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Chapter 4 Stoichiometry of Chemical Reactions175Chapter 4Stoichiometry of ChemicalReactionsFigure 4.1 Many modern rocket fuels are solid mixtures of substances combined in carefully measured amountsand ignited to yield a thrust-generating chemical reaction. (credit: modification of work by NASA)Chapter Outline4.1 Writing and Balancing Chemical Equations4.2 Classifying Chemical Reactions4.3 Reaction Stoichiometry4.4 Reaction Yields4.5 Quantitative Chemical AnalysisIntroductionSolid-fuel rockets are a central feature in the world’s space exploration programs, including the new Space LaunchSystem being developed by the National Aeronautics and Space Administration (NASA) to replace the retired SpaceShuttle fleet (Figure 4.1). The engines of these rockets rely on carefully prepared solid mixtures of chemicalscombined in precisely measured amounts. Igniting the mixture initiates a vigorous chemical reaction that rapidlygenerates large amounts of gaseous products. These gases are ejected from the rocket engine through its nozzle,providing the thrust needed to propel heavy payloads into space. Both the nature of this chemical reaction and therelationships between the amounts of the substances being consumed and produced by the reaction are criticallyimportant considerations that determine the success of the technology. This chapter will describe how to symbolizechemical reactions using chemical equations, how to classify some common chemical reactions by identifyingpatterns of reactivity, and how to determine the quantitative relations between the amounts of substances involved inchemical reactions—that is, the reaction stoichiometry.

176Chapter 4 Stoichiometry of Chemical Reactions4.1 Writing and Balancing Chemical EquationsBy the end of this section, you will be able to: Derive chemical equations from narrative descriptions of chemical reactions. Write and balance chemical equations in molecular, total ionic, and net ionic formats.The preceding chapter introduced the use of element symbols to represent individual atoms. When atoms gain or loseelectrons to yield ions, or combine with other atoms to form molecules, their symbols are modified or combined togenerate chemical formulas that appropriately represent these species. Extending this symbolism to represent both theidentities and the relative quantities of substances undergoing a chemical (or physical) change involves writing andbalancing a chemical equation. Consider as an example the reaction between one methane molecule (CH4) and twodiatomic oxygen molecules (O2) to produce one carbon dioxide molecule (CO2) and two water molecules (H2O). Thechemical equation representing this process is provided in the upper half of Figure 4.2, with space-filling molecularmodels shown in the lower half of the figure.Figure 4.2 The reaction between methane and oxygen to yield carbon dioxide in water (shown at bottom) may berepresented by a chemical equation using formulas (top).This example illustrates the fundamental aspects of any chemical equation:1. The substances undergoing reaction are called reactants, and their formulas are placed on the left side of theequation.2. The substances generated by the reaction are called products, and their formulas are placed on the right sightof the equation.3. Plus signs ( ) separate individual reactant and product formulas, and an arrow ( ) separates the reactantand product (left and right) sides of the equation.4. The relative numbers of reactant and product species are represented by coefficients (numbers placedimmediately to the left of each formula). A coefficient of 1 is typically omitted.It is common practice to use the smallest possible whole-number coefficients in a chemical equation, as is done inthis example. Realize, however, that these coefficients represent the relative numbers of reactants and products, and,therefore, they may be correctly interpreted as ratios. Methane and oxygen react to yield carbon dioxide and waterin a 1:2:1:2 ratio. This ratio is satisfied if the numbers of these molecules are, respectively, 1-2-1-2, or 2-4-2-4, or3-6-3-6, and so on (Figure 4.3). Likewise, these coefficients may be interpreted with regard to any amount (number)unit, and so this equation may be correctly read in many ways, including:This content is available for free at http://cnx.org/content/col11760/1.9

