volume of liquid nitrogen in the 1.5-L container. We are given that the density of liquid nitrogen is 0.807 g/mL.
Volume of liquid nitrogen = mass of liquid nitrogen / density of liquid nitrogen
The mass of liquid nitrogen can be calculated using the density and volume:
Mass of liquid nitrogen = density x volume of liquid nitrogen
Given that the volume is 1.5 L and the density is 0.807 g/mL:
Mass of liquid nitrogen = 0.807 g/mL x (1.5 L x 1000 mL/L)
= 0.807 g/mL x 1500 mL
= 1210.5 g
Now, let's calculate the volume of the closet. The dimensions of the closet are given as 1.2 m by 1.2 m by 1.8 m.
Volume of closet = length x width x height
= 1.2 m x 1.2 m x 1.8 m
= 2.59 m^3
Since we know the volume of the closet, we can now calculate the percent (by volume) of air that would be displaced if all the liquid nitrogen evaporated.
Percent (by volume) of air displaced = (Volume of liquid nitrogen / Volume of closet) x 100
Using the values we calculated:
Percent (by volume) of air displaced = (1.5 L / 2.59 m^3) x 100
= (1500 mL / 2.59 m^3) x 100
= 579.15 mL / m^3 x 100
Therefore, if all the liquid nitrogen evaporated into the closet, it would displace approximately 579.15 mL of air per cubic meter, expressed as a percentage.