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The fraction of a material lacking the specified long-range crystalline order. It is a structural measure, not directly a dissolved mass fraction or radionuclide release fraction.

The amount fraction of component $i$ is $x_i=n_i/{\sum }_j{n}_j$, where $n_i$ is its amount of substance. It is dimensionless and the fractions sum to one for a complete composition specification.

For an ideal gas mixture at common temperature and pressure, amount fraction equals partial-pressure fraction. It generally differs from mass fraction because different species have different molar masses. For one mole each of hydrogen and oxygen molecules, both amount fractions are one half, although their masses are very different. The composition basis must therefore accompany a quoted concentration.

Analytical sampling selects and collects material from a larger target for chemical measurement. It connects the material actually measured with the batch, location or time period about which a conclusion is wanted. A small, well-measured portion need not represent the larger material merely because its instrument reading is precise.

An original two-region example has90% of a batch's mass at $1\mathrm{mg}\mathrm{k}{\mathrm{g}}^{-1}$ and10% at $100\mathrm{mg}\mathrm{k}{\mathrm{g}}^{-1}$ of an analyte. The batch-average mass fraction isTaking equal masses from the two regions instead produces $50.5\mathrm{mg}\mathrm{k}{\mathrm{g}}^{-1}$. That sample answers a different weighted question. Probability sampling or a justified stratified sampling design can connect selection probabilities and weights to the intended target.

A sampling increment is an individual collected portion. Combining increments and reducing material to a laboratory portion can introduce further variation, so the protocol should state where, when, how much and how material was handled. Repeated readings of one prepared solution chiefly test later measurement stages.

For an original nested model, let independent collected portions have sampling variance ${\sigma }_s^2$, and repeated analyses within a portion have variance ${\sigma }_a^2$. Averaging $m$ analyses on each of $n$ independent portions givesWith stipulated ${\sigma }_s=4$, ${\sigma }_a=1$, $n=4$ and $m=3$ in compatible units, the mean's standard uncertainty is approximately2.02. Increasing laboratory replication alone cannot eliminate the sampling component. Correlated portions or shared biases require an expanded model.

A primary collaborative trial had multiple samplers collect wheat and green coffee from bulk lots. Its contrasting findings for between-sampler and within-condition variation demonstrate why analytical sampling uncertainty needs a design that actually varies the collection stage.^[ref]

The atmospheric metallicity of a giant planet describes its atmospheric inventory of elements heavier than hydrogen and helium. It must specify a convention: an elemental abundance ratio relative to hydrogen, an enhancement relative to a reference composition, or a total heavy-element mass fraction are related but different quantities. A quoted enrichment also needs to identify its reference, such as the host star.

Atmospheric retrieval estimates molecular abundances, which must then be connected to elemental inventories through a model of chemical equilibrium or disequilibrium chemistry in an exoplanet atmosphere. Atmospheric condensate rainout can hide elements in particles below the observed levels. Thus an atmospheric enrichment need not directly equal the heavy-element fraction of the whole exoplanet interior.

A binary mixture is a mixture with two specified chemical components. Water mixed with ethanol is a familiar example. “Binary” counts the components used to describe composition, rather than the number of thermodynamic phases: two components can form one homogeneous mixture or coexist in distinct thermodynamic phases.^[ref]

For two nonreacting components with amounts of substance $n_A,n_B$, the amount fractions satisfyOnly one composition coordinate is independent. In an original preparation using1mole of ethanol and3moles of water, $x_{\mathrm{ethanol}}=1/4$. Using rounded molar masses46.07and18.015grams per mole gives the ethanol mass fractionThus25percent by amount of substance and about46percent by mass describe the same preparation. A composition percentage without its basis is ambiguous. The calculation uses component masses, without assuming additive liquid volume.

Hexane and water illustrate why component count and phase count differ. Their limited mutual solubility permits two liquid thermodynamic phases, each containing some of the other component. A primary compiled experiment equilibrated the liquids by overnight shaking, sampled the aqueous portion with a microsyringe, and measured dissolved hydrocarbon by gas chromatography with flame-ionization detection.^[ref] The liquid immiscibility article develops a lever rule calculation distinguishing each phase's composition from the overall composition.

A binary mixture is not automatically an ideal solution. Interactions between unlike molecules can change activities, mixing enthalpy and phase stability. Stating temperature, pressure and the composition basis is therefore part of specifying the system, rather than optional experimental detail.

