Chemical Relationships

Chemical Equations: Using shorthand to show balanced reactions

Chemical equations are an efficient way to describe chemical reactions. This module explains the shorthand notation used to express how atoms are rearranged to make new compounds during a chemical reaction. It shows how balanced chemical equations convey proportions of each reactant and product involved. The module traces the development of chemical equations over the past four centuries as our understanding of chemical processes grew. A look at chemical equations reveals that nothing is lost and nothing is gained in a typical chemical reaction–matter simply changes form.

Imagine that you’re traveling in an exotic place and your rusty car muffler falls off. You need to find a place where you can buy a replacement, and you don’t speak the local language. Take a moment now to draw a sketch that conveys that you’re searching for a shop where you can get a new part installed. Maybe you include a car, a muffler, a storefront, and a person holding a screwdriver or other tool.

Then look at your picture: think about what kind of understanding you and the viewer need to share in order for you to convey your message. If you showed the same picture to someone 500 years ago, they’d have no idea what a car is, let alone what a muffler does or that there are people who specialize in installing them. But you and your 21st-century viewer can translate your sketch because of shared knowledge you have about cars.

Chemical equations play a similar role for people conveying messages about what happens during a chemical reaction. You probably remember that In a chemical reaction, bonds between atoms in a compound are broken, and the atoms rearrange to form new compounds, either releasing or consuming energy in the process (see our Chemical Reactions module).

As an example, let’s consider what happened to the muffler. Simply saying it rusted isn’t much of an explanation. You could say iron reacted with oxygen to produce rust. That's better, but not very precise. What, exactly, is rust? Chemically, it’s iron oxide, but iron forms many types of oxides. So we need a very specific way to express the chemical reaction that to led to our muffler’s demise.

Writing chemistry in shorthand

That’s what chemical equations are for: they’re a type of shorthand used to precisely communicate exactly what’s happening in the reaction. In the most basic sense, a chemical equation describes the type and amount of each substance that reacts (the reactants) to form a given amount of specific substances produced (the products). Reactants will always react in proportions given in the equation. If the supply of one reactant runs out, the excess of the other will remain unreacted.

The shorthand that explains our rusty car part is this:

4Fe + 3O2




The number in front of an atom or molecule, which we call the coefficient, tells us the relative amounts of each substance involved in or produced by the reaction. The numbers in subscript refer specifically to the element that’s in front of them.

In other words, 4 iron atoms in the muffler reacted with 3 oxygen molecules in the air. Each of these oxygen molecules contains 2 oxygen atoms. When the chemical bonds reassemble and these reactants combine, the result is 2 molecules of a specific iron oxide that contains 2 iron atoms and 3 oxygen atoms—a.k.a rust.

Plenty of the iron in this muffler combined with oxygen in the environment, creating rust and leaving holes in the muffler where the iron has been consumed.

image ©Raymond Webber

This equation conveys something much deeper than numbers of particles, though: it captures the centuries-long accumulation of knowledge about what our universe is made of and how matter interacts. Like an elegant poem (or like your rusty muffler drawing), a chemical equation conveys a world of complex concepts in just a few expressions.

Comprehension Checkpoint
If one reactant is completely consumed, the remaining reactant will

A brief history of the chemical equation

As our understanding of chemical processes deepened over time, chemical equations slowly became more sophisticated. Ultimately, such equations played a role in the recognition of chemistry as its own important science, separate from medicine, alchemy (which was popular in the 17th and 18th centuries), and physics.

The first known written chemical equation—which is really more of a diagram—appeared in what’s considered to be the first chemistry textbook, the Tyrocinium Chymicum (meaning “Begin Chemistry”). It was penned by French scientist and teacher Jean Beguin in Paris in 1615, and describes what Beguin observed when he heated antimony sulfide with a chloride of mercury. The mercury became vapor, leaving behind a residue of antimony oxychloride.

While Beguin’s diagram looks very different than modern chemical equations (and it isn’t entirely correct), it reflects an understanding of reactants and products in a chemical reaction.

Figure 2: This drawing, from Jean Beguin’s Tyrocinium Chymicum, shows what the author believed was happening when antimony sulfide reacts with mercury chloride. The diagram conveys an understanding that a chemical reaction begins with specific reactants and produces specific products.

