Chapter 8: Stoichiometry of Chemical Reactions

8.2 Precipitation Reactions and Solublity

Learning Outcomes

  • Define precipitation chemical reactions
  • Classify chemical reactions as precipitation or not  given appropriate descriptions or chemical equations
  • Write and balance chemical equations in molecular, total ionic, and net ionic formats
  • 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 chapter 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 section 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 module 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 8.2.1).

Table 8.2.1: Patterns of Solubility of Ionic Compounds
Contains these ions Exceptions
Soluble Ionic Compounds


group I cations:

Li+ , Na+, K+, Rb+, Cs+

group VII anions:

Cl, Br, I

compounds with Ag+, Hg22+, and Pb2+
F compounds with group 2 metal cations, Pb2+ and Fe3+

C2H3O2, HCO3

NO3, ClO3

SO42- compounds with Ag+, Ba2+, Ca2+, Hg22+, Pb2+ and Sr2+
Insoluble Ionic Compounds

CO32-, CrO42-

PO43-, S2-

compounds with group 1 cations and NH4+
OH compounds with group 1 cations and Ba2+

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:


A photograph is shown of a yellow green opaque substance swirled through a clear, colorless liquid in a test tube.
Figure 8.2.1. A precipitate of [latex]\ce{PbI2}[/latex] forms when solutions containing [latex]\ce{Pb2+}[/latex] and [latex]\ce{I−}[/latex] are mixed. (credit: Der Kreole/Wikimedia Commons)

Lead iodide is a bright yellow solid that was formerly used as an artist’s pigment known as iodine yellow (Figure 8.2.1). The properties of pure [latex]\ce{PbI2}[/latex] crystals make them useful for fabrication of X-ray and gamma ray detectors.

The solubility guidelines in Table 8.2.1 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 [latex]\ce{Ag+}[/latex], [latex]\ce{NO-}[/latex], [latex]\ce{Na+}[/latex], and [latex]\ce{F-}[/latex] ions. Aside from the two ionic compounds originally present in the solutions, [latex]\ce{AgNO3}[/latex] and [latex]\ce{NaF}[/latex], two additional ionic compounds may be derived from this collection of ions: [latex]\ce{NaNO3}[/latex] and [latex]\ce{AgF}[/latex]. 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:

[latex]\begin{array}{l}\text{NaF(}aq\text{)}+{\text{AgNO}}_{3}\text{(}aq\text{)}\rightarrow\text{AgF(}s\text{)}+\text{NaN}{\text{O}}_{3}\text{(}aq\text{)}\text{(molecular)}\\ {\text{Ag}}^{\text{+}}\text{(}aq\text{)}+{\text{F}}^{-}\text{(}aq\text{)}\rightarrow\text{AgF(}s\text{)}\text{(net ionic)}\end{array}[/latex]

Example 8.2.1: 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.

  1. potassium sulfate and barium nitrate
  2. lithium chloride and silver acetate
  3. lead nitrate and ammonium carbonate
Show Solution
  1. 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 [latex]\text{Ba}^{2+}(\text{aq})+\text{SO}_{4}^{2−}(\text{aq})⟶\text{BaSO}_{4}(\text{s})[/latex]
  2. 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 [latex]{\text{Ag}}^{\text{+}}\text{(}aq\text{)}+{\text{Cl}}^{-}\text{(}aq\text{)}\rightarrow\text{AgCl(}s\text{)}[/latex].
  3. 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 [latex]\text{Pb}^{2+}(\text{aq})+\text{CO}_{3}^{2−}(\text{aq})⟶\text{PbCO}_{3}(\text{s})[/latex]

Check Your Learning

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 earlier). These notations are illustrated in the example equation here:

[latex]2\text{Na(}s\text{)}+2{\text{H}}_{2}\text{O(}l\text{)}\rightarrow 2\text{NaOH(}aq\text{)}+{\text{H}}_{2}\text{(}g\text{)}[/latex]

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 later.

