# Problem: Liquid nitrogen has a density of 0.808 g/mL and boils at 77 K. Researchers often purchase liquid nitrogen in insulated 177 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 177 L of liquid nitrogen in a tank accidentally vaporized in a lab that measured 12.00 m m 12.00 m imes 3.50 m .What maximum fraction of the air in the room could be displaced by the gaseous nitrogen?

🤓 Based on our data, we think this question is relevant for Professor Kidwell's class at HARPER COLLEGE.

###### FREE Expert Solution

We’re being asked to determine the maximum fraction of the air in the room could be displaced by the gaseous nitrogen given the room dimensions.

Recall that density is the ratio of the mass and volume of an object:

$\overline{){\mathbf{density}}{\mathbf{=}}\frac{\mathbf{mass}}{\mathbf{volume}}}$

Also, the volume of a rectangular prism is given by:

$\overline{){\mathbf{V}}{\mathbf{=}}{\mathbf{L}}{\mathbf{×}}{\mathbf{W}}{\mathbf{×}}{\mathbf{H}}}$

where:

L = length

W = Width

H = height

###### Problem Details

Liquid nitrogen has a density of 0.808 g/mL and boils at 77 K. Researchers often purchase liquid nitrogen in insulated 177 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 177 L of liquid nitrogen in a tank accidentally vaporized in a lab that measured 12.00 m m 12.00 m 3.50 m .

What maximum fraction of the air in the room could be displaced by the gaseous nitrogen?