A Medley of Potpourri

Main isotopes			Decay
	abundance	half-life (t_1/2)	mode	product
¹⁷⁷Ta	synth	56.56 h	β⁺	¹⁷⁷Hf
¹⁷⁸Ta	synth	2.36 h	β⁺	¹⁷⁸Hf
¹⁷⁹Ta	synth	1.82 y	ε	¹⁷⁹Hf
¹⁸⁰Ta	synth	8.125 h	ε	¹⁸⁰Hf
¹⁸⁰Ta	synth	8.125 h	β⁻	¹⁸⁰W
^180mTa	0.0120%	stable
¹⁸¹Ta	99.988%	stable
¹⁸²Ta	synth	114.43 d	β⁻	¹⁸²W
¹⁸³Ta	synth	5.1 d	β⁻	¹⁸³W

Tantalum is a chemical element; it has symbol Ta and atomic number 73. It is named after Tantalus, a figure in Greek mythology. Tantalum is a very hard, ductile, lustrous, blue-gray transition metal that is highly corrosion-resistant. It is part of the refractory metals group, which are widely used as components of strong high-melting-point alloys. It is a group 5 element, along with vanadium and niobium, and it always occurs in geologic sources together with the chemically similar niobium, mainly in the mineral groups tantalite, columbite and coltan.

The chemical inertness and very high melting point of tantalum make it valuable for laboratory and industrial equipment such as reaction vessels and vacuum furnaces. It is used in tantalum capacitors for electronic equipment such as computers. It is being investigated for use as a material for high-quality superconducting resonators in quantum processors.

History

Tantalum was discovered in Sweden in 1802 by Anders Ekeberg, in two mineral samples – one from Sweden and the other from Finland. One year earlier, Charles Hatchett had discovered columbium (now niobium). In 1809, the English chemist William Hyde Wollaston compared the oxides of columbium and tantalum, columbite and tantalite. Although the two oxides had different measured densities of 5.918 g/cm³ and 7.935 g/cm³, he concluded that they were identical and kept the name tantalum. After Friedrich Wöhler confirmed these results, it was thought that columbium and tantalum were the same element. This conclusion was disputed in 1846 by the German chemist Heinrich Rose, who argued that there were two additional elements in the tantalite sample, and he named them after the children of Tantalus: niobium (from Niobe), and pelopium (from Pelops). The supposed element "pelopium" was later identified as a mixture of tantalum and niobium, and it was found that the niobium was identical to the columbium already discovered in 1801 by Hatchett.

The differences between tantalum and niobium were demonstrated unequivocally in 1864 by Christian Wilhelm Blomstrand, and Henri Etienne Sainte-Claire Deville, as well as by Louis J. Troost, who determined the empirical formulas of some of their compounds in 1865. Further confirmation came from the Swiss chemist Jean Charles Galissard de Marignac, in 1866, who proved that there were only two elements. These discoveries did not stop scientists from publishing articles about the so-called ilmenium until 1871. De Marignac was the first to produce the metallic form of tantalum in 1864, when he reduced tantalum chloride by heating it in an atmosphere of hydrogen. Early investigators had only been able to produce impure tantalum, and the first relatively pure ductile metal was produced by Werner von Bolton in Charlottenburg in 1903. Wires made with metallic tantalum were used for light bulb filaments until tungsten replaced it in widespread use.

The name tantalum was derived from the name of the mythological Tantalus, the father of Niobe in Greek mythology. In the story, he had been punished after death by being condemned to stand knee-deep in water with perfect fruit growing above his head, both of which eternally tantalized him. (If he bent to drink the water, it drained below the level he could reach, and if he reached for the fruit, the branches moved out of his grasp.) Anders Ekeberg wrote "This metal I call tantalum ... partly in allusion to its incapacity, when immersed in acid, to absorb any and be saturated."

For decades, the commercial technology for separating tantalum from niobium involved the fractional crystallization of potassium heptafluorotantalate away from potassium oxypentafluoroniobate monohydrate, a process that was discovered by Jean Charles Galissard de Marignac in 1866. This method has been supplanted by solvent extraction from fluoride-containing solutions of tantalum.

