Liquid nitrogen has a density of 0.808 g/mL and boils at 77 K. Researchers often purchase liquid nitrogen in insulated 195-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 195 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 bythe gaseous nitrogen?

The nswer to the question is

The maximum fraction of the air in the room that could be displaced by the gaseous nitrogen is 0.548 or 54.8 %

Explanation:

To solve the question we note that

The density of the liquid nitrogen = 0.808g/mL and the volume is 195 L tank (vaporised)

Therefore since density = mass/volume we have

mass = Density × volume = 0.808 g/mL × 195 L × 1000 ml/L =157560 g

In gaseous form the liquid nitrogen density =1.15 g/L

That is density = mass/volume and volume = mass/density = 157560 g/(1.15g/L)  or

volume = 137008.69565 L

The dimension of the room = 10 m × 10 m × 2.5 m = 250 m³ and

1 m³ is equivalent to 1000 L, therefore 250 m³ = 250 m³  × 1000 L/m³ = 250000L

Therefore fraction of the volume occupied by the gaseous nitrogen =

137008.69565 L/250000 L = 0.548

Therefore the gaseous nitrogen occpies 54.8% of the room