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Chapter 4 Stoichiometry of Chemical Reactions

4.2  Reaction Stoichiometry

Learning Objectives

By the end of this section, you will be able to:

  • Explain the concept of stoichiometry as it pertains to chemical reactions
  • Use balanced chemical equations to derive stoichiometric factors relating amounts of reactants and products
  • Perform stoichiometric calculations involving mass, moles, and solution molarity

A balanced chemical equation provides a great deal of information in a very succinct format. Chemical formulas provide the identities of the reactants and products involved in the chemical change, allowing classification of the reaction. As seen in Chapter 4, Introduction, the relationships between the amounts of the substances being consumed and produced are critical. Coefficients provide the relative numbers of these chemical species, allowing a quantitative assessment of the relationships between the amounts of substances consumed and produced by the reaction. These quantitative relationships are known as the reaction’s stoichiometry, a term derived from the Greek words stoicheion (meaning “element”) and metron (meaning “measure”). In this module, the use of balanced chemical equations for various stoichiometric applications is explored.

The general approach to using stoichiometric relationships is similar in concept to the way people go about many common activities. Food preparation, for example, offers an appropriate comparison. A recipe for making eight pancakes calls for 1 cup pancake mix, 3/4 cup milk, and one egg. The “equation” representing the preparation of pancakes per this recipe is:

1 cup mix + 3/4 cup milk + 1 egg → 8 pancakes

If two dozen pancakes are needed for a big family breakfast, the ingredient amounts must be increased proportionally according to the amounts given in the recipe. For example, the number of eggs required to make 24 pancakes is:

24pancakes1egg8pancakes=3eggs

Balanced chemical equations are used in much the same fashion to determine the amount of one reactant required to react with a given amount of another reactant, or to yield a given amount of product, and so forth. The coefficients in the balanced equation are used to derive stoichiometric factors that permit computation of the desired quantity. To illustrate this idea, consider the production of ammonia by reaction of hydrogen and nitrogen:

N2(g) + 3 H2(g) → 2 NH3(g)

This equation shows ammonia molecules are produced from hydrogen molecules in a 2:3 ratio, and stoichiometric factors may be derived using any amount (number) unit:

2NH3molecules3H2moleculesor2dozNH3molecules3dozH2moleculesor2molNH3molecules3molH2molecules

These stoichiometric factors can be used to compute the number of ammonia molecules produced from a given number of hydrogen molecules, or the number of hydrogen molecules required to produce a given number of ammonia molecules. Similar factors may be derived for any pair of substances in any chemical equation.

Example 4.3 − Moles of Reactant Required in a Reaction

How many moles of I2 are required to react with 0.429 mol of Al according to the following equation (Figure 4.4)?

2 Al + 3 I2 → 2 AlI3

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Three-stage chemical reaction sequence showing a powder igniting into purple and orange smoke.
Figure 4.4. Aluminum and iodine react to produce aluminum iodide. The heat of the reaction vaporizes some of the solid iodine as a purple vapor. (credit: modification of work by Mark Ott)

Solution

Referring to the balanced chemical equation, the stoichiometric factor relating the two substances of interest is [latex]\frac {3 \: mol \: I_2}{2 \: mol \: Al}[/latex]. The molar amount of iodine is derived by multiplying the provided molar amount of aluminum by this factor:

Flowchart showing conversion from moles of Al to moles of I₂ via a stoichiometric factor.
The image shows a horizontal flowchart with two beige rectangular boxes connected by a thick gray arrow pointing from left to right. The left box contains the text “Moles of Al,” while the right box contains the text “Moles of I₂.” Above the arrow, there is a label stating “Stoichiometric factor,” indicating a conversion or relationship between the two sets of moles.

molI2=0.429molAl3molI22molAl=0.644molI2

 

Check Your Learning

Example 4.4 − Number of Product Molecules Generated by a Reaction

How many carbon dioxide molecules are produced when 0.75 mol of propane is combusted according to this equation?

C3H8 + 5 O2 → 3 CO2 + 4 H2O

 

Solution

The approach here is the same as for the previous example, though the absolute number of molecules is requested, not the number of moles of molecules. This will simply require use of the moles-to-numbers conversion factor, Avogadro’s number.

The balanced equation shows that carbon dioxide is produced from propane in a 3:1 ratio:

3molCO21molC3H8

Using this stoichiometric factor, the provided molar amount of propane, and Avogadro’s number,

0.75molC3H83molCO21molC3H86.022×1023CO2moleculesmolCO2
=1.4×1024CO2molecules

Diagram showing a conversion from moles of C₃H₈ to molecules of CO₂ through stoichiometric factor and Avogadro's number.
The image is a diagram illustrating a chemical conversion process. It consists of three rectangular boxes connected by arrows, set against a light blue background. The first box on the left is labeled “Moles of C₃H₈.” An arrow labeled “Stoichiometric factor” points to the middle box, which is labeled “Moles of CO₂.” From the middle box, another arrow labeled “Avogadro’s number” points to the rightmost box labeled “Molecules of CO₂.” All boxes and labels are in a soft beige color with dark gray text.

