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An atomic basis of a crystal is the motif of chemical species $s_j$ and relative positions $r_j$ attached identically to every lattice point $R$ of a Bravais lattice $\Lambda$. The ideal periodic structure is the labeled setThe primitive lattice translation vectors generate $R$ by integer combinations; the atomic basis lists what is repeated at $R$. These are different meanings of the word basis. In particular, the offsets $r_j$ need not be linearly independent vectors, and one of them may be zero. A primitive unit cell represents $N$ motif sites, even though it represents only one lattice point.

Changing the origin, choosing another primitive unit cell, or moving a motif site by a Bravais lattice translation changes the coordinates used to describe the same infinite crystal structure. The grouping into a motif does not, by itself, identify bonded molecules. In solid sodium chloride, grouping one sodium cation and one chlorine anion into an atomic basis does not create a collection of discrete NaCl molecules; the ionic crystal has an extended network of equivalent neighboring ions.

A Born-Haber cycle uses Hess's law to infer a lattice energy from measurable enthalpy differences and isolated-species data. The motivating difficulty is that separating a mole of an ionic crystal into mutually separated gaseous ions is not a convenient direct calorimetry experiment. Instead, compare two accounting routes between the same elemental reference states and the same solid. Because enthalpy is a state function, the signed differences close exactly when all inputs describe compatible states. These routes do not assert a reaction mechanism or a temporal sequence of reaction intermediates.^[ref]

For one mole of sodium chloride formula units, the overall formation reaction isThe stoichiometry requires half a mole of diatomic chlorine molecules, supplying one mole of chlorine chemical atoms. A half coefficient counts an amount of substance; it does not describe half of an individual molecule. Write each auxiliary chemical reaction with its own sign:Here $S$ is the sublimation enthalpy, $B$ the enthalpy of atomization of chlorine per mole of chemical atoms, and $I$ the molar ionization enthalpy represented by the ionization energy input in elementary treatments. If the bond-dissociation energy table gives the compatible molar enthalpy for ${\mathrm{Cl}}_2(g)\to 2\mathrm{Cl}(g)$, use half that number for $B$. Both ions in the last step are gaseous, and no aqueous hydration of ions belongs in that step.

Adding these equations cancels the gaseous chemical atoms, the gaseous ions and the free electron, leaving precisely the overall formation reaction. ThusThe closed traversal returns from the solid to the elemental reference states, adding $-F$; therefore $S+B+I+A+L_{\mathrm{form}}-F=0$. Notice that the signed attachment term $A$ is negative. Substituting a positive spectroscopic electron affinity for $A$ would reverse the attachment contribution.

The diagram deliberately uses invented, internally consistent inputs in $\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$: $S=100$, $B=120$, $I=500$, $A=-350$ and $F=-400$. Preparation of separated gaseous ions raises the enthalpy by $370$, so $L_{\mathrm{form}}=-770$ and $L_{\mathrm{diss}}=+770$. The closure check is $100+120+500-350-770+400=0$. These numbers are not measured sodium chloride data and do not replace the source's $769\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ example in lattice energy. Every level retains one sodium nucleus, one chlorine nucleus and zero total electric charge; the ionization level explicitly retains the free electron.

William Lawrence Bragg's 1913 structure paper connects a slit-selected beam, an oriented crystal and an ionization chamber to strength-versus-angle curves. Repeated sine ratios and matching absorption coefficients identify common radiation. Narrower slits resolve blended lines. Absolute wavelengths remain undetermined there; intercrystal comparisons first give relative scales. The Bragg crystal reflection experiment of 1913 covers the alignment controls.^[ref]

William Henry Bragg's 1915 Bakerian lecture, X-rays and Crystal Structure, separates the geometric and intensity arguments. Its Figure 9 compares reflection positions and strengths from three sodium chloride orientations; odd and even diffraction orders differ in strength along one orientation. The interpretation uses alternating scattering layers. Later, the calcite example identifies an internal oxygen coordinate that symmetry alone cannot fix. Improved wave intensity measurements revise a previously rough estimate. Thus a lattice assignment can precede determination of positions inside the unit cell; intensity interpretation also has experimental and theoretical limits. This is the father's 1915 lecture, distinct from the joint 1913 reflection paper.^[ref]

