Chapter 4 Chemical Reactions and Equations

4.1 The Chemical Equation

A chemical reaction expresses a chemical change. For example, one chemical property of hydrogen is that it will react with oxygen to make water. We can write that as follows:

hydrogen reacts with oxygen to make water

We can represent this chemical change more succinctly as

hydrogen + oxygen → water

where the + sign means that the two substances interact chemically with each other and the → symbol implies that a chemical reaction takes place. But substances can also be represented by chemical formulas. Remembering that hydrogen and oxygen both exist as diatomic molecules, we can rewrite our chemical change as

H₂ + O₂ → H₂O

This is an example of a chemical equationA concise way of representing a chemical reaction., which is a concise way of representing a chemical reaction. The initial substances are called reactantsAn initial substance in a chemical equation., and the final substances are called productsA final substance in a chemical equation..

Unfortunately, it is also an incomplete chemical equation. The law of conservation of matter says that matter cannot be created or destroyed. In chemical equations, the number of atoms of each element in the reactants must be the same as the number of atoms of each element in the products. If we count the number of hydrogen atoms in the reactants and products, we find two hydrogen atoms. But if we count the number of oxygen atoms in the reactants and products, we find that there are two oxygen atoms in the reactants but only one oxygen atom in the products.

What can we do? Can we change the subscripts in the formula for water so that it has two oxygen atoms in it? No; you cannot change the formulas of individual substances because the chemical formula for a given substance is characteristic of that substance. What you can do, however, is to change the number of molecules that react or are produced. We do this one element at a time, going from one side of the reaction to the other, changing the number of molecules of a substance until all elements have the same number of atoms on each side.

To accommodate the two oxygen atoms as reactants, let us assume that we have two water molecules as products:

H₂ + O₂ → 2H₂O

The 2 in front of the formula for water is called a coefficientA number in a chemical equation indicating more than one molecule of the substance.. Now there is the same number of oxygen atoms in the reactants as there are in the product. But in satisfying the need for the same number of oxygen atoms on both sides of the reaction, we have also changed the number of hydrogen atoms on the product side, so the number of hydrogen atoms is no longer equal. No problem—simply go back to the reactant side of the equation and add a coefficient in front of the H₂. The coefficient that works is 2:

2H₂ + O₂ → 2H₂O

There are now four hydrogen atoms in the reactants and also four atoms of hydrogen in the product. There are two oxygen atoms in the reactants and two atoms of oxygen in the product. The law of conservation of matter has been satisfied. When the reactants and products of a chemical equation have the same number of atoms of all elements present, we say that an equation is balancedA condition when the reactants and products of a chemical equation have the same number of atoms of all elements present.. All proper chemical equations are balanced. If a substance does not have a coefficient written in front of it, it is assumed to be 1. Also, the convention is to use all whole numbers when balancing chemical equations. This sometimes makes us do a bit more “back and forth” work when balancing a chemical equation.

Many chemical equations also include phase labels for the substances: (s) for solid, (ℓ) for liquid, (g) for gas, and (aq) for aqueous (i.e., dissolved in water). Special conditions, such as temperature, may also be listed above the arrow. For example,

$${\text{2NaHCO}}_{\text{3}}\text{(s)} \stackrel{\text{200}\text{°C}}{\to } {\text{Na}}_{\text{2}}{\text{CO}}_{\text{3}}\text{(s)}+{\text{CO}}_{\text{2}}\text{(g)}+{\text{H}}_{\text{2}}\text{O}(\ell )$$

4.2 Types of Chemical Reactions: Single- and Double-Displacement Reactions

Up to now, we have presented chemical reactions as a topic, but we have not discussed how the products of a chemical reaction can be predicted. Here we will begin our study of certain types of chemical reactions that allow us to predict what the products of the reaction will be.

A single-replacement reactionA chemical reaction in which one element is substituted for another element in a compound. is a chemical reaction in which one element is substituted for another element in a compound, generating a new element and a new compound as products. For example,

2HCl(aq) + Zn(s) → ZnCl₂(aq) + H₂(g)

is an example of a single-replacement reaction. The hydrogen atoms in HCl are replaced by Zn atoms, and in the process a new element—hydrogen—is formed. Another example of a single-replacement reaction is

2NaCl(aq) + F₂(g) → 2NaF(s) + Cl₂(g)

Here the negatively charged ion changes from chloride to fluoride. A typical characteristic of a single-replacement reaction is that there is one element as a reactant and another element as a product.