Check Your Learning

These examples illustrate the ease with which the amounts of substances involved in a chemical reaction of known stoichiometry may be related. Directly measuring numbers of atoms and molecules is, however, not an easy task, and the practical application of stoichiometry requires that we use the more readily measured property of mass.

Example 4.5 − Relating Masses of Reactants and Products

What mass of sodium hydroxide, NaOH, would be required to produce 16 g of the antacid milk of magnesia [magnesium hydroxide, Mg(OH)2] by the following reaction?

MgCl2(aq) + 2 NaOH(aq) → Mg(OH)2(s) + 2 NaCl(aq)

 

Solution

The approach used previously in Example 4.3 and Example 4.4 is likewise used here; that is, we must derive an appropriate stoichiometric factor from the balanced chemical equation and use it to relate the amounts of the two substances of interest. In this case, however, masses (not molar amounts) are provided and requested, so additional steps of the sort learned in the previous chapter are required.

16gMg(OH)21molMg(OH)258.3gMg(OH)22molNaOH1molMg(OH)240.0gNaOHmolNaOH
=22gNaOH 

The calculations required are outlined in this flowchart:

Flowchart converting mass to moles for Mg(OH)₂ and NaOH with a stoichiometric factor.
The image depicts a flowchart with a light blue background outlining the process of converting mass to moles for two chemical substances: magnesium hydroxide (Mg(OH)₂) and sodium hydroxide (NaOH). There are four rectangular boxes connected by arrows. The top left box is labeled “Mass of Mg(OH)₂” with an arrow pointing to the top right box labeled “Moles of Mg(OH)₂.” Below this, the bottom left box is labeled “Mass of NaOH” connected by an arrow to the bottom right box labeled “Moles of NaOH.” An additional vertical arrow connects the “Moles of Mg(OH)₂” box to the “Moles of NaOH” box with the label “Stoichiometric factor.” Arrows between “Mass of Mg(OH)₂” and “Moles of Mg(OH)₂,” and between “Mass of NaOH” and “Moles of NaOH” are labeled “Molar mass.”

Check Your Learning

Example 4.6 − Relating Masses of Reactants

What mass of oxygen gas, O2, from the air is consumed in the combustion of 702 g of octane, C8H18, one of the principal components of gasoline?

2 C8H18 + 25 O2 → 16 CO2 + 18 H2O

 

Solution

The approach required here is the same as for the Example 4.5, differing only in that the provided and requested masses are both for reactant species.

702gC8H181molC8H18114.23gC8H1825molO22molC8H1832.00gO2molC8H18
=2.46×103gO2

Flowchart showing conversion between mass and moles with C₈H₁₈ and O₂.
The image is a flowchart depicting the conversion of mass to moles using molar mass and stoichiometric factors. It consists of four rectangular boxes arranged in a square layout with connecting arrows. The top-left box contains the text “Mass of C₈H₁₈,” and an arrow labeled “Molar mass” points right to the top-right box that reads “Moles of C₈H₁₈.” From this box, another arrow labeled “Stoichiometric factor” points downward to the bottom-right box titled “Moles of O₂.” Finally, an arrow labeled “Molar mass” extends left from this box to the bottom-left box, which states “Mass of O₂.” The boxes and arrows are set against a light blue background.

Check Your Learning

These examples illustrate just a few instances of reaction stoichiometry calculations. Numerous variations on the beginning and ending computational steps are possible depending upon what particular quantities are provided and sought (volumes, solution concentrations, and so forth). Regardless of the details, all these calculations share a common essential component: the use of stoichiometric factors derived from balanced chemical equations. Figure 4.5 provides a general outline of the various computational steps associated with many reaction stoichiometry calculations.

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Flow chart depicting the relationships between moles, mass, volume, and number of particles for substances A and B.
Figure 4.5. The flowchart depicts the various computational steps involved in most reaction stoichiometry calculations.

Chemistry in Everyday Life

Airbags

Airbags (Figure 4.6) are a safety feature provided in most automobiles since the 1990s. The effective operation of an airbag requires that it be rapidly inflated with an appropriate amount (volume) of gas when the vehicle is involved in a collision. This requirement is satisfied in many automotive airbag systems through the use of explosive chemical reactions, one common choice being the decomposition of sodium azide, NaN3. When sensors in the vehicle detect a collision, an electrical current is passed through a carefully measured amount of NaN3 to initiate its decomposition:

2 NaN3(s) → 3 N2(g) + 2 Na(s)

This reaction is very rapid, generating gaseous nitrogen that can deploy and fully inflate a typical airbag in a fraction of a second (~0.03–0.1 s). Among many engineering considerations, the amount of sodium azide used must be appropriate for generating enough nitrogen gas to fully inflate the air bag and ensure its proper function. For example, a small mass (~100 g) of NaN3 will generate approximately 50 L of N2.

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Interior of a car with deployed front airbags and a visible "E" marker on the passenger seat.
Figure 4.6. Airbags deploy upon impact to minimize serious injuries to passengers. (credit: Jon Seidman)

License

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4.2 Reaction Stoichiometry Copyright © by Nicole Bouvier-Brown; Saori Shiraki; J. Ryan Hunt; and Emily Jarvis is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.