OpenStax: General Chemistry
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4 Stoichiometry of Chemical Reactions
4.1 Writing and Balancing Chemical Equations
4.2 Classifying Chemical Reactions
4.3 Reaction Stoichiometry
4.4 Reaction Yields
4.5 Quantitative Chemical Analysis
Many modern rocket fuels are solid mixtures of substances combined in carefully measured amounts and ignited to yield a thrust-generating chemical reaction. (credit: modification of work by NASA)
Solid-fuel rockets are a central feature in the world’s space exploration programs, including the new Space Launch System being developed by the National Aeronautics and Space Administration (NASA) to replace the retired Space Shuttle fleet (Figure 4.1). The engines of these rockets rely on carefully prepared solid mixtures of chemicals combined in precisely measured amounts. Igniting the mixture initiates a vigorous chemical reaction that rapidly generates 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 the relationships between the amounts of the substances being consumed and produced by the reaction are critically important considerations that determine the success of the technology. This chapter will describe how to symbolize chemical reactions using chemical equations, how to classify some common chemical reactions by identifying patterns of reactivity, and how to determine the quantitative relations between the amounts of substances involved in chemical reactions—that is, the reaction stoichiometry.
4.1 Writing and Balancing Chemical Equations
By 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 lose electrons to yield ions, or combine with other atoms to form molecules, their symbols are modified or combined to generate chemical formulas that appropriately represent these species. Extending this symbolism to represent both the identities and the relative quantities of substances undergoing a chemical (or physical) change involves writing and balancing a chemical equation. Consider as an example the reaction between one methane molecule (CH4) and two diatomic oxygen molecules (O2) to produce one carbon dioxide molecule (CO2) and two water molecules (H2O). The chemical equation representing this process is provided in the upper half of Figure 4.2, with space-filling molecular models shown in the lower half of the figure.
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 the equation.
2. The substances generated by the reaction are called products, and their formulas are placed on the right sight of the equation.
3. Plus signs (+) separate individual reactant and product formulas, and an arrow (→) separates the reactant and product (left and right) sides of the equation.
4. The relative numbers of reactant and product species are represented by coefficients (numbers placed immediately 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 in this 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 water in 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, or 3-6-3-6, 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:
- One methane molecule and two oxygen molecules react to yield one carbon dioxide molecule and two water molecules.
- One dozen methane molecules and two dozen oxygen molecules react to yield one dozen carbon dioxide molecules and two dozen water molecules.
- One mole of methane molecules and 2 moles of oxygen molecules react to yield 1 mole of carbon dioxide molecules and 2 moles of water molecules.
The chemical equation described in section 4.1 is balanced, meaning that equal numbers of atoms for each element involved in the reaction are represented on the reactant and product sides. This is a requirement the equation must satisfy to be consistent with the law of conservation of matter. It may be confirmed by simply summing the numbers of atoms on either side of the arrow and comparing these sums to ensure they are equal. Note that the number of atoms for a given element is calculated by multiplying the coefficient of any formula containing that element by the element’s subscript in the formula. If an element appears in more than one formula on a given side of the equation, the number of atoms represented in each must be computed and then added together. For example, both product species in the example reaction, CO2 and H2O, contain the element oxygen, and so the number of oxygen atoms on the product side of the equation is
The equation for the reaction between methane and oxygen to yield carbon dioxide and water is confirmed to be balanced per this approach, as shown here:
A balanced chemical equation often may be derived from a qualitative description of some chemical reaction by a fairly simple approach known as balancing by inspection. Consider as an example the decomposition of water to yield molecular hydrogen and oxygen. This process is represented qualitatively by an unbalanced chemical equation:
Comparing the number of H and O atoms on either side of this equation confirms its imbalance:
The numbers of H atoms on the reactant and product sides of the equation are equal, but the numbers of O atoms are not. To achieve balance, the coefficients of the equation may be changed as needed. Keep in mind, of course, that the formula subscripts define, in part, the identity of the substance, and so these cannot be changed without altering the qualitative meaning of the equation. For example, changing the reactant formula from H2O to H2O2 would yield balance in the number of atoms, but doing so also changes the reactant’s identity (it’s now hydrogen peroxide and not water). The O atom balance may be achieved by changing the coefficient for H2O to 2.
The H atom balance was upset by this change, but it is easily reestablished by changing the coefficient for the H2 product to 2.
These coefficients yield equal numbers of both H and O atoms on the reactant and product sides, and the balanced equation is, therefore:
Balancing Chemical Equations
Write a balanced equation for the reaction of molecular nitrogen (N2) and oxygen (O2) to form dinitrogen pentoxide.
First, write the unbalanced equation.
Next, count the number of each type of atom present in the unbalanced equation.
Though nitrogen is balanced, changes in coefficients are needed to balance the number of oxygen atoms. To balance the number of oxygen atoms, a reasonable first attempt would be to change the coefficients for the O2 and N2O5 to integers that will yield 10 O atoms (the least common multiple for the O atom subscripts in these two formulas).
The N atom balance has been upset by this change; it is restored by changing the coefficient for the reactant N2 to 2.
The numbers of N and O atoms on either side of the equation are now equal, and so the equation is balanced.
Check Your Learning
Write 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 on the right side of the equation.)
It is sometimes convenient to use fractions instead of integers as intermediate coefficients in the process of balancing a chemical equation. When balance is achieved, all the equation’s coefficients may then be multiplied by a whole number to convert the fractional coefficients to integers without upsetting the atom balance. For example, consider the reaction of ethane (C2H6) with oxygen to yield H2O and CO2, represented by the unbalanced equation:
Following the usual inspection approach, one might first balance C and H atoms by changing the coefficients for the two product species, as shown:
This results in seven O atoms on the product side of the equation, an odd number—no integer coefficient can be used with the O2 reactant to yield an odd number, so a fractional coefficient, 7/2, is used instead to yield a provisional balanced equation:
A conventional balanced equation with integer-only coefficients is derived by multiplying each coefficient by 2:
Finally with regard to balanced equations, recall that convention dictates use of the smallest whole-number coefficients. Although the equation for the reaction between molecular nitrogen and molecular hydrogen to produce ammonia is, indeed, balanced,
the coefficients are not the smallest possible integers representing the relative numbers of reactant and product molecules. Dividing each coefficient by the greatest common factor, 3, gives the preferred equation:
Link to Learning
Use this interactive tutorial for additional practice balancing equations.
Additional Information in Chemical Equations
The physical states of reactants and products in chemical equations very often are indicated with a parenthetical abbreviation following the formulas. Common abbreviations include s for solids, l for liquids, g for gases, and aq for substances dissolved in water (aqueous solutions, as introduced in the preceding chapter). These notations are illustrated in the example equation here:
This equation represents the reaction that takes place when sodium metal is placed in water. The solid sodium reacts with liquid water to produce molecular hydrogen gas and the ionic compound sodium hydroxide (a solid in pure form, but readily dissolved in water).
Special conditions necessary for a reaction are sometimes designated by writing a word or symbol above or below the equation’s arrow. For example, a reaction carried out by heating may be indicated by the uppercase Greek letter delta (Δ) over the arrow.
Other examples of these special conditions will be encountered in more depth in later chapters.
Equations for Ionic Reactions
Given the abundance of water on earth, it stands to reason that a great many chemical reactions take place in aqueous media. When ions are involved in these reactions, the chemical equations may be written with various levels of detail appropriate to their intended use. To illustrate this, consider a reaction between ionic compounds taking place in an aqueous solution. When aqueous solutions of CaCl2 and AgNO3 are mixed, a reaction takes place producing aqueous Ca(NO3)2 and solid AgCl:
This balanced equation, derived in the usual fashion, is called a molecular equation because it doesn’t explicitly represent the ionic species that are present in solution. When ionic compounds dissolve in water, they may dissociate into their constituent ions, which are subsequently dispersed homogenously throughout the resulting solution (a thorough discussion of this important process is provided in the chapter on solutions). Ionic compounds dissolved in water are, therefore, more realistically represented as dissociated ions, in this case:
Unlike these three ionic compounds, AgCl does not dissolve in water to a significant extent, as signified by its physical state notation, s.
