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?

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Midnightwolf12 Midnightwolf12

02-09-2017
Chemistry

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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?

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Tringa0 Tringa0 · Answer 1 · 2019-07-01T06:13:15+02:00

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 Eduard22sly · Answer 2 · 2021-09-17T16:11:42+02:00

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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