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)?

Dec 2, 2015

$\text{0.78 atm}$

Explanation:

As you know, the partial pressure exerted by a gas that's part of a gaseous mixture depends on two things

• the total pressure of the mixture
• the mole fraction of that gas

Your equation will look like this

color(blue)(P_"gas" = chi_"gas" xx P_"total")" ", where

${P}_{\text{gas}}$ - the partial pressure of a gas
${\chi}_{\text{gas}}$ - the mole fraction of that gas
${P}_{\text{total}}$ - the total pressure of the mixture

In this case, you know that the total pressure of the mixture is equal to $\text{1.0 atm}$. Now, in order to find a gas' mole fraction, you need to know

• the number of moles of that gas present in the mixture
• the total number of moles present in the mixture

You don't know exactly how many moles of the mixture you have, but you do know one important thing.

More specifically, you know that 78.0% of all the molecules present in the mixture are nitrogen molecules, 21.0% are oxygen molecules, and 1% are molecules of other gases.

As you know, a mole is simply a very large collection of molecules. In order to have one mole of a substance, you need to have $6.022 \cdot {10}^{23}$ molecules of that substance.

This means that the actual number of moles is not important here, because the ratio that exists between the number of molecules is equivalent to the ratio that exists between the number of moles.

So, if you have $100$ moles of air, you know that $78$ will be moles of nitrogen, $21$ will be moles of oxygen, and $1$ mole will be other gases.

So, let's say that you have $x$ moles of gas. You can say that the mole fraction of nitrogen will be

chi_(N_2) = ("number of moles of N"_2)/"total number of moles"

The number of moles of nitrogen will be

x color(red)(cancel(color(black)("moles air"))) * "78 moles of N"_2/(100color(red)(cancel(color(black)("moles air")))) = 78/100x" moles N"_2

The partial pressure of nitrogen will thus be

P_(N_2) = 78/100 * "1.0 atm" = color(green)("0.78 atm")