Characteristics

Physical properties

Tantalum is dark (blue-gray), dense, ductile, very hard, easily fabricated, and highly conductive of heat and electricity. The metal is highly resistant to corrosion by acids: at temperatures below 150 °C tantalum is almost completely immune to attack by the normally aggressive aqua regia. It can be dissolved with hydrofluoric acid or acidic solutions containing the fluoride ion and sulfur trioxide, as well as with molten potassium hydroxide. Tantalum's high melting point of 3017 °C (boiling point 5458 °C) is exceeded among the elements only by tungsten, rhenium and osmium for metals, and carbon.

Tantalum exists in two crystalline phases, alpha and beta. The alpha phase is stable at all temperatures up to the melting point and has body-centered cubic structure with lattice constant a = 0.33029 nm at 20 °C. It is relatively ductile, has Knoop hardness 200–400 HN and electrical resistivity 15–60 μΩ⋅cm. The beta phase is hard and brittle; its crystal symmetry is tetragonal (space group P42/mnm, a = 1.0194 nm, c = 0.5313 nm), Knoop hardness is 1000–1300 HN and electrical resistivity is relatively high at 170–210 μΩ⋅cm. The beta phase is metastable and converts to the alpha phase upon heating to 750–775 °C. Bulk tantalum is almost entirely alpha phase, and the beta phase usually exists as thin films obtained by magnetron sputtering, chemical vapor deposition or electrochemical deposition from a eutectic molten salt solution.

Isotopes

Natural tantalum consists of two stable isotopes: ^180mTa (0.012%) and ¹⁸¹Ta (99.988%). ^180mTa (m denotes a metastable state) is predicted to decay in three ways: isomeric transition to the ground state of ¹⁸⁰Ta, beta decay to ¹⁸⁰W, or electron capture to ¹⁸⁰Hf. However, radioactivity of this nuclear isomer has never been observed, and only a lower limit on its half-life of 2.9×10¹⁷ years has been set. The ground state of ¹⁸⁰Ta has a half-life of only 8 hours. ^180mTa is the only naturally occurring nuclear isomer (excluding radiogenic and cosmogenic short-lived nuclides). It is also the rarest primordial isotope in the Universe, taking into account the elemental abundance of tantalum and isotopic abundance of ^180mTa in the natural mixture of isotopes (and again excluding radiogenic and cosmogenic short-lived nuclides).

Tantalum has been examined theoretically as a "salting" material for nuclear weapons (cobalt is the better-known hypothetical salting material). An external shell of ¹⁸¹Ta would be irradiated by the intensive high-energy neutron flux from a hypothetical exploding nuclear weapon. This would transmute the tantalum into the radioactive isotope ¹⁸²Ta, which has a half-life of 114.4 days and produces gamma rays with approximately 1.12 million electron-volts (MeV) of energy apiece, which would significantly increase the radioactivity of the nuclear fallout from the explosion for several months. Such "salted" weapons have never been built or tested, as far as is publicly known, and certainly never used as weapons.

Tantalum can be used as a target material for accelerated proton beams for the production of various short-lived isotopes including ⁸Li, ⁸⁰Rb, and ¹⁶⁰Yb.

Chemical compounds

Tantalum forms compounds in oxidation states −III to +V. Most commonly encountered are oxides of Ta(V), which includes all minerals. The chemical properties of Ta and Nb are very similar. In aqueous media, Ta only exhibit the +V oxidation state. Like niobium, tantalum is barely soluble in dilute solutions of hydrochloric, sulfuric, nitric and phosphoric acids due to the precipitation of hydrous Ta(V) oxide. In basic media, Ta can be solubilized due to the formation of polyoxotantalate species.

Oxides, nitrides, carbides, sulfides

Tantalum pentoxide (Ta₂O₅) is the most important compound from the perspective of applications. Oxides of tantalum in lower oxidation states are numerous, including many defect structures, and are lightly studied or poorly characterized.

