Food for thought

If you don't eat enough, you lose weight. Assuming you're hanging around the surface of the Earth, losing weight means you're losing mass.

Where does it go?

Many of my students (and many adults) think that the food (mass) gets converted to energy, and that explains the weight loss. While this does happen--the sun's light comes from fusion--we would not survive long if we were nuclear furnaces.

So where does it go?

High school science mostly exists in a Newtonian universe, and that's as it should be. While e = mc2 has become a cultural icon, you really don't need to know much about it in biology, except to know that's how the sun has managed to bathe us with the energy needed for life for over 4 billion years.

(There are huge reasons to know the consequences of our knowledge, but the consequences are far more easily grasped than the physics behind it.)

I announce first day of class that in Room B362, we live in a Newtonian universe. The amount of mass, or stuff, in a closed system (nothing gets in, nothing gets out) stays the same. Forever.

This is a big deal, the heart of chemistry--despite all the fizzing and hissing and heat and bubbling and light--when all is said and done, you have exactly the same amount of stuff at the end of a reaction that you started with. The stuff has different qualities--but the total amount of stuff stays the same.

A child may rationally think, Ah, well, it's easy--we poop! Except for a squirt or two of bile, though, what you poop is mostly the stuff you couldn't digest--stuff that never got inside of you beyond traveling through the open tube between your mouth and you anus. A lot of this stuff is digested by bacteria partying in your gut--they grow and reproduce, but the stuff of bacteria ultimately comes from the stuff that never truly enters you.

If you don't eat, and if you carefully weigh your stool each day, the total weight of you and your stool will still go down.

Where did the missing mass go?

A gallon of gasoline weighs just over 6 pounds. The carbon dioxide produced from a gallon of gasoline weighs around 3 times as much! How is this possible?

When you burn something, you are adding oxygen to fuel, and rearranging the atoms of both. In a clean burn, you end up with just water and carbon dioxide. Gasoline is made up of multiple compounds, about a fifth of it is octane ("oct-" means 8 carbons, "-ane" means all single bonds):

2C8H18 + 25O2 -> 16CO2 + 18H20

Gasoline compounds have no oxygen atoms--they are added during combustion. Every carbon atom ends up combined with oxygen has mass.

The energy released was energy "held" by electron arrangements in the gasoline--the electrons are in different configurations but they are exactly the same otherwise. (A ball on a table is exactly the same as a ball on the floor, but the ball on the table has more potential energy.)

Energy had to be put into the system to get the electrons in their high energy configurations--which is what plants do with sunlight using water and carbon dioxide, essentially the reverse of combustion. When you burn gasoline, you are releasing the energy that was transformed from ancient sunlight.

It seems as though the gasoline has less mass after we burn it, since all we see is a tiny bit of water trickling out the tail pipe. Just about all the exhaust today is invisible water vapor and carbon dioxide. For whatever reason, most of us do not think of invisible gasses as having any mass.

So where does the carbon in gasoline go? Through the exhaust and into the air. It's as real as solid oak, but we do not perceive it as such.

For most of us, the tank was full, we drove around, and now the tank is empty. We infer, incorrectly, that the gasoline "disappeared." It did not--it merely transformed when combined with oxygen.

So what about food?

Breathe on your hand, what comes out? CO2 and water vapor. (OK, mostly nitrogen, then unconsumed oxygen, a smidgeon of argon, and then carbon dioxide, but certainly more carbon dioxide than what you breathed in.)  The same stuff spewed out by your ULEV car engine.

If you are starving, that carbon came from, well, you. You are breathing out particles of yourself, particles released as you combined pieces of yourself with oxygen to allow electrons to settle down into more comfortable positions, releasing energy as they did so,

Yes, I know, your nitrogen gets converted to urea, and urea as well as ketones can be peed out. I'll save that part for AP Biology class.

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