FMA and Chemistry- Equivalent Exchange Stoicheometry


            Fullmetal Alchemist is one of the greatest manga/anime ever made. One of the reasons for this greatness is how consistent the world is, especially when it comes to one of the center points of the story: Alchemy and how it works. Alchemy was a scientific discipline at one point in history; Isaac Newton believed and wrote several papers on alchemy. It was eventually eclipsed by chemistry because chemistry was able to make better predictions.


While the alchemy in Fullmetal Alchemist does not completely line up with the historical alchemy, some of its principles line up with modern chemistry. One of these principles is arguably the most important; the Law of Equivalent Exchange. This law states that to obtain something, something of equal value must be lost. Or in more precise terms, your end product has to have the same mass as your starting materials. Lets demonstrate this with a simple example from Fullmetal Alchemist. In Chapter 38 of the manga, Roy Mustang demonstrates the ability to split water into its base elements, Hydrogen (H2) and Oxygen (O2). So the chemical formula for this reaction would be:

H2O → H2 + O2

            Already we can see a problem with this, since there is one oxygen on one side of the equation, (which are called the reactants or reactant) and 2 oxygen on the other side, (which are called the products). We must then change the number of molecules on one or both sides to make sure we have the same number of atoms on both sides of the equation.

Since we have more Hydrogen atoms than we do Oxygen, lets balance the Oxygen first. If we have 2 water molecules as reactants, then Oxygen will be balanced

2H2O → H2 + O2

            So now we have the oxygen balanced but not the hydrogen. The simplest way to balance the hydrogen is to add another hydrogen molecule so that we have 4 Hydrogen atoms on each side.

2H2O → 2H2 + O2

            This method also works on more complex equations as well. Just make sure to start by balancing the least represented element, and work your way up to the most represented element. Now that the equation is balanced it is more useful to us.

            Now, if Roy knows how much hydrogen gas he wants, he can figure out how much water he needs.

Chem Photo1

The equation shows that for every 2 molecules of water, we would get 2 molecules of hydrogen and one molecule of oxygen. The practical problem is that you can’t directly measure the number of molecules of a substance. However, mass, volume, temperature, and pressure can be measured directly so we would have to relate the number of molecules to one of those measurements. Fortunately, there is a relation between the number of molecules and the mass of a substance, and that is the unit known as a mol (mole). A mol is defined as 6.02 x 10^23 molecules.

So lets say that Roy wants to make a Kg of Hydrogen so that he can set something on fire. (Hydrogen is a flammable gas after all,) He has 20 Kg of water to make hydrogen, how much of that 20 Kg would he need to brake down to get 1 Kg of hydrogen?

Lets start with how many moles are in 1 Kg of Hydrogen. To convert mass into moles we need to know the atomic mass (which can be found on the periodic table of elements). The atomic mass of Hydrogen is 1 and since there are 2 atoms in 1 molecule of Hydrogen, the atomic mass of molecular Hydrogen is 2.

step 1

The measured mass must be in grams to convert to moles so 1 Kg becomes 1000 grams; this is then divided by 2 to give us 500 grams per mole. Since a mole is a measure of the number of molecules of a substance, then water must have the same number of moles as Hydrogen according to our equation.

step 2

So now we have to convert from moles back to grams by multiplying by the atomic mass of water. Using the periodic table and the chemical formula for water, we find that the atomic mass is 18. we multiply 18 by 500 and we get 9000 grams or 9 Kg of water.

step 3

So the moral of the story is, water does not make you safe from the Flame Alchemist.



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