Tantalates, compounds containing [TaO₄]³⁻ or [TaO₃]⁻ are numerous. Lithium tantalate (LiTaO₃) adopts a perovskite structure. Lanthanum tantalate (LaTaO₄) contains isolated TaO³⁻
₄ tetrahedra.

As in the cases of other refractory metals, the hardest known compounds of tantalum are nitrides and carbides. Tantalum carbide, TaC, like the more commonly used tungsten carbide, is a hard ceramic that is used in cutting tools. Tantalum(III) nitride is used as a thin film insulator in some microelectronic fabrication processes.

The best studied chalcogenide is Tantalum sulfide (TaS₂), a layered semiconductor, as seen for other transition metal dichalcogenides. A tantalum-tellurium alloy forms quasicrystals.

Halides

Tantalum halides span the oxidation states of +5, +4, and +3. Tantalum pentafluoride (TaF₅) is a white solid with a melting point of 97.0 °C. The anion [TaF₇]^2- is used for its separation from niobium. The chloride TaCl
₅, which exists as a dimer, is the main reagent in synthesis of new Ta compounds. It hydrolyzes readily to an oxychloride. The lower halides TaX
₄ and TaX
₃, feature Ta-Ta bonds.

Organotantalum compounds

Organotantalum compounds include pentamethyltantalum, mixed alkyltantalum chlorides, alkyltantalum hydrides, alkylidene complexes as well as cyclopentadienyl derivatives of the same. Diverse salts and substituted derivatives are known for the hexacarbonyl [Ta(CO)₆]⁻ and related isocyanides.

Occurrence

Tantalum is estimated to make up about 1 ppm or 2 ppm of the Earth's crust by weight. There are many species of tantalum minerals, only some of which are so far being used by industry as raw materials: tantalite (a series consisting of tantalite-(Fe), tantalite-(Mn) and tantalite-(Mg)), microlite (now a group name), wodginite, euxenite (actually euxenite-(Y)), and polycrase (actually polycrase-(Y)). Tantalite (Fe, Mn)Ta₂O₆ is the most important mineral for tantalum extraction. Tantalite has the same mineral structure as columbite (Fe, Mn) (Ta, Nb)₂O₆; when there is more tantalum than niobium it is called tantalite and when there is more niobium than tantalum is it called columbite (or niobite). The high density of tantalite and other tantalum containing minerals makes the use of gravitational separation the best method. Other minerals include samarskite and fergusonite.

Australia was the main producer of tantalum prior to the 2010s, with Global Advanced Metals (formerly known as Talison Minerals) being the largest tantalum mining company in that country. They operate two mines in Western Australia, Greenbushes in the southwest and Wodgina in the Pilbara region. The Wodgina mine was reopened in January 2011 after mining at the site was suspended in late 2008 due to the global financial crisis. Less than a year after it reopened, Global Advanced Metals announced that due to again "... softening tantalum demand ...", and other factors, tantalum mining operations were to cease at the end of February 2012. Wodgina produces a primary tantalum concentrate which is further upgraded at the Greenbushes operation before being sold to customers. Whereas the large-scale producers of niobium are in Brazil and Canada, the ore there also yields a small percentage of tantalum. Some other countries such as China, Ethiopia, and Mozambique mine ores with a higher percentage of tantalum, and they produce a significant percentage of the world's output of it. Tantalum is also produced in Thailand and Malaysia as a by-product of the tin mining there. During gravitational separation of the ores from placer deposits, not only is cassiterite (SnO₂) found, but a small percentage of tantalite also included. The slag from the tin smelters then contains economically useful amounts of tantalum, which is leached from the slag.

World tantalum mine production has undergone an important geographic shift since the start of the 21st century when production was predominantly from Australia and Brazil. Beginning in 2007 and through 2014, the major sources of tantalum production from mines dramatically shifted to the Democratic Republic of the Congo, Rwanda, and some other African countries. Future sources of supply of tantalum, in order of estimated size, are being explored in Saudi Arabia, Egypt, Greenland, China, Mozambique, Canada, Australia, the United States, Finland, and Brazil.

