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 transform 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.
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 the following sections of this chapter.