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12.1: Mole Ratios

Difficulty Level: At Grade Created by: CK-12

Lesson Objectives

• Be able to calculate the number of moles, molecules, or atoms in a sample.
• Be able to describe mole ratios for reactants and products of a given chemical reaction.
• Understand stoichiometry and stoichiometric coefficients.
• Be able to calculate the moles of reactants needed or products generated for a reaction based on its balanced chemical equation.

Lesson Vocabulary

• mole ratio: When the relative amounts of two reaction components are expressed as a ratio.
• stoichiometry: Calculations involving the relative amounts of various reactants and products that participate in a chemical reaction.

1. Calculate molar masses for the following compounds:
1. H2O
2. NH3
3. CH4
2. Calculate the mass (in grams) of the following samples:
1. 2.6 moles of water.
2. 1.4 x 1023 atoms of sulfur.

Introduction

When making a batch of chocolate chip cookies, a baker must pay careful attention to the amounts of ingredients he uses. The flour, sugar, butter, and chocolate chips must be measured and used in the correct ratios in order for the cookies to bake well. If the baker only has a certain amount of flour, only a certain amount of cookies can be made. Similarly, in chemical reactions, the resulting product is based on the initial moles of reactants present. In this lesson, you will learn how to calculate and account for the amounts of reactants and products in a given chemical reaction.

Mole Ratios: Equating Changes in Amount

We previously saw that mass is conserved for any chemical reaction. Atoms present during the beginning of a chemical reaction must be present at the end as well, even though they may be arranged in different ways. Consider the reaction between iron and oxygen to produce iron(III) oxide:

4Fe(s) + 3O2(g) → 2Fe2O3(s)

According to this equation 4 moles of iron will react with 3 moles of oxygen gas (O2) to produce 2 moles of iron(III) oxide, Fe2O3, as a product. Of course, we do not need exactly 4 moles of iron or 3 moles of oxygen for this reaction to occur. Rather, this equation tells us the ratio in which these reactants combine to make a particular product.

When we express the relative amounts of two reaction components as a ratio, we refer to this as a mole ratio or a stoichiometric ratio. Mole ratios can be made between two reactants, two products, or one of each. For example, the following mole ratios can be obtained by looking at the balanced equation shown above:

4 mol Fe3 mol O2 or 3 mol O24 mol Fe\begin{align*}\frac{4 \ \text{mol Fe}}{3 \ \text{mol O}_2} \ or \ \frac{3 \ \text{mol O}_2}{4 \ \text{mol Fe}}\end{align*}

4 mol Fe2 mol Fe2O3 or 2 mol Fe2O34 mol Fe\begin{align*}\frac{4 \ \text{mol Fe}}{2 \ \text{mol Fe}_2\text{O}_3} \ or \ \frac{2 \ \text{mol Fe}_2\text{O}_3}{4 \ \text{mol Fe}}\end{align*}

3 mol O22 mol Fe2O3 or 3 mol O22 mol Fe2O3\begin{align*}\frac{3 \ \text{mol O}_2}{2 \ \text{mol Fe}_2\text{O}_3} \ or \ \frac{3 \ \text{mol O}_2}{2 \ \text{mol Fe}_2\text{O}_3}\end{align*}

Stoichiometry refers to the calculations involving mole ratios to determine the relative amounts of reactants needed to produce a given amount of product. Consider the reaction of sodium chloride with silver nitrate:

AgNO3(aq) + NaCl(aq) → AgCl(s) + NaNO3(aq)

Silver chloride is an important compound that is commonly used in the production of photographic film. It also has many other uses, such as an antidote for mercury poisoning, a component of pottery glazes, and a reference standard for electrochemistry setups. It can be produced according to the reaction shown above. Now we will practice use of mole ratios and stoichiometry to determine the amounts of products and reactants necessary in our reaction.

Example 12.1

How many moles of each reactant are needed to produce 0.5 mol of silver chloride?

For this problem, we need to relate moles of each reactant to moles of the product silver chloride. The mole ratio of silver nitrate to silver chloride is constructed as follows:

As shown above, we would need 0.5 mol of silver nitrate to produce 0.5 mol of silver chloride.

We could also express the moles of silver chloride in terms of sodium chloride, our other reactant. Here is how we would do this:

Therefore, we would also need 0.5 mol of sodium chloride in order to produce 0.5 mol of silver chloride. Notice that in each case, we use the mole ratio to relate moles of reactants to moles of products.

Not all reactions have 1:1 ratios between reactants and products. For instance, the reaction between lead(II) nitrate and sodium chloride produces the precipitate lead(II) chloride and aqueous sodium nitrate:

Pb(NO3)2(aq) + 2NaCl(aq) → PbCl2(s) + 2 NaNO3(aq)

Lead(II) chloride is commonly used in the production of decorative glass, called Aurene. It also has many other uses. For example, it is used in the production of paints and in industrial processes that remove unwanted metals.

Example 12.2

If we wanted to make 0.5 mol of lead(II) chloride, how many moles of each reactant would be needed?

First, we will relate moles of the reactant sodium chloride to the desired product. The mole ratio between these two substances can be used as a conversion factor as follows:

0.5 mol PbCl2 × (2 mol NaCl1 mol PbCl2\begin{align*}\mathrm{\frac{2 \ \text{mol NaCl}}{1 \ \text{mol PbCl}_2}}\end{align*}) = 1 mol NaCl

In order to produce 0.5 mol of lead(II) chloride, we would need 1 mol of sodium chloride. The necessary amount of the other reactant can be calculated in the same way:

0.5 mol PbCl2 × (1 mol Pb(NO3)21 mol PbCl2\begin{align*}\mathrm{\frac{1 \ \text{mol Pb}(\text{NO}_3)_2}{1 \ \text{mol PbCl}_2}}\end{align*}) = 0.5 mol Pb(NO3)2

We can use mole ratios to determine the amounts of reactants needed to produce a given amount of product. As we will see in the next lesson, we can also convert these amounts into masses using our understanding of molar mass.

Lesson Summary

• Mole ratios can be derived from a balanced chemical equation. These ratios can then be used to determine the amounts of each substance involved in a given chemical reaction.
• Stoichiometry refers to calculations involving the relative amounts of various reactants and products that participate in a chemical reaction.

Lesson Review Questions

1. Aluminum reacts with oxygen to produce aluminum oxide as follows: 4Al + 3O2 → 2Al2O3
1. If you use 2.3 moles of Al, how many moles of Al2O3 can you make?
2. If you want 3.9 moles of Al2O3, how many moles of O2 are needed?
2. In the presence of sulfuric acid, metallic iron forms iron(III) sulfate: 2Fe + 3H2SO4 → Fe2(SO4)3 + 3H2
1. How many moles of hydrogen will be produced when you use 1.7 moles of iron?
2. How much sulfuric acid is needed to produce 2.8 moles of iron(III) sulfate?
3. Write the mole ratios for reactants in terms of products for the following equation: 2 Mg + O2 → 2 MgO
4. How many moles of each reactant are needed to produce 2.5 mol of aluminum oxide by the following reaction? 4 Al + 3 O2 → 2 Al2O3
5. How many moles of each reactant would be necessary to produce 2.6 mol of barium sulfate by the following reaction? BaCl2 + Na2SO4 → BaSO4 + 2NaCl

Points to Consider

• If you know how many moles of product a reaction yielded, can you find the mass of reactants used in the initial reaction?

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