Elements and Compounds

Every pure substance in nature falls into one of two categories: elements or compounds. This distinction matters for two reasons. It tells you whether a substance can be broken down further by ordinary chemical means. It also sets up the entire language chemists use to write formulas and equations. Building on the idea of a Classification of Matter: Pure Substances and Mixtures, this article zooms into the "pure substance" branch. It splits that branch cleanly in two. You will learn how chemical symbols encode identity. You will also learn how subscripts in a formula encode ratio. Then you'll see why the composition of a compound is always fixed. This rule is so important it has its own name: the law of definite proportions. These ideas are the grammar you need first. Only then can quantities like The Atomic Mass Unit and Atomic Weight and Molar Mass mean anything numerically precise.

Key takeaways

An element is a pure substance made of only one type of atom; it cannot be decomposed into simpler substances by chemical reactions.
A compound is a pure substance made of two or more elements chemically combined in a fixed, definite ratio.
Elements are represented by one- or two-letter chemical symbols (Na, O, Fe); compounds are represented by chemical formulas (H₂O, NaCl, C₆H₁₂O₆).
Subscripts in a formula give the whole-number ratio of atoms of each element in one formula unit or molecule.
The law of definite proportions says a given compound always has the same elemental composition by mass, no matter its source or how much of it you have.
Key idea: elements are the indivisible chemical building blocks; compounds are fixed-ratio combinations of those blocks, and formulas are the precise bookkeeping system that records the ratio.

The core insight

A pure substance is either an element (one kind of atom) or a compound (a fixed-ratio combination of two or more elements). Chemical formulas are not approximate labels — every subscript is an exact, reproducible integer ratio, which is why the same compound made in any lab, anywhere, has the identical composition.

The physical picture

Start from a single sample of matter that has already passed the test of being "pure" — meaning it has uniform composition and fixed properties throughout, as distinguished from a mixture. The next question chemistry asks is simple: can this pure substance be broken into anything simpler using chemical processes (heating, electrolysis, reaction with another substance) without changing what element the atoms are? If the answer is no, the substance is an element. Every atom in a sample of pure iron is an iron atom; there is no chemical operation that turns part of that iron into something else while leaving iron behind. As of now, 118 elements are recognized, each with a unique atomic number (number of protons) and a unique one- or two-letter symbol — often derived from Latin or Greek names (Na for natrium, sodium; Fe for ferrum, iron; Pb for plumbum, lead) or from the English name (O for oxygen, C for carbon). If the answer is yes — the substance decomposes chemically into two or more simpler substances — then it is a compound. Water (H₂O) decomposes by electrolysis into hydrogen gas and oxygen gas; table salt (NaCl) can be produced from and decomposed back toward sodium metal and chlorine gas. Crucially, a compound is not merely a physical blend of its elements: the properties of NaCl (a brittle white crystalline solid) bear no resemblance to sodium (a soft reactive metal) or chlorine (a toxic yellow-green gas). Chemical combination creates a new substance with its own identity. The ratio in which elements combine is not arbitrary — it is fixed for a given compound. Water is always 11.19% hydrogen and 88.81% oxygen by mass, whether it comes from a glacier, a raindrop, or a laboratory synthesis. This constancy is captured by the law of definite proportions (also called the law of constant composition), first argued clearly by Joseph Proust around 1799.

Figure

Classifying a pure substance as element or compound

The second figure shows how a chemical formula encodes composition using water as the running example, since its ratio (2 H : 1 O) is simple enough to check by eye.

Figure

Reading the formula H2O

The core relations

Formulas encode a fixed atomic ratio, and that ratio is the same quantity used later to build molar masses and reaction stoichiometry. The defining relation for a compound's formula is the whole-number atom ratio itself.

\text{Formula } \mathrm{A}_x\mathrm{B}_y \;\Rightarrow\; \frac{\text{atoms of A}}{\text{atoms of B}} = \frac{x}{y}, \quad x,y \in \mathbb{Z}^+

where:

$\mathrm{A}_x\mathrm{B}_y$ is a general formula for a compound of elements A and B,
$x$ and $y$ are subscripts, always positive integers (a subscript of 1 is never written explicitly),
the ratio $x:y$ is identical in every pure sample of that compound, regardless of the sample's total mass.

The law of definite proportions restates this at the mass level, using the elements' relative atomic masses (foreshadowing The Atomic Mass Unit and Atomic Weight):

\frac{\text{mass of A}}{\text{mass of B}} = \frac{x \cdot M_A}{y \cdot M_B} = \text{constant for a given compound}

where:

$M_A$ , $M_B$ are the atomic masses of elements A and B (in atomic mass units, defined elsewhere),
the right-hand side depends only on the compound's identity ( $x$ , $y$ , $M_A$ , $M_B$ ), never on sample size.