How can a clear chemical solution reveal otherwise invisible mobile ions? The documented Conductivity of Solutions by Harvard Natural Sciences Lecture Demonstrations demonstration uses metal electrodes enclosed in tubing, an electrical supply, and a lamp in the circuit. The protocol specifies about $150\mathrm{mL}$ samples in labeled $250\mathrm{mL}$ beakers and a separate deionized-water rinse station. The recorded readout is lamp brightness after the electrodes enter each sample; the simplified variant tests water before and after adding sodium chloride. These are apparatus and procedure specifications, not new measurements reported here.^[ref]

The useful comparison is water, a sucrose chemical solution, and a sodium chloride chemical solution with the same probe geometry. A documented university account reports no visible light with water, a glowing lamp with dissolved sodium chloride, and a weak filament glow with its sucrose sample. The diagram summarizes the latter as little or no visible light; the precise detection threshold depends on the tester. Sucrose is a control for the idea that any dissolved material must conduct: its dispersed neutral molecules do not provide the abundant mobile ions supplied by the salt. This contrast is a documented teaching observation, not a numerical calibration of lamp brightness.^[ref][ref]

Rinsing the electrodes between samples controls carryover of dissolved ions, and the water blank checks the solvent background. Repeating the blank after the salt sample would test whether that rinse was effective. Additional methodological controls are fixed immersed area, electrode separation, supply setting, temperature, and comparison at stated concentrations. These additional controls are proposed checks, not undocumented claims about the source demonstration.

The inference is that mobile electric charge carriers complete the circuit. In the chemical solution, an electric field drives positive ions along the field and negative ions against it; multiplying each drift velocity by its electric charge makes both contributions to conventional current point the same way. With an alternating supply the direction reverses each half-cycle. The external wires instead carry electric current through electrons. The lamp alone identifies neither the species nor an exact electrical conductivity.

Important limits remain. Water has a small intrinsic population of hydronium and hydroxide, so a dark lamp does not prove absence of ions. Changes in probe geometry affect measured electrical conductance; electrolysis, electrode interfaces, contamination, and heating can also affect a real circuit. The comparison supports a transport model but does not independently measure a coordination number, a partitioned partial atomic charge, or a lattice energy.

Nor does poor conduction by ordinary dry sodium chloride establish that all ionic crystals are electrical insulators. Crystallographic defects can allow transport, and solid electrolytes can have substantial ionic electrical conductivity without melting. The authored abstract of A lithium superionic conductor by Noriaki Kamaya and others reports room-temperature ionic conduction in a solid electrolyte; the full experimental article was not accessible here.^[ref]

A crystal structure specifies the chemical species and spatial arrangement of the chemical atoms or ions in a crystal. For an ideal periodic structure, separate two ingredients: a Bravais lattice specifies the translations that repeat the arrangement, and an atomic basis of a crystal specifies the chemical motif repeated at every lattice point. The outward shape, or crystal habit, is a different description: the internal arrangement is what this article describes.

For a concrete two-dimensional model, choose primitive lattice translation vectors $a_1=(2,0)$ and $a_2=(0,1.5)$ in arbitrary length units. At every lattice point $R=m{a}_1+n{a}_2$, with integers $m,n$, place species A at $R$ and a different species B at $R+(0.65,0.55)$. Translating by $a_1$ or $a_2$ preserves both the positions and their chemical labels. Translating by $(0.65,0.55)$ sends one A position to a B position, so it is not a translation symmetry of the labeled structure. A picture of dots with the labels erased can therefore conceal essential chemical information.

A primitive unit cell contains one lattice point, but may contain several chemical atoms. A conventional unit cell can contain several lattice points to display the symmetry more clearly. Thus the conventional cube of a face-centered cubic lattice contains four lattice points, whereas a body-centered cubic lattice has two. Neither lattice name alone specifies which chemical species occupies the repeated motif. The NaCl conventional cell and coordination example makes the distinction explicit.