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:

[latex]\begin{array}{l}{\text{CaCl}}_{2}\text{(}aq\text{)}\rightarrow{\text{Ca}}^{\text{2+}}\text{(}aq\text{)}+2{\text{Cl}}^{-}\text{(}aq\text{)}\\ 2{\text{AgNO}}_{3}\text{(}aq\text{)}\rightarrow 2{\text{Ag}}^{\text{+}}\text{(}aq\text{)}+2{\text{NO}}_{3}{}^{-}\text{(}aq\text{)}\\ \text{Ca}{\text{(}{\text{NO}}_{3}\text{)}}_{2}\text{(}aq\text{)}\rightarrow{\text{Ca}}^{\text{2+}}\text{(}aq\text{)}+2{\text{NO}}_{3}{}^{-}\text{(}aq\text{)}\end{array}[/latex]

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 [latex]{\text{NO}}_{3}{}^{-}\text{(}aq\text{)}[/latex]. 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:

[latex]\begin{array}{c}\cancel{{\text{Ca}}^{\text{2+}}\text{(}aq\text{)}}+2{\text{Cl}}^{-}\text{(}aq\text{)}+2{\text{Ag}}^{\text{+}}\text{(}aq\text{)}+\cancel{2{\text{NO}}_{3}{}^{\text{-}}\text{(}aq\text{)}}\rightarrow\cancel{{\text{Ca}}^{\text{2+}}\text{(}aq\text{)}}+\cancel{2{\text{NO}}_{3}{}^{-}\text{(}aq\text{)}}+2\text{AgCl(}s\text{)}\\ 2{\text{Cl}}^{-}\text{(}aq\text{)}+2{\text{Ag}}^{\text{+}}\text{(}aq\text{)}\rightarrow 2\text{AgCl(}s\text{)}\end{array}[/latex]

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+.

Example 8.2.2: 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.

Show Solution

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:

[latex]{\text{CO}}_{2}\text{(}aq\text{)}+2{\text{Na}}^{\text{+}}\text{(}aq\text{)}+2{\text{OH}}^{\text{-}}\text{(}aq\text{)}\rightarrow 2{\text{Na}}^{\text{+}}\text{(}aq\text{)}+{\text{CO}}_{3}{}^{\text{2-}}\text{(}aq\text{)}+{\text{H}}_{2}\text{O(}l\text{)}[/latex]

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:

[latex]\begin{array}{l}{\text{CO}}_{2}\text{(}aq\text{)}+\cancel{2{\text{Na}}^{\text{+}}\text{(}aq\text{)}}+2{\text{OH}}^{\text{-}}\text{(}aq\text{)}\rightarrow 2\cancel{{\text{Na}}^{\text{+}}\text{(}aq\text{)}}+{\text{CO}}_{3}{}^{\text{2-}}\text{(}aq\text{)}+{\text{H}}_{2}\text{O(}l\text{)}\\ {\text{CO}}_{2}\text{(}aq\text{)}+2{\text{OH}}^{\text{-}}\text{(}aq\text{)}\rightarrow{\text{CO}}_{3}{}^{\text{2-}}\text{(}aq\text{)}+{\text{H}}_{2}\text{O(}l\text{)}\end{array}[/latex]

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Key Concepts and Summary

Chemical reactions are classified according to similar patterns of behavior. A large number of important reactions are included in three categories: precipitation, acid-base, and oxidation-reduction (redox). Precipitation reactions involve the formation of one or more insoluble products. Acid-base reactions involve the transfer of hydrogen ions between reactants. Redox reactions involve a change in oxidation number for one or more reactant elements. Writing balanced equations for some redox reactions that occur in aqueous solutions is simplified by using a systematic approach called the half-reaction method.

