The law of conservation of mass

Where does all this stuff come from? This rock? That cow? Your heart? Not the things themselves, mind you, but what they’re made of: the atoms that are the fabric of all things. To answer that question, we look to the law of conservation of mass. This law says take an isolated system defined by a boundary that matter and energy cannot cross. Inside this system, mass, a.k.a. matter and energy, can neither be created nor destroyed. The universe, to the best of our knowledge, is an isolated system.

But before we get to that, let’s look at a much smaller and simpler one. Here we have six carbon atoms, 12 hydrogen atoms, and 18 oxygen atoms. With a little energy, our molecules can really get moving. These atoms can bond together to form familiar molecules. Here’s water, and here’s carbon dioxide. We can’t create or destroy mass. We’re stuck with what we’ve got, so what can we do? Ah, they have a mind of their own. Let’s see. They’ve formed more carbon dioxide and water, six of each.

Add a little energy, and we can get them to reshuffle themselves to a simple sugar, and some oxygen gas. Our atoms are all accounted for: 6 carbon, 12 hydrogen, and 18 oxygen. The energy we applied is now stored in the bonds between atoms. We can rerelease that energy by breaking that sugar back into water and carbon dioxide, and still, same atoms. Let’s put a few of our atoms aside and try something a little more explosive. This here is methane, most commonly associated with cow flatulence, but also used for rocket fuel.

If we add some oxygen and a little bit of energy, like you might get from a lit match, it combusts into carbon dioxide, water and even more energy. Notice our methane started with four hydrogen, and at the end we still have four hydrogen captured in two water molecules. For a grand finale, here’s propane, another combustible gas. We add oxygen, light it up, and boom. More water and carbon dioxide.

This time we get three CO2s because the propane molecule started with three carbon atoms, and they have nowhere else to go. There are many other reactions we can model with this small set of atoms, and the law of conservation of mass always holds true. Whatever matter and energy go into a chemical reaction are present and accounted for when it’s complete. So if mass can’t be created or destroyed, where did these atoms come from in the first place? Let’s turn back the clock and see.

Further, further, further, too far. Okay, there it is. The Big Bang. Our hydrogen formed from a high-energy soup of particles in the three minutes that followed the birth of our universe. Eventually, clusters of atoms accumulated and formed stars. Within these stars, nuclear reactions fused light elements, such as hydrogen and helium, to form heavier elements, such as carbon and oxygen. At first glance, these reactions may look like they’re breaking the law because they release an astounding amount of energy, seemingly out of nowhere. However, thanks to Einstein’s famous equation, we know that energy is equivalent to mass.

It turns out that the total mass of the starting atoms is very slightly more than the mass of the products, and that loss of mass perfectly corresponds to the gain in energy, which radiates out from the star as light, heat and energetic particles. Eventually, this star went supernova and scattered its elements across space.

Long story short, they found each other and atoms from other supernovas, formed the Earth, and 4.6 billion years later got scooped up to play their parts in our little isolated system. But they’re not nearly as interesting as the atoms that came together to form you, or that cow, or this rock. And that is why, as Carl Sagan famously told us, we are all made of star stuff.

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