Not all proposed single-replacement reactions will occur between two given reactants. This is most easily demonstrated with fluorine, chlorine, bromine, and iodine. Collectively, these elements are called the halogens and are in the next-to-last column on the periodic table (see Figure 4.1 "Halogens on the Periodic Table"). The elements on top of the column will replace the elements below them on the periodic table but not the other way around. Thus, the reaction represented by

CaI₂(s) + Cl₂(g) → CaCl₂(s) + I₂(s)

will occur, but the reaction

CaF₂(s) + Br₂(ℓ) → CaBr₂(s) + F₂(g)

will not because bromine is below fluorine on the periodic table. This is just one of many ways the periodic table helps us understand chemistry.

Chemical reactivity trends are easy to predict when replacing anions in simple ionic compounds—simply use their relative positions on the periodic table. However, when replacing the cations, the trends are not as straightforward. This is partly because there are so many elements that can form cations; an element in one column on the periodic table may replace another element nearby, or it may not. A list called the activity seriesA list of elements that will replace elements below them in single-replacement reactions. does the same thing the periodic table does for halogens: it lists the elements that will replace elements below them in single-replacement reactions. A simple activity series is shown below.

Using the activity series is similar to using the positions of the halogens on the periodic table. An element on top will replace an element below it in compounds undergoing a single-replacement reaction. Elements will not replace elements above them in compounds.

A double-replacement reactionA chemical reaction in which parts of two ionic compounds are exchanged. occurs when parts of two ionic compounds are exchanged, making two new compounds. A characteristic of a double-replacement equation is that there are two compounds as reactants and two different compounds as products. An example is

CuCl₂(aq) + 2AgNO₃(aq) → Cu(NO₃)₂(aq) + 2AgCl(s)

There are two equivalent ways of considering a double-replacement equation: either the cations are swapped, or the anions are swapped. (You cannot swap both; you would end up with the same substances you started with.) Either perspective should allow you to predict the proper products, as long as you pair a cation with an anion and not a cation with a cation or an anion with an anion.

Predicting whether a double-replacement reaction occurs is somewhat more difficult than predicting a single-replacement reaction. However, there is one type of double-replacement reaction that we can predict: the precipitation reaction. A precipitation reactionA chemical reaction in which two ionic compounds are dissolved in water and form a new ionic compound that does not dissolve. occurs when two ionic compounds are dissolved in water and form a new ionic compound that does not dissolve; this new compound falls out of solution as a solid precipitateA solid that falls out of solution in a precipitation reaction.. The formation of a solid precipitate is the driving force that makes the reaction proceed.

To judge whether double-replacement reactions will occur, we need to know what kinds of ionic compounds form precipitates. For this, we use solubility rulesGeneral statements that predict which ionic compounds dissolve and which do not., which are general statements that predict which ionic compounds dissolve (are soluble) and which do not (are not soluble or insoluble). Table 4.1 "Some Useful Solubility Rules" lists some general solubility rules. We need to consider each ionic compound (both the reactants and the possible products) in light of the solubility rules in Table 4.1 "Some Useful Solubility Rules". If a compound is soluble, we use the (aq) label with it, indicating it dissolves. If a compound is not soluble, we use the (s) label with it and assume that it will precipitate out of solution. If everything is soluble, then no reaction will be expected.

For example, consider the possible double-replacement reaction between Na₂SO₄ and SrCl₂. The solubility rules say that all ionic sodium compounds are soluble and all ionic chloride compounds are soluble except for Ag⁺, Hg₂²⁺, and Pb²⁺, which are not being considered here. Therefore, Na₂SO₄ and SrCl₂ are both soluble. The possible double-replacement reaction products are NaCl and SrSO₄. Are these soluble? NaCl is (by the same rule we just quoted), but what about SrSO₄? Compounds of the sulfate ion are generally soluble, but Sr²⁺ is an exception: we expect it to be insoluble—a precipitate. Therefore, we expect a reaction to occur, and the balanced chemical equation would be

Na₂SO₄(aq) + SrCl₂(aq) → 2NaCl(aq) + SrSO₄(s)

You would expect to see a visual change corresponding to SrSO₄ precipitating out of solution (Figure 4.2 "Double-Replacement Reactions").

