## 6.4 Mole-Mole Relationships in Chemical Reactions

### Learning Objective

1. Use a balanced chemical reaction to determine molar relationships between the substances.

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 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:

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. The study of the numerical relationships between the reactants and the products in balanced chemical reactions is called stoichiometry.

### Example 7

How many moles of oxygen react with hydrogen to produce 27.6 mol of H2O? The balanced equation is as follows:

2H2 + O2 → 2H2O

Solution

Because we are dealing with quantities of H2O and O2, we will use a ratio that relates those two substances. Because we are given an amount of H2O and want to determine an amount of O2, we will use the ratio that has H2O in the denominator (so it cancels) and O2 in the numerator (so it is introduced in the answer). Thus,

To produce 27.6 mol of H2O, 13.8 mol of O2 react.

### Skill-Building Exercise

1. Using 2H2 + O2 → 2H2O, how many moles of hydrogen react with 3.07 mol of oxygen to produce H2O?

### Concept Review Exercise

1. How do we relate molar amounts of substances in chemical reactions?

1. Amounts of substances in chemical reactions are related by their coefficients in the balanced chemical equation.

### Key Takeaway

• The balanced chemical reaction can be used to determine molar relationships between substances.

### Exercises

1. List the molar ratios you can derive from this balanced chemical equation:

NH3 + 2O2 → HNO3 + H2O
2. List the molar ratios you can derive from this balanced chemical equation

2C2H2 + 5O2 → 4CO2 + 2H2O
3. Given the following balanced chemical equation,

6NaOH + 3Cl2 → NaClO3 + 5NaCl + 3H2O

how many moles of NaCl can be formed if 3.77 mol of NaOH were to react?

4. Given the following balanced chemical equation,

C5H12 + 8O2 → 5CO2 + 6H2O

how many moles of H2O can be formed if 0.0652 mol of C5H12 were to react?

5. Balance the following unbalanced equation and determine how many moles of H2O are produced when 1.65 mol of NH3 react.

NH3 + O2 → N2 + H2O
6. Trinitrotoluene [C6H2(NO2)2CH3], also known as TNT, is formed by reacting nitric acid (HNO3) with toluene (C6H5CH3):

HNO3 + C6H5CH3 → C6H2(NO2)2CH3 + H2O

Balance the equation and determine how many moles of TNT are produced when 4.903 mol of HNO3 react.

7. Chemical reactions are balanced in terms of molecules and in terms of moles. Are they balanced in terms of dozens? Defend your answer.

8. Explain how a chemical reaction balanced in terms of moles satisfies the law of conservation of matter.