What is the difference between an empirical and a molecular formula?

The difference between an empirical formula and a molecular formula is the information each one provides. An empirical formula gives the simplest whole-number ratio of atoms of each element in a compound, while a molecular formula gives the actual number of atoms of each element in one molecule.

For example, glucose has the molecular formula C₆H₁₂O₆, but its empirical formula is CH₂O. Dividing all the molecular subscripts by 6 produces the simplest ratio 1:2:1. This distinction is central to IB Chemistry stoichiometry, particularly when using percentage composition, experimental mass data, and molar mass to identify a compound.

Empirical vs molecular formula at a glance

The formulas can sometimes be identical. Water is H₂O in both empirical and molecular terms because the subscripts 2 and 1 have no common factor. Carbon dioxide, CO₂, is another example.

This means that a molecular formula is not necessarily more complicated than an empirical formula. It is simply intended to report a different type of information.

What is an empirical formula?

An empirical formula expresses the simplest possible whole-number ratio of the elements in a compound. The IUPAC definition of empirical formula similarly describes it as the simplest possible formula expressing a compound's composition.

Consider hydrogen peroxide, H₂O₂. Each molecule contains two hydrogen atoms and two oxygen atoms, but the ratio 2:2 simplifies to 1:1. Its empirical formula is therefore HO.

An empirical formula does not establish:

• the actual number of atoms in a molecule
• the size or molar mass of the molecule
• how the atoms are bonded
• the compound's structural or displayed formula
• whether two samples with the same empirical formula are the same substance

For instance, ethene, C₂H₄, and butene, C₄H₈, both have the empirical formula CH₂. Their empirical formulas are identical because their carbon-to-hydrogen ratios are identical, but their molecular formulas and molecular masses differ.

Empirical formulas are especially appropriate for ionic compounds. Sodium chloride forms an extended ionic lattice rather than separate NaCl molecules, so NaCl represents the simplest ratio of Na⁺ to Cl⁻ ions. Calling NaCl a molecular formula would therefore be chemically inaccurate.

What is a molecular formula?

A molecular formula states the actual number of atoms of each element in one discrete molecule. Benzene, for example, has the molecular formula C₆H₆ because one benzene molecule contains six carbon atoms and six hydrogen atoms.

The molecular formula must be a positive whole-number multiple of the empirical formula:

molecular formula = (empirical formula)ₙ

Here, n is a positive integer such as 1, 2, 3, or 6. For benzene, the empirical formula is CH and n = 6, giving C₆H₆.

A molecular formula still does not show how atoms are connected. Ethanol and methoxymethane both have the molecular formula C₂H₆O, but their atoms are connected differently. They are structural isomers, which demonstrates why a molecular formula should not be confused with a structural formula.

How the formulas relate in IB Chemistry stoichiometry

In the current IB Chemistry course, empirical and molecular formulas belong within Structure 1.4: Counting particles by mass: The mole. The official IB Chemistry subject brief for first assessment 2025 places the mole and related quantitative work within Structure 1.4 for both SL and HL.

Students are expected to understand the distinction, interconvert percentage composition by mass and empirical formula, and determine a molecular formula from an empirical formula and molar mass. These skills depend on a central stoichiometric principle: chemical formulas describe ratios of numbers of particles, not ratios of their masses.

That is why mass data must first be converted to moles. Ten grams of hydrogen atoms and ten grams of oxygen atoms do not represent equal numbers of atoms because oxygen atoms have a much greater molar mass.

For wider context, use the topic-wide IB Chemistry S1.4 Counting Particles by Mass notes. That resource connects formulas to molar mass, amount of substance, percentage composition, and other mole calculations without turning this single-concept explanation into a complete stoichiometry topic page.

How to find an empirical formula from percentage composition

Use this sequence:

1. Treat each percentage as a mass in a 100 g sample.
2. Convert each element's mass to moles using amount = mass ÷ molar mass.
3. Divide every mole value by the smallest mole value.
4. Convert the resulting ratio to the smallest whole numbers.
5. Use those whole numbers as subscripts in the empirical formula.

Assuming 100 g is a calculation convenience, not a claim about the real sample size. Because percentages are proportional, any sample mass would produce the same mole ratio.

Worked example: percentage composition to empirical formula

A compound contains 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen by mass. Determine its empirical formula.

Assume a 100 g sample:

The simplest mole ratio is approximately 1:2:1, so the empirical formula is CH₂O.

Notice that dividing the percentages directly would not work. The percentages represent mass proportions, whereas formula subscripts represent numbers of atoms. Division by molar mass performs the necessary mass-to-mole conversion.

For additional guided practice, RevisionDojo's empirical formula explanation focuses on organizing this calculation from raw composition data.

How to convert an empirical formula into a molecular formula

An empirical formula alone is not enough to determine a unique molecular formula. You also need the compound's molar mass, which may be given directly or obtained from another part of the question.

Calculate the multiplier using:

n = molar mass of compound ÷ empirical formula mass

The empirical formula mass is found by adding the relative atomic masses represented by the empirical formula. The resulting n should be a whole number, allowing for small differences caused by rounded experimental data.

Worked example: CH₂O to a molecular formula

A compound has the empirical formula CH₂O and a molar mass of 180.16 g mol⁻¹. Determine its molecular formula.