4.3 Ionic Equations: A Closer Look

For single-replacement and double-replacement reactions, many of the reactions included ionic compounds: compounds between metals and nonmetals or compounds that contained recognizable polyatomic ions. Now we take a closer look at reactions that include ionic compounds.

One important aspect about ionic compounds that differs from molecular compounds has to do with dissolving in a liquid, such as water. When molecular compounds, such as sugar, dissolve in water, the individual molecules drift apart from each other. When ionic compounds dissolve, the ions physically separate from each other. We can use a chemical equation to represent this process—for example, with NaCl:

$$\text{NaCl(s)} \stackrel{{\text{H}}_2\text{O}}{\to } {\text{Na}}^{+}\text{(aq)}+{\text{Cl}}^{-}\text{(aq)}$$

When NaCl dissolves in water, the ions separate and go their own way in solution; the ions are now written with their respective charges, and the (aq) phase label emphasizes that they are dissolved (Figure 4.3 "Ionic Solutions"). This process is called dissociationThe process of an ionic compound separating into ions when it dissolves.; we say that the ions dissociate.

All ionic compounds that dissolve behave this way. (This behavior was first suggested by the Swedish chemist Svante August Arrhenius [1859–1927] as part of his PhD dissertation in 1884. Interestingly, his PhD examination team had a hard time believing that ionic compounds would behave like this, so they gave Arrhenius a barely passing grade. Later, this work was cited when Arrhenius was awarded the Nobel Prize in Chemistry.) Keep in mind that when the ions separate, all the ions separate. Thus, when CaCl₂ dissolves, the one Ca²⁺ ion and the two Cl⁻ ions separate from each other:

$$\begin{array}{c}{\text{CaCl}}_{\text{2}}\text{(s)} \stackrel{{\text{H}}_2\text{O}}{\to } {\text{Ca}}^{\text{2}+}\text{(aq)}+{\text{Cl}}^{-}\text{(aq)}+{\text{Cl}}^{-}\text{(aq)}\\ \text{or}\\ {\text{CaCl}}_{\text{2}}\text{(s)} \stackrel{{\text{H}}_2\text{O}}{\to } {\text{Ca}}^{\text{2}+}\text{(aq)}+{\text{2Cl}}^{-}\text{(aq)}\end{array}$$

That is, the two chloride ions go off on their own. They do not remain as Cl₂ (that would be elemental chlorine; these are chloride ions); they do not stick together to make Cl₂⁻ or Cl₂²⁻. They become dissociated ions in their own right. Polyatomic ions also retain their overall identity when they are dissolved.

When chemicals in solution react, the proper way of writing the chemical formulas of the dissolved ionic compounds is in terms of the dissociated ions, not the complete ionic formula. A complete ionic equationA chemical equation in which the dissolved ionic compounds are written as separated ions. is a chemical equation in which the dissolved ionic compounds are written as separated ions. Solubility rules are very useful in determining which ionic compounds are dissolved and which are not. For example, when NaCl(aq) reacts with AgNO₃(aq) in a double-replacement reaction to precipitate AgCl(s) and form NaNO₃(aq), the complete ionic equation includes NaCl, AgNO₃, and NaNO₃ written as separated ions:

Na⁺(aq) + Cl⁻(aq) + Ag⁺(aq) + NO₃⁻(aq) → AgCl(s) + Na⁺(aq) + NO₃⁻(aq)

This is more representative of what is occurring in the solution.

