1.3 Elemental Composition of Pure Substances

Elemental composition connects the masses of the elements in a pure substance to its empirical formula, which is the lowest whole-number ratio of atoms in that compound. You use mass percentages, molar masses, and mole ratios to move from data to a formula. For AP Chemistry, show the mole-ratio step before writing the empirical formula.

Why This Matters for the AP Chemistry Exam

This topic builds the quantitative reasoning you use across the whole course. You will explain how mass data relates to the formula of a pure substance, which shows up when you analyze experimental results and justify claims about what a compound is made of. The skill paired with this topic is asking a testable question based on data, so expect to connect numbers to a clear conclusion about composition.

Empirical formula thinking also supports later work in stoichiometry, mixtures, and lab analysis. Getting comfortable converting between mass, moles, and atom ratios now makes those units much easier.

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Key Takeaways

• A pure substance has a fixed composition, made of one type of atom (element) or one type of molecule or formula unit (compound).
• The law of definite proportions means any pure sample of a compound has the same mass ratio of its elements, no matter the sample size.
• The empirical formula is the lowest whole number ratio of atoms in a compound; the molecular formula may be a whole number multiple of it.
• Use the same process every time: percent to grams, grams to moles, divide by the smallest, then multiply to whole numbers.
• A formula unit describes ionic compounds and network solids using the simplest ratio of ions or atoms, not separate molecules.
• Empirical formulas show ratios, not the actual atom count or arrangement in a molecule.

Pure Substances

A pure substance is made of a single type of atom or molecule, and its composition does not change from sample to sample. There are two kinds of pure substances:

• Elements are made of one type of atom, such as gold (Au). Every element discovered so far appears on the periodic table.
• Compounds are made of atoms of two or more different elements bonded in a fixed ratio.
  • Water is a compound that is always two hydrogen atoms to one oxygen atom, written H2O.
  • Table salt, sodium chloride (NaCl), is always one sodium ion to one chloride ion.

Molecules vs Formula Units

Some pure substances exist as individual molecules, while others are atoms or ions held together in fixed proportions described by a formula unit.

A formula unit is the lowest whole number ratio of atoms or ions that describes a compound. It is the smallest collection of atoms from which the formula can be written. For sodium chloride, the formula unit is 1:1, so for every sodium ion there is one chloride ion. This idea matters most for ionic compounds and network covalent solids (like SiO2), which do not exist as separate molecules. Formula units let you think about element proportions instead of counting individual particles, which is useful when converting between moles and number of particles.

Example Problem

How many formula units of KCl are in 1.76 mol KCl?

Use Avogadro's number to convert from moles to formula units:

1.76 mol KCl × (6.022 × 10^23 formula units / 1 mol) = 1.06 × 10^24 formula units KCl

Law of Definite Proportions

The law of definite proportions, also called the law of constant composition, states that the ratio of the masses of the constituent elements in any pure sample of a compound is always the same. Constituent elements are the elements that make up the compound.

No matter the size of a water sample, whether 100 g, 200 g, or 5000 g, the mass ratio of hydrogen to oxygen stays fixed and the atom ratio reduces to 2:1.

A recipe is a helpful way to picture this. A cookie recipe fixes the proportions of flour, butter, eggs, and chocolate chips. You can make 5 cookies or 100, but the proportion of ingredients stays the same. In the same way, the ratio of elements in a pure compound is fixed. If that ratio changed, you would have a different compound.

Empirical Formula

The empirical formula is the simplest whole number ratio of atoms of each element in a compound. It applies the law of definite proportions directly: because the ratio is always the same, you can express it in lowest terms.

Empirical vs Molecular Formula

The molecular formula of glucose is C6H12O6, but its empirical formula divides every subscript by 2 to give CH2O. Both describe the same substance, but they answer different questions. The molecular formula tells you the actual number of atoms in one molecule, while the empirical formula tells you the simplest ratio.

This means the empirical formula does not always show the real atom count or the arrangement of atoms. Any molecular formula that reduces to the same ratio, even something like C90H180O90, still has the empirical formula CH2O.

How to Use This on the AP Chemistry Exam

Problem Solving

A common task is finding an empirical formula from percent composition. Use this four step process:

Example: A carbohydrate containing C, H, and O has a composition of 33.3% C and 7.4% H. Find the empirical formula.

Step 1: Percent to grams. Assume a 100 g sample, so each percent becomes that many grams. That gives 33.3 g C and 7.4 g H. Oxygen was not given, but all elements must add to 100% of the mass. Subtract to find it:

100% - 33.3% - 7.4% = 59.3%, so 59.3 g O

Step 2: Grams to moles. Divide each mass by the element's molar mass (C = 12.01 g/mol, H = 1.008 g/mol, O = 16.00 g/mol).

• C: 33.3 g / 12.01 g/mol = 2.773 mol C
• H: 7.4 g / 1.008 g/mol = 7.34 mol H
• O: 59.3 g / 16.00 g/mol = 3.706 mol O

Keep extra digits until the end so rounding does not throw off later steps.

Step 3: Divide by the smallest. The smallest mole amount is carbon, 2.773 mol.

• C: 2.773 / 2.773 = 1
• H: 7.34 / 2.773 = 2.66
• O: 3.706 / 2.773 = 1.33

Step 4: Multiply to whole numbers. When values end in .5, .33/.66, or .25/.75, multiply all by 2, 3, or 4. Here the .33 and .66 mean you multiply everything by 3.

• C: 1 × 3 = 3
• H: 2.66 × 3 = 8
• O: 1.33 × 3 = 4

The empirical formula is C3H8O4. The question did not ask for the molecular formula, but any multiple of the empirical formula (such as C6H16O8) would have the same ratio.

Common Trap

Watch for a missing element. If a problem lists three elements but only gives two percentages, the remaining percent is whatever makes the total reach 100%. Forgetting to solve for that element is one of the most common mistakes on these problems.

Common Misconceptions

• Empirical formula equals molecular formula. They are only the same when the molecular formula is already in lowest terms. CH2O and C6H12O6 are different formulas for substances with the same simplest ratio.
• Rounding too early. Rounding mole values before the final step can change your ratios and give the wrong formula. Carry extra digits until the end.
• Treating decimals near a whole number as exact. A value like 2.66 is not 3; it signals you need to multiply all values by 3. Only round small experimental errors (like 1.98 to 2), not clear fractions.
• Assuming every compound is made of molecules. Ionic compounds and network solids are described by formula units, not separate molecules, so their formulas show the simplest ratio of ions or atoms.
• Confusing subscripts with coefficients. Subscripts in a formula set the fixed atom ratio inside a compound. They are not the same as the coefficients you place in front of formulas when balancing equations.

Related AP Chemistry Guides

• Unit 1 Overview: Atomic Structure and Properties
• 1.1 Moles and Molar Mass
• 1.2 Mass Spectra of Elements
• 1.7 Periodic Trends
• 1.4 Composition of Mixtures
• 1.6 Photoelectron Spectroscopy