First calculate the empirical formula mass:

CH₂O = 12.01 + 2(1.008) + 16.00 = 30.026 g mol⁻¹

Then calculate the multiplier:

n = 180.16 ÷ 30.026 ≈ 6.00

Multiply every subscript in CH₂O by 6:

molecular formula = C₆H₁₂O₆

A frequent mistake is multiplying only one subscript. The multiplier applies to the entire empirical formula because the molecule contains n complete empirical-formula units.

How to convert a molecular formula into an empirical formula

To move in the reverse direction, divide every subscript in the molecular formula by their highest common factor.

For example, consider butane:

• Molecular formula: C₄H₁₀
• Highest common factor of 4 and 10: 2
• Empirical formula: C₂H₅

For ethanoic acid, C₂H₄O₂, the highest common factor is 2, giving CH₂O. If the subscripts have no common factor greater than 1, the formula is already empirical.

Do not change the relative proportions while simplifying. C₆H₁₂O₆ can become CH₂O because all subscripts are divided by 6, but it cannot become CHO because that would change the atom ratio from 1:2:1 to 1:1:1.

Handling non-integer ratios

Experimental data rarely produce perfect integers. A calculated ratio might be 1.00:1.50 or 1.00:1.33 because the true ratio contains a simple fraction or because the measurements have been rounded.

Use small whole-number multipliers when the values are close to recognizable fractions:

Suppose dividing by the smallest amount gives C:H = 1.00:1.50. Multiplying both values by 2 produces 2:3, so the empirical formula is C₂H₃.

Do not round 1.50 directly to 2. That would produce a 1:2 ratio and alter the composition significantly. Conversely, a result such as 1.99 can normally be interpreted as 2 because the small difference is consistent with measurement or rounding uncertainty.

A combined IB-style example

A gaseous compound contains 85.6% carbon and 14.4% hydrogen by mass. Its molar mass is approximately 56.1 g mol⁻¹. Determine both formulas.

Assume 100 g and convert to moles:

The empirical formula is CH₂. Its empirical formula mass is approximately 14.03 g mol⁻¹.

n = 56.1 ÷ 14.03 ≈ 4

Multiplying both subscripts by 4 gives the molecular formula C₄H₈. The full chain of reasoning is therefore mass percentages to moles, moles to simplest ratio, empirical formula to empirical formula mass, and molar-mass ratio to molecular formula.

Common exam mistakes and how to avoid them

Confusing mass ratios with mole ratios

Formula subscripts represent atom ratios, so always convert grams or percentages to moles before simplifying. A neat table makes this conversion visible and reduces calculator errors.

Rounding too early

Keep several calculator digits during intermediate steps. Round only when identifying a chemically sensible whole-number ratio or reporting the final numerical answer.

Assuming the empirical and molecular formulas must differ

The multiplier n can equal 1. In that case, as with H₂O or CO₂, the empirical and molecular formulas are identical.

Finding n in the wrong order

Use compound molar mass ÷ empirical formula mass, not the reverse. Since a molecule contains one or more empirical units, n must be at least 1 and should be an integer.

Using molecular terminology for ionic solids

Ionic compounds contain extended lattices, not separate molecules. Their formulas state the simplest whole-number ratio of ions, so terms such as formula unit and relative formula mass are more appropriate.

Giving only a final formula

In constructed-response calculations, show the mass-to-mole conversions, division by the smallest value, empirical formula mass, and multiplier. Clear working can demonstrate a correct method even if a later arithmetic error affects the final formula.

The IB Chemistry Questionbank can be used to practise this layout, while the S1.4 flashcards help reinforce the definitions and calculation sequence. If a step remains unclear, Jojo AI for IB study support can help diagnose where a mass-to-mole or ratio calculation went wrong.

A reliable exam checklist

Before finalizing an answer, check that:

• all mass data were converted to moles
• all mole amounts were divided by the same smallest value
• any fractional ratio was removed by multiplying every value
• the empirical subscripts are the smallest possible whole numbers
• the empirical formula mass includes every atom shown
• n was calculated as compound molar mass divided by empirical formula mass
• n is close to a positive whole number
• every empirical subscript was multiplied by n
• the final molecular formula has a molar mass consistent with the value given

This final mass check is particularly powerful. If your proposed molecular formula has the wrong molar mass, either the empirical formula, the multiplier, or the arithmetic must be reconsidered.

Conclusion

The empirical formula gives the simplest whole-number atom ratio, whereas the molecular formula gives the actual number of each type of atom in a molecule. A molecular formula is always a whole-number multiple of its empirical formula, although that multiplier may be 1.

To obtain an empirical formula, convert composition data from mass to moles and simplify the mole ratio. To obtain a molecular formula, divide the compound's molar mass by the empirical formula mass and multiply every subscript by the resulting integer. RevisionDojo's S1.4 notes, flashcards, Questionbank, and Jojo AI are useful for turning this method into a reliable exam routine.

Sources and referenced URLs

• IUPAC Gold Book definition of empirical formula
• Official IB Chemistry subject page
• Official IB Chemistry subject brief for first assessment 2025
• OpenStax: Determining Empirical and Molecular Formulas
• RevisionDojo: IB Chemistry S1.4 Counting Particles by Mass notes
• RevisionDojo: Empirical Formula Explained Simply
• RevisionDojo: S1.4 empirical and molecular formula videos
• RevisionDojo: S1.4 Chemistry Questionbank
• RevisionDojo: S1.4 Chemistry flashcards
• RevisionDojo: Meet Jojo AI