The Misconception:

It is a common misconception that the very thick blanket of air covering the earth is mostly Oxygen, that the air we breathe in is just oxygen, and that the air we breathe out is just Carbon-dioxide.

The Truth:

In truth, the air we breathe is closer to 78% Nitrogen, 20% Oxygen and 2% other gases including Carbon-dioxide. When we exhale, this is changed to approximately 78% Nitrogen, 13-16% Oxygen, 4-6% Carbon-dioxide, and 1% other gases. The amount of Oxygen converted to Carbon-dioxide depends on physiological factors and duration of the breath (whether they were holding their breath or not).
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The content mixture of the gases really only changes for Oxygen and Carbon-dioxide. Also, the atmosphere is relatively very thin compared to the size of the earth.

The Source:

It is often analogized with fruit. Think of the Earth as an apple. The atmosphere is like the skin of the apple. However, this can easily be misinterpreted by people to think that like the skin it is on the outside of the fruit, but it must be very thick because the space is very far away from the Earth. (This starts to lead into another misconception about the Earth that this article will not delve into.)

Children's books, and descriptions of the process of breathing, talk about the oxygen required to live, how our lungs absorb the oxygen and we expel carbon-dioxide, and that other gases in the air make it hard to breathe. NASA has a children's picture book that includes these same tenets. It states, "giving animals, and you and me, the oxygen we need to breathe. More gases enter the atmosphere over time from the fuel we use to run our cars and heat our houses. Other gases come from a volcano's eruption or great forest fire, all giving off unhealthy gases that you and I don't want , or desire." All with the picture of a kid coughing because of all the things in the air that are not oxygen.

I think the root of the problem is oversimplification. As explained by Dr. Freudenrich, "You breathe in and out anywhere from 15 to 25 times per minute. Your lungs are complex organs, but what they do is take a gas that your body needs to get rid of (carbon dioxide) and exchange it for a gas that your body can use (oxygen)." This doesn't say anything about filtering out the other gases that are in the air, just that we need oxygen. He goes on to say, "The lungs and airways bring in fresh, oxygen-enriched air and get rid of waste carbon dioxide."

Even this interactive Info Lab at http://forces.si.edu/atmosphere/index.html seems to neglect the other gases in the air, although it does do a good job of showing what could happen with higher/lower mixtures of both oxygen and/or Carbon-dioxide.
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The Solution:

From a poll conducted on Facebook, this misconception is less prevalent among adults as it is with teenagers. 46% of respondents under the age of 14 agreed with this misconception, 38% of respondents between the ages of 15 and 18 agreed with this misconception, and only 17% of respondents above the age of 18 agreed with this misconception. This shows that as a person gets more education and can start to understand a more detailed description of the thin atmosphere surrounding the Earth, and the composition of it, but that there still persists a percentage of the population that does not understand these basic concepts.

Even though this is a misconception that has roots in the lives of every person alive every 2 to 4 seconds, it is not life-threatening to misunderstand what is in the air you breathe or how thick the atmosphere is. It is also fortunate that the education system already in place seems to root out the majority of the misinformation.