Explicitly representing all dissolved ions results in a complete ionic equation. In this particular case, the formulas for the dissolved ionic compounds are replaced by formulas for their dissociated ions:
Examining this equation shows that two chemical species are present in identical form on both sides of the arrow, Ca2+(aq) and NO3−(aq). These spectator ions—ions whose presence is required to maintain charge neutrality—are neither chemically nor physically changed by the process, and so they may be eliminated from the equation to yield a more succinct representation called a net ionic equation:
Following the convention of using the smallest possible integers as coefficients, this equation is then written:
This net ionic equation indicates that solid silver chloride may be produced from dissolved chloride and silver(I) ions, regardless of the source of these ions. These molecular and complete ionic equations provide additional information, namely, the ionic compounds used as sources of Cl− and Ag+.
Molecular and Ionic Equations
When carbon dioxide is dissolved in an aqueous solution of sodium hydroxide, the mixture reacts to yield aqueous sodium carbonate and liquid water. Write balanced molecular, complete ionic, and net ionic equations for this process.
Begin by identifying formulas for the reactants and products and arranging them properly in chemical equation form:
Balance is achieved easily in this case by changing the coefficient for NaOH to 2, resulting in the molecular equation for this reaction:
The two dissolved ionic compounds, NaOH and Na2CO3, can be represented as dissociated ions to yield the complete ionic equation:
Finally, identify the spectator ion(s), in this case Na+(aq), and remove it from each side of the equation to generate the net ionic equation:
Check Your Learning
Diatomic chlorine and sodium hydroxide (lye) are commodity chemicals produced in large quantities, along with diatomic hydrogen, via the electrolysis of brine, according to the following unbalanced equation:
Write balanced molecular, complete ionic, and net ionic equations for this process.
1. What does it mean to say an equation is balanced? Why is it important for an equation to be balanced?
Click here to see the answer to Question 4.1
2. Consider molecular, complete ionic, and net ionic equations. (a) What is the difference between these types of equations? (b) In what circumstance would the complete and net ionic equations for a reaction be identical?
3. Balance the following equations: (a) PCl(s) + HO(l) → POCl(l) + HCl(aq) (b) Cu(s) + HNO(aq) → Cu(NO)(aq) + HO(l) + NO(g) (c) H(g) + I(s) → HI(s) (d) Fe(s) + O(g) → FeO(s) (e) Na(s) + HO(l) → NaOH(aq) + H(g) (f) (NH) CrO(s) → CrO(s) + N(g) + HO(g) (g) P(s) + Cl(g) → PCl(l) (h) PtCl(s) → Pt(s) + Cl(g)
Click here to see the answer to Question 4.3
4. Balance the following equations: (a) Ag(s) + H S(g) + O(g) → AgS(s) + HO(l) (b) P(s) + O(g) → PO (s) (c) Pb(s) + HO(l) + O(g) → Pb(OH)(s) (d) Fe(s) + HO(l) → FeO(s) + H(g) (e) ScO(s) + SO(l) → Sc(SO)(s) (f) Ca(PO)(aq) + HPO(aq) → Ca(HPO)(aq) (g) Al(s) + HSO(aq) → Al(SO)(s) + H(g) (h) TiCl(s) + HO(g) → TiO(s) + HCl(g)
5. Write a balanced molecular equation describing each of the following chemical reactions. (a) Solid calcium carbonate is heated and decomposes to solid calcium oxide and carbon dioxide gas. (b) Gaseous butane, CH, reacts with diatomic oxygen gas to yield gaseous carbon dioxide and water vapor. (c) Aqueous solutions of magnesium chloride and sodium hydroxide react to produce solid magnesium hydroxide and aqueous sodium chloride. (d) Water vapor reacts with sodium metal to produce solid sodium hydroxide and hydrogen gas.
Click here to see the answer to Question 4.5
6. Write a balanced equation describing each of the following chemical reactions. (a) Solid potassium chlorate, KClO, decomposes to form solid potassium chloride and diatomic oxygen gas. (b) Solid aluminum metal reacts with solid diatomic iodine to form solid AlI. (c) When solid sodium chloride is added to aqueous sulfuric acid, hydrogen chloride gas and aqueous sodium sulfate are produced. (d) Aqueous solutions of phosphoric acid and potassium hydroxide react to produce aqueous potassium dihydrogen phosphate and liquid water.
7. Colorful fireworks often involve the decomposition of barium nitrate and potassium chlorate and the reaction of the metals magnesium, aluminum, and iron with oxygen. (a) Write the formulas of barium nitrate and potassium chlorate. (b) The decomposition of solid potassium chlorate leads to the formation of solid potassium chloride and diatomic oxygen gas. Write an equation for the reaction. (c) The decomposition of solid barium nitrate leads to the formation of solid barium oxide, diatomic nitrogen gas, and diatomic oxygen gas. Write an equation for the reaction. (d) Write separate equations for the reactions of the solid metals magnesium, aluminum, and iron with diatomic oxygen gas to yield the corresponding metal oxides. (Assume the iron oxide contains Fe ions.)
Click here to see the answer to Question 4.7
8. Fill in the blank with a single chemical formula for a covalent compound that will balance the equation:
9. Aqueous hydrogen fluoride (hydrofluoric acid) is used to etch glass and to analyze minerals for their silicon content. Hydrogen fluoride will also react with sand (silicon dioxide). (a) Write an equation for the reaction of solid silicon dioxide with hydrofluoric acid to yield gaseous silicon tetrafluoride and liquid water. (b) The mineral fluorite (calcium fluoride) occurs extensively in Illinois. Solid calcium fluoride can also be prepared by the reaction of aqueous solutions of calcium chloride and sodium fluoride, yielding aqueous sodium chloride as the other product. Write complete and net ionic equations for this reaction.
Click here to see the answer to Question 4.9
10. A novel process for obtaining magnesium from sea water involves several reactions. Write a balanced chemical equation for each step of the process. (a) The first step is the decomposition of solid calcium carbonate from seashells to form solid calcium oxide and gaseous carbon dioxide. (b) The second step is the formation of solid calcium hydroxide as the only product from the reaction of the solid calcium oxide with liquid water. (c) Solid calcium hydroxide is then added to the seawater, reacting with dissolved magnesium chloride to yield solid magnesium hydroxide and aqueous calcium chloride. (d) The solid magnesium hydroxide is added to a hydrochloric acid solution, producing dissolved magnesium chloride and liquid water. (e) Finally, the magnesium chloride is melted and electrolyzed to yield liquid magnesium metal and diatomic chlorine gas.
11. From the balanced molecular equations, write the complete ionic and net ionic equations for the following: (a) KCO(aq) + Ba(OH)(aq) → 2KOH(aq) + BaCO(s) (b) Pb(NO)(aq) + HSO(aq) → PbSO(s) + 2HNO(aq) (c) CaCO(s) + HSO(aq) → CaSO(s) + CO(g) + HO(l)
Click here to see the answer to Question 4.11
4.2 Classifying Chemical Reactions
By the end of this section, you will be able to:
- Define three common types of chemical reactions (precipitation, acid-base, and oxidation-reduction)
- Classify chemical reactions as one of these three types given appropriate descriptions or chemical equations
- Identify common acids and bases
- Predict the solubility of common inorganic compounds by using solubility rules
- Compute the oxidation states for elements in compounds
Humans interact with one another in various and complex ways, and we classify these interactions according to common patterns of behavior. When two humans exchange information, we say they are communicating. When they exchange blows with their fists or feet, we say they are fighting. Faced with a wide range of varied interactions between chemical substances, scientists have likewise found it convenient (or even necessary) to classify chemical interactions by identifying common patterns of reactivity. This module will provide an introduction to three of the most prevalent types of chemical reactions: precipitation, acid-base, and oxidation-reduction.
Precipitation Reactions and Solubility Rules
A precipitation reaction is one in which dissolved substances react to form one (or more) solid products. Many reactions of this type involve the exchange of ions between ionic compounds in aqueous solution and are sometimes referred to as double displacement, double replacement, or metathesis reactions. These reactions are common in nature and are responsible for the formation of coral reefs in ocean waters and kidney stones in animals. They are used widely in industry for production of a number of commodity and specialty chemicals. Precipitation reactions also play a central role in many chemical analysis techniques, including spot tests used to identify metal ions and gravimetric methods for determining the composition of matter (see the last module of this chapter).
