One of the great defining principles of physics is that many of its most important properties unwaveringly obey an important principle: Under easily specified conditions, they are ​conserved​, meaning that the total amount of these quantities contained within the system you’ve chosen never changes.

Four common quantities in physics are characterized by having laws of conservation that apply to them. These are ​energy​, ​momentum​, ​angular momentum​ and ​mass​. The first three of these are quantities often specific to mechanics problems, but mass is universal, and the discovery – or demonstration, as it were – that mass is conserved, while confirming some long-held suspicions in the science world, was vital to prove.

The ​law of conservation of mass​ states that, in a ​closed system​ (including the whole universe), mass can neither be created nor destroyed by chemical or physical changes. In other words, ​total mass is always conserved​. The cheeky maxim "What goes in, must come out!" appears to be a literal scientific truism, as nothing has ever been shown to simply vanish with no physical trace.

All of the components of all of the molecules in every skin cell you've ever shed, with their oxygen, hydrogen, nitrogen, sulfur and carbon atoms, still exist. Just as the mystery science fiction show ​The X-Files​ declares about the truth, all mass that ever was "is out there ​somewhere​."

It could be called instead “the law of conservation of matter” because, absent gravity, there is nothing special in the world about especially “massive” objects; more on this important distinction follows, as its relevance is difficult to overstate.

The discovery of the law of conservation of mass was made in 1789 by the French scientist Antoine Lavoisier; others had come up with the idea before, but Lavoisier was first to prove it.

At the time, much of the prevailing belief in chemistry about atomic theory still came from the ancient Greeks, and thanks to more recent ideas, it was thought that something within fire ("​phlogiston​") was actually a substance. This, scientists reasoned, explained why a pile of ashes is lighter than whatever was burned to produce the ashes.

Lavoisier heated ​mercuric oxide​ and noted that the amount the chemical's weight decreased was equal to the weight of the oxygen gas released in the chemical reaction.

Before chemists could account for the masses of things that were difficult to track, such as water vapor and trace gases, they could not adequately test any matter conservation principles even if they suspected such laws were indeed in operation.

In any case, this led Lavoisier to state that matter must be conserved in chemical reactions, meaning the total amount of matter on each side of a chemical equation is the same. This means the total number of atoms (but not necessarily the total number of molecules) in the reactants must equal the amount in the products, regardless of the nature of the chemical change.

• "​The mass of the products in chemical equations is equal to the mass of the reactants​" is the basis of stoichiometry, or the accounting process by which chemical reactions and equations are mathematically balanced in terms of both mass and number of atoms on each side. 

One difficulty people can have with the law of conservation of mass is that the limits of your senses make some aspects of the law less intuitive.

For example, when you eat a pound of food and drink a pound of fluid, you might weigh the same six or so hours later even if you don’t go to the bathroom. This is in part because carbon compounds in food are converted to carbon dioxide (CO₂) and exhaled gradually in the (usually invisible) vapor in your breath.

At its core, as a chemistry concept, the law of conservation of mass is integral to understanding physical science, including physics. For instance, in a momentum problem about collision, we can assume the total mass in the system has not changed from what it was before the collision to something different after the collision because mass – like momentum and energy – is conserved.

The ​law of conservation of energy​ states that total energy of an isolated system never changes, and that can be expressed in a number of ways. One of these is KE (kinetic energy) + PE (potential energy) + internal energy (IE) = a constant. This law follows from the first law of thermodynamics and assures that energy, like mass, cannot be created or destroyed.

• The sum of KE and PE is called ​mechanical energy,​ and is constant in systems in which only conservative forces act (that is, when no energy is "wasted" in the form of frictional or heat losses).

​Momentum​ (m​v​) and ​angular momentum​ (​L​ = m​vr​) are also conserved in physics, and the relevant laws strongly determine much of the behavior of particles in classical analytical mechanics.

The heating of calcium carbonate, or CaCO₃, produces a calcium compound while liberating a mysterious gas. Let's say you have 1 kg (1,000 g) of CaCO₃, and you discover that when this is heated, 560 grams of the calcium compound remain.

What is the likely composition of the remaining calcium chemical substance, and what is the compound that was liberated as gas?

First, since this is essentially a chemistry problem, you'll need to refer to a periodic table of elements (see Resources for an example).

You are told that you have that initial 1,000 g of CaCO₃. From the molecular masses of the constituent atoms in the table, you see that Ca = 40 g/mol, C = 12 g/mol, and O = 16 g/mol, making the molecular mass of calcium carbonate as a whole 100 g/mol (remember there are three oxygen atoms in CaCO₃). However, you have 1,000 g of CaCO₃, which is 10 moles of the substance.

In this example, the calcium product has 10 moles of Ca atoms; because each Ca atom is 40 g/mol, you have 400 g total of Ca that you can safely assume was left after the CaCO₃ was heated. For this example, the remaining 160 g (560 – 400) of post-heating compound represents 10 moles of oxygen atoms. This must leave 440 g of mass as a liberated gas.

The balanced equation must have the form

and the "?" gas must contain carbon and oxygen in some combination; it must have 20 moles of oxygen atoms – you already have 10 moles of oxygen atoms to the left of the + sign – and therefore 10 moles of carbon atoms. The "?" is CO_2. (In today's science world, you have heard of carbon dioxide, making this problem something of a trivial exercise. But think to a time when even scientists didn't even know what was in "air.")

Physics students might be confused by the famous ​conservation of mass-energy equation​ ​E = mc​² postulated by Albert Einstein in the early 1900s, wondering if it defies the law of conservation of mass (or energy), since it seems to imply mass can be converted to energy and vice versa.

Neither law is violated; instead, the law affirms that mass and energy are actually different forms of the same thing.

It is kind of like measuring them in different units given the situation.

You perhaps cannot help but unconsciously equate mass with weight for the reasons described above – mass is only weight when gravity is in the mix, but when in your experience is gravity ​not​ present (when you're on Earth and not in a zero-gravity chamber)?

It is hard, then, to conceive of matter as just stuff, like energy in its own right, that obeys certain fundamental laws and principles.

Also, just as energy can change forms between kinetic, potential, electrical, thermal and other types, matter does the same thing, though the different forms of matter are called ​states​: solid, gas, liquid and plasma.

If you can filter how your own senses perceive the differences in these quantities, you might be able to appreciate that there are few actual differences in the physics.

Being able to tie major concepts together in the "hard sciences" may seem arduous at first, but it is always exciting and rewarding in the end.