A companion idea, the law of multiple proportions, compares two different compounds formed from the same two elements:

\frac{\text{mass of A per fixed mass of B in compound 1}}{\text{mass of A per fixed mass of B in compound 2}} = \text{small whole-number ratio}

where:

"compound 1" and "compound 2" are two distinct compounds built from the same pair of elements (for example CO and CO₂),
the fixed mass of B is held the same basis (commonly 1 g) in both compounds for the comparison,
the resulting ratio being a small whole number is direct evidence that atoms combine in discrete integer counts, not continuously.

Derivation AFrom mass percentages to a mass ratio, and checking the law of multiple proportions

Goal. Show how raw mass-percent data for two carbon–oxygen compounds reduces to a small whole-number ratio, verifying that composition is fixed and quantized.

Step 1. State the data. Suppose careful decomposition experiments give: compound 1 is 42.9% carbon and 57.1% oxygen by mass; compound 2 is 27.3% carbon and 72.7% oxygen by mass. (These are the real values for carbon monoxide and carbon dioxide, rounded to three significant figures.)

Step 2. Fix the mass of oxygen at 1.00 g in each compound and find the corresponding mass of carbon. For compound 1, the mass ratio of carbon to oxygen is

\frac{m_C}{m_O}\Big|_1 = \frac{42.9}{57.1} = 0.751

so per 1.00 g of oxygen, compound 1 contains 0.751 g of carbon.

Step 3. Repeat for compound 2.

\frac{m_C}{m_O}\Big|_2 = \frac{27.3}{72.7} = 0.3755

so per 1.00 g of oxygen, compound 2 contains 0.375 g (to three sig figs) of carbon.

Step 4. Compare the two masses of carbon that combine with the same 1.00 g of oxygen.

\frac{(m_C/m_O)_1}{(m_C/m_O)_2} = \frac{0.751}{0.3755} = 2.00

Step 5. Interpret. The ratio comes out to 2.00, a small whole number, exactly as the law of multiple proportions predicts. This matches the known formulas: compound 1 is CO (one oxygen per carbon) and compound 2 is CO₂ (two oxygens per carbon), so for the same amount of carbon, compound 2 needs twice the oxygen — equivalently, for the same oxygen, compound 1 carries twice the carbon. The whole-number result is not a coincidence; it is the mass-level fingerprint of atoms combining in fixed integer counts, which is exactly what the subscripts in a chemical formula are recording.

Limiting-case check. If a hypothetical "compound 3" had the same mass ratio as compound 1 (0.751), the ratio in Step 4 would collapse to 1.00 — the correct signal that it is not a distinct compound but the same substance, CO, restated. A ratio that is not close to a small integer (say, 1.37) would instead flag an arithmetic or measurement error, since real compounds obey the law exactly within experimental precision.

Worked examples

Example 1 — Classifying substances and reading formulas. A sample is analyzed and found to be entirely aluminum atoms (atomic number 13, all identical). A second sample is found to contain aluminum and oxygen atoms combined as Al₂O₃, in a fixed 2:3 ratio throughout. Task: classify each sample and state the atom ratio for the second. Step 1: The first sample contains only one kind of atom (aluminum), so by definition it is an element, symbol Al. Step 2: The second sample contains two different elements (Al and O) chemically combined in one fixed ratio, so it is a compound, formula Al₂O₃. Step 3: Read the subscripts directly:

\frac{\text{Al atoms}}{\text{O atoms}} = \frac{2}{3}

So for every 2 aluminum atoms there are exactly 3 oxygen atoms, in any sample of pure Al₂O₃, whether it is a milligram of rust-like powder or a kilogram block of aluminum oxide ceramic. Limiting case: if a sample instead contained aluminum atoms alone with no oxygen present anywhere, the "ratio" question would not apply — that sample is simply the element Al, illustrating that the ratio concept is meaningful only once two or more elements are chemically combined.

Example 2 — Applying the law of definite proportions numerically. A 15.0 g sample of pure magnesium oxide (MgO) is analyzed and found to contain 9.05 g of magnesium and 5.95 g of oxygen. A second, independently prepared 42.0 g sample of magnesium oxide is available. Predict the mass of oxygen it contains.

Step 1. Find the fixed mass ratio of magnesium to oxygen from the first sample.

\frac{m_{Mg}}{m_O} = \frac{9.05\text{ g}}{5.95\text{ g}} = 1.521

Step 2. Because MgO is a compound, the law of definite proportions guarantees this ratio holds in every pure sample of MgO, including the second one. Let $m_{Mg}'$ and $m_O'$ be the masses in the 42.0 g sample, with

m_{Mg}' + m_O' = 42.0\text{ g}, \qquad \frac{m_{Mg}'}{m_O'} = 1.521

Step 3. Substitute $m_{Mg}' = 1.521\, m_O'$ into the total mass equation.