The extent to which a substance may be dissolved in water, or any solvent, is quantitatively expressed as its solubility, defined as the maximum concentration of a substance that can be achieved under specified conditions. Substances with relatively large solubilities are said to be soluble. A substance will precipitate when solution conditions are such that its concentration exceeds its solubility. Substances with relatively low solubilities are said to be insoluble, and these are the substances that readily precipitate from solution. More information on these important concepts is provided in the text chapter on solutions. For purposes of predicting the identities of solids formed by precipitation reactions, one may simply refer to patterns of solubility that have been observed for many ionic compounds (Table 4.1).
A vivid example of precipitation is observed when solutions of potassium iodide and lead nitrate are mixed, resulting in the formation of solid lead iodide:
This observation is consistent with the solubility guidelines: The only insoluble compound among all those involved is lead iodide, one of the exceptions to the general solubility of iodide salts.
The net ionic equation representing this reaction is:
Lead iodide is a bright yellow solid that was formerly used as an artist’s pigment known as iodine yellow (Figure 4.4). The properties of pure PbI2 crystals make them useful for fabrication of X-ray and gamma ray detectors.
The solubility guidelines in Table 4.2 may be used to predict whether a precipitation reaction will occur when solutions of soluble ionic compounds are mixed together. One merely needs to identify all the ions present in the solution and then consider if possible cation/anion pairing could result in an insoluble compound. For example, mixing solutions of silver nitrate and sodium fluoride will yield a solution containing Ag+, NO3−, Na+, and F− ions. Aside from the two ionic compounds originally present in the solutions, AgNO3 and NaF, two additional ionic compounds may be derived from this collection of ions: NaNO3 and AgF. The solubility guidelines indicate all nitrate salts are soluble but that AgF is one of the exceptions to the general solubility of fluoride salts. A precipitation reaction, therefore, is predicted to occur, as described by the following equations:
Predicting Precipitation Reactions
Predict the result of mixing reasonably concentrated solutions of the following ionic compounds. If precipitation is expected, write a balanced net ionic equation for the reaction.
(a) potassium sulfate and barium nitrate
(b) lithium chloride and silver acetate
(c) lead nitrate and ammonium carbonate
(a) The two possible products for this combination are KNO3 and BaSO4. The solubility guidelines indicate BaSO4 is insoluble, and so a precipitation reaction is expected. The net ionic equation for this reaction, derived in the manner detailed in the previous module, is
(b) The two possible products for this combination are LiC2H3O2 and AgCl. The solubility guidelines indicate AgCl is insoluble, and so a precipitation reaction is expected. The net ionic equation for this reaction, derived in the manner detailed in the previous module, is
(c) The two possible products for this combination are PbCO3 and NH4NO3. The solubility guidelines indicate PbCO3 is insoluble, and so a precipitation reaction is expected. The net ionic equation for this reaction, derived in the manner detailed in the previous module, is
Check Your Learning
Which solution could be used to precipitate the barium ion, Ba2+, in a water sample: sodium chloride, sodium hydroxide, or sodium sulfate? What is the formula for the expected precipitate?
Answer: sodium sulfate, BaSO4
An acid-base reaction is one in which a hydrogen ion, H+, is transferred from one chemical species to another. Such reactions are of central importance to numerous natural and technological processes, ranging from the chemical transformations that take place within cells and the lakes and oceans, to the industrial-scale production of fertilizers, pharmaceuticals, and other substances essential to society. The subject of acid-base chemistry, therefore, is worthy of thorough discussion, and a full chapter is devoted to this topic later in the text.
For purposes of this brief introduction, we will consider only the more common types of acid-base reactions that take place in aqueous solutions. In this context, an acid is a substance that will dissolve in water to yield hydronium ions, H3O+. As an example, consider the equation shown here:
The process represented by this equation confirms that hydrogen chloride is an acid. When dissolved in water, H3O+ ions are produced by a chemical reaction in which H+ ions are transferred from HCl molecules to H2O molecules (Figure 4.5).
The nature of HCl is such that its reaction with water as just described is essentially 100% efficient: Virtually every HCl molecule that dissolves in water will undergo this reaction. Acids that completely react in this fashion are called strong acids, and HCl is one among just a handful of common acid compounds that are classified as strong (Table 4.2). A far greater number of compounds behave as weak acids and only partially react with water, leaving a large majority of dissolved molecules in their original form and generating a relatively small amount of hydronium ions. Weak acids are commonly encountered in nature, being the substances partly responsible for the tangy taste of citrus fruits, the stinging sensation of insect bites, and the unpleasant smells associated with body odor. A familiar example of a weak acid is acetic acid, the main ingredient in food vinegars:
When dissolved in water under typical conditions, only about 1% of acetic acid molecules are present in the ionized form, CH3CO2− (Figure 4.6). (The use of a double-arrow in the equation above denotes the partial reaction aspect of this process, a concept addressed fully in the chapters on chemical equilibrium.)
A base is a substance that will dissolve in water to yield hydroxide ions, OH−. The most common bases are ionic compounds composed of alkali or alkaline earth metal cations (groups 1 and 2) combined with the hydroxide ion—for example, NaOH and Ca(OH)2. When these compounds dissolve in water, hydroxide ions are released directly into the solution. For example, KOH and Ba(OH)2 dissolve in water and dissociate completely to produce cations (K+ and Ba2+, respectively) and hydroxide ions, OH−. These bases, along with other hydroxides that completely dissociate in water, are considered strong bases.
Consider as an example the dissolution of lye (sodium hydroxide) in water:
This equation confirms that sodium hydroxide is a base. When dissolved in water, NaOH dissociates to yield Na+ and OH− ions. This is also true for any other ionic compound containing hydroxide ions. Since the dissociation process is essentially complete when ionic compounds dissolve in water under typical conditions, NaOH and other ionic hydroxides are all classified as strong bases.
Unlike ionic hydroxides, some compounds produce hydroxide ions when dissolved by chemically reacting with water molecules. In all cases, these compounds react only partially and so are classified as weak bases. These types of compounds are also abundant in nature and important commodities in various technologies. For example, global production of the weak base ammonia is typically well over 100 metric tons annually, being widely used as an agricultural fertilizer, a raw material for chemical synthesis of other compounds, and an active ingredient in household cleaners (Figure 4.7). When dissolved in water, ammonia reacts partially to yield hydroxide ions, as shown here:
This is, by definition, an acid-base reaction, in this case involving the transfer of H+ ions from water molecules to ammonia molecules. Under typical conditions, only about 1% of the dissolved ammonia is present as NH4+ ions.
The chemical reactions described in which acids and bases dissolved in water produce hydronium and hydroxide ions, respectively, are, by definition, acid-base reactions. In these reactions, water serves as both a solvent and a reactant. A neutralization reaction is a specific type of acid-base reaction in which the reactants are an acid and a base, the products are often a salt and water, and neither reactant is the water itself:
To illustrate a neutralization reaction, consider what happens when a typical antacid such as milk of magnesia (an aqueous suspension of solid Mg(OH)2) is ingested to ease symptoms associated with excess stomach acid (HCl):
Note that in addition to water, this reaction produces a salt, magnesium chloride.
Writing Equations for Acid-Base Reactions
Write balanced chemical equations for the acid-base reactions described here:
(a) the weak acid hydrogen hypochlorite reacts with water
(b) a solution of barium hydroxide is neutralized with a solution of nitric acid
(a) The two reactants are provided, HOCl and H2O. Since the substance is reported to be an acid, its reaction with water will involve the transfer of H+ from HOCl to H2O to generate hydronium ions, H3O+ and hypochlorite ions, OCl−.
A double-arrow is appropriate in this equation because it indicates the HOCl is a weak acid that has not reacted completely.
(b) The two reactants are provided, Ba(OH)2 and HNO3. Since this is a neutralization reaction, the two products will be water and a salt composed of the cation of the ionic hydroxide (Ba2+) and the anion generated when the acid transfers its hydrogen ion (NO3−).
Check Your Learning
Write the net ionic equation representing the neutralization of any strong acid with an ionic hydroxide. (Hint: Consider the ions produced when a strong acid is dissolved in water.)
