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)?

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: 

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

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

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

Where:

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

P_Total= Total Pressure = 1 atm

X_i= mole fraction of a gas = mole fraction of Nitrogen