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25 January, 00:30

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?

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  1. 25 January, 00:53
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    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 %

    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
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