Question

Air is about 78.0% nitrogen molecules and 21.0% oxygen molecules. Several other gases make up the remaining 1% of air molecules.

Answer 1

The partial pressure of the component of a gas mixture is equal to the product of the total pressure and its molar ratio in the mixture. Assuming that the gas behaves as real, the partial pressure of nitrogen is 0.78 of 1 atm which is equal to 0.78 atm. 

Answer 2

The partial pressure of a gas in a mixture follow the equation: $P_i = x_i\cdot P_T$

In case of air, at a total pressure of 1 atm, the partial fraction of nitrogen is 0,78, because $x_i = \frac{78}{100} = 0,78$

The partial pressure of nitrogen will be:

$P_{N_2} = 0,78\cdot 1\ atm = \bf 0,78\ atm$