Status as a conflict resource

Tantalum is considered a conflict resource. Coltan, the industrial name for a columbite–tantalite mineral from which niobium and tantalum are extracted, can also be found in Central Africa, which is why tantalum is being linked to warfare in the Democratic Republic of the Congo (formerly Zaire). According to an October 23, 2003 United Nations report, the smuggling and exportation of coltan has helped fuel the war in the Congo, a crisis that has resulted in approximately 5.4 million deaths since 1998 – making it the world's deadliest documented conflict since World War II. Ethical questions have been raised about responsible corporate behavior, human rights, and endangering wildlife, due to the exploitation of resources such as coltan in the armed conflict regions of the Congo Basin. The United States Geological Survey reports in its yearbook that this region produced a little less than 1% of the world's tantalum output in 2002–2006, peaking at 10% in 2000 and 2008. USGS data published in January 2021 indicated that close to 40% of the world's tantalum mine production came from the Democratic Republic of the Congo, with another 18% coming from neighboring Rwanda and Burundi.

Production and fabrication

Several steps are involved in the extraction of tantalum from tantalite. First, the mineral is crushed and concentrated by gravity separation. This is generally carried out near the mine site.

Refining

The refining of tantalum from its ores is one of the more demanding separation processes in industrial metallurgy. The chief problem is that tantalum ores contain significant amounts of niobium, which has chemical properties almost identical to those of Ta. A large number of procedures have been developed to address this challenge.

In modern times, the separation is achieved by hydrometallurgy. Extraction begins with leaching the ore with hydrofluoric acid together with sulfuric acid or hydrochloric acid. This step allows the tantalum and niobium to be separated from the various non-metallic impurities in the rock. Although Ta occurs as various minerals, it is conveniently represented as the pentoxide, since most oxides of tantalum(V) behave similarly under these conditions. A simplified equation for its extraction is thus:

Ta₂O₅ + 14 HF → 2 H₂[TaF₇] + 5 H₂O

Completely analogous reactions occur for the niobium component, but the hexafluoride is typically predominant under the conditions of the extraction.

Nb₂O₅ + 12 HF → 2 H[NbF₆] + 5 H₂O

These equations are simplified: it is suspected that bisulfate (HSO₄⁻) and chloride compete as ligands for the Nb(V) and Ta(V) ions, when sulfuric and hydrochloric acids are used, respectively. The tantalum and niobium fluoride complexes are then removed from the aqueous solution by liquid-liquid extraction into organic solvents, such as cyclohexanone, octanol, and methyl isobutyl ketone. This simple procedure allows the removal of most metal-containing impurities (e.g. iron, manganese, titanium, zirconium), which remain in the aqueous phase in the form of their fluorides and other complexes.

Separation of the tantalum from niobium is then achieved by lowering the ionic strength of the acid mixture, which causes the niobium to dissolve in the aqueous phase. It is proposed that oxyfluoride H₂[NbOF₅] is formed under these conditions. Subsequent to removal of the niobium, the solution of purified H₂[TaF₇] is neutralised with aqueous ammonia to precipitate hydrated tantalum oxide as a solid, which can be calcined to tantalum pentoxide (Ta₂O₅).

Instead of hydrolysis, the H₂[TaF₇] can be treated with potassium fluoride to produce potassium heptafluorotantalate:

H₂[TaF₇] + 2 KF → K₂[TaF₇] + 2 HF

Unlike H₂[TaF₇], the potassium salt is readily crystallized and handled as a solid.

K₂[TaF₇] can be converted to metallic tantalum by reduction with sodium, at approximately 800 °C in molten salt.

K₂[TaF₇] + 5 Na → Ta + 5 NaF + 2 KF

In an older method, called the Marignac process, the mixture of H₂[TaF₇] and H₂[NbOF₅] was converted to a mixture of K₂[TaF₇] and K₂[NbOF₅], which was then separated by fractional crystallization, exploiting their different water solubilities.