You may notice that in a complete ionic equation, some ions do not change their chemical form; they stay exactly the same on the reactant and product sides of the equation. For example, in

Na⁺(aq) + Cl⁻(aq) + Ag⁺(aq) + NO₃⁻(aq) → AgCl(s) + Na⁺(aq) + NO₃⁻(aq)

the Ag⁺(aq) and Cl⁻(aq) ions become AgCl(s), but the Na⁺(aq) ions and the NO₃⁻(aq) ions stay as Na⁺(aq) ions and NO₃⁻(aq) ions. These two ions are examples of spectator ionsAn ion that does nothing in the overall course of a chemical reaction., ions that do nothing in the overall course of a chemical reaction. They are present, but they do not participate in the overall chemistry. It is common to cancel spectator ions (something also done with algebraic quantities) on the opposite sides of a chemical equation:

$$\cancel{{\text{Na}}^{+}\text{(aq)}}+{\text{Cl}}^{-}\text{(aq)}+{\text{Ag}}^{+}\text{(aq)}+\cancel{ {\text{NO}}_{\text{3}}{}^{-}\text{(aq)}}\to \text{AgCl(s)}+\cancel{{\text{Na}}^{+}\text{(aq)}}+\cancel{{\text{NO}}_{\text{3}}{}^{-}\text{(aq)}}$$

What remains when the spectator ions are removed is called the net ionic equationA chemical equation with the spectator ions removed., which represents the actual chemical change occurring between the ionic compounds:

Cl⁻(aq) + Ag⁺(aq) → AgCl(s)

It is important to reiterate that the spectator ions are still present in solution, but they don’t experience any net chemical change, so they are not written in a net ionic equation.

4.4 Composition, Decomposition, and Combustion Reactions

Three classifications of chemical reactions will be reviewed in this section. Predicting the products in some of them may be difficult, but the reactions are still easy to recognize.

A composition reactionA chemical reaction in which a single substance is produced from multiple reactants. (sometimes also called a combination reaction or a synthesis reaction) produces a single substance from multiple reactants. A single substance as a product is the key characteristic of the composition reaction. There may be a coefficient other than one for the substance, but if the reaction has only a single substance as a product, it can be called a composition reaction. In the reaction

2H₂(g) + O₂(g) → 2H₂O(ℓ)

water is produced from hydrogen and oxygen. Although there are two molecules of water being produced, there is only one substance—water—as a product. So this is a composition reaction.

A decomposition reactionA chemical reaction in which a single substance becomes more than one substance. starts from a single substance and produces more than one substance; that is, it decomposes. One substance as a reactant and more than one substance as the products is the key characteristic of a decomposition reaction. For example, in the decomposition of sodium hydrogen carbonate (also known as sodium bicarbonate),

2NaHCO₃(s) → Na₂CO₃(s) + CO₂(g) + H₂O(ℓ)

sodium carbonate, carbon dioxide, and water are produced from the single substance sodium hydrogen carbonate.

Composition and decomposition reactions are difficult to predict; however, they should be easy to recognize.

A combustion reactionA chemical reaction in which a reactant combines with oxygen to produce oxides of all other elements as products. occurs when a reactant combines with oxygen, many times from the atmosphere, to produce oxides of all other elements as products; any nitrogen in the reactant is converted to elemental nitrogen, N₂. Many reactants, called fuels, contain mostly carbon and hydrogen atoms, reacting with oxygen to produce CO₂ and H₂O. For example, the balanced chemical equation for the combustion of methane, CH₄, is as follows:

CH₄ + 2O₂ → CO₂ + 2H₂O

Kerosene can be approximated with the formula C₁₂H₂₆, and its combustion equation is

2C₁₂H₂₆ + 37O₂ → 24CO₂ + 26H₂O

Sometimes fuels contain oxygen atoms, which must be counted when balancing the chemical equation. One common fuel is ethanol, C₂H₅OH, whose combustion equation is

C₂H₅OH + 3O₂ → 2CO₂ + 3H₂O

If nitrogen is present in the original fuel, it is converted to N₂, not to a nitrogen-oxygen compound. Thus, for the combustion of the fuel dinitroethylene, whose formula is C₂H₂N₂O₄, we have

2C₂H₂N₂O₄ + O₂ → 4CO₂ + 2H₂O + 2N₂

4.5 Neutralization Reactions

In Chapter 3 "Atoms, Molecules, and Ions", Section 3.5 "Acids", we defined an acid as an ionic compound that contains H⁺ as the cation. This is slightly incorrect, but until additional concepts were developed, a better definition needed to wait. Now we can redefine an acid: an acidA compound that increases the amount of ${\text{H}}^{+}$ ions in an aqueous solution. is any compound that increases the amount of hydrogen ion (H⁺) in an aqueous solution. The chemical opposite of an acid is a base. The equivalent definition of a base is that a baseA compound that increases the amount of ${\text{OH}}^{-}$ ions in an aqueous solution. is a compound that increases the amount of hydroxide ion (OH⁻) in an aqueous solution. These original definitions were proposed by Arrhenius (the same person who proposed ion dissociation) in 1884, so they are referred to as the Arrhenius definition of an acid and a base, respectively.

