Midnightwolf12
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Air is 21% oxygen by volume. Oxygen has a density of 1.31 g/L. What is the volume in liters of a room that holds enough air to contain 55kg of oxygen?

Respuesta :

Answer:

199,927.29 L is the volume air that holds enough air to contain 55 kg of oxygen.

Explanation:

Density of oxygen = 1.31 g/L

Mass of oxygen gas,m = 55 kg = 55,000 g

Volume of the oxygen gas = V

Volume of the air = [tex]V_a[/tex]

[tex]Density=\frac{Mass}{Volume}[/tex]

[tex]1.31 g/L=\frac{55,000 g}{V}[/tex]

V = 41.984.732 L

Air is 21% oxygen by volume.That is in 100 L of air 21 L of oxygen  is present.

So, when oxygen gas is 41.984.732 L the volume of the air will be:

[tex]21\%=\frac{41.984.732 L}{V_a}\times 100[/tex]

[tex]V_a=199,927.29 L[/tex]

199,927.29 L is the volume air that holds enough air to contain 55 kg of oxygen.

Eduard22sly

The volume of the room that can hold enough air containing 55 Kg of oxygen is 199927.29 L

We'll begin by converting 55 kg of oxygen to grams (g). This can be obtained as follow:

1 Kg = 1000 g

Therefore,

55 kg = 55 × 1000

55 Kg = 55000 g

Next, we shall determine the volume of oxygen. This can be obtained as follow:

Mass of oxygen = 55000 kg

Density of oxygen = 1.31 g/L

Volume of oxygen =?

[tex]Density = \frac{mass}{volume} \\\\1.31 = \frac{55000 }{volume}[/tex]

Cross multiply

1.31 × Volume = 55000

Divide both side by 1.31

Volume = 55000 / 1.31

Volume of oxygen = 41984.73 L

Finally, we shall determine the volume of the room by calculating the volume of air. This can be obtained as follow:

Volume of oxygen = 41984.73 L

Percentage of oxygen in air = 21%

Volume of air =?

[tex]Percentage of oxygen =\frac{volume of oxygen}{Volume of air} * 100[/tex]

21% = [tex]\frac{41984.73}{Volume of air}[/tex]

[tex]0.21 = \frac{41984.73}{Volume of air }[/tex]

Cross multiply

0.21 × Volume of air = 41984.73

Divide both side by 0.21

[tex]Volume of air = \frac{41984.73}{0.21}\\\\[/tex]

Volume of air = 199927.29 L

Therefore, we can conclude that the volume of the room that can hold enough air containing 55 Kg of oxygen is 199927.29 L

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