Link to Learning
Explore the microscopic view of strong and weak acids and bases.
Earth’s atmosphere contains about 20% molecular oxygen, O2, a chemically reactive gas that plays an essential role in the metabolism of aerobic organisms and in many environmental processes that shape the world. The term oxidation was originally used to describe chemical reactions involving O2, but its meaning has evolved to refer to a broad and important reaction class known as oxidation-reduction (redox) reactions. A few examples of such reactions will be used to develop a clear picture of this classification.
Some redox reactions involve the transfer of electrons between reactant species to yield ionic products, such as the reaction between sodium and chlorine to yield sodium chloride:
It is helpful to view the process with regard to each individual reactant, that is, to represent the fate of each reactant in the form of an equation called a half-reaction:
These equations show that Na atoms lose electrons while Cl atoms (in the Cl2 molecule) gain electrons, the “s” subscripts for the resulting ions signifying they are present in the form of a solid ionic compound. For redox reactions of this sort, the loss and gain of electrons define the complementary processes that occur:
In this reaction, then, sodium is oxidized and chlorine undergoes reduction. Viewed from a more active perspective, sodium functions as a reducing agent (reductant), since it provides electrons to (or reduces) chlorine. Likewise, chlorine functions as an oxidizing agent (oxidant), as it effectively removes electrons from (oxidizes) sodium.
Some redox processes, however, do not involve the transfer of electrons. Consider, for example, a reaction similar to the one yielding NaCl:
The product of this reaction is a covalent compound, so transfer of electrons in the explicit sense is not involved. To clarify the similarity of this reaction to the previous one and permit an unambiguous definition of redox reactions, a property called oxidation number has been defined. The oxidation number (or oxidation state) of an element in a compound is the charge its atoms would possess if the compound was ionic. The following guidelines are used to assign oxidation numbers to each element in a molecule or ion.
1. The oxidation number of an atom in an elemental substance is zero.
2. The oxidation number of a monatomic ion is equal to the ion’s charge.
3. Oxidation numbers for common nonmetals are usually assigned as follows:
- Hydrogen: +1 when combined with nonmetals, −1 when combined with metals
- Oxygen: −2 in most compounds, sometimes −1 (so-called peroxides, O22−), very rarely −1/2 (so-called superoxides, O2−), positive values when combined with F (values vary)
- Halogens: −1 for F always, −1 for other halogens except when combined with oxygen or other halogens (positive oxidation numbers in these cases, varying values)
4. The sum of oxidation numbers for all atoms in a molecule or polyatomic ion equals the charge on the molecule or ion.
Note: The proper convention for reporting charge is to write the number first, followed by the sign (e.g., 2+), while oxidation number is written with the reversed sequence, sign followed by number (e.g., +2). This convention aims to emphasize the distinction between these two related properties.
Assigning Oxidation Numbers
Follow the guidelines in this section of the text to assign oxidation numbers to all the elements in the following species:
(a) According to guideline 1, the oxidation number for H is +1.
Using this oxidation number and the compound’s formula, guideline 4 may then be used to calculate the oxidation number for sulfur:
(b) Guideline 3 suggests the oxidation number for oxygen is −2.
Using this oxidation number and the ion’s formula, guideline 4 may then be used to calculate the oxidation number for sulfur:
(c) For ionic compounds, it’s convenient to assign oxidation numbers for the cation and anion separately.
According to guideline 2, the oxidation number for sodium is +1.
Assuming the usual oxidation number for oxygen (−2 per guideline 3), the oxidation number for sulfur is calculated as directed by guideline 4:
Check Your Learning
Assign oxidation states to the elements whose atoms are underlined in each of the following compounds or ions:
Answer: (a) N, +5; (b) Al, +3; (c) N, −3; (d) P, +5
Using the oxidation number concept, an all-inclusive definition of redox reaction has been established. Oxidation-reduction (redox) reactions are those in which one or more elements involved undergo a change in oxidation number. (While the vast majority of redox reactions involve changes in oxidation number for two or more elements, a few interesting exceptions to this rule do exist Example 4.6.) Definitions for the complementary processes of this reaction class are correspondingly revised as shown here:
oxidation = increase in oxidation number
reduction = decrease in oxidation number
Returning to the reactions used to introduce this topic, they may now both be identified as redox processes. In the reaction between sodium and chlorine to yield sodium chloride, sodium is oxidized (its oxidation number increases from 0 in Na to +1 in NaCl) and chlorine is reduced (its oxidation number decreases from 0 in Cl2 to −1 in NaCl). In the reaction between molecular hydrogen and chlorine, hydrogen is oxidized (its oxidation number increases from 0 in H2 to +1 in HCl) and chlorine is reduced (its oxidation number decreases from 0 in Cl2 to −1 in HCl).
Several subclasses of redox reactions are recognized, including combustion reactions in which the reductant (also called a fuel) and oxidant (often, but not necessarily, molecular oxygen) react vigorously and produce significant amounts of heat, and often light, in the form of a flame. Solid rocket-fuel reactions such as the one depicted in Figure 4.1 are combustion processes. A typical propellant reaction in which solid aluminum is oxidized by ammonium perchlorate is represented by this equation:
Link to Learning
Watch a brief video showing the test firing of a small-scale, prototype, hybrid rocket engine planned for use in the new Space Launch System being developed by NASA. The first engines firing at 3 s (green flame) use a liquid fuel/oxidant mixture, and the second, more powerful engines firing at 4 s (yellow flame) use a solid mixture.
Single-displacement (replacement) reactions are redox reactions in which an ion in solution is displaced (or replaced) via the oxidation of a metallic element. One common example of this type of reaction is the acid oxidation of certain metals:
Metallic elements may also be oxidized by solutions of other metal salts; for example:
This reaction may be observed by placing copper wire in a solution containing a dissolved silver salt. Silver ions in solution are reduced to elemental silver at the surface of the copper wire, and the resulting Cu2+ ions dissolve in the solution to yield a characteristic blue color (Figure 4.8).
Describing Redox Reactions
Identify which equations represent redox reactions, providing a name for the reaction if appropriate. For those reactions identified as redox, name the oxidant and reductant.
(a) ZnCO3(s) → ZnO(s)+CO2(g)
(b) 2Ga(l)+3Br2(l) → 2GaBr3(s)
(c) 2H2O2(aq) → 2H2O(l)+O2(g)
(d) BaCl2(aq)+K2SO4(aq) → BaSO4(s)+2KCl(aq)
(e) C2H4(g)+3O2(g) → 2CO2(g)+2H2O(l)
Redox reactions are identified per definition if one or more elements undergo a change in oxidation number.
(a) This is not a redox reaction, since oxidation numbers remain unchanged for all elements.
(b) This is a redox reaction. Gallium is oxidized, its oxidation number increasing from 0 in Ga(l) to +3 in GaBr3(s). The reducing agent is Ga(l). Bromine is reduced, its oxidation number decreasing from 0 in Br2(l) to −1 in GaBr3(s). The oxidizing agent is Br2(l).
(c) This is a redox reaction. It is a particularly interesting process, as it involves the same element, oxygen, undergoing both oxidation and reduction (a so-called disproportionation reaction). Oxygen is oxidized, its oxidation number increasing from −1 in H2O2(aq) to 0 in O2(g). Oxygen is also reduced, its oxidation number decreasing from −1 in H2O2(aq) to −2 in H2O(l). For disproportionation reactions, the same substance functions as an oxidant and a reductant.
(d) This is not a redox reaction, since oxidation numbers remain unchanged for all elements.
(e) This is a redox reaction (combustion). Carbon is oxidized, its oxidation number increasing from −2 in C2H4(g) to +4 in CO2(g). The reducing agent (fuel) is C2H4(g). Oxygen is reduced, its oxidation number decreasing from 0 in O2(g) to −2 in H2O(l). The oxidizing agent is O2(g).
Check Your Learning
This equation describes the production of tin(II) chloride:
Is this a redox reaction? If so, provide a more specific name for the reaction if appropriate, and identify the oxidant and reductant.
Answer: Yes, a single-replacement reaction. Sn(s)is the reductant, HCl(g) is the oxidant.
