Part A: Lavender Oil 

We will do a practice run of the math and concepts with lavender oil before tackling T.rex. (In Part B the lavender scent will represent a dinosaur's breath).

1. Put a drop of scent such as Lavender oil on a tissue in the corner of a room. Leave it for a couple of hours and go out of the room. When you return, can you smell the scent? The scent has spread throughout the room and into your nose. Just think how finely spread this drop is through all the air of the room.

One drop of lavender oil contains about 2 x 1020 molecules. 

That is 2 with twenty zeroes after it! or 200,000,000,000,000,000,000 molecules. A big bunch. 

2. Next we will see how this scent is spread throughout the room. (In part B, the room will represent the earth's atmosphere). We will assume the lavender spreads throughout a room sized 5 meters x 5 meters square by 4 meters high. The room air volume would be 5x5x4 = 100 cubic meters. We will convert this to liters because we can understand this amount better since, if we think of it, a giant soda bottle contains 2 liters. One cubic meter contains 1,000 liters by definition. 

So our standard room contains:

100 x 1,000 = 100,000 Liters or 1 x 105  liters

the number of lavender molecules for every liter is the number of lavender molecules divided by the volume of liters in the room:

3. Now we will see how many of these scent molecules enter your lungs when you breathe! (In part B this number will represent the amount of dino breath in your lungs).

In your lungs, each breath is about a half liter. This contains molecules of oxygen, nitrogen, carbon dioxide, water vapor, scent, pollution and a trace of other gases.

So we will divide the answer from item 2 by two to get 1 x 1015   which is 1,000,000,000,000,000 or one quadrillion molecules of lavender in each breath! 

Another way to say this is five thousand-million-million lavender molecules in each breath!

Part B: T.rex

We will apply this to our dinosaur.

1. A large T.rex dinosaur breathed about 10 breaths a minute and 3.5 liters each breath, more or less = 35 liters a minute.

Since each liter contains 25x1021 molecules of air, the dino breathed 35 x 25x1021 = 8.75 x 1023 molecules a minute.

These molecules spread all through the atmosphere after some time. The atmosphere contains 4 x 1018  liters.

So there are this many dino molecules from one minute's breath in one liter of atmosphere, assuming it stays there.

 so there are 2 x 105 molecules of T.rex's minute of breath per liter of air, or 200,000 molecules from a minute's breath.

3. Each of our own breath is about half liter, so divide this by two and get 1 x 105  molecules from T.rex

So in your lungs right now there are an estimated 100,000 molecules from one minute of T.rex breath.

4. But what about photosynthesis? Doesn't this transform the carbon dioxide that the T.rex exhaled into solid sugar, and remove T.rex  breath from getting back into our own lungs? Yes, as you saw in the Lego lesson, the atoms of carbon, oxygen, and hydrogen cycle between different molecules but do not disappear. Some are stored as a solid in plant matter: glucose and other substances. However, of these molecules, only about 10-15% of the carbon, hydrogen, and oxygen molecules from air ended up stored in woodland, coal, oil, and chalk. 

The important thing for the T.rex question is that most of the air we breathe in and out does not get used for cellular respiration, but just gets breathed out again without change. We breathe in 21% oxygen, and breathe out 16% oxygen. So we recycle most of the oxygen unchanged. As a result, over 85% of the free oxygen that ever existed in air from the first time it was produced by green bacteria is still in the atmosphere today. 

Because the size of the molecules of cellular respiration and photosynthesis are so very, very small, the exhaled molecules spread out evenly throughout all of the atmosphere. Over time, these molecules connect us to nearly all living organisms through our breath, including us to T. rex.