Try It

  1. Use the following equations to answer the next four questions:
    • [latex]{\text{H}}_{2}\text{O(}s\text{)}\rightarrow{\text{H}}_{2}\text{O(}l\text{)}[/latex]
    • [latex]{\text{Na}}^{+}\text{(}aq\text{)}+{\text{Cl}}^{-}\text{(}aq\text{)}{\text{Ag}}^{+}\text{(}aq\text{)}+{\text{NO}}_{3}{}^{-}\text{(}aq\text{)}\rightarrow\text{AgCl(}s\text{)}+{\text{Na}}^{+}\text{(}aq\text{)}+{\text{NO}}_{3}{}^{-}\text{(}aq\text{)}[/latex]
    • [latex]{\text{CH}}_{3}\text{OH(}g\text{)}+{\text{O}}_{2}\text{(}g\text{)}\rightarrow{\text{CO}}_{2}\text{(}g\text{)}+{\text{H}}_{2}\text{O(}g\text{)}[/latex]
    • [latex]2{\text{H}}_{2}\text{O(}l\text{)}\rightarrow 2{\text{H}}_{2}\text{(}g\text{)}+{\text{O}}_{2}\text{(}g\text{)}[/latex]
    • [latex]{\text{H}}^{\text{+}}\text{(}aq\text{)}+{\text{OH}}^{-}\text{(}aq\text{)}\rightarrow{\text{H}}_{2}\text{O(}l\text{)}[/latex]
    1. Which equation describes a physical change?
    2. Which equation identifies the reactants and products of a combustion reaction?
    3. Which equation is not balanced?
    4. Which is a net ionic equation?
  2. Write the molecular, total ionic, and net ionic equations for the following reactions:
    1. [latex]\text{Ca}{\text{(OH)}}_{2}\text{(}aq\text{)}+{\text{HC}}_{2}{\text{H}}_{3}{\text{O}}_{2}\text{(}aq\text{)}\rightarrow[/latex]
    2. [latex]{\text{H}}_{3}{\text{PO}}_{4}\text{(}aq\text{)}+{\text{CaCl}}_{2}\text{(}aq\text{)}\rightarrow[/latex]
  3. Great Lakes Chemical Company produces bromine, Br2, 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 Cl2.
Show Selected Solutions
  1. [latex]\text{2NaBr(}aq\text{)}+{\text{Cl}}_{2}\text{(}g\text{)}\rightarrow 2\text{NaCl(}aq\text{)}+{\text{Br}}_{2}\text{(}l\text{)}[/latex]


complete ionic equation: chemical equation in which all dissolved ionic reactants and products, including spectator ions, are explicitly represented by formulas for their dissociated ions

combustion reaction: vigorous redox reaction producing significant amounts of energy in the form of heat and, sometimes, light

half-reaction: an equation that shows whether each reactant loses or gains electrons in a reaction.

insoluble: of relatively low solubility; dissolving only to a slight extent

molecular equation: chemical equation in which all reactants and products are represented as neutral substances

neutralization reaction: reaction between an acid and a base to produce salt and water

net ionic equation: chemical equation in which only those dissolved ionic reactants and products that undergo a chemical or physical change are represented (excludes spectator ions)

oxidation: process in which an element’s oxidation number is increased by loss of electrons

oxidation-reduction reaction: (also, redox reaction) reaction involving a change in oxidation number for one or more reactant elements

oxidation number: (also, oxidation state) the charge each atom of an element would have in a compound if the compound were ionic

oxidizing agent: (also, oxidant) substance that brings about the oxidation of another substance, and in the process becomes reduced

precipitate: insoluble product that forms from reaction of soluble reactants

precipitation reaction: reaction that produces one or more insoluble products; when reactants are ionic compounds, sometimes called double-displacement or metathesis

reactant: substance undergoing a chemical or physical change; shown on the left side of the arrow in a chemical equation

reduction: process in which an element’s oxidation number is decreased by gain of electrons

reducing agent: (also, reductant) substance that brings about the reduction of another substance, and in the process becomes oxidized

salt: ionic compound that can be formed by the reaction of an acid with a base that contains a cation and an anion other than hydroxide or oxide

single-displacement reaction: (also, replacement) redox reaction involving the oxidation of an elemental substance by an ionic species

soluble: of relatively high solubility; dissolving to a relatively large extent

solubility: the extent to which a substance may be dissolved in water, or any solvent

spectator ion: ion that does not undergo a chemical or physical change during a reaction, but its presence is required to maintain charge neutrality

strong acid: acid that reacts completely when dissolved in water to yield hydronium ions

strong base: base that reacts completely when dissolved in water to yield hydroxide ions

weak acid: acid that reacts only to a slight extent when dissolved in water to yield hydronium ions

weak base: base that reacts only to a slight extent when dissolved in water to yield hydroxide ions



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