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:

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

where:

L = length

W = Width

H = height

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?

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