Balancing Redox Reactions via the Half-Reaction Method
Redox reactions that take place in aqueous media often involve water, hydronium ions, and hydroxide ions as reactants or products. Although these species are not oxidized or reduced, they do participate in chemical change in other ways (e.g., by providing the elements required to form oxyanions). Equations representing these reactions are sometimes very difficult to balance by inspection, so systematic approaches have been developed to assist in the process. One very useful approach is to use the method of half-reactions, which involves the following steps:
1. Write the two half-reactions representing the redox process.
2. Balance all elements except oxygen and hydrogen.
3. Balance oxygen atoms by adding H2O molecules.
4. Balance hydrogen atoms by adding H+ ions.
5. Balance charge by adding electrons.
6. If necessary, multiply each half-reaction’s coefficients by the smallest possible integers to yield equal numbers of electrons in each.
7. Add the balanced half-reactions together and simplify by removing species that appear on both sides of the equation.
8. For reactions occurring in basic media (excess hydroxide ions), carry out these additional steps:
a. Add OH− ions to both sides of the equation in numbers equal to the number of H+ ions.
b. On the side of the equation containing both H+ and OH− ions, combine these ions to yield water molecules.
c. Simplify the equation by removing any redundant water molecules.
9. Finally, check to see that both the number of atoms and the total charges2 are balanced.
Balancing Redox Reactions in Acidic Solution
Write a balanced equation for the reaction between dichromate ion and iron(II) to yield iron(III) and chromium(III) in acidic solution.
Step 1. Write the two half-reactions.
Each half-reaction will contain one reactant and one product with one element in common.
Step 2. Balance all elements except oxygen and hydrogen. The iron half-reaction is already balanced, but the chromium half-reaction shows two Cr atoms on the left and one Cr atom on the right. Changing the coefficient on the right side of the equation to 2 achieves balance with regard to Cr atoms.
Step 3. Balance oxygen atoms by adding H2O molecules. The iron half-reaction does not contain O atoms. The chromium half-reaction shows seven O atoms on the left and none on the right, so seven water molecules are added to the right side.
Step 4. Balance hydrogen atoms by adding H+ ions. The iron half-reaction does not contain H atoms. The chromium half-reaction shows 14 H atoms on the right and none on the left, so 14 hydrogen ions are added to the left side.
Step 5. Balance charge by adding electrons. The iron half-reaction shows a total charge of 2+ on the left side (1 Fe2+ ion) and 3+ on the right side (1 Fe3+ ion). Adding one electron to the right side bring that side’s total charge to (3+) + (1−) = 2+, and charge balance is achieved.
The chromium half-reaction shows a total charge of (1 × 2−) + (14 × 1+) = 12+ on the left side
(1 Cr2O72− ion and 14 H+ ions). The total charge on the right side is (2 × 3+) = 6 + (2 Cr3+ ions). Adding six electrons to the left side will bring that side’s total charge to (12+ + 6−) = 6+, and charge balance is achieved.
Step 6. Multiply the two half-reactions so the number of electrons in one reaction equals the number of electrons in the other reaction. To be consistent with mass conservation, and the idea that redox reactions involve the transfer (not creation or destruction) of electrons, the iron half-reaction’s coefficient must be multiplied by 6.
Step 7. Add the balanced half-reactions and cancel species that appear on both sides of the equation.
Only the six electrons are redundant species. Removing them from each side of the equation yields the simplified, balanced equation here:
A final check of atom and charge balance confirms the equation is balanced.
Check Your Learning
In acidic solution, hydrogen peroxide reacts with Fe2+ to produce Fe3+ and H2O. Write a balanced equation for this reaction.
Answer: H 2 O 2(aq) + 2H +(aq) + 2Fe 2+ → 2H 2 O(l) + 2Fe 3+
12. Use the following equations to answer the next five questions: i. HO(s) → HO(l) ii. Na (aq) + Cl (aq) Ag +(aq) + NO (aq) → AgCl(s) + Na (aq) + NO (aq) iii. CHOH(g) + O(g) → CO(g) + HO(g) iv. 2HO(l) → 2H(g) + O(g) v. H +(aq) + OH (aq) → HO(l) (a) Which equation describes a physical change? (b) Which equation identifies the reactants and products of a combustion reaction? (c) Which equation is not balanced? (d) Which is a net ionic equation?
13. Indicate what type, or types, of reaction each of the following represents: (a) Ca(s) + Br(l) → CaBr(s) (b) Ca (OH)(aq) + 2HBr(aq) → CaBr(aq) + 2HO(l) (c) CH(l) + 9O(g) → 6CO(g) + 6HO(g)
Click here to see the answer to Question 4.13
14. Indicate what type, or types, of reaction each of the following represents: (a) HO(g) + C(s) → CO(g) + H(g) (b)KClO(s) → 2KCl(s) + 3O(g) (c) Al(OH)(aq) + 3HCl(aq) → AlBr(aq) + 3HO(l) (d) Pb(NO)(aq) + HSO(aq) → PbSO(s) + 2HNO(aq)
15. Silver can be separated from gold because silver dissolves in nitric acid while gold does not. Is the dissolution of silver in nitric acid an acid-base reaction or an oxidation-reduction reaction? Explain your answer.
Click here to see the answer to Question 4.15
16. Determine the oxidation states of the elements in the following compounds: (a) NaI (b) GdCl (c) LiNO (d) HSe (e) MgSi (f) RbO, rubidium superoxide (g) HF
17. Determine the oxidation states of the elements in the compounds listed. None of the oxygen-containing compounds are peroxides or superoxides. (a) HPO (b) Al(OH) (c) SeO (d) KNO (e) InS (f) PO
Click here to see the answer to Question 4.17
18. Determine the oxidation states of the elements in the compounds listed. None of the oxygen-containing compounds are peroxides or superoxides. (a) HSO (b) Ca(OH) (c) BrOH (d) ClNO (e) TiCl (f) NaH
19. Classify the following as acid-base reactions or oxidation-reduction reactions: (a) NaS(aq) + 2HCl(aq) → 2NaCl(aq) + H S(g) (b)Na(s) + 2HCl(aq) → 2NaCl(aq) + H(g) (c) Mg(s) + Cl(g) → MgCl(s) (d) MgO(s) + 2HCl(aq) → MgCl(aq) + HO(l) (e) KP(s) + 2O(g) → KPO(s) (f) 3KOH(aq) + HPO(aq) → KPO(aq) + 3HO(l)
Click here to see the answer to Question 4.19
20. Identify the atoms that are oxidized and reduced, the change in oxidation state for each, and the oxidizing and reducing agents in each of the following equations: (a) Mg(s) + NiCl(aq) → MgCl(aq) + Ni(s) (b) PCl(l) + Cl(g) → PCl(s) (c) (g) + 3O(g) → 2CO(g) + 2HO(g) (d) Zn(s) + HSO(aq) → ZnSO(aq) + H(g) (e) 2KSO(s) + I(s) → KSO(s) + 2KI(s) (f) 3Cu(s) + 8HNO(aq) → 3Cu(NO)(aq) + 2NO(g) + 4HO(l)
21. Complete and balance the following acid-base equations: (a) HCl gas reacts with solid Ca(OH)(s). (b) A solution of Sr(OH) is added to a solution of HNO.
Click here to see the answer to Question 4.21
22. Complete and balance the following acid-base equations: (a) A solution of HClO is added to a solution of LiOH. (b) Aqueous HSO reacts with NaOH. (c) Ba(OH) reacts with HF gas.
23. Complete and balance the following oxidation-reduction reactions, which give the highest possible oxidation state for the oxidized atoms. (a) Al(s) + F(g) → (b) Al(s) + CuBr(aq) → (single displacement) (c) P(s) + O(g) → (d) Ca(s) + HO(l) → (products are a strong base and a diatomic gas)
Click here to see the answer to Question 4.23
24. Complete and balance the following oxidation-reduction reactions, which give the highest possible oxidation state for the oxidized atoms. (a) K(s) + HO(l) → (b) Ba(s) + HBr(aq) → (c) Sn(s) + I(s) →
25. Complete and balance the equations for the following acid-base neutralization reactions. If water is used as a solvent, write the reactants and products as aqueous ions. In some cases, there may be more than one correct answer, depending on the amounts of reactants used. (a) Mg(OH)(s) + HClO(aq) → (b) SO(g) + HO(l) → (assume an excess of water and that the product dissolves) (c) SrO(s) + HSO(l) →
Click here to see the answer to Question 4.25
26. When heated to 700-800 °C, diamonds, which are pure carbon, are oxidized by atmospheric oxygen. (They burn!) Write the balanced equation for this reaction.
