A chemical formula uses element symbols and numerical subscripts to represent the composition of a molecule or compound. This universal shorthand conveys the substance’s identity by showing which atoms are present and in what quantity. The molecular formula displays the exact number of atoms of each element in a single molecule, such as \(H_2O\) for water. This is distinct from the empirical formula, which only shows the simplest whole-number ratio of atoms. For example, the molecular formula for glucose, \(C_6H_{12}O_6\), reduces to the empirical formula \(CH_2O\).
Formulas for Binary Covalent Compounds
Writing the formulas for binary covalent compounds, which are formed exclusively between two nonmetals, is a straightforward process based directly on the compound’s name. This naming system utilizes Greek prefixes to indicate the precise number of atoms for each element in the molecule. The prefix is translated into the subscript that follows the element’s symbol.
The element listed first in the name corresponds to the first symbol in the formula. Conventionally, the prefix “mono-” is never used for the first element, but it is used for the second element when only one atom is present. For example, carbon dioxide translates to \(CO_2\), and dinitrogen tetroxide is written as \(N_2O_4\).
Formulas for Binary Ionic Compounds
Forming the chemical formula for a binary ionic compound, which consists of a metal and a nonmetal, relies on the principle of electrical neutrality. These compounds are composed of cations and anions. The total positive charge must exactly cancel out the total negative charge, resulting in a net charge of zero. To achieve this charge balance, chemists employ the crisscross method.
First, write the symbol and charge of the cation, followed by the anion. The numerical value of the cation’s charge becomes the subscript for the anion, and vice versa. For instance, \(Ca^{2+}\) and \(Cl^{1-}\) ions produce the formula \(CaCl_2\). If the charges are equal in magnitude, such as \(Na^{1+}\) and \(Cl^{1-}\), they cancel one-to-one, and the formula is simply \(NaCl\), with the subscript ‘1’ omitted. The resulting subscripts must be reduced to the lowest possible whole-number ratio.
Incorporating Polyatomic Ions and Variable Charges
Polyatomic Ions
The rules for ionic compounds become slightly more complex when dealing with polyatomic ions. A polyatomic ion is a tightly bound group of two or more atoms that acts as a single unit with an overall electrical charge, such as the sulfate ion, \(SO_4^{2-}\). The same charge-balancing crisscross method is used. If a subscript greater than one is needed, the entire polyatomic ion’s formula must be enclosed in parentheses, and the subscript is placed outside. For example, \(Ca^{2+}\) combining with \(NO_3^{-}\) results in \(Ca(NO_3)_2\).
Variable Charges
Certain metals, particularly transition metals, exhibit variable charges. The specific charge of the metal cation is indicated by a Roman numeral in the compound’s name. For example, Iron(III) oxide indicates the iron cation has a \(3+\) charge (\(Fe^{3+}\)). This charge is used in the crisscross method with the anion (e.g., \(O^{2-}\)), resulting in \(Fe_2O_3\). This Roman numeral ensures the correct charge neutrality is maintained in the resulting formula.
Specific Notations (Acids and Hydrates)
Acids
The formula for an inorganic acid is always written with hydrogen first because acids release hydrogen ions (\(H^{+}\)) when dissolved in water. The number of hydrogen atoms is determined by the negative charge of the accompanying anion, ensuring the molecule remains electrically neutral. The nomenclature of the acid dictates the formula of the anion: an anion name ending in “-ate” corresponds to an acid ending in “-ic acid,” while an anion ending in “-ite” corresponds to an acid ending in “-ous acid.”
Hydrates
Hydrates are compounds that have water molecules chemically incorporated into their crystal structure. The formula is written by first stating the formula for the anhydrous (water-free) compound, followed by a centered dot, a coefficient indicating the number of water molecules, and finally the formula for water, \(H_2O\). This coefficient is determined by a Greek prefix attached to the word “hydrate” in the name. Therefore, copper(II) sulfate pentahydrate is written as \(CuSO_4 \cdot 5H_2O\).