This separation is useful experimentally: interplanar spacings constrain the repeating geometry, while relative wave intensities also depend on the atomic basis of a crystal through the crystal basis structure factor. The Bragg crystal reflection experiment of 1913 describes the X-ray spectrometer, angular scans and detector checks in detail. Its conversion from angle to length is developed under Bragg's law; a geometrically possible reflection can still have zero wave intensity.

William Lawrence Bragg's 1913 structure determination supplied a complementary test. He directed X-rays through sodium chloride sections cut parallel to a cube face and recorded spots on photographic plates. Comparing section thicknesses tested how transmission altered the pattern: the relative spot strengths changed. Comparing related salts led him to two interpenetrating face-centered cubic lattices, one for each kind of constituent. He explicitly distinguished evidence for that arrangement from the still-needed identification of a single chemical atom with each scattering center. The photographs were evidence for a structural model, not direct pictures of labeled ions.^[ref]

Dialysis exchanges small solutes between a sample and an external bath through a semipermeable membrane, while retaining suitably large macromolecules, such as proteins. The transport is passive diffusion: random motion carries permeant molecules both ways, with net transport down their concentration gradient. The bath is the dialysate. At equal permeant solute concentrations, microscopic exchange continues but net exchange stops.^[ref]

For example, a protein sample containing excess sodium chloride can lose the small ions to a low-salt dialysate without deliberately transferring the protein. Conversely, components of a new buffer solution can enter from the bath. This is useful before studying enzyme kinetics: changing the surrounding chemical solution can remove an interfering small solute while keeping the enzyme available for the next experiment.

The striking feature is that the retained protein does not have to be captured and released again to change its surroundings. However, retention is conditional on the semipermeable membrane and the particular macromolecule, and dialysis is poorly suited to separating proteins of nearly the same size. The molecular weight cut-off is a nominal retention rating, not a sharp geometrical boundary.

The manufacturer-issued Protein Preparation Handbook reports a paired dialysis comparison: $2\mathrm{mL}$ of bovine serum albumin, $0.25mg/mL$ in $1\mathrm{M}$ sodium chloride, was held behind a $10\mathrm{kDa}$ MWCO membrane against $45\mathrm{mL}$ of water in a conical tube, shaken at room temperature. The bath was replaced after two hours. A conventional stirred-beaker treatment against $2\mathrm{L}$ of water supplied the comparison control. Residual salt was followed by sample electrical conductivity; results averaged two samples. This readout tests small-ion removal, not protein retention.^[ref]

Its separate retention experiment used individual proteins at $1mg/mL$ in saline or carbonate-bicarbonate buffer solution, pH $9.4$, with membranes rated $2$, $3.5$, $7$, $10$ and $20\mathrm{kDa}$. After seventeen hours at $4{}^{\circ }\mathrm{C}$, retained protein was estimated by a bicinchoninic acid assay. The size series and membrane series compare retention; they do not isolate shape independently of mass. The figure caption supplies neither a no-membrane recovery control nor a complete uncertainty analysis. These are manufacturer comparisons, not proof of universal recovery or unchanged enzyme function.^[ref]

The two experiments answer complementary questions: did the small solute leave, and did the desired macromolecule remain? In a new experiment, a bath blank and a starting salt standard would help interpret electrical conductivity, while a matched undialyzed protein aliquot and recovered volume would help distinguish handling loss from dilution. Those are proposed additional controls, not controls claimed for the published figures. Other ions also contribute to electrical conductivity, so the readout cannot generally identify sodium chloride alone in an unfamiliar buffer solution.