1.521\, m_O' + m_O' = 42.0 \;\Rightarrow\; 2.521\, m_O' = 42.0

Step 4. Solve for the oxygen mass.

m_O' = \frac{42.0}{2.521} = 16.66\text{ g}

Step 5. The magnesium mass follows by difference.

m_{Mg}' = 42.0 - 16.66 = 25.34\text{ g}

Sanity/limiting check: the mass percent of oxygen should match both samples: $5.95/15.0 = 39.7\%$ and $16.66/42.0 = 39.7\%$ — identical, confirming the compound's composition is fixed regardless of sample size. If instead the two computed percentages disagreed, that would signal either a measurement error or that the two samples were not the same pure compound (perhaps one contained an impurity, making it technically a mixture rather than a pure compound).

Limiting cases & common traps

Situation	Correct view	Common trap
A metal alloy like brass (Cu + Zn)	Mixture — composition varies continuously; not a compound	Assuming any combination of two elements is automatically a compound
Diatomic elements: O₂, N₂, H₂, Cl₂	Still elements — only one type of atom is present, just bonded in pairs	Mistaking a formula with a subscript (O₂) for a compound because it "has a subscript"
Isotopes of the same element (e.g. ¹²C and ¹³C)	Still the same element — atomic number, not mass, defines the element	Thinking different atomic masses mean different elements
Water vs. hydrogen peroxide (H₂O vs H₂O₂)	Two distinct compounds, related by the law of multiple proportions	Assuming "more oxygen" just means "more concentrated water"
A solution of salt in water	Mixture (homogeneous) — proportions can vary	Confusing a homogeneous mixture with a compound because it looks uniform

The chemist behind it

The clean split between elements and compounds, and the insistence that a compound's composition is fixed rather than adjustable, owes its rigor largely to Joseph Louis Proust. Working in Spain in the final years of the eighteenth century, Proust performed careful gravimetric analyses of compounds such as copper carbonate, showing that no matter how the sample was prepared — natural mineral or laboratory synthesis — the ratio of copper to carbon to oxygen by mass came out the same every time. This stood in direct opposition to the rival view, championed by Claude Louis Berthollet, that compounds could have continuously variable composition depending on how they were made. The Proust–Berthollet dispute ran for years and was ultimately settled in Proust's favor, cementing the law of definite proportions as a cornerstone of chemical theory — and setting the stage for John Dalton's atomic theory, which explained why the ratios must be fixed: atoms combine in small whole-number counts, and a compound's formula simply records that count.

Origins · 1 minJoseph Louis Proust and how this was discovered

Joseph Louis Proust

1754–1826 · Analytical chemistry in Spain during the atomic-theory revolution

Proust trained in Paris and spent much of his career in Madrid, where royal patronage supported an unusually well-equipped laboratory. His painstaking mass analyses of compounds like copper carbonate and tin oxides provided the empirical backbone later cited by Dalton, whose atomic theory gave the law of definite proportions its physical explanation: fixed mass ratios exist because atoms of definite mass combine in fixed whole-number counts.

Ask the tutor: If I know the mass percent of each element in an unknown compound, how do I work backward to find its actual chemical formula?

Are diatomic molecules like N₂ or Cl₂ compounds?

No. A diatomic molecule made of only one element — N₂, O₂, H₂, Cl₂, F₂, Br₂, I₂ — is still an element. The defining test for a compound is the presence of two or more different elements combined in fixed ratio; bonding two atoms of the same element together does not create a new substance with different chemical identity from that element.

How many elements are there, and can new ones be discovered?

As of the current periodic table, 118 elements have been confirmed and named, filling all seven periods. Elements beyond atomic number 118 are being sought in laboratories through nuclear synthesis, but they are typically extremely unstable and decay within fractions of a second, so "discovery" here means detection rather than isolation of a bulk sample.

Can the same two elements form more than one compound?

Yes, routinely. Carbon and oxygen form both CO and CO₂; nitrogen and oxygen form at least NO, NO₂, N₂O, N₂O₃, N₂O₄, and N₂O₅, each with its own fixed composition and distinct properties. The law of multiple proportions is precisely the tool for comparing such families of compounds.

Is a chemical formula the same thing as a molecular structure?

Not quite. A formula such as C₂H₆O only reports the atom counts (2 carbons, 6 hydrogens, 1 oxygen); it does not say how the atoms are arranged. That formula in fact corresponds to two different compounds with different structures and different properties, ethanol and dimethyl ether — a reminder that formulas encode composition, while structural formulas (introduced alongside bonding topics) encode connectivity.

Why does any of this matter for later topics like molar mass?

Because molar mass calculations add up atomic masses according to exactly the subscripts in a formula. Getting the element/compound distinction and the meaning of subscripts right here is what makes later quantitative work — converting grams to moles, balancing equations, computing percent composition — reliable rather than guesswork.