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# Solution: Air is about 78.0% nitrogen molecules and 21.0% oxygen molecules. Several other gases make up the remaining 1% of air molecules. What is the partial pressure of nitrogen in air at atmospheric pressure (1.0 atm)?

###### Problem

Air is about 78.0% nitrogen molecules and 21.0% oxygen molecules. Several other gases make up the remaining 1% of air molecules. What is the partial pressure of nitrogen in air at atmospheric pressure (1.0 atm)?

###### Solution

We are asked to calculate the partial pressure of Nitrogen in the air at 1 atm.

Recall that Dalton's Law of Partial Pressure states that the total pressure of a mixture of gases can be defined as the sum of the pressures of each individual gas

$\overline{){{\mathbf{P}}}_{\mathbf{t}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}}{\mathbf{=}}{{\mathbf{P}}}_{{\mathbf{1}}}{\mathbf{+}}{{\mathbf{P}}}_{{\mathbf{2}}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{+}}{{\mathbf{P}}}_{{\mathbf{n}}}}$

Therefore, the partial pressure of an individual gas is equal to the total pressure multiplied by the mole fraction of that gas, as in:

$\overline{){{\mathbf{P}}}_{{\mathbf{i}}}{\mathbf{=}}{{\mathbf{P}}}_{\mathbf{t}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}}{{\mathbf{\chi }}}_{{\mathbf{1}}}}$

Where:

Pi = Partial Pressure of a gas = Partial Pressure of Nitrogen gas = unknown = x

PTotal= Total Pressure = 1 atm

Xi= mole fraction of a gas = mole fraction of Nitrogen

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