You may recognize that, based on the description of a hydrogen atom, an H⁺ ion is a hydrogen atom that has lost its lone electron; that is, H⁺ is simply a proton. Do we really have bare protons moving about in aqueous solution? No. What is more likely is that the H⁺ ion has attached itself to one (or more) water molecule(s). To represent this chemically, we define the hydronium ion${\text{H}}_3{\text{O}}^{+}\left(\text{aq}\right)$, a water molecule with an extra hydrogen ion attached to it. as H₃O⁺, which represents an additional proton attached to a water molecule. We use the hydronium ion as the more logical way a hydrogen ion appears in an aqueous solution, although in many chemical reactions H⁺ and H₃O⁺ are treated equivalently.

The reaction of an acid and a base is called a neutralization reactionThe reaction of an acid with a base to produce water and a salt.. Although acids and bases have their own unique chemistries, the acid and base cancel each other’s chemistry to produce a rather innocuous substance—water. In fact, the general reaction between an acid and a base is

acid + base → water + salt

where the term saltAny ionic compound that is formed from a reaction between an acid and a base. is generally used to define any ionic compound (soluble or insoluble) that is formed from a reaction between an acid and a base. (In chemistry, the word salt refers to more than just table salt.) For example, the balanced chemical equation for the reaction between HCl(aq) and KOH(aq) is

HCl(aq) + KOH(aq) → H₂O(ℓ) + KCl(aq)

where the salt is KCl. By counting the number of atoms of each element, we find that only one water molecule is formed as a product. However, in the reaction between HCl(aq) and Mg(OH)₂(aq), additional molecules of HCl and H₂O are required to balance the chemical equation:

2HCl(aq) + Mg(OH)₂(aq) → 2H₂O(ℓ) + MgCl₂(aq)

Here, the salt is MgCl₂. (This is one of several reactions that take place when a type of antacid—a base—is used to treat stomach acid.)

Neutralization reactions are one type of chemical reaction that proceeds even if one reactant is not in the aqueous phase. For example, the chemical reaction between HCl(aq) and Fe(OH)₃(s) still proceeds according to the equation

3HCl(aq) + Fe(OH)₃(s) → 3H₂O(ℓ) + FeCl₃(aq)

even though Fe(OH)₃ is not soluble. When one realizes that Fe(OH)₃(s) is a component of rust, this explains why some cleaning solutions for rust stains contain acids—the neutralization reaction produces products that are soluble and wash away. (Washing with acids like HCl is one way to remove rust and rust stains, but HCl must be used with caution!)

Complete and net ionic reactions for neutralization reactions will depend on whether the reactants and products are soluble, even if the acid and base react. For example, in the reaction of HCl(aq) and NaOH(aq),

HCl(aq) + NaOH(aq) → H₂O(ℓ) + NaCl(aq)

the complete ionic reaction is

H⁺(aq) + Cl⁻(aq) + Na⁺(aq) + OH⁻(aq) → H₂O(ℓ) + Na⁺(aq) + Cl⁻(aq)

The Na⁺(aq) and Cl⁻(aq) ions are spectator ions, so we can remove them to have

H⁺(aq) + OH⁻(aq) → H₂O(ℓ)

as the net ionic equation. If we wanted to write this in terms of the hydronium ion, H₃O⁺(aq), we would write it as

H₃O⁺(aq) + OH⁻(aq) → 2H₂O(ℓ)

With the exception of the introduction of an extra water molecule, these two net ionic equations are equivalent.