A complex medium is a culture medium containing ingredients whose complete molecular composition is not specified. Common examples include yeast extract and peptone. A recipe can state the mass of such an ingredient precisely while leaving the amounts of its individual molecular constituents incompletely known.^[ref]

That distinction can be expressed quantitatively. In a constructed example, two hypothetical extracts are each present at $10\mathrm{g}{\mathrm{L}}^{-1}$. Suppose a constituent X has mass fraction $0.01$ in the first extract and $0.02$ in the second. Its mass concentration is then respectivelyEqual masses of the whole mixture therefore permit a twofold difference in X. These fractions are invented to illustrate the information missing from an ingredient-level specification; they are not measurements of commercial extracts.

A defined medium makes individual chemical inputs easier to track. A complex medium can instead provide many growth-supporting constituents together, which can be useful when an organism's requirements are incompletely characterized.^[ref] Neither classification by itself establishes the outcome of a bacterial culture experiment.

For an observed change in growth, the useful questions include which ingredient was varied, what was measured about its chemical composition, and whether other conditions were matched. The word complex describes incomplete compositional specification; it does not mean that every measured property of the preparation is unknown.

A composite sample is formed by combining material from several collected portions into one mixture, from which material for laboratory measurement is taken. It can represent an aggregate composition when the collection and mixing weights match the intended target. IUPAC describes compositing as preparation of a mixture from several samples; combining them does not by itself prove representativeness.^[ref]

Suppose sampling increments have masses $m_i$ and analyte mass fractions $c_i$. With complete transfer, no chemical change and adequate mixing, conservation of analyte givesEqual increment masses produce an arithmetic mean; unequal masses produce a mass-weighted mean. Weights chosen to represent different parts of the sampling target can differ from the fractions accidentally collected.

An original example shows what is lost. Four equal-mass portions with concentrations $(0,0,0,40)$ milligrams per kilogram give the same composite concentration, 10 milligrams per kilogram, as portions with concentrations $(10,10,10,10)$. A single composite measurement cannot distinguish a localized high value from uniform composition. It addresses the weighted average, not the maximum or the spatial distribution.

The uncertainty of that average depends on dependence between portions. For a random concentration vector with covariance matrix $\Sigma$ and fixed mixing weights,For four equal-weight portions each with standard deviation 2 concentration units and common pairwise correlation coefficient 0.25, this givesand standard deviation about 1.32 units. Assuming independence would instead give 1 unit. This stipulated model concerns collected-material variation; common losses or measurement errors can add other contributions.^[ref]

A practical protocol specifies increment selection, mixing proportions, mixing procedure and reduction to a test portion. Loss of volatile material, segregation of particles or incomplete mixing can make the analysed portion differ from the intended composite. Replicate readings of one final solution test later measurement stages; independent composites are needed to investigate variability introduced during collection and pooling.

Concentration quantifies how much of a named constituent is present relative to a specified sample measure. In chemical terminology, volumetric concentrations use the final mixture volume: mass concentration is mass per volume and molar concentration is amount of substance per volume. Mass fraction and amount fraction instead compare a constituent with the corresponding total quantity in the mixture.^[ref]

The distinction matters in transport models. If an isolated sample expands without exchanging constituents, its volumetric concentration decreases even though its composition fractions stay fixed. A scalar called concentration in an advection model may represent a fraction instead, so its definition must be stated.

Conservation applies to the transported constituent amount. Reactions, diffusion and exchange then determine how the chosen concentration changes relative to its carrier and denominator.

For electrically neutral, fully ionized stellar matter with electrons and Positrons as its charged leptons, the electron fraction in stellar matter is the net electron number per baryon:Here $n_i$ is the number density of nuclear species $i$, $Z_i$ its atomic number, $A_i$ its mass number, and $n_b$ the total baryon number density. Charge neutrality equates the net negative lepton charge to the total proton charge. The subtraction of Positrons matters in hot matter containing abundant thermally produced Positrons; ordinary electron number alone need not equal nuclear charge.^[ref]

Neglecting small nuclear mass defect corrections, isotope mass fractions $X_i$ give $Y_e={\sum }_i{X}_i{Z}_i/A_i$. Pure fully ionized helium-4 therefore has $Y_e=1/2$. Strong interactions and electromagnetic reactions preserve this proton fraction, whereas electron capture and beta-plus decay reduce it and beta-minus decay can increase it. The total proton-to-neutron number ratio is $Y_e/(1-Y_e)$; electron-positron pair production changes neither of those baryon counts. If other charged leptons such as muons are appreciably populated, their charge must also be included in the neutrality equation.

