3.7 Writing and Balancing Chemical Equations

A chemical equation is a shorthand description of a chemical reaction, using symbols and formulas to represent the elements and compounds involved. This shorthand description, based on experiments, shows that a reaction occurred, identifies all the substances involved in the reaction, and establishes the formulas of these substances.

For the reaction of carbon with a plentiful source of oxygen, as we have noted, the sole product is carbon dioxide. We can write an equation for this reaction:

The plus sign indicates that carbon and oxygen react, and the arrow, usually read as “yields,” points to the result of their reaction: carbon dioxide. We generally call the starting substances in a reaction the reactants and the substances formed in the reaction, the products. The reactants appear to the left of the arrow in an equation, and the products appear to the right of the arrow.

Occasionally, we may need to indicate the physical form of the reactants and products, and we use these symbols to do this:

These parenthetical symbols are attached to the formulas of the reactants and products:

If it is necessary to heat a mixture of reactants to bring about a chemical reaction, we sometimes denote this by placing a capital Greek letter delta, above the yield arrow. Sometimes the temperature or other conditions under which the reaction is carried out are also noted above the yield arrow:

The equation

can be interpreted in several ways. We can use it as a qualitative description of the reaction, as in “solid carbon and gaseous oxygen react to form gaseous carbon dioxide.” We can give a microscopic interpretation, as in “one carbon atom reacts with one oxygen molecule to form one molecule of carbon dioxide gas.” However, because we must usually work at the macroscopic level, the most useful interpretation of the equation is based on enormously large numbers of atoms and molecules, specifically the numbers found in a mole of substance: 1 mol (12.01 g) of carbon reacts with 1 mol (32.00 g) of oxygen gas to produce 1 mol (44.01 g) of carbon dioxide. This molar interpretation is at the heart of the quantitative calculations based on chemical equations, as we will see in Section 3.8.

The equation for the reaction of carbon and oxygen to form carbon dioxide is deceptively easy to write. If we try something similar for the reaction of hydrogen and oxygen to form water, however, we run into a bit of a problem. The following equation does not conform to the law of conservation of mass, and therefore it is not balanced:

(not balanced)

Two O atoms in the form of an O2 molecule are shown on the left side of the equation, but there is only one O atom, in the H2O molecule, on the right side. More O atoms are present on the reactant side than on the product side, but we know that atoms cannot be created or destroyed in a chemical reaction. We should not assume that H2 and O2 molecules react in a 1:1 ratio. They don’t, as we show in the molecular interpretation in Figure 3.6, where we illustrate how to balance the equation so that it agrees with the law of conservation of mass. However, we don’t need to draw molecular pictures to balance equations; we can work directly with the equation and use stoichiometric coefficients to adjust the ratios of the reactants and products. Stoichiometric coefficients are numbers placed in front of formulas in a chemical equation to balance the equation; they indicate the combining ratios of the reactants and the ratios in which products are formed. A stoichiometric coefficient multiplies everything in the formula that follows it. If there is no coefficient before a formula, the coefficient 1 is understood.

To balance the equation

(not balanced)

we can begin by placing the stoichiometric coefficient 2 in front of the formula H2O, in order to balance the oxygen:

(O balanced, H not balanced)

Balancing an Equation activity
3D Model - Water
FIGURE 3.6 Balancing the chemical equation for the reaction of hydrogen with oxygen to form water.
(a) Incorrect: There is no evidence for the presence of atomic oxygen as a product. A reactant or product having a chemical formula different from the formula of any substance in the original equation cannot be introduced for the purpose of balancing an equation. (b) Incorrect: The product of the reaction is water, H2O, not hydrogen peroxide, H2O2. A formula cannot be changed in order to balance a chemical equation. (c) Correct: An equation can be balanced only through the use of correct formulas and coefficients.

Now we have two oxygen atoms on each side of the equation, but our added 2 increases the number of H atoms on the right to four at the same time that it increases the number of O atoms to two. This is a problem because there are only two H atoms on the left. We can correct this imbalance by placing another stoichiometric coefficient 2 in front of the H2 on the left. The equation is now balanced:


with four H atoms and two O atoms on each side of the arrow.

The point made in Figure 3.6 is extremely important: We can balance an equation only by adjusting coefficients. We cannot do so by changing any subscripts in the formulas or by adding or removing a reactant or product from the equation. This might balance the equation, but it would no longer describe the desired reaction.

The method we just described is called balancing by inspection. The following simple strategies reduce the trial-and-error aspect of the method.

In any case, the most important step in any strategy is to check an equation to ensure that it is indeed balanced: For each element, the same number of atoms must appear on each side of the arrow. To phrase this most important point another way, atoms are conserved in chemical reactions.

Our main interest in this section has been simply balancing equations. It is much more important, however, to be able to predict whether a chemical reaction will occur and then to write an equation to represent it. We will introduce a number of new ideas in later chapters to show how to make such predictions.

Example 3.13
Example 3.14
Example 3.15
Example 3.16