5.2 Chemical Equations

Water (H₂O) is composed of hydrogen and oxygen. Suppose we imagine a process in which we take some elemental hydrogen (H₂) and elemental oxygen (O₂) and let them react to make water. The statement

hydrogen and oxygen react to make water

is one way to represent that process, which is called a chemical reactionA representation of a chemical change.. Figure 5.1 "The Formation of Water" shows a rather dramatic example of this very reaction.

To simplify the writing of reactions, we use formulas instead of names when we describe a reaction. We can also use symbols to represent other words in the reaction. A plus sign connects the initial substances (and final substances, if there is more than one), and an arrow (→) represents the chemical change:

H₂ + O₂ → H₂O

This statement is one example of a chemical equationAn abbreviated way of using symbols to represent a chemical change., an abbreviated way of using symbols to represent a chemical change. The substances on the left side of the arrow are called reactantsA substance on the left side of the arrow in a chemical equation., and the substances on the right side of the arrow are called productsA substance on the right side of the arrow in a chemical equation.. It is not uncommon to include a phase label with each formula—(s) for solid, (ℓ) for liquid, (g) for gas, and (aq) for a substance dissolved in water, also known as an aqueous solution. If we included phase labels for the reactants and products, under normal environmental conditions, the reaction would be as follows:

H₂(g) + O₂(g) → H₂O(ℓ)

This equation is still not complete because it does not satisfy the law of conservation of matter. Count the number of atoms of each element on each side of the arrow. On the reactant side, there are two H atoms and two O atoms; on the product side, there are two H atoms and only one oxygen atom. The equation is not balanced because the number of oxygen atoms on each side is not the same (Figure 5.2 "Balanced—Yes or No?").

To make this chemical equation conform to the law of conservation of matter, we must revise the amounts of the reactants and the products as necessary to get the same number of atoms of a given element on each side. Because every substance has a characteristic chemical formula, we cannot change the chemical formulas of the individual substances. For example, we cannot change the formula for elemental oxygen to O. However, we can assume that different numbers of reactant molecules or product molecules may be involved. For instance, perhaps two water molecules are produced, not just one:

H₂(g) + O₂(g) → 2H₂O(ℓ)

The 2 preceding the formula for water is called a coefficientA number that gives the number of molecules of a substance in a balanced chemical equation.. It implies that two water molecules are formed. There are now two oxygen atoms on each side of the equation.

Unfortunately, by inserting the coefficient 2 in front of the formula for water, we have also changed the number of hydrogen atoms on the product side as well. As a result, we no longer have the same number of hydrogen atoms on each side. This can be easily fixed, however, by putting a coefficient of 2 in front of the diatomic hydrogen reactant:

2H₂(g) + O₂(g) → 2H₂O(ℓ)

Now we have four hydrogen atoms and two oxygen atoms on each side of the equation. The law of conservation of matter is satisfied because we now have the same number of atoms of each element in the reactants and in the products. We say that the reaction is balancedA property of a chemical equation when there are the same number of atoms of each element in the reactants and products. (Figure 5.3 "Balanced—Yes or No?"). The diatomic oxygen has a coefficient of 1, which typically is not written but assumed in balanced chemical equations.

Proper chemical equations should be balanced. Writing balanced reactions is a chemist’s way of acknowledging the law of conservation of matter.

How does one balance a chemical equation, starting with the correct formulas of the reactants and products? Basically, a back-and-forth approach is adopted, counting the number of atoms of one element on one side, checking the number of atoms of that element on the other side, and changing a coefficient if necessary. Then check another element, going back and forth from one side of the equation to another, until each element has the same number of atoms on both sides of the arrow. In many cases, it does not matter which element is balanced first and which is balanced last, as long as all elements have the same number of atoms on each side of the equation.

For example, to balance the equation

CH₄ + Cl₂ → CCl₄ + HCl

we might choose to count the carbon atoms first, finding that both sides are balanced with one carbon atom. The reactant side has four hydrogen atoms, so the product side must also have four hydrogen atoms. We fix this by putting a 4 in front of the HCl:

CH₄ + Cl₂ → CCl₄ + 4HCl

Now each side has four hydrogen atoms. The product side has a total of eight chlorine atoms (four from the CCl₄ and four from the four molecules of HCl), so we need eight chlorine atoms as reactants. Because elemental chlorine is a diatomic molecule, we need four chlorine molecules to get a total of eight chlorine atoms. We add another 4 in front of the Cl₂ reactant:

CH₄ + 4Cl₂ → CCl₄ + 4HCl

Now we check: each side has one carbon atom, four hydrogen atoms, and eight chlorine atoms. The chemical equation is balanced.