Liquid nitrogen has a density of 0.808 g/mL and boils at 77 K. Researchers often

Question

Liquid nitrogen has a density of 0.808 g/mL and boils at 77 K. Researchers often purchase liquid nitrogen in insulated 201 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 201 L of liquid nitrogen in a tank accidentally vaporized in a lab that measured 11.00 m × 11.00 m × 3.50 m.

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

Explanation / Answer

mass of liquid N = volume * density of liq N
                  = (201000 mL) * (0.808)
                  =162408 g

when N vapourises , its mass doesn't change
mass of liquid N = mass of gaseous N

Volume of gas N =   mass of gaseous N /density of gaseous N
    = 162408/1.15
     = 141,224 L

Volume of room = 11*11*3.5 = 423.5 m^3
                        = 423.5*1000 L
                   

Fraction of room occupied = 141224 /(423.5*1000 )
                                       = 0.33

Answer: 0.33

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