Beguin revealed the beginnings of an understanding of what occurs in a chemical reaction, but not an explanation of why. More than a century passed before new diagrams revealed deeper insights into the phenomena that drive reactions.

These insights came from William Cullen, who was also a teacher, and founded the chemistry department at the University of Glasgow in 1747. His hand-written lecture notes contain diagrams using arrows and letters, indicating four different types of reactions:

Figure 3: Drawings in a set of undated lecture notes written by William Cullen in the mid-18th century. Cullen developed the drawings in the hope that they would help his students better understand chemical reactions.

image ©University of Glasgow Library

The diagram on the lower left described what Cullen called a “single elective attraction,” or what we now call a single replacement reaction, one that involves a single element taking the place of another element within a compound. (For more on reaction types, see our Chemical Equations module. The upper left is his diagram for a double replacement reaction, or one that involves the exchange of a component from each of two different compounds. In both cases, the reactions produce precipitates, indicated by the squiggly lines.

The two diagrams on the right relate to the dissolution of salts. The prevailing wisdom during Cullen’s time was that “elective attractions,” which we now know as charge, caused a metal in one substance to be attracted to another substance. The metals swapped places, forming either a new solid precipitate or dissolving in solution (sometimes producing a solution that displayed new properties).

While he didn’t have all the details right, Cullen’s thinking was on track, and his diagrams represent an important step toward what is now a common generic chemical equation:

A + B C + D

We may take this simple type of equation for granted now, but at the time, it demonstrated some very perceptive ideas about what is actually happening during a chemical reaction. Remember, atoms and molecules were still not understood in Cullen’s time. It took a trio of chemists working over the next 50 years to clarify the picture that gave us the modern chemical equation. So, to grasp the idea that substances combined and were exchanged in chemical reactions is really significant.

In 1774, French chemist Antoine Lavoisier made an important observation – he noted that while substances in a chemical reaction changed form in ways described by Cullen, the mass of the system did not change. In other words, the amount of each element present remained the same, meaning that matter and mass are conserved. This is a crucial concept that will be important when we discuss balancing chemical reactions – all elements have to be fully accounted for at the start and at the end of a chemical reaction.

Around the same time as Lavosier, Joseph Proust, another Frenchman, was working extensively with copper carbonate. He found that regardless of how he changed the ratio of starting reactants – adding more copper sometimes, or more carbon or oxygen at others, the copper, carbon, and oxygen all reacted together in a constant ratio. His insight brought us the law of definite proportions: in any given compound, the elements occur in fixed ratios, regardless of their source. (Visit our module on Chemical Reactions to learn more about the work of these scientists). Again, this seems obvious to us today as we know that elements only react together in certain ways, but Proust completed his work before it was widely recognized that atoms and compounds existed.

Finally, in 1803, English chemist John Dalton tied these threads together by proposing that matter is made of atoms of unique substances that could not be created or destroyed (see our module Early Ideas about Matter for more information). He showed that each element could combine with multiple others to form different compounds, and always in whole number ratios.

This knowledge, taken together, provided the foundation for the chemical notation we use today. Chemical equations aren’t like mathematical equations, which have been around much longer. While the quantity of each element must be equal on both sides of the equation, you will never see an “equals” sign in a chemical equation. That’s because a chemical equation describes a process of change.

Comprehension Checkpoint
Chemical equations are written basically the same way today as they were in the 17th century.

Conservation of mass: a balancing act

Like all other reactions, the creation of the rusty muffler is an example of chemical change:

Fe + O2 Fe2O3
Reactants Yield Products

Again, iron and oxygen combine to form a specific iron oxide. The arrow indicates that this reaction proceeds to the right as it is written, meaning that iron oxide is formed. In some cases, the reaction can also go backward, and we use a double arrow showing that some reactions go in both directions. Unfortunately for the muffler, that’s not the case here.

Now look at the equation more closely: How many iron atoms are on the reactant side (left) versus the product side (right)? How many oxygen atoms? You will see that they’re not equal as the equation is currently written.

However, we know from the law of conservation of matter that atoms can’t be created or destroyed. In other words, we can’t just get rid of an iron atom or create an oxygen atom to make the equation work. Nor can we change the subscripts in the reaction, because doing so would suggest that we are starting with a different reactant or obtaining a different product.

What we can do is adjust the numbers of reactant and product components (iron atoms and/or oxygen molecules on the left side and iron oxide molecules on the right), because doing so doesn’t imply creating or destroying matter. It’s a way of bookkeeping – in order to produce a molecule that has two iron atoms, you need to find a source of those atoms.

