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Chemical Formulas and Equations
From Grolier's New Book of Knowledge

Scientists, like artists, strive to express information in a clear, concise way. In writing, for example, we try to translate ideas and feelings into easily understood sentences. In mathematics, we turn numerical truths and mysteries into equations. In painting or photography, we may turn an entire experience into a single image.

So it is in chemistry. As chemists, we use the shorthand of chemical formulas to represent all known substances. We describe how these substances interact and transform with chemical equations. Like mathematics and fine art, chemical formulas and equations transcend language and span national boundaries. They represent an international vocabulary useful to scientists and students around the world.

SYMBOLS AND FORMULAS

Chemistry's dramatic cast of actors consists of all the known elements, although some make far-more-frequent appearances than do others. Each of these elements has its own symbol, consisting of one or two letters. The letter C, for example, stands for the element carbon. The letters Cl stand for chlorine, H for hydrogen, He for helium, and so on.

The symbols of some elements are more obscure than others. Hg, for instance, stands for mercury, Fe for iron, and Sn for tin. The symbols for these and several other elements are abbreviations of Greek or Latin names. Mercury's symbol of Hg stands for hydrargyrum, from the Greek word meaning "liquid silver." Fe comes from the first two letters of ferrum, the Latin word for iron. Sn comes from the Latin stannum, meaning tin.

More than an abbreviation, a chemcial symbol can represent a quantity—specifically one atom of an element. So O can stand for a single atom of oxygen, Cl for a single atom of chlorine, and so on. In reality, however, oxygen never exists in single-atom form. Like several other elements—such as chlorine, fluorine, and hydrogen—oxygen in its pure form always exists as paired atoms, called diatomic molecules.

Molecules are combinations of more than one atom—be they of the same or different elements. To indicate that a molecule contains more than one atom of an element, we use a subscript number—that is, a small figure immediately below and to the right of a chemical symbol. So O2 stands for two atoms of oxygen, Br2 for two atoms of bromine, and so on. To read this abbreviation aloud, you would pronounce all letters and subscripts, as in "O-two" and "B-R-two," respectively. When any symbol is written in this way, it indicates that the atoms represented are joined by chemical bonds.

When two or more different elements form a substance, it is called a compound. A compound is written using two or more symbols with subscripts to show how many of each element are present in each molecule of the compound. So H2O means "a molecule consisting of two atoms of hydrogen and one atom of oxygen"—namely, water. CO2 stands for "a molecule consisting of one atom of carbon and two atoms of oxygen"—or carbon dioxide. Compounds are read aloud in the same way. So NaCl is read "N-A-C-L."

The above abbreviations for compounds and diatomic molecules are called formulas. A chemical formula always tells us what elements are contained in a compound (using symbols), and the ratio of these atoms to one another (the subscripts). The chemical formula for water, for example, points out that there are always two atoms of hydrogen with every atom of oxygen: H2O.

Using these symbols, we can indicate any kind of molecule, no matter how complicated. A single molecule of cane sugar, for example, consists of 45 atoms—12 atoms of carbon, 22 of hydrogen, and 11 of oxygen. We write this C12H22O11.

CHEMICAL EQUATIONS

Like a mathematical equation, a chemical equation represents a process and a result. In this case, we are looking at the result of a chemical change. The equation shows us the substance or substances entering this change—the reactants. It also gives us the substance or substances formed from the change—the products. The process in which chemical reactants change into new products is called the chemical reaction.

Here is how we would write the chemical change that occurs when mercuric oxide yields mercury and oxygen:

HgO → Hg + O2

This chemical equation says that our reactant consists of a molecule made up of one atom of mercury bound to one atom of oxygen, and that it has yielded (→) two products—namely, a single atom of mercury and a molecule consisting of two oxygen atoms. However, there is something fundamentally wrong with the above equation. It is not balanced.

Balancing. The law of conservation of matter states that in ordinary chemical reactions (nonnuclear reactions), matter is never lost or created. This means that the sum total of the atoms on the reactant side of a chemical equation must equal the sum total of the same atoms, in the same proportions, on the product side. These atoms may "change partners," so to speak, to form new molecules. But none disappear, nor do any new "partners" enter the dance.

 

So what of our equation HgO → Hg + O2? We have one atom of mercury and one atom of oxygen in the reactant, but one atom of mercury and two atoms of oxygen in the product. Clearly, when a single molecule of mercuric oxide breaks into mercury and oxygen, only one atom of each element is produced.

To balance our equation, we need two molecules of mercuric oxide. We express this as 2HgO. When it breaks apart, these two molecules yield the two oxygen atoms we need to balance the equation, as well as two mercury atoms. The resulting equation is as follows:

2HgO → 2Hg + O2

In other words, "two molecules of mercuric oxide (HgO) yield two atoms of mercury and a molecule made up of two united oxygen atoms." Our equation is balanced.

Note that in the product, we wrote 2Hg, not Hg2. This indicates that the mercury atoms exist independently of one another. Hg2 would have indicated that the two mercury atoms were bound together to form a diatomic molecule—in this case, a molecule that does not even exist. This is an important principle in balancing chemical equations: we can change only the number of molecules, not the nature of the molecules themselves.

Equations with Added Information. The equation 2HgO → 2Hg + O2 shows us the atoms and molecules involved in a chemical change, as well as their ratios. But it reveals nothing about the physical state of the reactants and products, nor does it tell us conditions under which this reaction takes place.