27. The military has experimented with lasers that produce very intense light when fluorine combines explosively with hydrogen. What is the balanced equation for this reaction?
Click here to see the answer to Question 4.27
28. Write the molecular, total ionic, and net ionic equations for the following reactions: (a) Ca(OH)(aq) + HCHO(aq) → (b) HPO(aq) + CaCl(aq) →
29. Great Lakes Chemical Company produces bromine, Br, from bromide salts such as NaBr, in Arkansas brine by treating the brine with chlorine gas. Write a balanced equation for the reaction of NaBr with Cl.
Click here to see the answer to Question 4.29
30. In a common experiment in the general chemistry laboratory, magnesium metal is heated in air to produce MgO. MgO is a white solid, but in these experiments it often looks gray, due to small amounts of MgN, a compound formed as some of the magnesium reacts with nitrogen. Write a balanced equation for each reaction.
31. Lithium hydroxide may be used to absorb carbon dioxide in enclosed environments, such as manned spacecraft and submarines. Write an equation for the reaction that involves 2 mol of LiOH per 1 mol of CO. (Hint: Water is one of the products.)
Click here to see the answer to Question 4.31
32. Calcium propionate is sometimes added to bread to retard spoilage. This compound can be prepared by the reaction of calcium carbonate, CaCO, with propionic acid, CHCOH, which has properties similar to those of acetic acid. Write the balanced equation for the formation of calcium propionate.
33. Complete and balance the equations of the following reactions, each of which could be used to remove hydrogen sulfide from natural gas: (a) Ca(OH)(s) + H S(g) → (b) Na)CO(aq) + H S(g) →
Click here to see the answer to Question 4.33
34. Copper(II) sulfide is oxidized by molecular oxygen to produce gaseous sulfur trioxide and solid copper(II) oxide. The gaseous product then reacts with liquid water to produce liquid hydrogen sulfate as the only product. Write the two equations which represent these reactions.
35. Write balanced chemical equations for the reactions used to prepare each of the following compounds from the given starting material(s). In some cases, additional reactants may be required. (a) solid ammonium nitrate from gaseous molecular nitrogen via a two-step process (first reduce the nitrogen to ammonia, then neutralize the ammonia with an appropriate acid) (b) gaseous hydrogen bromide from liquid molecular bromine via a one-step redox reaction (c) gaseous HS from solid Zn and S via a two-step process (first a redox reaction between the starting materials, then reaction of the product with a strong acid)
Click here to see the answer to Question 4.35
36. Calcium cyclamate Ca(CHNHSO) is an artificial sweetener used in many countries around the world but is banned in the United States. It can be purified industrially by converting it to the barium salt through reaction of the acid CHNHSOH with barium carbonate, treatment with sulfuric acid (barium sulfate is very insoluble), and then neutralization with calcium hydroxide. Write the balanced equations for these reactions.
37. Complete and balance each of the following half-reactions (steps 2–5 in half-reaction method): (a) Sn (aq) → Sn (aq) (b) [Ag(NH) (aq) → Ag(s) + NH(aq) (c) HgCl(s) → Hg(l) + Cl (aq) (d) HO(l) → O(g) (in acidic solution) (e) IO (aq) → I(s) (f) SO (aq) →SO (aq) (in acidic solution) (g) MnO (aq) → Mn (aq) (in acidic solution) (h) Cl (aq) → ClO (aq) (in basic solution)
Click here to see the answer to Question 4.37
38. Complete and balance each of the following half-reactions (steps 2–5 in half-reaction method): (a) Cr (aq) → Cr (aq) (b) Hg(l) + Br (aq) → HgBr (aq) (c) ZnS(s) → Zn(s) + S (aq) (d) H(g) → HO(l) (in basic solution) (e) H(g) → HO +(aq) (in acidic solution) (f) NO (aq) → HNO(aq) (in acidic solution) (g) MnO(s) → MnO (aq) (in basic solution) (h) Cl (aq) → ClO (aq) (in acidic solution)
39. Balance each of the following equations according to the half-reaction method: (a) Sn (aq) + Cu (aq) → Sn (aq) + Cu +(aq) (b) H S(g) + Hg (aq) → Hg(l) + S(s) (in acid) (c) CN (aq) + ClO(aq) → CNO (aq) + Cl (aq) (in acid) (d) Fe (aq) + Ce (aq) → Fe (aq) + Ce (aq) (e) HBrO(aq) → Br (aq) + O(g) (in acid)
Click here to see the answer to Question 4.39
40. Balance each of the following equations according to the half-reaction method: (a) Zn(s) + NO (aq) → Zn (aq) + N(g) (in acid) (b) Zn(s) + NO (aq) → Zn (aq) + NH(aq) (in base) (c) CuS(s) + NO (aq) → Cu (aq) + S(s) + NO(g) (in acid) (d) NH(aq) + O(g) → NO(g) (gas phase) (e) Cl(g) + OH (aq) → Cl (aq) + ClO (aq) (in base) (f) HO(aq) + MnO (aq) → Mn (aq) + O(g) (in acid) (g) NO(g) → NO (aq) + NO (aq) (in base) (h) Fe (aq) + I (aq) → Fe (aq) + I(aq)
41. Balance each of the following equations according to the half-reaction method: (a) MnO (aq) + NO (aq) → MnO(s) + NO (aq) (in base) (b) MnO (aq) → MnO (aq) + MnO(s) (in base) (c) Br(l) + SO(g) → Br (aq) +SO (aq) (in acid)
Click here to see the answer to Question 4.41
4.3 Reaction Stoichiometry
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. 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
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
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:
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:
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.
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 (see Figure 4.9)?
Referring to the balanced chemical equation, the stoichiometric factor relating the two substances of interest is
The molar amount of iodine is derived by multiplying the provided molar amount of aluminum by this factor:
Check Your Learning
How many moles of Ca(OH)2 are required to react with 1.36 mol of H3PO4 to produce Ca3(PO4)2 according to the equation 3Ca(OH)2 + 2H3 PO4 → Ca3 (PO4)2 + 6H2 O?
Answer: 2.04 mol
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?
The approach here is the same as for Example 4.8, 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:
Using this stoichiometric factor, the provided molar amount of propane, and Avogadro’s number,
Check Your Learning
How many NH3 molecules are produced by the reaction of 4.0 mol of Ca(OH)2 according to the following equation:
Answer: 4.8 × 1024 NH3 molecules
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.
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?
The approach used previously in Example 4.8 and Example 4.9 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. The calculations required are outlined in this flowchart:
Check Your Learning
What mass of gallium oxide, Ga2O3, can be prepared from 29.0 g of gallium metal? The equation for the reaction is 4Ga + 3O2 → 2Ga2 O3.
Answer: 39.0 g
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?
The approach required here is the same as for the Example 4.10, differing only in that the provided and requested masses are both for reactant species.
Check Your Learning
What mass of CO is required to react with 25.13 g of Fe2O3 according to the equation Fe2 O3 + 3CO → 2Fe + 3CO2 ?
Answer: 13.22 g
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 4.10 provides a general outline of the various computational steps associated with many reaction stoichiometry calculations.
Chemistry in Everyday Life
Airbags (Figure 4.11) 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 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:
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.
42. Write the balanced equation, then outline the steps necessary to determine the information requested in each of the following: (a) The number of moles and the mass of chlorine, Cl, required to react with 10.0 g of sodium metal, Na, to produce sodium chloride, NaCl. (b) The number of moles and the mass of oxygen formed by the decomposition of 1.252 g of mercury(II) oxide. (c) The number of moles and the mass of sodium nitrate, NaNO, required to produce 128 g of oxygen. (NaNO is the other product.) (d) The number of moles and the mass of carbon dioxide formed by the combustion of 20.0 kg of carbon in an excess of oxygen. (e) The number of moles and the mass of copper(II) carbonate needed to produce 1.500 kg of copper(II) oxide. (CO is the other product.)
