Liquid nitrogen has a density of 0.808 g/mL and boils at 77 K

Question: 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 for the tank. Suppose that all 175 L of liquid in a tank accidentally vaporized in lab that measured 10.00 m x 10.00 m x 2.50 m. What maximum fraction of the air in the room is displaced by the gaseous nitrogen?

First you want to convert the given information to the same measurements. 175 L of liquid nitrogen equals 175000 mL.

In order to find the mass you multiply the density of the liquid nitrogen (0.808 g/mL) by the volume of the tank (175000mL) which equates to 141400 g.

After vaporization:

Plug in the given: density (1.15 g/L) multiplied by the mass (141400g) equals to the volume of 122956 g/L.

In order to find the measurement of the room you multiply the three numbers which equals 250 cm³   then multiply it by 1000 L/m to get 250000.

Then you take the volume (122956 g/L) and divide it by 250000 to get 0.492 which approximates to 49% is the fraction of the air that is displaced.