Electrolysis

Tantalum can also be refined by electrolysis, using a modified version of the Hall–Héroult process. Instead of requiring the input oxide and output metal to be in liquid form, tantalum electrolysis operates on non-liquid powdered oxides. The initial discovery came in 1997 when Cambridge University researchers immersed small samples of certain oxides in baths of molten salt and reduced the oxide with electric current. The cathode uses powdered metal oxide. The anode is made of carbon. The molten salt at 1,000 °C (1,830 °F) is the electrolyte. The first refinery has enough capacity to supply 3–4% of annual global demand.

Fabrication and metalworking

All welding of tantalum must be done in an inert atmosphere of argon or helium in order to shield it from contamination with atmospheric gases. Tantalum is not solderable. Grinding tantalum is difficult, especially so for annealed tantalum. In the annealed condition, tantalum is extremely ductile and can be readily formed as metal sheets.

Applications

Electronics

The major use for tantalum, as the metal powder, is in the production of electronic components, mainly capacitors and some high-power resistors. Tantalum electrolytic capacitors exploit the tendency of tantalum to form a protective oxide surface layer, using tantalum powder, pressed into a pellet shape, as one "plate" of the capacitor, the oxide as the dielectric, and an electrolytic solution or conductive solid as the other "plate". Because the dielectric layer can be very thin (thinner than the similar layer in, for instance, an aluminium electrolytic capacitor), a high capacitance can be achieved in a small volume. Because of the size and weight advantages, tantalum capacitors are attractive for portable telephones, personal computers, automotive electronics and cameras.

Alloys

Tantalum is also used to produce a variety of alloys that have high melting points, strength, and ductility. Alloyed with other metals, it is also used in making carbide tools for metalworking equipment and in the production of superalloys for jet engine components, chemical process equipment, nuclear reactors, missile parts, heat exchangers, tanks, and vessels. Because of its ductility, tantalum can be drawn into fine wires or filaments, which are used for evaporating metals such as aluminium.

Tantalum is inert against most acids except hydrofluoric acid and hot sulfuric acid, and hot alkaline solutions also cause tantalum to corrode. This property makes it a useful metal for chemical reaction vessels and pipes for corrosive liquids. Heat exchanging coils for the steam heating of hydrochloric acid are made from tantalum. Tantalum was extensively used in the production of ultra high frequency electron tubes for radio transmitters. Tantalum is capable of capturing oxygen and nitrogen by forming nitrides and oxides and therefore helped to sustain the high vacuum needed for the tubes when used for internal parts such as grids and plates.

Surgical uses

Medical researcher Gerald L. Burke at the Los Angeles Orthopaedic Hospital first discovered in 1938 that tantalum is bio-inert in human tissue and could be used safely as an orthopaedic implant material. Burke also demonstrated perhaps the other most appreciated characteristic of tantalum in surgical procedures: tantalum would permanently bond to bone with no degradation of the surrounding bone. Later, Burke's team working with a team from the California Institute of Technology led by John Norton Wilson showed that tantalum, while hard enough to be fabricated into surgical tools, could also be fabricated in a form sufficiently ductile, yet still sufficiently strong to be drawn into fine threads that could be used for non-scarring sutures. Burke's team in 1940 was the first to propose the use of tantalum for arthroplasty procedures, the repair of intertrochanteric fractures, and for jaw repairs and dental implants. Burke's initial biological research results were confirmed and credited in greater detail by the Harvard Medical School in a series of neurological experiments using powdered tantalum implants. More than 50 years later, researchers were still refining and documenting their understanding of the basic surgical procedures developed by Burke after his pioneering discoveries.

Nowadays, in spite of the cost, tantalum is still widely used in making surgical instruments and implants, and new procedures continue to be developed. For example, porous tantalum coatings are used in the construction of titanium implants due to tantalum's exceptional ability to form a direct bond to hard tissue. Because tantalum is a non-ferrous, non-magnetic metal, tantalum implants are considered to be acceptable for patients undergoing MRI procedures.

