Molecular and Empirical Formulae: An Introduction

Introduction

Glucose has the formula C₆H₁₂O₆, but its atoms are in the ratio 1 : 2 : 1, which could be written CH₂O. Both formulae are correct, but they tell you different things. The first gives the real number of atoms in one molecule; the second gives only the simplest ratio. Chemists call these the molecular formula and the empirical formula . Knowing the difference helps you understand what experiments can reveal about a compound and how formulae of ionic substances are written.

Core explanation

Molecular formula. The molecular formula shows the actual number of atoms of each element in one molecule. Hydrogen peroxide is H₂O₂ because each molecule really contains two hydrogen and two oxygen atoms.

Empirical formula. The empirical formula shows the simplest whole-number ratio of atoms. To find it from a molecular formula, divide all the subscripts by their highest common factor.

Compound Molecular formula Divide by Empirical formula --- --- --- --- hydrogen peroxide H₂O₂ 2 HO ethane C₂H₆ 2 CH₃ glucose C₆H₁₂O₆ 6 CH₂O benzene C₆H₆ 6 CH butane C₄H₁₀ 2 C₂H₅ water H₂O 1 H₂O carbon dioxide CO₂ 1 CO₂

Sometimes they are the same. If the subscripts cannot be simplified, the molecular and empirical formulae are identical, as for water, carbon dioxide and methane, CH₄.

Different compounds can share an empirical formula. Ethyne, C₂H₂, and benzene, C₆H₆, are very different substances, but both have the empirical formula CH. Glucose, C₆H₁₂O₆, and methanal, CH₂O, share the empirical formula CH₂O. An empirical formula alone cannot always identify a compound.

Ionic compounds. Ionic compounds do not contain molecules; they form giant lattices. Their formulae therefore always give the simplest ratio of ions, which is an empirical formula. That is why we write MgO rather than Mg₂O₂, and CaCl₂ for calcium chloride.

Why empirical formulae matter. Experiments that measure the masses of elements combining in a compound reveal only the ratio of atoms, not the size of the molecule. So analysis first gives an empirical formula. To find the molecular formula, chemists also need the mass of one molecule, which tells them how many empirical units it contains.

Linking the two. The molecular formula is always a whole-number multiple of the empirical formula: C₆H₁₂O₆ is 6 × CH₂O.

Step-by-step reasoning

To find an empirical formula from a molecular formula:

1. Write down all the subscripts, remembering that a missing subscript is 1. 2. Find the largest number that divides into all of them exactly. 3. Divide every subscript by that number. 4. Write the new formula, leaving out any subscript of 1.

Visual explanation

Picture a glucose molecule broken into six identical groups, each containing one black carbon ball, two white hydrogen balls and one red oxygen ball. Each group is one CH₂O unit; six of them together make the full C₆H₁₂O₆ molecule.

Real-world analogy

A molecular formula is like the full guest list for a party: 6 adults and 12 children. The empirical formula is the ratio: 1 adult for every 2 children. The ratio is useful, but it does not tell you how big the party is.

Real-world example

When forensic or food scientists analyse an unknown compound, combustion analysis tells them the masses of carbon, hydrogen and oxygen present. This gives the empirical formula first. A second technique, such as mass spectrometry, measures the molecule's mass, allowing them to decide between possibilities such as CH₂O and C₆H₁₂O₆.

Why?

Why can analysis give only the empirical formula at first? Measuring the proportions of elements tells you the ratio of atoms, and that ratio is the same whether molecules contain one unit or six. Only knowing the mass of an individual molecule reveals how many units it has.

Common misconception

"The empirical formula is just a shorter way of writing the molecular formula." They carry different information. The empirical formula loses the actual atom numbers, so CH could be ethyne or benzene. Only the molecular formula tells you which molecule it is.

Worked example

Question: Find the empirical formula of octane, C₈H₁₈.

Reasoning: The subscripts are 8 and 18. The highest common factor is 2. Dividing gives 4 and 9.

Answer: The empirical formula is C₄H₉.

Quick check

1. What is the empirical formula of ethene, C₂H₄? Answer: CH₂, found by dividing both subscripts by 2.

Exam focus

Be able to define both formulae precisely: molecular is the actual number of atoms in a molecule; empirical is the simplest whole-number ratio. Simplify by dividing by the highest common factor, not just by 2. Remember that ionic formulae are always empirical.

Advanced insight

Given an empirical formula and the relative mass of a molecule, you can find the molecular formula. For example, CH₂O has a relative mass of 30; if the molecule has a relative mass of 180, it contains 180 ÷ 30 = 6 units, giving C₆H₁₂O₆. You will use this method once you have learned about relative formula mass.

Summary

The molecular formula gives the actual number of atoms of each element in one molecule; the empirical formula gives the simplest whole-number ratio. Divide the subscripts by their highest common factor to get the empirical formula. Different compounds can share an empirical formula, and ionic compounds are always written with empirical formulae.

Practice questions

1. Define empirical formula. Answer: The simplest whole-number ratio of atoms of each element in a compound. 2. Give the empirical formulae of C₂H₆, C₆H₆ and N₂O₄. Answer: CH₃, CH and NO₂. 3. Why is the formula of magnesium oxide written MgO and not Mg₂O₂? Answer: Magnesium oxide is ionic and has no molecules, so its formula gives the simplest ratio of ions, which is 1 : 1. 4. Ethyne is C₂H₂ and benzene is C₆H₆. What do they have in common, and why can they not be told apart by empirical formula alone? Answer: Both have the empirical formula CH, because their atoms are in the same 1 : 1 ratio; only the molecular formula shows that ethyne has 2 of each atom and benzene 6.