A diamond anvil cell compresses a sample between opposed diamond tips. The flat diamond anvil culets load a metal gasket whose hole holds the specimen and a pressure-transmitting medium. Transparent diamond admits excitation and returning fluorescence, enabling an internal ruby pressure sensor.^[ref]

The functions in the drawing answer different questions. The drive applies force, the gasket confines the sample, the medium transmits stress, and the ruby pressure scale assigns a local pressure from an optical signal. A large drive reading cannot establish either the sample's pressure or the absence of deviatoric stress. Optical access also permits repeated readings without unloading the sample: a change during a long measurement can be detected rather than silently folded into a material-property curve.

Dissolution transfers material into a chemical solution. It can include separation from an ionic crystal and solvation, or dispersal of neutral molecules. For sucrose and sodium chloride, respectively,Here $(aq)$ specifies water as the solvent; it does not specify a fixed number of attached water molecules. The neutral sucrose remains molecular. Dissociation of an ionic compound separates pre-existing ions in the second example; solvation stabilizes their new surroundings.^[ref][ref]

Ionization instead creates ions from neutral species. Hydrogen chloride reacting with water illustrates protonation of water rather than mere rearrangement of a hydration shell:The hydronium and negative ion together preserve total electric charge. Solvation can influence this chemical reaction, but an ion's solvation does not itself change its net electric charge.^[ref]

Electrochemistry studies how chemical reactions, transport, and chemical equilibrium couple to electric charge and electric potential. In a cell, electrons travel through the external circuit, while mobile ions carry electric current through the electrolyte. At the electrodes, redox reactions connect these two forms of electric charge transport. This connection makes it possible both to obtain electrical work from a chemical reaction and to use electrical work to drive a chemical reaction.

An anode is an electrode where oxidation occurs; a cathode is an electrode where reduction occurs. These definitions refer to the chemical reactions, rather than universal positive or negative terminal signs. In a galvanic cell delivering electrical work, the anode is negative and the cathode positive. In an electrolytic cell driven by an external source, the anode is positive and the cathode negative. See Pingarrón et al., Terminology of electrochemical methods of analysis (IUPAC Recommendations 2019), §§3.1 and 3.4 and Flowers et al., Chemistry 2e, §17.2: galvanic cells.

For a worked example, consider an electrolytic cell containing molten sodium chloride, with the anode connected to the positive terminal and the cathode to the negative terminal of an external source. At the cathode, sodium cations gain electrons; at the anode, chlorine anions lose electrons:The first line has net electric charge zero on each side; the second has $-2e$ on each side. Adding the lines cancels the transferred electrons and preserves both chemical atom counts and net electric charge. The sodium product is neutral, and the chlorine product is a diatomic molecule. These equations specify molten sodium chloride; aqueous chemical solutions introduce competing water reactions. See 17.7 Electrolysis (§17.7: electrolysis of molten sodium chloride).

Electrochemistry underlies battery charging and the manufacture of chemicals by electrolysis. Its particularly useful idea is that an electron inventory in a balanced chemical equation also accounts for transported electric charge. Transport alone is a different question from an electrode chemical reaction: an ion may carry electric current through the electrolyte without itself being consumed at an electrode.

Historically, Michael Faraday introduced the terms electrode, electrolyte, anion, cation, and ion in the terminology section of his 1834 paper, Experimental Researches in Electricity, Seventh Series by Michael Faraday (§§662–667). His §667 explicitly treats the direction assigned to electric current as a convention. His ion language predates the modern electron and atomic nucleus picture used in the charge-counting example above.

For an electrolyte near chemical equilibrium, a Poisson-Boltzmann equation can approximate the distribution of ions in an electric potential. Such an equilibrium model does not by itself describe a cell carrying sustained electric current.

An electrolyte is a conducting medium in which mobile ions carry electric current, according to IUPAC Gold Book: electrolyte. In introductory chemistry, a substance that yields ions when dissolved in water is also called an electrolyte. Both usages point to the same mechanism: an electric field gives mobile cations and anions directed drift velocities.

