Formulae and Homologous Series

Spec Mapping — OCR H432 Module 4.1.1 — Basic concepts of organic chemistry, covering empirical, molecular, general, structural, displayed and skeletal formulae; the homologous-series concept (shared functional group, common general formula, gradual physical-property trends, identical chemistry); the saturated/unsaturated distinction; and the aliphatic/alicyclic/aromatic classification (refer to the official OCR H432 specification document for exact wording).

Organic chemists use several distinct types of formula to represent the same molecule, each emphasising a different aspect of its structure: the atom count alone, the simplest whole-number ratio, the connectivity pattern, every individual bond, or just the carbon skeleton with heteroatoms picked out. Each format has its place. The homologous-series concept then groups related compounds into families that share a general formula and a functional group, so that one piece of chemistry covers thousands of compounds. This lesson formalises both ideas — the five formula types and the homologous-series machinery — and shows how they connect. Mastering this material is what lets you decode any organic-chemistry question on the OCR H432 paper from a single line of structural notation, and what lets you predict the physical properties of a compound you have never seen before from the chain length and functional group alone.

Key Definition: a homologous series is a family of organic compounds with the same functional group and the same general formula ( $C_nH_{2n+2}$ for alkanes, $C_nH_{2n}$ for alkenes, $C_nH_{2n+1}OH$ for alcohols, etc.), in which successive members differ by an additional $-CH_2-$ unit, share identical chemistry but show gradually changing physical properties (boiling point, viscosity, volatility, solubility).

1. Types of Formulae

1.1 Empirical Formula

The empirical formula gives the simplest whole-number ratio of atoms of each element in a compound.

Key Definition — Empirical formula: The simplest whole-number ratio of atoms of each element present in a compound.

Example: glucose has a molecular formula C₆H₁₂O₆ but an empirical formula CH₂O.

1.2 Molecular Formula

The molecular formula gives the actual number of atoms of each element present in one molecule.

Key Definition — Molecular formula: The actual number of atoms of each element in a molecule.

Example: butane is C₄H₁₀; the empirical formula is C₂H₅.

1.3 General Formula

The general formula expresses the ratio of atoms for any member of a homologous series using n for the number of carbons.

Homologous series	General formula
Alkane	CₙH₂ₙ₊₂
Alkene (one C=C)	CₙH₂ₙ
Cycloalkane	CₙH₂ₙ
Alcohol (saturated, one OH)	CₙH₂ₙ₊₁OH
Haloalkane (one halogen)	CₙH₂ₙ₊₁X
Carboxylic acid	CₙH₂ₙO₂
Ketone / aldehyde	CₙH₂ₙO

1.4 Structural Formula

A structural formula shows the minimum detail needed to unambiguously identify the molecule — it shows which atoms are joined to which, without drawing every bond.

Examples:

Propan-2-ol: CH₃CH(OH)CH₃
Butan-1-ol: CH₃CH₂CH₂CH₂OH
Methylpropane: (CH₃)₃CH

1.5 Displayed Formula

A displayed formula shows every bond and every atom explicitly. You draw every C–H and every C–C single bond individually.

Ethanol displayed (every C–H, C–C, C–O and O–H bond drawn as a separate line):

1.6 Skeletal Formula

A skeletal formula is the most compact representation. Carbon atoms are implied at every vertex and line end; hydrogen atoms on carbons are implied (each carbon is assumed to have enough H atoms to complete four bonds). Functional groups and heteroatoms are shown explicitly.

(Four zig-zag carbons with –OH on the terminal carbon.)

graph LR
  A["Molecular formula<br/>C2H6O"] --> B["Empirical formula<br/>C2H6O cannot simplify"]
  A --> C["Structural formula<br/>CH3CH2OH"]
  A --> D["Displayed formula<br/>all bonds shown"]
  A --> E["Skeletal formula<br/>vertices imply C"]

1.7 When each format is examined

OCR examiners use precise verbs. "State the empirical formula" expects a simplest ratio with no further detail. "Draw the displayed formula" demands every C–H bond drawn explicitly — a structural or skeletal answer loses marks. "Draw the skeletal formula" allows the compact form but every heteroatom must still appear. When the question says simply "give the formula", any unambiguous representation is acceptable. Reading the verb is half the mark.

2. The Homologous Series Concept

A homologous series is a family of organic compounds which:

share the same general formula;
have the same functional group;
show a gradual trend in physical properties (boiling point, density, solubility) with increasing chain length;
show similar chemical reactions because of the shared functional group;
differ from adjacent members by CH₂ (one methylene unit).

2.1 Worked Example — The Alkane Series

Name	Molecular formula	Boiling point / °C	State at room temp
Methane	CH₄	−162	Gas
Ethane	C₂H₆	−89	Gas
Propane	C₃H₈	−42	Gas
Butane	C₄H₁₀	−1	Gas
Pentane	C₅H₁₂	36	Liquid
Hexane	C₆H₁₄	69	Liquid
Octane	C₈H₁₈	126	Liquid
Decane	C₁₀H₂₂	174	Liquid

Each successive alkane differs by CH₂ (adding about 14 g mol⁻¹). Boiling point rises steadily because larger molecules have more electrons, larger surface area, and therefore stronger London (dispersion) forces — more energy is required to overcome them.

