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To lower the chance of suffering from decompression sickness (the bends), scuba divers use a mixture of gases in their air tank (typically oxygen and nitrogen gas in recreational dives). Assuming no other gas is present besides oxygen and nitrogen, if the mole fraction of oxygen present is 0.21, what is the partial pressure of nitrogen gas if the total pressure is 111.7 atm

Respuesta :

Answer: The partial pressure of nitrogen gas if the total pressure is 111.7 atm is 88.243 atm.

Explanation:

Given: Mole fraction of oxygen = 0.21

Total pressure = 111.7 atm

It is known that the sum of moles fractions is always equal to 1. So, mole fraction of nitrogen is calculated as follows.

Mole fraction of nitrogen + mole fraction of oxygen = 1

Mole fraction of nitrogen = 1 - mole fraction of oxygen

Mole fraction of nitrogen = 1 - 0.21

Mole fraction of nitrogen = 0.79

Now, formula used to calculate the partial pressure of nitrogen is as follows.

[tex]P_{N} = X_{N} \times P_{total}[/tex]

where,

[tex]P_{N}[/tex] = partial pressure of nitrogen

[tex]X_{N}[/tex] = mole fraction of nitrogen

[tex]P_{total}[/tex] = total pressure

Substitute the values into above formula as follows.

[tex]P_{N} = X_{N} \times P_{total}\\= 0.79 \times 111.7 atm\\= 88.243 atm[/tex]

Thus, we can conclude that the partial pressure of nitrogen gas if the total pressure is 111.7 atm is 88.243 atm.

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