Chemical Formulas: Empirical, Molecular, and Structural

A chemical formula uses element symbols and numbers to represent a substance: the empirical formula gives the simplest whole-number ratio of atoms, the molecular formula gives the actual number of atoms in a molecule, and the structural formula shows how the atoms are connected. In brief: glucose has the molecular formula C₆H₁₂O₆, the empirical formula CH₂O and a structural formula that shows a ring or chain of carbon atoms with OH groups; ethanol and dimethyl ether share the molecular formula C₂H₆O but have different structural formulas.

Different types of formulas answer different questions. The empirical formula is the simplest, the molecular formula is more informative, and the structural formula explains properties and reactions. This article defines each type, explains how to convert between them, describes how to write condensed and skeletal structures, includes a comparison table, works through calculations and gives a short history.

What is an empirical formula?

The empirical formula shows the elements in a compound and their simplest whole-number ratio. It is found by experiment from the masses of the elements in a sample, so it is the first formula that chemists determine for a new compound. To find it from a molecular formula, divide all the subscripts by their greatest common factor. For hydrogen peroxide, H₂O₂, the factor is 2 and the empirical formula is HO. For glucose, C₆H₁₂O₆, the factor is 6 and the empirical formula is CH₂O.

What is a molecular formula?

The molecular formula gives the actual number of atoms of each element in one molecule. It is always a whole-number multiple of the empirical formula: molecular formula = (empirical formula)_n, where n = molar mass ÷ empirical formula mass. To find the molecular formula, you need the molar mass of the compound as well as the empirical formula. Some compounds have the same empirical formula but different molecular formulas: formaldehyde (CH₂O), acetic acid (C₂H₄O₂) and glucose (C₆H₁₂O₆) all have the empirical formula CH₂O.

What is a structural formula?

A structural formula shows which atoms are bonded to which. Several kinds are used.

Full structural (displayed) formula: shows every atom and every bond as a line. In ethanol, the carbon atoms are in a chain, and an OH group is attached to the second one.
Condensed structural formula: writes the atoms in groups along the chain, such as CH₃CH₂OH for ethanol and CH₃OCH₃ for dimethyl ether.
Skeletal formula: a line drawing in which the ends and corners of lines are carbon atoms, and hydrogen atoms bonded to carbon are not shown. It is widely used for organic molecules.
Lewis structure: shows valence electrons as dots and bonds as lines.
Ball-and-stick and space-filling models: show the three-dimensional arrangement.

Formulas of common substances

Empirical, molecular and condensed structural formulas
Substance	Empirical	Molecular	Condensed structural
Water	H₂O	H₂O	H–O–H
Hydrogen peroxide	HO	H₂O₂	H–O–O–H
Ethane	CH₃	C₂H₆	CH₃CH₃
Benzene	CH	C₆H₆	Ring of six CH groups
Acetic acid	CH₂O	C₂H₄O₂	CH₃COOH
Glucose	CH₂O	C₆H₁₂O₆	Chain or ring with five OH groups
Ethanol	C₂H₆O	C₂H₆O	CH₃CH₂OH

What is the formula of an ionic compound?

Ionic compounds do not consist of separate molecules but of a lattice of ions. Their formulas are empirical formulas that give the simplest ratio of ions, and the smallest unit is called a formula unit. The formula for sodium chloride, NaCl, tells us that there is one sodium ion for each chloride ion. Calcium chloride, CaCl₂, has two chloride ions for each calcium ion. Network solids, such as silicon dioxide (SiO₂) and diamond (C), also use empirical formulas.

Worked examples

From molecular to empirical. C₄H₈O₂: the greatest common factor of 4, 8 and 2 is 2. The empirical formula is C₂H₄O.
From masses to empirical formula. A hydrocarbon contains 2.40 g of carbon and 0.60 g of hydrogen. Moles of C = 2.40 ÷ 12.01 = 0.200 mol. Moles of H = 0.60 ÷ 1.008 = 0.595 mol. Divide by the smaller number: C = 0.200 ÷ 0.200 = 1.00 and H = 0.595 ÷ 0.200 = 2.98, which is about 3. The empirical formula is CH₃.
From empirical to molecular. The molar mass of the compound in example 2 is 30.1 g/mol. The empirical formula mass of CH₃ is 12.01 + 3 × 1.008 = 15.03 g/mol. n = 30.1 ÷ 15.03 = 2.00. The molecular formula is C₂H₆, which is ethane.
Molar mass from a formula. Glucose, C₆H₁₂O₆: 6 × 12.01 + 12 × 1.008 + 6 × 16.00 = 72.06 + 12.10 + 96.00 = 180.16 g/mol.
Counting atoms. One molecule of glucose has 6 + 12 + 6 = 24 atoms. In 3C₆H₁₂O₆ there are 3 × 24 = 72 atoms, of which 18 are carbon.
Formula from a name and structure. The condensed structure CH₃CH₂COOH has 3 carbon atoms, 2 + 3 + 1 = 6 hydrogen atoms and 2 oxygen atoms. The molecular formula is C₃H₆O₂ (propanoic acid).

Why do structural formulas matter?

Compounds with the same molecular formula but different structures are called isomers, and they have different properties. Ethanol (CH₃CH₂OH) is a liquid that boils at 78 °C and mixes with water. Dimethyl ether (CH₃OCH₃) has the same formula C₂H₆O but is a gas at room temperature, with a boiling point of about −24 °C. A molecular formula alone cannot tell them apart, so organic chemists rely on structural formulas.

How did formulas develop?

Jöns Jacob Berzelius introduced the use of letters for elements and subscript numbers in the early 1800s. Originally he wrote the numbers as superscripts, and the subscript convention became standard later. Justus von Liebig and Friedrich Wöhler discovered in 1823 to 1828 that silver cyanate and silver fulminate have the same composition but different properties, an observation that led Berzelius to the concept of isomerism. In 1858, August Kekulé and Archibald Scott Couper proposed that carbon forms four bonds and that atoms are connected in a structure, and Alexander Butlerov used the term “chemical structure” in 1861.

Which mistakes are common?

Mistake 1: Using the empirical formula as the molecular formula

The molecular formula needs the molar mass. CH₂O could be formaldehyde or glucose.

Mistake 2: Reducing the formula of an ionic compound incorrectly

The formula of an ionic compound is already the simplest ratio. Do not change subscripts to match a molecule.

Mistake 3: Ignoring the structure when comparing isomers

The same formula can describe several substances with different properties.

Mistake 4: Confusing subscripts and coefficients

Subscripts are inside the formula, and coefficients show the number of units in an equation.