 

If we stored a chunk of mercuric oxide in a sealed container at room temperature, it would continue to exist as mercuric oxide indefinitely. To make solid mercuric oxide decompose, we need heat. Moreover, the resulting products come in the form of a liquid and a gas. We can show all this succinctly as follows:


This more-informative equation explains that "when heated, solid mercuric oxide yields liquid mercury and oxygen gas." In this instance, heat is the special condition required for the chemical change to occur. In other reactions, other special conditions may be required. A common example is the presence of a catalyst—a chemical that increases the speed of a reaction without itself undergoing a chemical change.

For instance, the catalyst manganese dioxide (MnO2) will cause hydrogen peroxide (H2O2) to rapidly decompose at room temperature. Since manganese dioxide is neither a reactant nor a product in the resulting chemical change, we show it above the arrow in our equation:


In the above equation, the abbreviation “aq” means that the hydrogen peroxide is in an aqueous solution (in water).

EXPRESSING REVERSIBLE REACTIONS

The chemical equation 2HgO → 2Hg + O2 tells us what happens to mercuric oxide when heated. But it does not show how complete the reaction is—that is, whether all of the mercuric oxide decomposes into elemental mercury and molecular oxygen.

If mercuric oxide is heated in a closed container, two reactions take place at the same time. As the mercuric oxide decomposes into mercury and oxygen (2HgO → 2Hg + O2), some of the mercury and oxygen reacts to re-form mercuric oxide (2Hg + O2 → 2HgO). We call this a reversible reaction.

We indicate a reversible reaction by using two opposite arrows in our equation. In this case, the forward-pointing arrow shows the decomposition of our original reactant, and the back-pointing arrow shows the recombination of the products—that is, the reverse process. We express this as follows:


Let us follow what actually happens here:

We begin by heating mercuric oxide in a closed tube from which the air has been removed. So at first, there is neither elemental mercury nor oxygen in the tube. Therefore, our reaction can only go forward.

However, as mercury and oxygen are formed, the reverse reaction can begin. It does so slowly at first, but gradually mercury and oxygen accumulate as the decomposition of mercuric oxide is sped by heat. As a greater concentration of mercury and oxygen develops, the speed of the reverse reaction increases.

In this way, the reverse reaction continues to accelerate until the mercuric oxide is being re-formed at precisely the same speed as it is decomposing. A reversible reaction at this stage is said to be in chemical equilibrium.

In some cases, the reaction mixture at equilibrium consists mainly of reactants; in other cases, of products. The ratio depends on the nature of the chemicals involved and on conditions such as heat or the presence of catalysts. One way chemists force a reversible reaction to completion is by continuously removing one or more of the products. In our mercuric oxide example, this can be done by simply drawing off the oxygen gas from our closed container, leaving behind liquid mercury. Under these circumstances, mercuric oxide will completely decompose, and we return to our original, one-way equation: .


THE MOLE AND AVOGADRO'S NUMBER

Just as a recipe describes how to successfully assemble ingredients such as flour, eggs, and baking soda into a product such as pancakes, a chemical equation tells us how to prepare a given substance. In order to avoid costly waste, a chemist, pharmacist, or student must know the precise amounts of each reactant needed to produce a desired product.

Yet clearly, it is not practical to assemble products one or two molecules at a time, as represented by our sample equation 2HgO → 2Hg + O2. In order to create products in useful amounts, we need to work with billions upon billions of atoms. How do we go about calculating such mind-boggling amounts?

Luckily, much of the work has been done for us, by the great 19th-century Italian chemist Amedeo Avogadro. Around the year 1810, Avogadro calculated that 18 grams of water contain 602,000,000,000,000,000,000,000 molecules of H2O. Thankfully, this can be abbreviated as 6.02 × 1023. Far from a random number, this huge figure gives us the most fundamental unit of measurement in all of chemistry—the mole. By definition, a mole is the amount of a substance that contains Avogadro's number of particles. For most elements, the mass in grams of one mole (called the molar mass) is equal to the element's atomic mass, found on the periodic table.

If the element forms a diatomic molecule such as O2, for example, then the molar mass is twice the element's atomic mass in grams. In this case, oxygen has an atomic mass of 16, so its diatomic molecules (O2) have a molar mass of 32. This tells us that one mole of oxygen weighs 32 grams.

Similarly, we can calculate the molar mass of HgO by adding the atomic masses of each atom in the compound: 201 grams for Hg and 16 grams for O equals 217 grams.

Importantly, a mole of any substance always contains the same number of molecules (or atoms). What is that number? You guessed it: 6.02 × 1023, or Avogadro's number.

Thanks to Avogadro's number and the unit of measure we call the mole, anyone can easily measure out a known quantity of atoms or molecules with an accurate scale.

Because of this simple method of translating atoms and molecules to moles, a chemical equation tells us precisely what amount of each reactant is required to yield a given product, or conversely, how much product we will get for any given amount of reactants. For example: the equation 2HgO → 2Hg + O2 could also be stated as "Two moles of mercuric oxide (2 × 217 = 434 grams) yield two moles of mercury (2 × 201 = 402 grams) and one mole of molecular oxygen (32 grams)."

The area of chemistry that deals with Avogadro's laws and the weight relationships in a chemical reaction is called stoichiometry (stoy-kee-ahm'-uhtree). The term comes from the Greek words for "first principle" and "to measure." It is one of the cornerstones on which the science of chemistry is built.