Let’s see how this works with the reaction that creates rust.

Fe + O2 Fe2O3

We already know that the numbers of each type of atom aren’t equal on each side of the reaction. To address this, we can add coefficients in front of the reactants and products to adjust the number of particles and create a balanced equation. (If there is no coefficient, it means there is only one of that type of particle.)

Let’s look at the reaction atom by atom.

Fe + O2 Fe2O3
↑ 1 iron ↑ 2 iron

Since the rust molecule has two iron atoms, we must balance the Fe atoms by adding the coefficient “2” in front of the iron atom on the reactant side, since that is the only place where iron appears on the left side of the equation. Now we have two irons on each side of the equation.

2Fe + O2 Fe2O3
↑ 2 iron ↑ 2 iron

Moving on to the oxygen atoms, we find two on the left side of the equation, but three on the right side. We could mathematically balance the equation by using one and a half oxygen molecules, since each molecule is made up of two oxygen atoms. To better understand this, picture one oxygen molecule as two atoms bonded together O-O, therefore 1.5 oxygen molecules (O-O and O-O) provides three oxygen atoms:

2Fe + 1.5O2 Fe2 O3
↑ 3 oxygen ↑ 3 oxygen

In the real world, though, oxygen doesn’t occur in half-molecules. We can solve this conundrum by simply multiplying all the coefficients by two:

4Fe + 3O2 2Fe2O3
↑ 4 iron ↑ 6 oxygen ↑ 4 iron & 6 oxygen

Now we have 4 atoms of iron on the left side, and 4 (2 molecules, each containing 2 iron atoms) on the right side. For oxygen, there are 6 atoms on the left side (3 molecules of 2 atoms each) and 6 on the right side (2 molecules containing 3 oxygen atoms). Now we have a balanced equation.

Comprehension Checkpoint
To create a balanced equation, we can

Balanced equations indicate proportions

Along with telling us exactly how much of a chemical compound is involved in a reaction, balanced chemical equations tell us is the proportions of “ingredients” required to make a particular product. It’s a bit like a recipe. Let’s say you’re making a batch of cookies. The recipe calls for:

  • 2 cups of flour
  • 1 cup of sugar

and promises you a batch of 12 cookies. You can follow the recipe and use 2 cups of flour and 1 cup of sugar and expect 12 cookies, or you can double the recipe and use 4 cups of flour and 2 cups of sugar and expect 24 cookies (or you can triple the recipe, or half it, or so on).

Similarly, to make a “batch” of 2 rust molecules, you need 4 iron atoms and 3 oxygen molecules:

4Fe + 3O2 2Fe2O3
↑ 4 iron ↑ 3 oxygen
↑ 2 rust

So, for every four atoms of iron and three molecules of oxygen, we get two molecules of rust. Much as you would do with a cookie recipe, you could double this: start with eight iron atoms and six oxygen molecules and make four molecules of rust. No matter how many times you multiply it, the base proportion always remains constant.

In the real world of chemistry, though, we don’t deal with individual atoms and molecules; there are a lot more than two molecules of rust on a muffler that falls off a car. That’s where the concept of the mole comes in handy. A mole is a quantity of particles, specifically a mole is 6.022 x 1023 particles. In other words, one mole of iron atoms contains 6.022 x 1023 atoms. Four moles of iron atoms contain four times that amount, or 28.088 x 1023 iron atoms. (To brush up on your mole math, see our module, The Mole and Atomic Mass).

Note that when we were balancing the equation, we were thinking about the numbers of individual atoms on each side, attending to the law of conservation of matter that we can’t create or destroy atoms. When we’re thinking about proportions, however, we’re thinking about the coefficients in front of the particles, which represent the number of moles of each type of particle consumed or produced. These coefficients tell us how many moles of product can be produced with the number of moles of reactant present at the beginning of the reaction.


A chemical equation is an ingeniously compact way of communicating a lot of information in a short sequence of parts. Modern chemical equations reflect our understanding of matter being composed of atoms and of chemical reactions as a process of breaking bonds and rearranging atoms into new compounds. Mass is conserved in a chemical reaction, and the number of particles on each side of the equation must reflect this. A balanced equation also communicates the proportions of products and reactants involved in that reaction.

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