Ethylene-vinyl acetate, abbreviated EVA, is a copolymer made from the monomers Ethylene and vinyl acetate. Its chain contains ethylene-derived units $-\mathrm{C}{\mathrm{H}}_2-\mathrm{C}{\mathrm{H}}_2-$ and vinyl-acetate-derived units $-\mathrm{C}{\mathrm{H}}_2-\mathrm{CH}(\mathrm{OCOC}{\mathrm{H}}_3)-$. The polymerization joins the carbon skeletons while retaining the acetate side group. Consequently ethylene-vinyl acetate denotes a family of compositions and chain lengths, rather than one small molecule with a unique molar mass.^[ref][ref]

A useful distinction is between the mole fraction of incorporated vinyl acetate units and their mass fraction. Write $x=N_{\mathrm{VA}}/(N_{\mathrm{VA}}+N_{\mathrm{E}})$. Ignoring the contribution of chain ends for sufficiently long chains, the unit molar masses are $M_{\mathrm{E}}=28.05\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$ and $M_{\mathrm{VA}}=86.09\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$. ThusA chain population with 20% of its units derived from vinyl acetate has about 43.4% of its mass in those units. Conversely, 20% by mass corresponds to only about 7.53% of the units. The difference comes from the roughly threefold unit-mass ratio. Here $x$ describes the incorporated chain composition; incorporated composition versus feed composition in EVA is a separate issue from this arithmetic conversion.^[ref]

The manufacturer's EVA 2018 datasheet illustrates actual reporting practice: its typical vinyl acetate content is 18.2% by mass. That value characterizes the named product and does not define every ethylene-vinyl acetate material.^[ref]

A particularly revealing application is laser capture microdissection. The 1996 report placed a transparent thermoplastic ethylene-vinyl acetate film on a histological section. A carbon dioxide laser pulse activated a chosen region of the film, whose local adhesion transferred selected cells for subsequent analysis. This connects a polymer processing response to spatially selective sampling of tissue; the report's film is not identified with the commercial grade cited above.^[ref]

An exoplanet bulk-composition ternary diagram represents three component mass fractions by one point inside a triangle. If the components have fractions $x_1,x_2,x_3$, then $x_i\ge 0$ and $x_1+x_2+x_3=1$. Each vertex is a pure component, an edge excludes the opposite component, and the centre corresponds to equal thirds. The fractions are barycentric coordinates relative to the vertices.

For an illustrative iron-rock-water model, measured mass and radius restrict the allowed part of the triangle through an exoplanet interior calculation. They need not select a unique point, making exoplanet interior-composition degeneracy visible. The diagram is conditional on the chosen three components: an unmodelled hydrogen-helium envelope cannot automatically be interpreted as more of one of those solid components.

A finite population total adds a specified numerical value over every labelled unit in a fixed, finite population $U=\{1,\dots ,N\}$:The target must specify both the population and the measured variable. It may be a total inventory mass, the total number of employees across establishments, or the sum of a binary property. If $y_i\in \{0,1\}$, the total counts units having the property; it is not automatically the population size $N$. A finite population mean is $\overline{Y}=T/N$, when $N$ is known and positive.

An original inventory has four containers holding $3,7,10,20\mathrm{kg}$ of a material. The total is $40\mathrm{kg}$ and the finite population mean is $10\mathrm{kg}$ per container. Giving every container the same mass fraction of an analyte is a separate assumption: the total analyte mass instead requires summing each container's mass multiplied by its own mass fraction. The target follows the physical quantity being added.

When only a sample $S$ is observed, the unweighted sample sum is generally not an unbiased estimator of $T$. Using inclusion indicators $I_i$ and inclusion probabilities ${\pi }_i$ givesIf every ${\pi }_i>0$, the Horvitz-Thompson estimator instead satisfiesThis is a consequence of the sampling design, without requiring the fixed population values to follow a statistical distribution.^[ref] A full census removes sample-selection variation, but imperfect measurement can still make the recorded sum differ from the intended physical total.

Freeze-drying, also called lyophilization, removes water from a frozen material chiefly by sublimation: solid water passes directly into vapor. Reduced pressure makes that route useful without requiring the whole sample to pass through a liquid-water stage. Primary drying concerns removal of ice by sublimation; secondary drying concerns removal of residual sorbed water by desorption.^[ref]

A hypothetical mass balance separates water removal from the measurement convention. Suppose a $1.000\mathrm{g}$ specimen contains $0.200\mathrm{g}$ of dry solids and $0.800\mathrm{g}$ of water. If its final mass is $0.210\mathrm{g}$, with no solids lost or chemical change, the residual water is $0.010\mathrm{g}$. Its wet-mass mass fraction iswhereas water relative to dry solids is $0.010/0.200=5\%$.

