A chemical compound is a substance formed when two or more different elements are chemically bonded together, represented by a chemical formula. The chemical formula expresses the exact number of each type of atom that makes up one unit of that compound. The process of counting atoms involves interpreting the numerical indicators within the formula, which precisely define the composition of the substance.
Deciphering the Chemical Formula
The primary indicator of an atom’s count is the subscript, the small number written to the lower right of an element’s symbol. This subscript specifies how many atoms of that particular element are present in a single molecule or formula unit. For example, in the formula for water, $\text{H}_2\text{O}$, the subscript ‘2’ next to the hydrogen symbol ($\text{H}$) indicates that there are two hydrogen atoms in that molecule.
When an element symbol does not have a subscript written after it, the number of atoms is understood to be one, a value which chemists typically do not write out. In the water example, the oxygen symbol ($\text{O}$) has no subscript, meaning there is just one oxygen atom present. Similarly, the formula for table salt, $\text{NaCl}$, indicates one sodium atom ($\text{Na}$) and one chlorine atom ($\text{Cl}$), as no subscripts are present for either element.
Counting Atoms in Grouped Elements (Parentheses)
Chemical formulas often use parentheses to group together a specific cluster of atoms, such as a polyatomic ion. A subscript is placed outside the closing parenthesis to indicate how many of those entire groups are present in the compound. This external subscript functions as a multiplier for every atom inside the parentheses.
To find the total count of an atom within a parenthetical group, the atom’s internal subscript is multiplied by the subscript outside the parentheses. For instance, in calcium nitrate, $\text{Ca}(\text{NO}_3)_2$, the subscript ‘2’ outside the parentheses means the entire nitrate group ($\text{NO}_3$) is present twice. Nitrogen ($\text{N}$) has an implied subscript of one, so its total count is $1 \times 2 = 2$ atoms, and oxygen ($\text{O}$) with an inside subscript of three results in $3 \times 2 = 6$ oxygen atoms. The calcium atom ($\text{Ca}$) is not inside the parentheses, so its count remains one.
Accounting for Multiple Molecules (Coefficients)
The coefficient is the large number placed at the very front of the entire compound formula. It represents the number of separate molecules or formula units of the compound being considered. This number multiplies the count of every atom throughout the entire formula.
If a simple formula like water ($\text{H}_2\text{O}$) has a coefficient, such as $3\text{H}_2\text{O}$, the coefficient ‘3’ signifies three separate water molecules. This coefficient must be multiplied by the subscript of each atom: the two hydrogen atoms ($2 \times 3 = 6$ total $\text{H}$ atoms) and the one oxygen atom ($1 \times 3 = 3$ total $\text{O}$ atoms). The coefficient is the final multiplier applied after all internal subscripts and parenthetical rules have been addressed.
Putting It All Together: Complex Examples
Counting atoms in a complex formula requires integrating the rules of subscripts, parentheses, and coefficients in a specific order. Consider the example $2\text{Al}_2(\text{SO}_4)_3$, which represents two units of aluminum sulfate. The first step involves calculating the count of atoms within the parentheses (the sulfate group, $\text{SO}_4$).
The subscript ‘3’ outside the parentheses multiplies the internal counts. The one sulfur atom becomes three ($1 \times 3 = 3$), and the four oxygen atoms become twelve ($4 \times 3 = 12$). Aluminum ($\text{Al}$) is outside the parentheses and has a subscript of ‘2’. The final step is to apply the external coefficient of ‘2’ to the entire molecule’s atom counts.
The coefficient doubles the counts for every element: aluminum goes from two to four ($2 \times 2 = 4$), sulfur goes from three to six ($3 \times 2 = 6$), and oxygen goes from twelve to twenty-four ($12 \times 2 = 24$). This systematic multiplication ensures an accurate final tally of all atoms in the compound, resulting in a total of 34 atoms. This three-step approach—internal subscripts, parenthetical multiplication, and final coefficient scaling—is necessary for deciphering any chemical formula.