2.2 Trends in Physical Properties

As chain length increases within a series:

Boiling point rises — due to stronger London forces between larger molecules.
Viscosity increases — longer chains tangle more.
Volatility decreases — fewer molecules escape to the vapour phase.
Density generally increases slightly.
Solubility in water decreases (for hydrocarbons this is already very low; for alcohols, the hydrocarbon "tail" becomes dominant and hydrogen bonding becomes proportionally less significant).

2.3 Branching and Boiling Point

Two isomers with the same molecular formula can differ significantly in boiling point because of differences in surface area and therefore in London force strength:

Isomer	B.p. / °C
Pentane (straight)	36
2-methylbutane	28
2,2-dimethylpropane	10

More branched molecules are more spherical, have less surface contact between molecules, and therefore lower boiling points.

2.4 The general-formula machinery

Adding one –CH₂– unit corresponds to adding 14 g mol⁻¹ to the molar mass. For alkanes this also adds approximately 20–30 °C to the boiling point (the increment shrinks as molecules get larger). The arithmetic of $C_nH_{2n+2}$ is more than a tidy mnemonic: it expresses the fact that an acyclic saturated hydrocarbon with $n$ carbons has $4n$ valences from carbon (each C has 4) and $n - 1$ of these are used in C–C bonds (counting bonds, not atoms). The remaining $4n - 2(n-1) = 2n + 2$ valences must be filled by hydrogen — hence the formula. Each ring or pi-bond costs two hydrogens, which is why cycloalkanes share $C_nH_{2n}$ with alkenes (one ring, no double bond, vs no ring, one double bond — both single degrees of unsaturation).

2.5 Worked check — does C₈H₁₈ fit the alkane formula?

Substitute n = 8 into $C_nH_{2n+2}$ : $C_8H_{18}$ . Yes — octane (or any of its 17 isomers) satisfies the formula. By contrast C₈H₁₆ has 2n hydrogens, so it must be a cycloalkane (e.g., cyclooctane), an alkene (e.g., oct-1-ene), or contain one ring/double bond — degree of unsaturation = 1. Whenever you meet an unfamiliar molecular formula, run the general-formula check first.

2.6 Boiling-point trend — quantitative scaling

Within a homologous series the increment in boiling point per added –CH₂– can be approximated by a saturating function: each new methylene raises the b.p. by about 30 °C for n = 1→2 in alkanes, 25 °C for n = 2→3, 20 °C for n = 3→4 and so on, eventually plateauing at around 20 °C per methylene by the long-chain limit. The diminishing return is because fractional polarisability gain per added carbon decreases — adding the 20th methylene to a long chain is a smaller relative change in molecular size than adding the second methylene to ethane.

For alcohols the increments are slightly larger because hydrogen bonding still dominates intermolecular forces for short chains; by ~C8 the alcohols look more like alkanes plus a constant offset (~80 °C above the equivalent alkane) than like a hydrogen-bonded ensemble. OCR mark schemes accept "London forces increase with chain length / electron count" — but if you can quote the saturating trend in passing it tightens an A* answer.

3. Saturated vs Unsaturated

Saturated compounds contain only single C–C bonds. Alkanes are saturated.
Unsaturated compounds contain at least one C=C or C≡C multiple bond. Alkenes and alkynes are unsaturated.

A saturated compound has the maximum possible number of hydrogen atoms for a given number of carbons. Each additional degree of unsaturation (or ring) removes two hydrogens.

The chemical consequence is dramatic: saturated compounds (alkanes) only undergo a small number of reactions (combustion; free-radical substitution with halogens under UV light), whereas unsaturated compounds — by virtue of their reactive pi-electrons — undergo electrophilic addition with bromine, hydrogen halides, water (acid-catalysed), hydrogen (with a Ni or Pt catalyst), and ozonolysis. Sketching the saturation count for an unknown compound therefore narrows the universe of reactions to a manageable subset before any further data is examined. The 1832 Liebig–Wöhler tests on benzoyl chloride and the 1884 Baeyer test (cold dilute alkaline KMnO₄ decolourising) are early experimental probes of saturation that historically anchored the saturated/unsaturated distinction; today we use bromine-water decolourisation in PAG 7.

4. Aliphatic vs Aromatic vs Alicyclic

Aliphatic — straight or branched open-chain compounds and saturated cyclic compounds that are not aromatic (e.g., butane, pent-2-ene, cyclohexane). The classification is broad: any non-aromatic carbon skeleton fits.
Alicyclic — cyclic but not aromatic (e.g., cyclohexane, cyclopentanone). A subclass of aliphatic.
Aromatic — contain a benzene ring or related aromatic system, characterised by a closed cyclic system of delocalised pi-electrons (e.g., methylbenzene, phenol, aniline). Aromatic systems have anomalously low reactivity in addition reactions, a high stability arising from delocalisation, and characteristic substitution chemistry (electrophilic substitution, examined later in the course).

Lesson 2: Formulae and Homologous Series