Chapter 4 Stoichiometry of Chemical Reactions177 One methane molecule and two oxygen molecules react to yield one carbon dioxide molecule and two watermolecules. One dozen methane molecules and two dozen oxygen molecules react to yield one dozen carbon dioxidemolecules and two dozen water molecules. One mole of methane molecules and 2 moles of oxygen molecules react to yield 1 mole of carbon dioxidemolecules and 2 moles of water molecules.Figure 4.3 Regardless of the absolute number of molecules involved, the ratios between numbers of molecules arethe same as that given in the chemical equation.Balancing EquationsThe chemical equation described in section 4.1 is balanced, meaning that equal numbers of atoms for each elementinvolved in the reaction are represented on the reactant and product sides. This is a requirement the equation mustsatisfy to be consistent with the law of conservation of matter. It may be confirmed by simply summing the numbersof atoms on either side of the arrow and comparing these sums to ensure they are equal. Note that the number ofatoms for a given element is calculated by multiplying the coefficient of any formula containing that element by theelement’s subscript in the formula. If an element appears in more than one formula on a given side of the equation, thenumber of atoms represented in each must be computed and then added together. For example, both product species inthe example reaction, CO2 and H2O, contain the element oxygen, and so the number of oxygen atoms on the productside of the equation is 2 O atoms 1 O atom 1 CO 2 molecule CO 2 molecule 2 H 2 O molecule H 2 O molecule 4 O atomsThe equation for the reaction between methane and oxygen to yield carbon dioxide and water is confirmed to bebalanced per this approach, as shown here:CH 4 2O 2 CO 2 2H 2 OElementReactantsProductsBalanced?C1 1 11 1 11 1, yesH4 1 42 2 44 4, yesO2 2 4(1 2) (2 1) 44 4, yes

178Chapter 4 Stoichiometry of Chemical ReactionsA balanced chemical equation often may be derived from a qualitative description of some chemical reaction by afairly simple approach known as balancing by inspection. Consider as an example the decomposition of water to yieldmolecular hydrogen and oxygen. This process is represented qualitatively by an unbalanced chemical equation:H2 O H2 O2(unbalanced)Comparing the number of H and O atoms on either side of this equation confirms its imbalance:ElementReactantsProductsBalanced?H1 2 21 2 22 2, yesO1 1 11 2 21 2, noThe numbers of H atoms on the reactant and product sides of the equation are equal, but the numbers of O atomsare not. To achieve balance, the coefficients of the equation may be changed as needed. Keep in mind, of course, thatthe formula subscripts define, in part, the identity of the substance, and so these cannot be changed without alteringthe qualitative meaning of the equation. For example, changing the reactant formula from H2O to H2O2 would yieldbalance in the number of atoms, but doing so also changes the reactant’s identity (it’s now hydrogen peroxide and notwater). The O atom balance may be achieved by changing the coefficient for H2O to 2.2H 2 O H 2 O 2(unbalanced)ElementReactantsProductsBalanced?H2 2 41 2 24 2, noO2 1 21 2 22 2, yesThe H atom balance was upset by this change, but it is easily reestablished by changing the coefficient for the H2product to 2.2H 2 O 2H 2 O 2(balanced)ElementReactantsProductsBalanced?H2 2 42 2 24 4, yesO2 1 21 2 22 2, yesThese coefficients yield equal numbers of both H and O atoms on the reactant and product sides, and the balancedequation is, therefore:2H 2 O 2H 2 O 2Example 4.1Balancing Chemical EquationsThis content is available for free at http://cnx.org/content/col11760/1.9

Chapter 4 Stoichiometry of Chemical Reactions179Write a balanced equation for the reaction of molecular nitrogen (N2) and oxygen (O2) to form dinitrogenpentoxide.SolutionFirst, write the unbalanced equation.N2 O2 N2 O5(unbalanced)Next, count the number of each type of atom present in the unbalanced equation.ElementReactantsProductsBalanced?N1 2 21 2 22 2, yesO1 2 21 5 52 5, noThough nitrogen is balanced, changes in coefficients are needed to balance the number of oxygen atoms. Tobalance the number of oxygen atoms, a reasonable first attempt would be to change the coefficients for theO2 and N2O5 to integers that will yield 10 O atoms (the least common multiple for the O atom subscripts inthese two formulas).N 2 5O 2 2N 2 O 5(unbalanced)ElementReactantsProductsBalanced?N1 2 22 2 42 4, noO5 2 102 5 1010 10, yesThe N atom balance has been upset by this change; it is restored by changing the coefficient for the reactantN2 to 2.2N 2 5O 2 2N 2 O 5ElementReactantsProductsBalanced?N2 2 42 2 44 4, yesO5 2 102 5 1010 10, yesThe numbers of N and O atoms on either side of the equation are now equal, and so the equation is balanced.Check Your LearningWrite a balanced equation for the decomposition of ammonium nitrate to form molecular nitrogen,molecular oxygen, and water. (Hint: Balance oxygen last, since it is present in more than one molecule onthe right side of the equation.)Answer: 2NH 4 NO 3 2N 2 O 2 4H 2 O

