Question

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?

Answer 1

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 %

Step-by-step 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