Coefficients are the numbers placed before the reactants in a chemical equation so that the number of atoms in the products on the right side of the equation are equal to the number of atoms in the reactants on the left side. If a written chemical reaction were not balanced in this manner, there would be no information available regarding the relationship between the reactants and products. Also known as stoichiometric coefficients, these numerical values demonstrate that the number of atoms on either side of the equation are equal to each other.
The need for balanced chemical equations is dictated by the law of conservation of mass. The law states that the quantity of each element involved in a chemical reaction does not change. For example, this is an unbalanced equation: N2 + O2 —> NO. The nitrogen atoms and oxygen atoms on the left-hand reactant side of the equation do not equal the number of atoms on the right-hand product side. Placing a coefficient of 2 before the product, however, will balance out the equation and is written as N2 + O2 —> 2NO.
In another example, once again involving atoms of nitrogen and oxygen, coefficients need to be added to both sides of the following unbalanced equation: N2 + O2 —> N2O3. In its unbalanced state, the equation does not show an equal number of nitrogen and oxygen atoms on both the left and right sides. There are two atoms each of nitrogen and oxygen on the left-hand reactant side, but the product side contains two nitrogen atoms and three oxygen atoms. This unbalanced equation violates the law of conservation of mass, but can be remedied by the proper placement of stoichiometric coefficients so that 2N2 + 3O2 —> 2N2O3. In its balanced form, the equation now shows four nitrogen and six oxygen atoms on both sides of the equation.