180Chapter 4 Stoichiometry of Chemical ReactionsIt is sometimes convenient to use fractions instead of integers as intermediate coefficients in the process of balancinga chemical equation. When balance is achieved, all the equation’s coefficients may then be multiplied by a wholenumber to convert the fractional coefficients to integers without upsetting the atom balance. For example, considerthe reaction of ethane (C2H6) with oxygen to yield H2O and CO2, represented by the unbalanced equation:C 2 H 6 O 2 H 2 O CO 2(unbalanced)Following the usual inspection approach, one might first balance C and H atoms by changing the coefficients for thetwo product species, as shown:C 2 H 6 O 2 3H 2 O 2CO 2(unbalanced)This results in seven O atoms on the product side of the equation, an odd number—no integer coefficient can be usedwith the O2 reactant to yield an odd number, so a fractional coefficient, 7 , is used instead to yield a provisional2balanced equation:C 2 H 6 7 O 2 3H 2 O 2CO 22A conventional balanced equation with integer-only coefficients is derived by multiplying each coefficient by 2:2C 2 H 6 7O 2 6H 2 O 4CO 2Finally with regard to balanced equations, recall that convention dictates use of the smallest whole-numbercoefficients. Although the equation for the reaction between molecular nitrogen and molecular hydrogen to produceammonia is, indeed, balanced,3N 2 9H 2 6NH 3the coefficients are not the smallest possible integers representing the relative numbers of reactant and productmolecules. Dividing each coefficient by the greatest common factor, 3, gives the preferred equation:N 2 3H 2 2NH 3Link to LearningUse this interactive tutorial (http://openstaxcollege.org/l/16BalanceEq) foradditional practice balancing equations.Additional Information in Chemical EquationsThe physical states of reactants and products in chemical equations very often are indicated with a parentheticalabbreviation following the formulas. Common abbreviations include s for solids, l for liquids, g for gases, and aqfor substances dissolved in water (aqueous solutions, as introduced in the preceding chapter). These notations areillustrated in the example equation here:2Na(s) 2H 2 O(l) 2NaOH(aq) H 2(g)This equation represents the reaction that takes place when sodium metal is placed in water. The solid sodium reactswith liquid water to produce molecular hydrogen gas and the ionic compound sodium hydroxide (a solid in pure form,but readily dissolved in water).This content is available for free at http://cnx.org/content/col11760/1.9

Chapter 4 Stoichiometry of Chemical Reactions181Special conditions necessary for a reaction are sometimes designated by writing a word or symbol above or below theequation’s arrow. For example, a reaction carried out by heating may be indicated by the uppercase Greek letter delta(Δ) over the arrow.ΔCaCO 3(s) CaO(s) CO 2(g)Other examples of these special conditions will be encountered in more depth in later chapters.Equations for Ionic ReactionsGiven the abundance of water on earth, it stands to reason that a great many chemical reactions take place in aqueousmedia. When ions are involved in these reactions, the chemical equations may be written with various levels of detailappropriate to their intended use. To illustrate this, consider a reaction between ionic compounds taking place in anaqueous solution. When aqueous solutions of CaCl2 and AgNO3 are mixed, a reaction takes place producing aqueousCa(NO3)2 and solid AgCl:CaCl 2(aq) 2AgNO 3(aq) Ca(NO 3) 2(aq) 2AgCl(s)This balanced equation, derived in the usual fashion, is called a molecular equation because it doesn’t explicitlyrepresent the ionic species that are present in solution. When ionic compounds dissolve in water, they may dissociateinto their constituent ions, which are subsequently dispersed homogenously throughout the resulting solution (athorough discussion of this important process is provided in the chapter on solutions). Ionic compounds dissolved inwater are, therefore, more realistically represented as dissociated ions, in this case:CaCl 2(aq) Ca 2 (aq) 2Cl (aq)2AgNO 3(aq) 2Ag (aq) 2NO 3 (aq)Ca(NO 3) 2(aq) Ca 2 (aq) 2NO 3 (aq)Unlike these three ionic compounds, AgCl does not dissolve in wa