# 4.12: Chemical Reactions and Chemical Equations

Learning Objectives
• Define chemical reaction.
• Define chemical equation.
• Explain the differences between a chemical reaction and a chemical equation.
• Identify the reactants and products in a chemical equation.
• Identify the states of matter in which chemicals participate in a chemical reaction.
• Identify the balancing coefficient that is associated with a particular chemical in a chemical equation.

Physical and chemical changes were defined, compared, and contrasted in the previous section of this chapter.  A physical change is defined as a transformation of the appearance of a substance that is not brought about by a corresponding change in the identity of that substance.  Because the all chemical identities remain constant during a physical change, only a limited number of processes, which will be studied in greater detail in Chapter 5 and Chapter 7, are classified as physical changes.

## Chemical Reactions and Chemical Equations

Both the physical properties and the chemical formula of a substance must be altered during a chemical change.  In other words, the identity of a chemical must be transformed during a chemical change.  At a molecular level, the composition of a chemical is defined by the types of atoms that it contains, as well as on the ratio in which those atoms are present.  Therefore, in order to alter the identity of a substance, one or more atoms that were present in the initial substance must be removed or new atoms must be introduced.  In order for the composition of a chemical to be changed in one or both of these ways, the bonds that exist between these atoms must also be altered.  Pre-existing bonds must be broken, so that the associated atoms can separate and rearrange.  Finally, new bonds and, therefore, new chemicals, are created.  The combination of these molecular-level processes, in which one set of substances is chemically changed into another through the breaking and making of bonds, is called a chemical reaction.

While the events that occur during a chemical reaction can be described verbally, these transformations are more often represented symbolically in a chemical equation.  While the terms "chemical reaction" and "chemical equation" sound similar and are related to one another, these phrases should not be interchanged, as their meanings are subtly different.  During a chemical reaction, a chemical change occurs by breaking the bonds within a substance, rearranging the atoms that had previously been connected, and then generating new bonds, in order to produce a new chemical.  In contrast, a chemical equation is the symbolic representation of the reaction process.  For example, hydrogen peroxide, H2O2, is relatively unstable and decomposes during a chemical reaction to form water, H2O, and molecular oxygen, O2.  The chemical equation that corresponds to this process is shown below.  While chemical reactions can be highly-complex, chemical equations are, in contrast, relatively straightforward.  The information that is represented in a chemical equation will be discussed in greater detail in the following paragraphs.

$$\ce{2 H_2O_2} \left( aq \right) \rightarrow \ce{2 H_2O} \left( l \right) + \ce{O_2} \left( g \right)$$

### Chemical Formulas as Reactants and Products

The most important symbol in a chemical equation is a reaction arrow, "$$\rightarrow$$," which can also be called a yield sign.  A reaction arrow, which represents the verbal phrase "reacts to form," indicates the point at which a chemical reaction has occurred.

Because a chemical equation is the symbolic representation of a chemical reaction, the chemicals that are being transformed and created are indicated using their formulas, not their chemical names.  As both elements and compounds can participate in chemical reactions, a chemical equation can include both elemental symbols and chemical formulas.  The chemicals that are present before a reaction has occurred are classified as reactants, and their formulas are written on the left side of a reaction arrow.  The chemical formulas for the final substances that are generated at the end of a chemical reaction, which are called products, are written on the right side of a reaction arrow.  If multiple reactants or products are involved in a particular reaction, a plus sign, "+", is used to separate their formulas.

The chemical reaction that is represented above has a single reactant, H2O2, as no plus sign is written on the left side of the reaction arrow.  Water, H2O, and molecular oxygen, O2, are the products of this reaction, as both of these formulas, which are written on the right side of the reaction arrow, are separated by a plus sign.

Recall that a chemical reaction is a combination of molecular-level processes, in which one set of substances is chemically changed into another.  In order to alter the identity of a material, one or more of its constituent atoms must be removed or new atoms must be introduced.  Therefore, the products of a chemical reaction must contain different types of atoms or altered elemental ratios, relative to the compositions that are found within the corresponding reactants.  Consequently, the elemental symbols or subscripts that are present in the formulas of the reactants in a chemical reaction must differ from those in the products.  In a chemical equation, the chemical formulas of the reactants and the products can be written in close, but separate, physical proximity, due to the presence of the reaction arrow.  As a result, the differences between these formulas, which reflect the chemical change that has occurred, can be readily-identified.

### States of Matter

As stated in Section 4.11, water can exist as a solid, a liquid, or a gas.  However, these terms, which describe the physical form of a substance, are neither uniquely-applicable to water nor the only states of matter that exist.  When considering chemical reactions, a fourth term, aqueous, can also be utilized.

The words "solid," "liquid," and "gas" are used to describe a single chemical, and their definitions all indicate the extent to which the appearance of that substance depends on its container.  A solid has both a definite volume and a definite shape.  As neither of these attributes is influenced by the vessel in which the substance is placed, both the volume and the shape of a solid are completely independent of its container.  In contrast, a liquid has a definite volume, but does not have a definite shape.  In other words, a substance that exists in its liquid state will occupy the same amount of space, regardless of the vessel in which it is poured.  However, a liquid will mold itself into the shape of its container.  For example, a liquid that is transferred into a cylindrical glass will take the form of a cylinder, but will reshape itself into a rectangle when poured into a rectangular pan.  Therefore, the shape, but not the volume, of a liquid is directly dependent on the vessel in which it is placed.  Finally, gaseous chemicals are unique, in that they completely fill their containers.  As a result, neither the volume nor the shape of a gas is intrinsic to the gas itself.  Instead, both of these attributes are dictated by the vessel occupied by the gas.