43. Determine the number of moles and the mass requested for each reaction in Exercise 4.42.
Click here to see the answer to Question 4.43
44. Write the balanced equation, then outline the steps necessary to determine the information requested in each of the following: (a) The number of moles and the mass of Mg required to react with 5.00 g of HCl and produce MgCl and H. (b) The number of moles and the mass of oxygen formed by the decomposition of 1.252 g of silver(I) oxide. (c) The number of moles and the mass of magnesium carbonate, MgCO, required to produce 283 g of carbon dioxide. (MgO is the other product.) (d) The number of moles and the mass of water formed by the combustion of 20.0 kg of acetylene, CH, in an excess of oxygen. (e) The number of moles and the mass of barium peroxide, BaO, needed to produce 2.500 kg of barium oxide, BaO (O is the other product.) (f)
45. Determine the number of moles and the mass requested for each reaction in Exercise 4.44.
Click here to see the answer to Question 4.45
46. H is produced by the reaction of 118.5 mL of a 0.8775-M solution of HPO according to the following equation: 2Cr + 2HPO → 3H + 2CrPO. (a) Outline the steps necessary to determine the number of moles and mass of H. (b) Perform the calculations outlined.
47. Gallium chloride is formed by the reaction of 2.6 L of a 1.44 M solution of HCl according to the following equation: 2Ga + 6HCl → 2GaCl + 3H. (a) Outline the steps necessary to determine the number of moles and mass of gallium chloride. (b) Perform the calculations outlined.
Click here to see the answer to Question 4.47
48. I is produced by the reaction of 0.4235 mol of CuCl according to the following equation: 2CuCl + 4KI → 2CuI + 4KCl + I. (a) How many molecules of I are produced? (b) What mass of I is produced?
49. Silver is often extracted from ores as K[Ag(CN)] and then recovered by the reaction 2K(aq) + Zn(s) → 2Ag(s) + Zn(CN) (aq) + 2KCN(aq) (a) How many molecules of Zn(CN) are produced by the reaction of 35.27 g of K[Ag(CN)]? (b) What mass of Zn(CN) is produced?
Click here to see the answer to Question 4.49
50. What mass of silver oxide, AgO, is required to produce 25.0 g of silver sulfadiazine, AgCHNSO, from the reaction of silver oxide and sulfadiazine? 2CHNSO + AgO → 2AgCHNSO + HO
51. Carborundum is silicon carbide, SiC, a very hard material used as an abrasive on sandpaper and in other applications. It is prepared by the reaction of pure sand, SiO, with carbon at high temperature. Carbon monoxide, CO, is the other product of this reaction. Write the balanced equation for the reaction, and calculate how much SiO is required to produce 3.00 kg of SiC.
Click here to see the answer to Question 4.51
52. Automotive air bags inflate when a sample of sodium azide, NaN, is very rapidly decomposed. (s) → 2Na(s) + 3N(g) What mass of sodium azide is required to produce 2.6 ft (73.6 L) of nitrogen gas with a density of 1.25 g/L?
53. Urea, CO(NH), is manufactured on a large scale for use in producing urea-formaldehyde plastics and as a fertilizer. What is the maximum mass of urea that can be manufactured from the CO produced by combustion of 1.00 × 10 kg of carbon followed by the reaction? CO(g) + 2NH(g) → CO (NH)(s) + HO(l) (answer in × 10 kg)
54. In an accident, a solution containing 2.5 kg of nitric acid was spilled. Two kilograms of NaCO was quickly spread on the area and CO was released by the reaction. Was sufficient NaCO used to neutralize all of the acid?
55. A compact car gets 37.5 miles per gallon on the highway. If gasoline contains 84.2% carbon by mass and has a density of 0.8205 g/mL, determine the mass of carbon dioxide produced during a 500-mile trip (3.785 liters per gallon). (answer in × 10 g CO)
56. What volume of a 0.750 M solution of hydrochloric acid, a solution of HCl, can be prepared from the HCl produced by the reaction of 25.0 g of NaCl with an excess of sulfuric acid? NaCl(s) + HSO(l) → HCl(g) + NaHSO(s)
57. What volume of a 0.2089 M KI solution contains enough KI to react exactly with the Cu(NO) in 43.88 mL of a 0.3842 M solution of Cu(NO)? 2Cu(NO) + 4KI → 2CuI + I + 4KNO (answer in mL KI solution)
58. A mordant is a substance that combines with a dye to produce a stable fixed color in a dyed fabric. Calcium acetate is used as a mordant. It is prepared by the reaction of acetic acid with calcium hydroxide. 2CHCO H + Ca(OH) → Ca(CHCO) + 2HO What mass of Ca(OH) is required to react with the acetic acid in 25.0 mL of a solution having a density of 1.065 g/mL and containing 58.0% acetic acid by mass?
59. The toxic pigment called white lead, Pb(OH)(CO), has been replaced in white paints by rutile, TiO. How much rutile (g) can be prepared from 379 g of an ore that contains 88.3% ilmenite (FeTiO) by mass? 2FeTiO + 4HCl + Cl → 2FeCl + 2TiO + 2HO
(answer in g TiO)
4.4 Reaction Yields
By the end of this section, you will be able to:
- Explain the concepts of theoretical yield and limiting reactants/reagents.
- Derive the theoretical yield for a reaction under specified conditions.
- Calculate the percent yield for a reaction.
The relative amounts of reactants and products represented in a balanced chemical equation are often referred to as stoichiometric amounts. All the exercises of the preceding module involved stoichiometric amounts of reactants. For example, when calculating the amount of product generated from a given amount of reactant, it was assumed that any other reactants required were available in stoichiometric amounts (or greater). In this module, more realistic situations are considered, in which reactants are not present in stoichiometric amounts.
Consider another food analogy, making grilled cheese sandwiches (Figure 4.12):
Stoichiometric amounts of sandwich ingredients for this recipe are bread and cheese slices in a 2:1 ratio. Provided with 28 slices of bread and 11 slices of cheese, one may prepare 11 sandwiches per the provided recipe, using all the provided cheese and having six slices of bread left over. In this scenario, the number of sandwiches prepared has been limited by the number of cheese slices, and the bread slices have been provided in excess.
Consider this concept now with regard to a chemical process, the reaction of hydrogen with chlorine to yield hydrogen chloride:
The balanced equation shows the hydrogen and chlorine react in a 1:1 stoichiometric ratio. If these reactants are provided in any other amounts, one of the reactants will nearly always be entirely consumed, thus limiting the amount of product that may be generated. This substance is the limiting reactant, and the other substance is the excess reactant. Identifying the limiting and excess reactants for a given situation requires computing the molar amounts of each reactant provided and comparing them to the stoichiometric amounts represented in the balanced chemical equation. For example, imagine combining 3 moles of H2 and 2 moles of Cl2. This represents a 3:2 (or 1.5:1) ratio of hydrogen to chlorine present for reaction, which is greater than the stoichiometric ratio of 1:1. Hydrogen, therefore, is present in excess, and chlorine is the limiting reactant. Reaction of all the provided chlorine (2 mol) will consume 2 mol of the 3 mol of hydrogen provided, leaving 1 mol of hydrogen unreacted.
An alternative approach to identifying the limiting reactant involves comparing the amount of product expected for the complete reaction of each reactant. Each reactant amount is used to separately calculate the amount of product that would be formed per the reaction’s stoichiometry. The reactant yielding the lesser amount of product is the limiting reactant. For the example in the previous paragraph, complete reaction of the hydrogen would yield
Complete reaction of the provided chlorine would produce
The chlorine will be completely consumed once 4 moles of HCl have been produced. Since enough hydrogen was provided to yield 6 moles of HCl, there will be unreacted hydrogen remaining once this reaction is complete. Chlorine, therefore, is the limiting reactant and hydrogen is the excess reactant (Figure 4.13).
Link to Learning
View this interactive simulation illustrating the concepts of limiting and excess reactants.
Identifying the Limiting Reactant
Silicon nitride is a very hard, high-temperature-resistant ceramic used as a component of turbine blades in jet engines. It is prepared according to the following equation:
Which is the limiting reactant when 2.00 g of Si and 1.50 g of N2 react?