Other uses

Bimetallic coins minted by the Bank of Kazakhstan with silver ring and tantalum center. These two feature the Apollo–Soyuz and the International Space Station

Tantalum was used by NASA to shield components of spacecraft, such as Voyager 1 and Voyager 2, from radiation. The high melting point and oxidation resistance led to the use of the metal in the production of vacuum furnace parts. Tantalum is extremely inert and is therefore formed into a variety of corrosion resistant parts, such as thermowells, valve bodies, and tantalum fasteners. Due to its high density, shaped charge and explosively formed penetrator liners have been constructed from tantalum. Tantalum greatly increases the armor penetration capabilities of a shaped charge due to its high density and high melting point. It is also occasionally used in precious watches e.g. from Audemars Piguet, F.P. Journe, Hublot, Montblanc, Omega, and Panerai. Tantalum oxide is used to make special high refractive index glass for camera lenses. Spherical tantalum powder, produced by atomizing molten tantalum using gas or liquid, is commonly used in additive manufacturing due to its uniform shape, excellent flowability, and high melting point.

Environmental issues

Tantalum receives far less attention in the environmental field than it does in other geosciences. Upper Crust Concentration (UCC) and the Nb/Ta ratio in the upper crust and in minerals are available because these measurements are useful as a geochemical tool. The latest value for upper crust concentration is 0.92 ppm, and the Nb/Ta(w/w) ratio stands at 12.7.

Little data is available on tantalum concentrations in the different environmental compartments, especially in natural waters where reliable estimates of ‘dissolved’ tantalum concentrations in seawater and freshwaters have not even been produced. Some values on dissolved concentrations in oceans have been published, but they are contradictory. Values in freshwaters fare little better, but, in all cases, they are probably below 1 ng L⁻¹, since ‘dissolved’ concentrations in natural waters are well below most current analytical capabilities. Analysis requires pre-concentration procedures that, for the moment, do not give consistent results. And in any case, tantalum appears to be present in natural waters mostly as particulate matter rather than dissolved.

Values for concentrations in soils, bed sediments and atmospheric aerosols are easier to come by. Values in soils are close to 1 ppm and thus to UCC values. This indicates detrital origin. For atmospheric aerosols the values available are scattered and limited. When tantalum enrichment is observed, it is probably due to loss of more water-soluble elements in aerosols in the clouds.

Pollution linked to human use of the element has not been detected. Tantalum appears to be a very conservative element in biogeochemical terms, but its cycling and reactivity are still not fully understood.

Precautions

Compounds containing tantalum are rarely encountered in the laboratory. The metal is highly biocompatible and is used for body implants and coatings, therefore attention may be focused on other elements or the physical nature of the chemical compound.

People can be exposed to tantalum in the workplace by breathing it in, skin contact, or eye contact. The Occupational Safety and Health Administration (OSHA) has set the legal limit (permissible exposure limit) for tantalum exposure in the workplace as 5 mg/m³ over an 8-hour workday. The National Institute for Occupational Safety and Health (NIOSH) has set a recommended exposure limit (REL) of 5 mg/m³ over an 8-hour workday and a short-term limit of 10 mg/m³. At levels of 2500 mg/m³, tantalum dust is immediately dangerous to life and health.

Gas

From Wikipedia, the free encyclopedia

Drifting smoke particles indicate the movement of the surrounding gas.

Gas is one of the four fundamental states of matter. The others are solid, liquid, and plasma. A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or compound molecules made from a variety of atoms (e.g. carbon dioxide). A gas mixture, such as air, contains a variety of pure gases. What distinguishes gases from liquids and solids is the vast separation of the individual gas particles. This separation usually makes a colorless gas invisible to the human observer.

The gaseous state of matter occurs between the liquid and plasma states, the latter of which provides the upper-temperature boundary for gases. Bounding the lower end of the temperature scale lie degenerative quantum gases which are gaining increasing attention. High-density atomic gases super-cooled to very low temperatures are classified by their statistical behavior as either Bose gases or Fermi gases. For a comprehensive listing of these exotic states of matter, see list of states of matter.