However, for the reaction between HCl(aq) and Cr(OH)₂(s), because chromium(II) hydroxide is insoluble, we cannot separate it into ions for the complete ionic equation:

2H⁺(aq) + 2Cl⁻(aq) + Cr(OH)₂(s) → 2H₂O(ℓ) + Cr²⁺(aq) + 2Cl⁻(aq)

The chloride ions are the only spectator ions here, so the net ionic equation is

2H⁺(aq) + Cr(OH)₂(s) → 2H₂O(ℓ) + Cr²⁺(aq)

4.6 Oxidation-Reduction Reactions

Consider this chemical reaction:

2Na(s) + Cl₂(g) → 2NaCl

The reactants are elements, and it is assumed that they are electrically neutral; they have the same number of electrons as protons. The product, however, is ionic; it is composed of Na⁺ and Cl⁻ ions. Somehow, the individual sodium atoms as reactants had to lose an electron to make the Na⁺ ion, while the chlorine atoms as reactants had to each gain an electron to become the Cl⁻ ion. This reaction involves the transfer of electrons between atoms.

In reality, electrons are lost by some atoms and gained by other atoms simultaneously. However, mentally we can separate the two processes. OxidationThe loss of one or more electrons by an atom; an increase in oxidation number. is defined as the loss of one or more electrons by an atom. ReductionThe gain of one or more electrons by an atom; a decrease in oxidation number. is defined as the gain of one or more electrons by an atom. In reality, oxidation and reduction always occur together; it is only mentally that we can separate them. Chemical reactions that involve the transfer of electrons are called oxidation-reduction (or redox) reactionsA chemical reaction that involves the transfer of electrons..

Redox reactions require that we keep track of the electrons assigned to each atom in a chemical reaction. How do we do that? We use an artificial count called the oxidation numberA number assigned to an atom that helps keep track of the number of electrons on the atom. to keep track of electrons in atoms. Oxidation numbers are assigned to atoms based on a series of rules. Oxidation numbers are not necessarily equal to the charge on the atom; we must keep the concepts of charge and oxidation numbers separate.

The rules for assigning oxidation numbers to atoms are as follows:

1. Atoms in their elemental state are assigned an oxidation number of 0.
2. Atoms in monatomic (i.e., one-atom) ions are assigned an oxidation number equal to their charge. Oxidation numbers are usually written with the sign first, then the magnitude, which differentiates them from charges.
3. In compounds, fluorine is assigned a −1 oxidation number; oxygen is usually assigned a −2 oxidation number (except in peroxide compounds [where it is −1] and in binary compounds with fluorine [where it is positive]); and hydrogen is usually assigned a +1 oxidation number (except when it exists as the hydride ion, H⁻, in which case rule 2 prevails).
4. In compounds, all other atoms are assigned an oxidation number so that the sum of the oxidation numbers on all the atoms in the species equals the charge on the species (which is zero if the species is neutral).

Let us work through a few examples for practice. In H₂, both hydrogen atoms have an oxidation number of 0, by rule 1. In NaCl, sodium has an oxidation number of +1, while chlorine has an oxidation number of −1, by rule 2. In H₂O, the hydrogen atoms each have an oxidation number of +1, while the oxygen has an oxidation number of −2, even though hydrogen and oxygen do not exist as ions in this compound as per rule 3. By contrast, by rule 3 in hydrogen peroxide (H₂O₂), each hydrogen atom has an oxidation number of +1, while each oxygen atom has an oxidation number of −1. We can use rule 4 to determine oxidation numbers for the atoms in SO₂. Each oxygen atom has an oxidation number of −2; for the sum of the oxidation numbers to equal the charge on the species (which is zero), the sulfur atom is assigned an oxidation number of +4. Does this mean that the sulfur atom has a 4+ charge on it? No, it only means that the sulfur atom is assigned a +4 oxidation number by our rules of apportioning electrons among the atoms in a compound.

All redox reactions occur with a simultaneous change in the oxidation numbers of some atoms. At least two elements must change their oxidation numbers. When an oxidation number of an atom is increased in the course of a redox reaction, that atom is being oxidized. When an oxidation number of an atom is decreased in the course of a redox reaction, that atom is being reduced. Oxidation and reduction are thus also defined in terms of increasing or decreasing oxidation numbers, respectively.

In this introduction to oxidation-reduction reactions, we are using straightforward examples. However, oxidation reactions can become quite complex; the following equation represents a redox reaction:

To demonstrate that this is a redox reaction, the oxidation numbers of the species being oxidized and reduced are listed; can you determine what is being oxidized and what is being reduced? This is also an example of a net ionic reaction; spectator ions that do not change oxidation numbers are not displayed in the equation.