In Chapter 5 “Introduction to Chemical Reactions”, you learned to balance chemical equations by comparing the numbers of each type of atom in the reactants and products. The coefficients in front of the chemical formulas represent the numbers of atoms, molecules, or formula units, depending on the type of substance. Here, we will extend the meaning of the coefficients in a chemical equation.

Consider the simple chemical equation

2H₂ + O₂ → 2H₂O

The convention for writing balanced chemical equations is to use the lowest whole-number ratio for the coefficients. However, the equation is balanced as long as the coefficients are in a 2:1:2 ratio. For example, this equation is also balanced if we write it as

4H₂ + 2O₂ → 4H₂O

The ratio of the coefficients is 4:2:4, which reduces to 2:1:2. The equation is also balanced if we were to write it as

22H₂ + 11O₂ → 22H₂O

because 22:11:22 also reduces to 2:1:2.

Suppose we want to use larger numbers. Consider the following coefficients:

12.044 × 10²³ H₂ + 6.022 × 10²³ O₂ → 12.044 × 10²³ H₂O

These coefficients also have the ratio 2:1:2 (check it and see), so this equation is balanced. But 6.022 × 10²³ is 1 mol, while 12.044 × 10²³ is 2 mol (and the number is written that way to make this more obvious), so we can simplify this version of the equation by writing it as

2 mol H₂ + 1 mol O₂ → 2 mol H₂O

We can leave out the word mol and not write the 1 coefficient (as is our habit), so the final form of the equation, still balanced, is

2H₂ + O₂ → 2H₂O

Now we interpret the coefficients as referring to molar amounts, not individual molecules. The lesson? Balanced chemical equations are balanced not only at the molecular level but also in terms of molar amounts of reactants and products. Thus, we can read this reaction as “two moles of hydrogen react with one mole of oxygen to produce two moles of water.”

By the same token, the ratios we constructed in Chapter 5 “Introduction to Chemical Reactions” can also be constructed in terms of moles rather than molecules. For the reaction in which hydrogen and oxygen combine to make water, for example, we can construct the following ratios:

[latex]\frac{2\text{ mol H}_2}{1\text{ mol O}_2}[/latex]   and   [latex]\frac{1\text{ mol O}_2}{2\text{ mol H}_2}[/latex]     and     [latex]\frac{2\text{ mol H}_2\text{O}}{1\text{ mol O}_2}[/latex]     and     [latex]\frac{1\text{ mol O}_2}{2\text{ mol H}_2\text{O}}[/latex]     and     [latex]\frac{2\text{ mol H}_2}{2\text{ mol H}_2\text{O}}[/latex]     and     [latex]\frac{2\text{ mol H}_2\text{O}}{2\text{ mol H}_2}[/latex]

We can use these ratios to determine what amount of a substance, in moles, will react with or produce a given number of moles of a different substance.  In these problems, it will not be necessary to write all of the ratios, just the one needed to solve the problem at hand. Writing all of the ratios from a balanced equation is a good reminder that the mole-to-mole ratio of various substances comes from the coefficients of a balanced equation. The study of the numerical relationships between the reactants and the products in balanced chemical reactions is called stoichiometry.