Online text: goldbook.iupac.org/terms/view/L03597

Online text: goldbook.iupac.org/terms/view/C00963

Online text: goldbook.iupac.org/terms/view/T06274

Online text: goldbook.iupac.org/terms/view/C00958

Online text: goldbook.iupac.org/terms/view/15441

Cited passages: IUPAC Gold Book entry for acid dissociation constant, definition and notes 1–2: standard concentration, conditional constants and dimensionless thermodynamic constant.

Online text: goldbook.iupac.org/terms/view/A00496

Cited passages: IUPAC Gold Book, atomic mass: ground-state rest mass of an atom.

Online text: goldbook.iupac.org/terms/view/A00102

Cited passages: IUPAC Gold Book, activation energy: empirical derivative definition and threshold-energy qualification; IUPAC Gold Book, activation energy: operational temperature-derivative definition; IUPAC Gold Book: activation energy.

Online text: goldbook.iupac.org/terms/view/C01458

Cited passages: IUPAC Gold Book, current efficiency: definition and exception for simultaneous anodic and cathodic reactions; IUPAC Gold Book, current efficiency: partial electrode currents and product yield; conditions excluding consecutive product-consuming reactions.

Online text: www.msterms.org/wiki/index.php/Aston_1922/Chapter_5

Cited passages: Chapter V, §§33–40: apparatus and photographic procedure; §§43 and 45–46: calibration, aperture comparisons, and accuracy.

An excited atom or ion above an electron-emission threshold can decay without a photon by ejecting an electron and leaving a more highly charged ion. This is autoionization. Its rate competes with radiative stabilization in dielectronic recombination; the inverse electron-capture channel is dielectronic capture.

A free electron is resonantly captured while exciting the ionic core, producing a doubly excited state above the parent-ion threshold. Capture becomes permanent recombination only if the state undergoes radiative stabilization rather than autoionization. For resonance $d$, entrance ion $i$, and Maxwellian electrons, ${\alpha }_d=(g_d/(2g_i))(h^2/(2\pi mkT){)}^{3/2}{e}^{-E_d/kT}{A}_{di}^a{A}_{\mathrm{stab}}^r/(A_{\mathrm{tot}}^a+A_{\mathrm{tot}}^r)$. Detailed balance determines the capture rate; a steady population balance determines the survival factor. The rate coefficient has dimensions volume per time.

Three-body recombination captures an electron while a second free electron carries away energy, the inverse of direct electron-impact ionization. Its rate scales as the parent-ion density times the square of electron density. It is usually negligible compared with two-body radiative recombination and dielectronic recombination in the low-density solar corona, but matters in sufficiently dense plasmas.

Many ionic crystals have high melting temperatures compared with small molecular solids, because reorganizing their strongly interacting ions costs energy. But melting leaves a dense liquid with interactions; it does not perform the complete separation defining a lattice energy. At fixed pressure, the transition occurs when the Gibbs free energies of the solid and liquid match. The relevant enthalpy and entropy differences both matter, so lattice energy alone is not a universal ordering of melting temperatures. Strong covalent bonds in extended networks can also give high melting temperatures.^[ref]

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]

For two point electric charges in vacuum, Coulomb's law gives the interaction potential energywith zero at infinite separation. Here $r_{ij}$ is the distance between them and ${ϵ}_0$ is the vacuum permittivity. Opposite signs give negative potential energy and attraction; equal signs give positive potential energy and repulsion. For a finite collection of distinct point electric charges, sum over $i<j$ to count each pair once. A bulk ionic crystal requires the extended lattice sum, including both signs, rather than multiplying one attractive pair by the coordination number.^[ref]

At short distances, overlapping electron density makes the simple point-charge picture inadequate. Quantum mechanics, including the Pauli exclusion principle, matters to the steep repulsive contribution. Pure attraction proportional to $-1/r$ would collapse as $r\to 0$; it cannot set an equilibrium spacing on its own. A useful illustrative model isHere $r$ scales an assumed fixed arrangement, $A$ packages its attractive contribution, and $B/r^n$ represents short-range repulsion. The constants have units energy times length and energy times length to the power $n$, respectively. This is a model, not a fitted description of a named salt.^[ref]

Differentiating gives $r_0=(nB/A{)}^{1/(n-1)}$ and $U^{\prime \prime }(r_0)=(n-1)A/r_0^3>0$, so the stationary spacing is a stable minimum. For the diagram's stipulated $n=9$, put $x=r/r_0$ and $E_0=A(1-1/n)/r_0>0$. ThenThe dimensionless curves show how competing interactions select a spacing. Their energy scale and exponent are synthetic; neither is a measured lattice energy or a melting prediction.

The bookkeeping steps $\mathrm{Na}\to {\mathrm{Na}}^{+}+e^{-}$ and $\mathrm{Cl}+e^{-}\to {\mathrm{Cl}}^{-}$ conserve electric charge and describe the electron inventories of separated species. They do not establish a chronological mechanism in which a labeled electron jumps between two pre-existing chemical atoms and becomes a classical object owned exclusively by one of them. In a bound material, quantum mechanics determines the electron density and the total energy.

Ionic bonding and a covalent bond are useful limiting descriptions with a continuum between them. Electronegativity helps anticipate unequal sharing of electron density, but a numerical cutoff does not measure a universal fraction of ionic bonding. A partial atomic charge depends on how the electron density is partitioned; integer formal charges are a bookkeeping convention. Using $\pm e$ in a point-charge model therefore does not claim that every partition of the actual electron density assigns exactly those values.^[ref][ref]

An ion pair is an associated cation and anion. An isolated ion pair lacks the extended neighbourhood of an ionic crystal. In a chemical solution, ion pairs can coexist with more widely separated ions; their abundance depends on conditions. A neutral gas-phase sodium chloride molecule can be treated as a discrete entity, with its own quantum mechanics and dissociation products. That use of molecule does not describe the constituents of ordinary solid sodium chloride.^[ref][ref]

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 salt is an assembly of cations and anions with zero total electric charge. Its constituents can be single chemical atoms or groups joined internally by covalent bonds. Thus ionic bonding and covalent bonds can occur in the same chemical substance, at different structural levels.^[ref]

Online text: pure.uva.nl/ws/files/4022576/36988_UBA002001360_11.pdf

Cited passages: Ion solvation in water: femtosecond spectroscopy of hydrogen-bond dynamics, chapter 8, §8.2 and §8.3, printed pp. 82–89, Figures 8.1–8.7; PDF text inspected, numerical decay-time OCR unreliable and not reproduced.