Liquid nitrogen has a density of 0.808 g/mL and boils at 77 K. Researchers often purchase liquid nitrogen in insulated 185 L tanks. The liquid vaporizes quickly to gaseous nitrogen (which has a density of 1.15 g/mL at room temperature and atmospheric pressure) when the liquid is removed from the tank. Suppose that all 185 L of liquid nitrogen in a tank accidentally vaporized in a lab that measured 10.00 m times 10.00 m times 3.50 m.
Part A
What maximum fraction of the air in the room could be displaced by the gaseous nitrogen?

37.14 %

Explanation:

Using the equation, mass, M = D1 * V1

= D2 * V2

Where,

D1 = density of the liquid Nitrogen

D2 = density of gaseous Nitrogen

V1 = volume of the liquid Nitrogen

V2 = volume of the gaseous Nitrogen

Calculating V2,

0.808 * 185 = 1.15 * V2

Volume of Nitrogen after expansion = 129.98 m3.

Volume = L * b * h

= 10 * 10 * 3.5

Volume of the room = 350 m3.

Fraction of air = volume of Nitrogen after expansion/volume of the room * 100

= 129.98/350 *100

= 37.14 %

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