176 Chapter 4 Stoichiometry of Chemical Reactions
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.
Figure 4.2 The reaction between methane and oxygen to yield carbon dioxide in water (shown at bottom) may be
represented by a chemical equation using formulas (top).
This example illustrates the fundamental aspects of any chemical equation:
1. The substances undergoing reaction are called reactants, and their formulas are placed on the left side of 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:
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,Chapter 4 Stoichiometry of Chemical Reactions 177
• 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.
Figure 4.3 Regardless of the absolute number of molecules involved, the ratios between numbers of molecules are
the same as that given in the chemical equation.
Balancing Equations
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
⎛ 2 O atoms ⎞ ⎛ 1 O atom ⎞
⎝1 CO 2 molecule × CO 2 molecule ⎠ + ⎝2 H 2 O molecule × H 2 O molecule ⎠ = 4 O atoms
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:
CH 4 + 2O 2 ⟶ CO 2 + 2H 2 O
Element Reactants Products Balanced?
C 1 × 1=1 1 × 1=1 1 = 1, yes
H 4 × 1=4 2 × 2=4 4 = 4, yes
O 2 × 2=4 (1 × 2) + (2 × 1) = 4 4 = 4, yes
, 178 Chapter 4 Stoichiometry of Chemical Reactions
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:
H2 O ⟶ H2 + O2 (unbalanced)
Comparing the number of H and O atoms on either side of this equation confirms its imbalance:
Element Reactants Products Balanced?
H 1 × 2=2 1 × 2=2 2 = 2, yes
O 1 × 1=1 1 × 2=2 1 ≠ 2, no
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.
2H 2 O ⟶ H 2 + O 2 (unbalanced)
Element Reactants Products Balanced?
H 2 × 2=4 1 × 2=2 4 ≠ 2, no
O 2 × 1=2 1 × 2=2 2 = 2, yes
The H atom balance was upset by this change, but it is easily reestablished by changing the coefficient for the H2
product to 2.
2H 2 O ⟶ 2H 2 + O 2 (balanced)
Element Reactants Products Balanced?
H 2 × 2=4 2 × 2=2 4 = 4, yes
O 2 × 1=2 1 × 2=2 2 = 2, yes
These coefficients yield equal numbers of both H and O atoms on the reactant and product sides, and the balanced
equation is, therefore:
2H 2 O ⟶ 2H 2 + O 2
Example 4.1
Balancing Chemical Equations
This content is available for free at http://cnx.org/content/col11760/1.9
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.
Figure 4.2 The reaction between methane and oxygen to yield carbon dioxide in water (shown at bottom) may be
represented by a chemical equation using formulas (top).
This example illustrates the fundamental aspects of any chemical equation:
1. The substances undergoing reaction are called reactants, and their formulas are placed on the left side of 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:
This content is available for free at http://cnx.org/content/col11760/1.9
,Chapter 4 Stoichiometry of Chemical Reactions 177
• 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.
Figure 4.3 Regardless of the absolute number of molecules involved, the ratios between numbers of molecules are
the same as that given in the chemical equation.
Balancing Equations
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
⎛ 2 O atoms ⎞ ⎛ 1 O atom ⎞
⎝1 CO 2 molecule × CO 2 molecule ⎠ + ⎝2 H 2 O molecule × H 2 O molecule ⎠ = 4 O atoms
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:
CH 4 + 2O 2 ⟶ CO 2 + 2H 2 O
Element Reactants Products Balanced?
C 1 × 1=1 1 × 1=1 1 = 1, yes
H 4 × 1=4 2 × 2=4 4 = 4, yes
O 2 × 2=4 (1 × 2) + (2 × 1) = 4 4 = 4, yes
, 178 Chapter 4 Stoichiometry of Chemical Reactions
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:
H2 O ⟶ H2 + O2 (unbalanced)
Comparing the number of H and O atoms on either side of this equation confirms its imbalance:
Element Reactants Products Balanced?
H 1 × 2=2 1 × 2=2 2 = 2, yes
O 1 × 1=1 1 × 2=2 1 ≠ 2, no
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.
2H 2 O ⟶ H 2 + O 2 (unbalanced)
Element Reactants Products Balanced?
H 2 × 2=4 1 × 2=2 4 ≠ 2, no
O 2 × 1=2 1 × 2=2 2 = 2, yes
The H atom balance was upset by this change, but it is easily reestablished by changing the coefficient for the H2
product to 2.
2H 2 O ⟶ 2H 2 + O 2 (balanced)
Element Reactants Products Balanced?
H 2 × 2=4 2 × 2=2 4 = 4, yes
O 2 × 1=2 1 × 2=2 2 = 2, yes
These coefficients yield equal numbers of both H and O atoms on the reactant and product sides, and the balanced
equation is, therefore:
2H 2 O ⟶ 2H 2 + O 2
Example 4.1
Balancing Chemical Equations
This content is available for free at http://cnx.org/content/col11760/1.9
