At room temperature and atmospheric pressure, oxygen and carbon dioxide are both gasses. In fact, they are close to what scientists call ideal gasses.

Ideal gasses are much more easy to understand than non-ideal gasses. For ideal gasses, the density of the gas (the weight for a given volume--basically the heaviness) is directly proportional to the mass of an individual molecule.

For oxygen, a molecule consists of two oxygen atoms, and has a weight of 2 x 16 = 32. For carbon dioxide, there is one carbon atom (weight 12) and two oxygen atoms (mass 16 x 2) for a total of 44. This means that carbon dioxide should be about 44/32 = 1.375 times as heavy as an equivalent volume of oxygen.

In reality, oxygen gas has a density of 1.429 grams/liter at the so-called standard pressure and temperature (basically room temperature and atmospheric pressure) while carbon dioxide has a density of 1.977 grams/liter. If you do the math, you will find that carbon dioxide is 1.383 times as heavy as oxygen. This means that the "ideal gas model" is very good in this case.

Incidentally, if you cooled these gasses down and pressurized them until they liquefied (liquid oxygen is used as rocket fuel, liquid carbon dioxide is used to carbonate soft drinks) you would get a different answer. Liquid oxygen is actually heavier than liquid carbon dioxide by a little bit. 1.149 grams/ milliliter for liquid oxygen at its boiling point versus 1.101 grams/ milliliter for liquid carbon dioxide.

If you cool even more and get solid oxygen and carbon dioxide, you would find that carbon dioxide is slightly heavier than a similar volume of solid oxygen. Solid carbon dioxide is also known as dry ice, and is used to keep thing cold when ordinary ice is not good enough.

What you are really interested is the density of the gas, rather than the weight. For most gases at atmospheric pressure, a given volume contains the same number of molecules at a given temperature. This is known as the ideal gas law. The density (or how "heavy") something is depends on the amount of mass per volume - a pound of lead and a pound of feathers has the same mass, but take up quite different volumes, and hence have quite different densities, with the leak having a high density (heavy) and the feathers having a low density (light).

For an ideal gas, the density is just the molecular weight of the gas, divided by the volume of a given number of molecules. Since a given number of molecules always takes up the same volume for a gas, the higher the molecular weight, the "heavier" the gas is, or the higher the density. Carbon dioxide has one carbon atom and two oxygen atoms, and a molecular weight of 44 grams per mole ( a certain number of molecules). The oxygen in the air is actually O₂, or molecular oxygen, with a molecular weight of 32. Hence, carbon dioxide has a higher density, or is heavier than oxygen. That is why you need to be careful with carbon dioxide. It can displace the oxygen in a room and lead to asphyxiation.

Carbon has an atomic weight of 12, oxygen in diatomic form(O₂) of 32 and CO₂ of 44. This means that the mass of 6x10²³ atoms of CARBON has a mass of 6 kilograms, the mass of 6x10²³ diatomic oxygen molecules is 32 kg, and for CO₂ it is 44kg. So carbon is the lightest and CO₂ the heaviest.

Well, what makes up oxygen gas? Oxygen gas is made up of two oxygen atoms stuck together. That's why you'll sometimes see O₂ when they mean oxygen (get it...two oxygens). Anyway, carbon dioxide is made up of two oxygen atoms and a carbon atom. So, which do you think is heavier?

The answer is carbon dioxide.

Bonus question: How much heavier is carbon dioxide than oxygen?

Well, oxygen molecules have two oxygen atoms. Carbon dioxide molecules have two oxygen atoms plus one carbon atom. So, which molecule do you think is heavier?

Oxygen has an atomic mass of 16 gram per mole. The gas oxygen that is in the "air" has the formula O₂. That means that there are two atoms of oxygen. The formula for carbon dioxide is CO₂, that means one atom of carbon and two atoms of oxygen. The atomic mass of carbon is 12 grams per mole.

So one mole of O₂ weights : 2 x 16 = 32 grams

One mole of carbon dioxide : 12 + (2 x 16) = 44 grams.

Which one is heavier?

I am going to help you answer this one for yourself. All gasses (like oxygen and carbon dioxide) have about the same number of molecules in, lets say a gallon of air. So the difference in weight of the gasses is in proportion to the difference in weight of the individual molecules.

Now, the each oxygen molecule has two oxygen atoms. Each carbon dioxide molecule has two oxygen atoms and one carbon atom. Even without knowing the weight of these atoms, can you tell now: which will be heavier? Write back with your answer!

That is an interesting question. Once, when I was at the Exploratorium, a science museum in San Francisco, I saw a great exhibit that actually answered your question perfectly! The exhibit had you blow a single soap bubble into a large tub with dry ice at the bottom. The soap bubble sank towards the bottom of the tub at first, as you would expect, but instead of hitting the bottom and popping, the bubble gradually stopped falling and finally sat suspended in the air! Dry ice gives off carbon dioxide gas, and so there was a thick layer of carbon dioxide in the bottom of the tub.

Because carbon dioxide is heavier than air, and the bubble was made of air, the bubble actually floated above the carbon dioxide layer because it was lighter. Eventually, the chill from the dry ice froze the soap on the surface of the bubble and the bubble sank to the bottom of the tub and stayed there, a perfect sphere of hollow ice.

If you've ever seen the smoke that comes off of dry ice, you probably already knew the answer to your question, as that "smoke" is actually carbon dioxide gas mixed with water vapor, and tends to "sink" and collect on the floor or on counter tops until it mixes with the air and disperses.

Here's an exercise: the chemical formula for molecular oxygen (the kind found in the atmosphere and which we breathe) is two oxygen atoms bound together (two atoms total), while the chemical formula for carbon dioxide is one carbon atom plus two oxygen atoms bound together (3 atoms total). If a carbon atoms weighs 12 atomic mass units, and oxygen atoms each weigh 16 atomic mass units, how much heavier is carbon dioxide than molecular oxygen?