4.22: Balancing Chemical Equations: Identifying a Balanced Chemical Equation

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Learning Objectives

Identify a balanced chemical equation.

In order to balance a chemical equation, the quantities of each type of element and polyatomic ion that are present in the reactants and the products of the reaction must be determined. Because polyatomic ions contain multiple atoms and generally react as indivisible units, any polyatomic ion that is present in both a reactant and a product in a given chemical equation should be treated as a singular entity. However, as explained in the solution to Example 4.20.1b, polyatomic ions are unable to remain unified in a decomposition reaction, as this type of transformation requires, by definition, that a reactant molecule be divided into simpler substances. Therefore, any polyatomic ion that is present in the reactant of a decomposition reaction should be divided into its constituent elements. After accounting for the polyatomic ions that are present in a reaction equation, any remaining elements should be considered individually. Finally, note that if a particular element appears in two distinctive places within a single chemical formula or within multiple formulas on the same side of the reaction arrow, the corresponding subscripts must be added, in order to accurately determine the quantity of that element that is present on that side of the reaction arrow.

For example, consider the following chemical equation. In order to balance this equation, coefficients should be written in the "blanks," as necessary.

___ \(\ce{HC_2H_3O_2} \left( g \right) \rightarrow\) ___ \(\ce{CH_4} \left( g \right) +\) ___ \(\ce{CO_2} \left( g \right)\)

The reactant in this reaction contains an acetate ion, C₂H₃O₂^-1, which is a polyatomic anion. However, this reaction is classified as a decomposition because only a single molecule, hydrogen acetate, HC₂H₃O₂, is represented on the left side of the reaction arrow. Because a decomposition requires that a reactant molecule be divided into simpler substances, polyatomic ions are unable to remain unified in this type of reaction. Therefore, when balancing this reaction, the elements found within the acetate ion, carbon, C, hydrogen, H, and oxygen, O, are treated separately. No additional elements are found within any of the given reactants or products, so only carbon, C, hydrogen, H, and oxygen, O, must be considered for this reaction.

The subscript that is present on carbon, C, in HC₂H₃O₂, indicates that a total of two carbons are present on the reactant side of this equation. However, carbon is present in both of the products that are generated during this reaction. In order to determine the true number of carbons that are present on the product side of this equation, the subscripts on both carbons, which are each unwritten "1"s, must be added. Therefore, a total of two carbons are also present on the product side of this equation.
Hydrogen, H, appears in two distinctive places within the reactant formula. In order to determine the true number of hydrogens that are present within this reactant, the subscripts on both hydrogens, which are an unwritten "1" and a "3," respectively, must be added. Therefore, a total of four hydrogens are initially present on the reactant side of this equation. The subscript that is present on hydrogen in carbon tetrahydride, CH₄, indicates that a total of four hydrogens are also present on the product side of this equation.
The subscript that is present on oxygen, O, in HC₂H₃O₂, indicates that a total of two oxygens are present on the reactant side of this equation. The subscript that is present on oxygen in carbon dioxide, CO₂, indicates that a total of two oxygens are also present on the product side of this equation.

The process of verbally summarizing the quantities of each type of element and polyatomic ion is cumbersome and time-consuming. Furthermore, the quantitative information is not readily-apparent in this format, due to the overwhelming number of words that are present. Therefore, summarizing these quantities using a tabular format is more efficient, and the resultant data is easily-interpretable, as shown below.

Element or Ion	Reactants	Products
C	2	2
H	4	4
O	2	2

In order for a component of a reaction to be balanced, the reactants and products of the reaction must contain identical total quantities of that type of element or polyatomic ion. Since both sides of the reaction contain equal amounts of carbon, C, this element is balanced. Hydrogen, H, and oxygen, O, are also balanced, because each of these elements is present in the same quantities on both sides of the reaction arrow.

Because all of the individual elements that are present within the given reaction are balanced, the overall equation is also balanced. A equation that is balanced does not require the incorporation of any coefficients, as the Law of Conservation of Matter is already upheld for the corresponding chemical reaction. As indicated previously, values of "1" are usually implicitly-understood in chemistry and should not be written the coefficient "blanks" in a chemical equation. Therefore, the equation that is presented above is chemically-correct, as written.