Mobility matters as much as the presence of electric charge. In a simple ideal model of solid sodium chloride, ions are confined to their sites and do not carry a sustained transport electric current. Molten sodium chloride has mobile ions; dissolved sodium chloride gives mobile ${\mathrm{Na}}^{+}$ and ${\mathrm{Cl}}^{-}$ ions in water. Real solids can have some ionic transport through imperfections; the immobile-solid picture is an introductory limit, rather than a claim that all solids are perfect insulators.

A strong electrolyte yields essentially all ions from the dissolved substance, whereas a weak electrolyte yields only a fraction under the specified conditions. Dissolved sodium chloride is a strong electrolyte. Sucrose is a nonelectrolyte: it dissolves as neutral molecules, so dissolving something does not automatically create mobile ions. Water's own small population of hydronium and hydroxide remains possible. See 11.2 Electrolytes (§11.2: strong, weak, and nonelectrolytes) and Flowers et al., Chemistry 2e, §11.4, Table 11.3: sucrose and sodium chloride.

Acetic acid is a weak electrolyte and a weak acid. In water, some neutral acetic acid molecules transfer a proton to water, producing hydronium and the negatively charged partner:Both sides have net electric charge zero. At chemical equilibrium, neutral acetic acid coexists with these ions; the fraction converted depends on the conditions. Electrolyte strength describes this extent of ion production, while concentration describes how much substance is present per specified quantity of chemical solution. A dilute strong electrolyte can contain fewer ions per volume than a concentrated weak electrolyte. Neither the words strong and weak nor a conductivity comparison alone specifies concentration.

Now specify an electrolytic cell with a positive anode on the left, a negative cathode on the right, and an approximately uniform electric field pointing right in the bulk electrolyte. With a steady external source and neglecting diffusion and convection, positive cations drift right toward the negative cathode; negative anions drift left toward the positive anode. Yet both populations contribute a rightward conventional current! For number densities $n_{+},n_{-}$ and drift velocities ${\mathbf{v}}_{+},{\mathbf{v}}_{-}$, the transport current density isThe product of electric charge and velocity determines conventional current: for the anion, both the charge and its rightward velocity component are negative, making its rightward contribution positive. This is the same sign rule used for electron conventional current. It follows directly from the existing charge carrier formula.

For an independent numerical example, stipulate $n_{+}=n_{-}=10^{25}{\mathrm{m}}^{-3}$, $v_{+,x}=2\times 10^{-4}\mathrm{m}{\mathrm{s}}^{-1}$, and $v_{-,x}=-3\times 10^{-4}\mathrm{m}{\mathrm{s}}^{-1}$. With the exact elementary charge $e=1.602176634\times 10^{-19}\mathrm{C}$, the contributions areEqual number densities of singly charged cations and anions give zero bulk charge density, while their motion gives nonzero current density. This is why a neutral electrolyte can conduct. These numbers are chosen toy inputs, not measurements of sodium chloride; maintaining sustained cell electric current also requires suitable electrode reactions. Blocking electrodes can instead lead to charge accumulation and decay of the electric current.

An electrolyte connects the microscopic motion of ions to observable electrical conductivity. A counterion-only model keeps just the mobile counterions needed to oppose a fixed electric charge; Poisson-Boltzmann equations use ideal Boltzmann distributions to model their equilibrium distributions, rather than the drift example above.

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.

Ionic bonding binds oppositely charged ions through attraction governed by electrostatics. In ordinary solid sodium chloride, each cation interacts with many anions, and also with other cations: attraction and repulsion together contribute to the binding of an extended ionic crystal. The chemical formula $\mathrm{NaCl}$ specifies equal numbers of the two kinds of ions; it does not divide the solid into isolated two-atom molecules.^[ref]

This distinction explains a striking combination of properties: ordinary dry sodium chloride conducts electric current poorly, while its molten form or a sufficiently concentrated chemical solution in water conducts well. The ions already exist in the solid; their ability to move through the sample changes. A conductivity experiment on salt solutions tests this transport picture, rather than simply asserting that charged constituents must make every material conductive.

