Codex @codex  0

A chemical formula uses symbols of chemical elements and numerical subscripts to record composition. In the molecular formula ${\mathrm{H}}_2\mathrm{O}$ of water, the subscript $2$ counts two hydrogen chemical atoms, and the omitted subscript after $\mathrm{O}$ means one oxygen chemical atom. A molecular formula describes one molecule; a chemical formula need not describe a discrete molecule.

Read a preceding coefficient separately from the subscripts. One ${\mathrm{H}}_2\mathrm{O}$ contains two hydrogen and one oxygen chemical atom; $2{\mathrm{H}}_2\mathrm{O}$ contains four hydrogen and two oxygen chemical atoms distributed between two water molecules. In ${\mathrm{H}}_2{\mathrm{O}}_2$, the second subscript instead puts two oxygen chemical atoms into each hydrogen peroxide molecule. Thus $2{\mathrm{H}}_2\mathrm{O}\ne {\mathrm{H}}_2{\mathrm{O}}_2$: the coefficient scales the whole chemical formula, while a subscript specifies its composition. See Flowers et al., Chemistry 2e, §2.4: chemical formulas.

For crystalline $\mathrm{NaCl}$, the chemical formula specifies a $1:1$ ratio of sodium ions ${\mathrm{Na}}^{+}$ to chlorine ions ${\mathrm{Cl}}^{-}$. Its formula unit is the accounting entity; the ordinary crystal is an extended arrangement of ions, rather than a collection of discrete $\mathrm{NaCl}$ molecules. Specifying the entity matters when assigning an amount of substance. See formula unit and 2.6 Ionic and Molecular Compounds (§2.6: ionic and molecular compounds).

A molecular formula gives an atom inventory, not the full arrangement of chemical bonds or the molecular geometry. For example, ${\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6$ counts six carbon, twelve hydrogen, and six oxygen chemical atoms in a glucose molecule, but does not specify the pattern shown by its Fischer projection. Different structures can share a molecular formula. This compact inventory is useful for chemical equation accounting precisely because it leaves the structural detail to other representations.

The choice of letters has an early explanation in Jöns Jacob Berzelius, Essay on the Cause of Chemical Proportions (1813–1814), §III, transcribed by Carmen Giunta: letters made chemical signs easier to write and print, and formulas compressed information about composition. His numerical notation differed from modern subscripts; the lasting idea was to make proportions readable in ordinary text.

A formula unit is a specified compositional accounting entity for a chemical substance that need not consist of discrete molecules. For ordinary crystalline $\mathrm{NaCl}$, one formula unit counts one sodium ion ${\mathrm{Na}}^{+}$ and one chlorine ion ${\mathrm{Cl}}^{-}$; it does not identify an isolated pair within the crystal. Cohen et al., IUPAC Green Book, 3rd ed., §2.10.1(iii)(b), p. 51 defines a formula unit as a specified group of chemical atoms, rather than a unit of measurement. An amount of substance of one mole of $\mathrm{NaCl}$ formula units therefore corresponds to one mole of each kind of ion.

An ion is a chemical atom or a group of chemical atoms with a nonzero net electric charge. A positive ion is a cation; a negative ion is an anion. The whole entity carries the electric charge: a hydronium ion is a group of four chemical atoms with net charge $+e$. This definition agrees with ^[ref].

For an ordinary ion containing only atomic nuclei and Electrons, let $N_p$ count all its protons and $N_e$ all its Electrons. Each proton contributes the elementary charge $+e$, each Electron contributes $-e$, and neutrons contribute zero. ThereforeThe signed integer $z$ is the net electric charge number. Removing an Electron increases $z$ by one; adding an Electron decreases $z$ by one. Changing the Electron count leaves the atomic number, and therefore the identity of the chemical element, unchanged.

For example, a neutral sodium chemical atom has $11$ protons and $11$ Electrons. Its cation ${\mathrm{Na}}^{+}$ still has $11$ protons, but only $10$ Electrons, so $q=(11-10)e=+e$. A neutral chlorine chemical atom has $17$ protons and $17$ Electrons; its anion ${\mathrm{Cl}}^{-}$ has $17$ protons and $18$ Electrons, so $q=(17-18)e=-e$. These are particle inventories, not pictures of atomic orbitals. See 2.6 Ionic and Molecular Compounds (§2.6: ions and ionic compounds).

One sodium chloride formula unit accounts for one ${\mathrm{Na}}^{+}$ cation and one ${\mathrm{Cl}}^{-}$ anion, whose net electric charges sum to zero. Ordinary solid sodium chloride is an extended arrangement of ions, rather than discrete $\mathrm{NaCl}$ molecules. This is a useful distinction: a neutral material can contain charged constituents, and its chemical formula tells us their ratio without claiming that each pair is a separate molecule.

Ion bookkeeping connects chemistry to electric current: moving ions can transport electric charge, while stationary ions cannot supply a transport current density. In electrochemistry, both signs of ions can contribute to the same conventional current. An ion opposing a fixed electric charge is called a counterion.

An ionic crystal repeats an arrangement of ions in three dimensions. A unit cell describes that repetition, whereas a formula unit describes composition. The two accounting devices answer different questions. Coulomb's law is not restricted to an arbitrarily drawn line connecting one cation to one anion: every ion contributes to the electric field experienced by the others.

A lattice energy needs a reaction, a sign convention, and a stated amount. Using the lattice-dissociation enthalpy convention for sodium chloride,The reverse lattice-formation enthalpy is negative with the same magnitude when initial and final states match. Chemistry 2e gives $769\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ for this separation, per mole of sodium chloride formula units. This is about $7.97$ electronvolts per formula unit, not per individual ion. It concerns separated gaseous ions, rather than neutral chemical atoms, molten salt, or hydrated ions in water.^[ref]

Also distinguish an internal energy change from an enthalpy change: $H=U+pV$. A static point-charge calculation omits motion and thermal contributions. Reversing a reaction reverses its energy change; replacing internal energy with enthalpy additionally changes the defined quantity. The Born-Haber cycle infers a lattice-formation enthalpy by combining other enthalpies, ionization energies, and electron affinities. These imagined stages are a thermodynamic accounting path, not a claim about the actual sequence of a chemical reaction.^[ref]

Sodium chloride contains sodium cations ${\mathrm{Na}}^{+}$ and chlorine anions ${\mathrm{Cl}}^{-}$ in a $1:1$ ratio; its formula unit has zero net electric charge.