Both percentages describe the same imagined sample with different denominators. The mass change establishes water removal under the assumptions, but does not independently prove that sublimation was the mechanism. That claim requires information about the material's phase and the physical process.

The stated mass or atom fraction of a selected fuel isotope. An isotope balance requires all streams to use the same convention; a mass fraction is not interchangeable with an atom fraction without conversion.

Gravimetric dilution determines a dilution from measured masses. A measured amount of a stock solution is combined with material containing none of the quantity being diluted. For a closed transfer and a homogeneous mixture, the conserved amount divided by the final mass determines the new mass-based concentration.

Let $m_s$ be the stock's net mass, $m_d$ the added net mass, and $M=m_s+m_d$. Define the stock fraction $f$ and the gravimetric dilution factor $F$ byIf the stock has solute mass fraction $w_s$, thenFor stipulated $m_s=2.000\mathrm{g}$, $m_d=18.000\mathrm{g}$ and $w_s=0.2000$, the final mass is $20.000\mathrm{g}$, $F=10$, and $\boxed{w_f=0.02000}$: 2% by mass. The solute mass is $0.4000\mathrm{g}$ before and after dilution. The net masses exclude their containers. This mass basis does not require an assumption that liquid volumes add.

The uncertainty of a gravimetric dilution depends on which readings share errors. For independently evaluated inputs $w_s,m_s,m_d$, first-order propagation of uncertainty givesHere $u$ denotes standard uncertainty. The sensitivity factors follow from the partial derivatives $\partial f/\partial m_s=m_d/M^2$ and $\partial f/\partial m_d=-m_s/M^2$. With a chosen independent $u(m_s)=u(m_d)=0.001\mathrm{g}$ at the example's nominal masses, the relative mass-ratio contribution is approximately 0.0453%. Adding an independent 0.5% relative stock-value contribution in quadrature gives approximately 0.502%. These are illustrative inputs, rather than a balance specification.^[ref]

If input errors have covariance, their cross terms must be retained. A useful exact check isA common multiplicative mass-scale factor therefore cancels from $f$. Counting it as two independent contributions would lose that correlation. Container subtraction, transfer losses and changes in composition require their own assessment; this cancellation establishes only the common-scale property.

For massic activity, the same conservation argument applies after expressing all activities at a common reference time. A 2000 NIST study compared massic activity ratios inferred from gravimetric dilution with independent liquid scintillation counting. Their agreement within reported uncertainties provided an experimental check on transferring standards through mass ratios.^[ref]

The gravimetric dilution factor is the ratio of final mixture mass to the stock mass used in a gravimetric dilution:Here $m_d$ is added diluent mass and $f$ is the retained stock mass fraction. For a diluent containing none of the component being measured, mass conservation gives final component mass fraction $w_f=w_s/F$. This mass-based relation avoids assuming that liquid volumes are additive. Its uncertainty follows from the same input masses and their covariance as the uncertainty of a gravimetric dilution.^[ref]

For an original two-step example, combine $2.000\mathrm{g}$ of stock with $18.000\mathrm{g}$ of diluent, giving $F_1=10$. After complete mixing, transfer $1.000\mathrm{g}$ of that mixture and add $4.000\mathrm{g}$ of diluent, giving $F_2=5$. The combined gravimetric dilution factor isIf the original stock has component mass fraction $0.2000$, the first mixture has $0.02000$ and the final mixture $0.004000$. The transferred gram contains $0.02000\mathrm{g}$ of the component; dividing by the final $5.000\mathrm{g}$ checks the result. This calculation requires a representative, homogeneous transferred portion and no component loss.

State whether a dilution number denotes $F$ or its reciprocal $f$: here a tenfold dilution means $F=10$ and $f=0.1$, not that ten parts of diluent were added per part of stock. The latter recipe gives $F=11$.

The humidity ratio $w$ is the mass of water vapor divided by the mass of dry air in a sample:It is commonly expressed as kilograms of water vapor per kilogram of dry air, or grams per kilogram. The denominator excludes the water vapor itself; the related specific humidity is a mass fraction of the entire moist sample.^[ref]

Using the ideal gas law for both components giveswhere $M_v,M_d$ are molar masses, $p_v$ is the water-vapor partial pressure, and $p$ is total pressure. At $p=101.325\mathrm{kPa}$ and $p_v=1.6\mathrm{kPa}$, this yields $w\approx 0.00998$, or about $9.98g/kg$ of dry air.^[ref]

Unlike relative humidity, the humidity ratio does not compare vapor pressure with saturation vapor pressure. Warming air without adding or removing water vapor can change its relative humidity while leaving $w$ unchanged. This distinction matters when comparing incoming and outgoing air in measurements of evaporation or biological heat loss.