Compute the provided molar amounts of reactants, and then compare these amounts to the balanced equation to identify the limiting reactant.
The provided Si:N2 molar ratio is:
The stoichiometric Si:N2 ratio is:
Comparing these ratios shows that Si is provided in a less-than-stoichiometric amount, and so is the limiting reactant.
Alternatively, compute the amount of product expected for complete reaction of each of the provided reactants. The 0.0712 moles of silicon would yield
while the 0.0535 moles of nitrogen would produce
Since silicon yields the lesser amount of product, it is the limiting reactant.
Check Your Learning
Which is the limiting reactant when 5.00 g of H2 and 10.0 g of O2 react and form water?
The amount of product that may be produced by a reaction under specified conditions, as calculated per the stoichiometry of an appropriate balanced chemical equation, is called the theoretical yield of the reaction. In practice, the amount of product obtained is called the actual yield, and it is often less than the theoretical yield for a number of reasons. Some reactions are inherently inefficient, being accompanied by side reactions that generate other products. Others are, by nature, incomplete (consider the partial reactions of weak acids and bases discussed earlier in this chapter). Some products are difficult to collect without some loss, and so less than perfect recovery will reduce the actual yield. The extent to which a reaction’s theoretical yield is achieved is commonly expressed as its percent yield:
Actual and theoretical yields may be expressed as masses or molar amounts (or any other appropriate property; e.g., volume, if the product is a gas). As long as both yields are expressed using the same units, these units will cancel when percent yield is calculated.
Calculation of Percent Yield
Upon reaction of 1.274 g of copper sulfate with excess zinc metal, 0.392 g copper metal was obtained according to the equation:
What is the percent yield?
The provided information identifies copper sulfate as the limiting reactant, and so the theoretical yield is found by the approach illustrated in the previous module, as shown here:
Using this theoretical yield and the provided value for actual yield, the percent yield is calculated to be
Check Your Learning
What is the percent yield of a reaction that produces 12.5 g of the Freon CF2Cl2 from 32.9 g of CCl4 and excess HF?
How Sciences Interconnect
Green Chemistry and Atom Economy
The purposeful design of chemical products and processes that minimize the use of environmentally hazardous substances and the generation of waste is known as green chemistry. Green chemistry is a philosophical approach that is being applied to many areas of science and technology, and its practice is summarized by guidelines known as the “Twelve Principles of Green Chemistry” (see details at this website). One of the 12 principles is aimed specifically at maximizing the efficiency of processes for synthesizing chemical products. The atom economy of a process is a measure of this efficiency, defined as the percentage by mass of the final product of a synthesis relative to the masses of all the reactants used:
Though the definition of atom economy at first glance appears very similar to that for percent yield, be aware that this property represents a difference in the theoretical efficiencies of different chemical processes. The percent yield of a given chemical process, on the other hand, evaluates the efficiency of a process by comparing the yield of product actually obtained to the maximum yield predicted by stoichiometry.
The synthesis of the common nonprescription pain medication, ibuprofen, nicely illustrates the success of a green chemistry approach (Figure 4.14). First marketed in the early 1960s, ibuprofen was produced using a six-step synthesis that required 514 g of reactants to generate each mole (206 g) of ibuprofen, an atom economy of 40%. In the 1990s, an alternative process was developed by the BHC Company (now BASF Corporation) that requires only three steps and has an atom economy of ~80%, nearly twice that of the original process. The BHC process generates significantly less chemical waste; uses less-hazardous and recyclable materials; and provides significant cost-savings to the manufacturer (and, subsequently, the consumer). In recognition of the positive environmental impact of the BHC process, the company received the Environmental Protection Agency’s Greener Synthetic Pathways Award in 1997.
60. The following quantities are placed in a container: 1.5 × 10 atoms of hydrogen, 1.0 mol of sulfur, and 88.0 g of diatomic oxygen. (a) What is the total mass in grams for the collection of all three elements? (b) What is the total number of moles of atoms for the three elements? (c) If the mixture of the three elements formed a compound with molecules that contain two hydrogen atoms, one sulfur atom, and four oxygen atoms, which substance is consumed first? (d) How many atoms of each remaining element would remain unreacted in the change described in (c)?
61. What is the limiting reactant in a reaction that produces sodium chloride from 8 g of sodium and 8 g of diatomic chlorine?
Click here to see the answer to Question 4.61
62. Which of the postulates of Dalton's atomic theory explains why we can calculate a theoretical yield for a chemical reaction?
63. A student isolated 25 g of a compound following a procedure that would theoretically yield 81 g. What was his percent yield? (answer in %)
64. A sample of 0.53 g of carbon dioxide was obtained by heating 1.31 g of calcium carbonate. What is the percent yield for this reaction? CaCO(s) → CaO(s) + CO(s)
65. Freon-12, CClF, is prepared from CCl by reaction with HF. The other product of this reaction is HCl. Outline the steps needed to determine the percent yield of a reaction that produces 12.5 g of CClF from 32.9 g of CCl. Freon-12 has been banned and is no longer used as a refrigerant because it catalyzes the decomposition of ozone and has a very long lifetime in the atmosphere. Determine the percent yield. (answer in %)
66. Citric acid, CHO, a component of jams, jellies, and fruity soft drinks, is prepared industrially via fermentation of sucrose by the mold Aspergillus niger. The equation representing this reaction is CHO + HO + 3O → 2CHO + 4HO What mass of citric acid is produced from exactly 1 metric ton (1.000 × 10 kg) of sucrose if the yield is 92.30%?
67. Toluene, CHCH, is oxidized by air under carefully controlled conditions to benzoic acid, CHCOH, which is used to prepare the food preservative sodium benzoate, CHCONa. What is the percent yield of a reaction that converts 1.000 kg of toluene to 1.21 kg of benzoic acid? 2CHCH + 3O → 2CHCO H + 2HO
(answer in %)
68. In a laboratory experiment, the reaction of 3.0 mol of H with 2.0 mol of I produced 1.0 mol of HI. Determine the theoretical yield in grams and the percent yield for this reaction.
69. Outline the steps needed to solve the following problem, then do the calculations. Ether, (CH)O, which was originally used as an anesthetic but has been replaced by safer and more effective medications, is prepared by the reaction of ethanol with sulfuric acid. 2CHOH + HSO → (CH) + HSO∙HO What is the percent yield of ether if 1.17 L (d = 0.7134 g/mL) is isolated from the reaction of 1.500 L of CHOH (d = 0.7894 g/mL)? (answer in %)
70. Outline the steps needed to determine the limiting reactant when 30.0 g of propane, , is burned with 75.0 g of oxygen. Determine the limiting reactant.
71. Outline the steps needed to determine the limiting reactant when 0.50 g of Cr and 0.75 g of HPO react according to the following chemical equation? 2Cr + 2HPO → 2CrPO + 3H Determine the limiting reactant.
Click here to see the answer to Question 4.71
72. What is the limiting reactant when 1.50 g of lithium and 1.50 g of nitrogen combine to form lithium nitride, a component of advanced batteries, according to the following unbalanced equation? Li + N → LiN
73. Uranium can be isolated from its ores by dissolving it as UO(NO), then separating it as solid UO(CO)∙3HO. Addition of 0.4031 g of sodium oxalate, NaCO, to a solution containing 1.481 g of uranyl nitrate, UO(NO), yields 1.073 g of solid UO(CO)∙3HO. NaCO + UO(NO) + 3HO → UO(CO)∙3HO + 2NaNO Determine the limiting reactant and the percent yield of this reaction.
Click here to see the answer to Question 4.73
74. How many molecules of CHCl can be prepared from 15 CH molecules and 8 Cl molecules?
75. How many molecules of the sweetener saccharin can be prepared from 30 C atoms, 25 H atoms, 12 O atoms, 8 S atoms, and 14 N atoms?
Click here to see the answer to Question 4.75
76. The phosphorus pentoxide used to produce phosphoric acid for cola soft drinks is prepared by burning phosphorus in oxygen. (a) What is the limiting reactant when 0.200 mol of P and 0.200 mol of O react according to P + 5O → PO