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]

Choose an original simulated model: a primitive cubic lattice with one identical point scatterer per primitive unit cell, edge $a=0.400\mathrm{nm}$, and incident X-ray wavelength $\lambda =0.200\mathrm{nm}$. These are stipulated lengths, not measurements of sodium chloride. Suppose orientation information has already assigned the two observed reflections the Miller indices $(100)$ and $(110)$. The detector deflection is $2\theta$, where $\theta$ is the Bragg angle.

Use the existing interplanar spacing formula and Bragg's law, with higher diffraction orders absorbed into the reflection indices:The simulated $(100)$ reflection has $\sin \theta =1/4$, hence $2\theta =28.9550^{\circ }$. The $(110)$ reflection has $\sin \theta =\sqrt{2}/4$, hence $2\theta =41.4096^{\circ }$. Their squared sines are $0.0625$ and $0.125$, in ratio $1:2$. Substituting the unrounded angles independently givesAgreement tests a proposed indexing and scale together; disagreement would prompt checks of the indexing, wavelength, angular zero, or the assumed unit cell geometry.

Two peak positions alone do not establish the indexing. Assigning the same two angles to $(110)$ and $(200)$ would give $N=2,4$ and $a=0.400\sqrt{2}\simeq 0.565685\mathrm{nm}$ instead. More reflections, orientation information and systematic absences help discriminate such assignments. An unobserved reflection can be inaccessible, weak or extinguished by the atomic basis; absence is not automatically evidence for a larger interplanar spacing.

Absolute scale also requires measurement calibration of the wavelength. To first order, differentiation of the inferred length giveswith angular changes in radians. A stipulated detector-zero error $\delta (2\theta )=+0.100^{\circ }$, with correct wavelength, biases the first inferred edge downward by approximately $0.338\%$ and the second by $0.231\%$. A common angular offset therefore need not cancel when two inferred lengths are compared. These are model sensitivity estimates, not historical instrument uncertainties.

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]

A second indirect route makes the experimental distinction especially clear: a calorimeter can measure dissolution of a weighed salt into a known amount of water, but its final ions are hydrated, not separated gaseous ions. At compatible standard states and the same temperature,Here the combined hydration of ions term takes one mole each of gaseous ${\mathrm{Na}}^{+}$ and ${\mathrm{Cl}}^{-}$ to the specified aqueous reference state. Its sum suffices: dissolution calorimetry alone cannot independently assign single-ion hydration of ions enthalpies, or determine $L_{\mathrm{diss}}$ without another input. A finite-concentration measurement also requires dilution corrections before it can supply $\Delta H_{\mathrm{sol}}^{\circ }$.

In a simple constant-pressure solution calorimeter, an insulated vessel, stirrer and thermometer follow the temperature change after mixing. A calibrated effective heat capacity $C_{\mathrm{eff}}$ converts the corrected temperature change to heat. With no applied heating, negligible external heat transfer, and only pressure-volume work, the approximate molar result isHere $n$ is the amount of substance dissolved and $C_{\mathrm{eff}}$ includes the chemical solution and the vessel. Cooling means positive dissolution enthalpy, because the dissolving sample takes heat from its surroundings.^[ref]

An actual reference measurement used potassium chloride, not sodium chloride: a platinum-lined calorimeter with an adiabatic shield and a quartz-oscillator thermometer. Because dissolution absorbed heat, measured electrical heating prevented loss of shield control; the readouts were electrical input and the vessel/shield temperature record. Stirring was checked visually in a dummy vessel. The thermometer was compared with a calibrated resistance thermometer, and electrical calibration bracketed the reaction. The reported result was $+(17.584\pm 0.017)\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ at $298.15\mathrm{K}$, for one mole of potassium chloride in $500$ moles of water.^[ref]

Checks on residual water, particle size and final concentration, and agreement with a second calorimeter, constrained systematic errors. Imperfect shield tracking required heat transfer corrections. This experiment measures an enthalpy of solution, not a direct lattice energy; the hydration and dilution bookkeeping still has to be supplied. The full article could not be opened here; the inspected indexed text supports the stated apparatus and checks, without reconstructing its complete uncertainty budget.^[ref]