Because a chemical equation is the symbolic representation of a chemical reaction, the state of matter in which each chemical exists is abbreviated by a single lower-case letter.  Furthermore, each of these letters is italicized, if possible, and enclosed in parentheses, in order to visually distinguish a substance's state of matter from its chemical formula.  Therefore, the solid, liquid, and gaseous states of matter are represented by "$$\left( s \right)$$," "$$\left( l \right)$$," and "$$\left( g \right)$$," respectively, in a chemical equation.

In many cases, two chemicals that are placed in the same container will spontaneously interact and undergo a chemical change.  However, some reactants are incompatible with one another in their natural states and must be dissolved in a liquid medium, called a solvent, in order to react.  While a variety of solid, liquid, and gaseous chemicals can serve as solvents, water is able to dissolve more substances than any other chemical.  As a result of this versatility, water is known as the "universal solvent" and, furthermore, is the most commonly-used solvent for chemical reactions.  Therefore, if a chemical cannot react in its natural state, it will often be dissolved in water and participate in an aqueous state, which is indicated by the abbreviation "$$\left( aq \right)$$" in a chemical equation.

In the chemical equation that is shown above, the symbol "$$\left( aq \right)$$" that directly follows the formula for hydrogen peroxide, H2O2, indicates that this chemical reacts in an aqueous state.  Water is generated as a liquid and molecular oxygen, O2, is evolved as a gas, as indicated by the "$$\left( l \right)$$" and "$$\left( g \right)$$," respectively, that are associated with the formulas for each of these products.

### Balancing Coefficients

The Law of Conservation of Matter is a fundamental principle that mandates that particles cannot be created or destroyed in the course of a chemical reaction.  Therefore, while the formulas of elements and compounds must change during a reaction, by definition, the relative quantity of each atom or ion involved in the reaction must be constant.  The subscripts that are present within a chemical formula are solely dependent on the elemental, ionic, or covalent nature of the corresponding substance and, therefore, cannot be altered to uphold the Law of Conservation of Matter.

As a result, most chemical equations require the incorporation of one or more balancing coefficients, which are often simply referred to as "coefficients," in order to account for any relative differences between the formulas of the reactants and products that are involved in the reaction.  A coefficient, which is written directly before the chemical formula with which it is associated, is defined as a whole-number value that indicates how many of the corresponding atom or molecule are involved in the overall chemical reaction.  The process of "balancing" a chemical equation, which requires the determination and interpretation of these coefficients, will be discussed and applied in a subsequent section of this chapter.

In the chemical equation that is shown above, the balancing coefficients that are associated with the formulas for hydrogen peroxide, H2O2, and water are both "2"s.  No numerical value is explicitly-associated with the final formula in this chemical equation.  As indicated previously, values of "1" are usually implicitly-understood in chemistry and, therefore, are not written when balancing a chemical reaction.  Therefore, the coefficient for molecular oxygen, O2, is understood to be an unwritten "1."

Example $$\PageIndex{1}$$

Consider the reaction that is represented by the following chemical equation.

$$\ce{4 NH_3} \left( g \right) + \ce{3 O_2} \left( g \right) \rightarrow \ce{2 N_2} \left( g \right) + \ce{6 H_2O} \left( g \right)$$

1. Identify the reactants in this reaction.
2. Identify the products of this reaction.
3. Identify the state of matter in which each chemical participates in this reaction.
4. Identify the value of the balancing coefficient that is associated with each chemical in this reaction.

Solutions

1. NH3 and O2 are the reactants in this reaction, because both of these formulas are written on the left side of the reaction arrow.  Furthermore, since these formulas are separated by a plus sign, each represents a unique reactant.
2. N2 and H2are the products of this reaction, because both of these formulas are written on the right side of the reaction arrow.  Furthermore, since these formulas are separated by a plus sign, each represents a unique product.
3. All of the chemicals participate in this reaction as gases, as indicated by the "$$\left( g \right)$$"s that are associated with all of the formulas in the given chemical equation.
4. A coefficient is written directly before the chemical formula with which it is associated.  Therefore, the coefficients that are associated with with NH3, O2, N2, and H2O are "4," "3," "2," and "6," respectively.
Exercise $$\PageIndex{1}$$

Consider the reaction that is represented by the following chemical equation.

$$\ce{K_2CO_3} \left( aq \right) + \ce{H_2O} \left( l \right) + \ce{CO_2} \left( g \right) \rightarrow \ce{2 KHCO_3} \left( aq \right)$$

1. How many unique products are generated at the end this reaction?
2. Is carbon dioxide a reactant or a product in this reaction?
3. How many chemicals participate in this reaction in the solid state of matter?
4. What is the value of the balancing coefficient that is associated with water in this reaction?
None of the chemicals participate in this reaction in the solid state of matter, because none of the given chemical formulas is associated with an "$$\left( s \right)$$."