For fully ionized hydrogen and helium with hydrogen mass fraction $x_H$, $n_e=(1+x_H)\rho /(2m_p)$ and ${\sum }_i{Z}_i^2{n}_i=\rho /m_p$. With the same unit Gaunt factor for both species, thermal bremsstrahlung at fixed electron number density is multiplied by $2/(1+x_H)$ relative to pure ionized hydrogen. The factor is one for pure hydrogen and two for pure helium.

The Mixture measurements and the Gibbs-Duhem constraint article describes the inspected acetone–chloroform preparation, apparatus, paired readouts, controls and sampling limits.^[ref]

That existing apparatus account supplies the experimental controls and limitations. Its refractive index calibration yields mass fractions, which must be converted to mole fractions. For a measured component-A mass fraction $w_A$ and component molar masses $M_A,M_B$,Apply this conversion separately to the flask sample and to completely condensed vapor to obtain $x_A$ and $y_A$. Comparing $y_{i}P$ with $x_i{p}_i^{\ast }(T)$ tests Raoult's law at the measured temperature; using the changing temperature at each composition is essential. The chosen A/B values above are unrelated to the protocol's substances.

The more general diagnostic, retaining an ideal gas vapor and negligible pure-liquid pressure correction, isThis follows by replacing $\ln x_i$ with $\ln (x_i{\gamma }_i)$ in the chemical potential subtraction used for Raoult's law. A reproducible discrepancy from ${\gamma }_i=1$ can expose failure of the ideal solution approximation, but interpreting it requires checking measurement uncertainty, representative paired sampling and the ideal gas approximation. Apparent agreement within uncertainty supports an approximation over the tested conditions; it cannot establish exact ideality at every composition.

Positive or negative deviations of component partial pressures require activity coefficients different from one under these assumptions. An azeotrope is also absent from the chosen unequal-vapor pressure model: the explicit inequality in ideal binary vapor composition gives $y_A>x_A$ throughout $0<x_A<1$. An interior equality would require $p_A^{\ast }=p_B^{\ast }$; in that degenerate case every composition has $y_A=x_A$, rather than an isolated enrichment reversal. Neither an azeotrope nor liquid phase separation should be inferred from the ideal curves.

Incorporated composition versus feed composition in EVA distinguishes the monomer mixture available to react from the units actually entering ethylene-vinyl acetate chains. Let $f$ be the mole fraction of vinyl acetate in the reacting monomer mixture, and $F$ its instantaneous fraction among newly incorporated units. Neither quantity is the mass fraction reported on a product datasheet. The copolymer composition equation relates instantaneous composition to the reacting mixture and monomer reactivity ratios; IUPAC explicitly notes that composition generally changes during the reaction.^[ref]

In the terminal model of copolymerization, the identity of the last unit controls addition-rate constants. Define $r_V=k_{VV}/k_{VE}$ and $r_E=k_{EE}/k_{EV}$, where the first subscript identifies the chain end and the second the incoming monomer. IUPAC defines these monomer reactivity ratios as homopropagation-to-cross-propagation rate-constant ratios.^[ref] Steady-state balance between the two chain-end types gives the familiar binary-model expressionFor an original illustration, stipulate $r_V=0.5$, $r_E=2$ and $f=0.2$. The numerator is 0.18 and denominator 1.62, so $F=1/9\approx 0.111$. These illustrative ratios are not measured kinetic constants for a commercial EVA grade. If both ratios were instead one, this model would give $F=f$ at every reacting-mixture composition.

The composition accumulated over a finite reaction interval is different again. Conversion bookkeeping for binary copolymers follows directly from conservation of monomer units. Normalize the initial total to one mole of units, let $X$ be the total molar conversion, and let $f_0$ and $f$ denote initial and remaining vinyl acetate fractions. Assuming no side losses and incorporation of every consumed monomer, the cumulative fraction isFor $f_0=0.20$, $X=0.50$ and remaining $f=0.30$, the polymer has $\overline{F}=0.10$. It is enriched in ethylene-derived units while the unreacted mixture becomes richer in vinyl acetate. At complete conversion, the overall incorporated fraction must return to $f_0$ under these assumptions, even if individual chains or earlier growth intervals differed.

An informative experiment therefore measures reacting-mixture composition, conversion and product composition separately. A low-conversion approximation needs evidence that composition drift is negligible over the actual interval; an initial feed label alone does not establish the chain composition. Convert incorporated mole fractions to mass fractions only after identifying which composition and reaction interval the measurement represents.