Elemental gases

The only chemical elements that are stable diatomic homonuclear molecular gases at STP are hydrogen (H₂), nitrogen (N₂), oxygen (O₂), and two halogens: fluorine (F₂) and chlorine (Cl₂). When grouped with the monatomic noble gases – helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and radon (Rn) – these gases are referred to as "elemental gases".

Etymology

The word gas was first used by the early 17th-century Flemish chemist Jan Baptist van Helmont. He identified carbon dioxide, the first known gas other than air. Van Helmont's word appears to have been simply a phonetic transcription of the Ancient Greek word χάος 'chaos' – the g in Dutch being pronounced like ch in "loch" (voiceless velar fricative, /x/) – in which case Van Helmont simply was following the established alchemical usage first attested in the works of Paracelsus. According to Paracelsus's terminology, chaos meant something like 'ultra-rarefied water'.

An alternative story is that Van Helmont's term was derived from "gahst (or geist), which signifies a ghost or spirit". That story is given no credence by the editors of the Oxford English Dictionary. In contrast, the French-American historian Jacques Barzun speculated that Van Helmont had borrowed the word from the German Gäscht, meaning the froth resulting from fermentation.

Physical characteristics

Because most gases are difficult to observe directly, they are described through the use of four physical properties or macroscopic characteristics: pressure, volume, number of particles (chemists group them by moles) and temperature. These four characteristics were repeatedly observed by scientists such as Robert Boyle, Jacques Charles, John Dalton, Joseph Gay-Lussac and Amedeo Avogadro for a variety of gases in various settings. Their detailed studies ultimately led to a mathematical relationship among these properties expressed by the ideal gas law (see § Ideal and perfect gas section below).

Gas particles are widely separated from one another, and consequently, have weaker intermolecular bonds than liquids or solids. These intermolecular forces result from electrostatic interactions between gas particles. Like-charged areas of different gas particles repel, while oppositely charged regions of different gas particles attract one another; gases that contain permanently charged ions are known as plasmas. Gaseous compounds with polar covalent bonds contain permanent charge imbalances and so experience relatively strong intermolecular forces, although the compound's net charge remains neutral. Transient, randomly induced charges exist across non-polar covalent bonds of molecules and electrostatic interactions caused by them are referred to as Van der Waals forces. The interaction of these intermolecular forces varies within a substance which determines many of the physical properties unique to each gas.A comparison of boiling points for compounds formed by ionic and covalent bonds leads us to this conclusion.

Compared to the other states of matter, gases have low density and viscosity. Pressure and temperature influence the particles within a certain volume. This variation in particle separation and speed is referred to as compressibility. This particle separation and size influences optical properties of gases as can be found in the following list of refractive indices. Finally, gas particles spread apart or diffuse in order to homogeneously distribute themselves throughout any container.

Macroscopic view of gases

When observing gas, it is typical to specify a frame of reference or length scale. A larger length scale corresponds to a macroscopic or global point of view of the gas. This region (referred to as a volume) must be sufficient in size to contain a large sampling of gas particles. The resulting statistical analysis of this sample size produces the "average" behavior (i.e. velocity, temperature or pressure) of all the gas particles within the region. In contrast, a smaller length scale corresponds to a microscopic or particle point of view.

Macroscopically, the gas characteristics measured are either in terms of the gas particles themselves (velocity, pressure, or temperature) or their surroundings (volume). For example, Robert Boyle studied pneumatic chemistry for a small portion of his career. One of his experiments related the macroscopic properties of pressure and volume of a gas. His experiment used a J-tube manometer which looks like a test tube in the shape of the letter J. Boyle trapped an inert gas in the closed end of the test tube with a column of mercury, thereby making the number of particles and the temperature constant. He observed that when the pressure was increased in the gas, by adding more mercury to the column, the trapped gas' volume decreased (this is known as an inverse relationship). Furthermore, when Boyle multiplied the pressure and volume of each observation, the product was constant. This relationship held for every gas that Boyle observed leading to the law, (PV=k), named to honor his work in this field.

There are many mathematical tools available for analyzing gas properties. Boyle's lab equipment allowed the use of just a simple calculation to obtain his analytical results. His results were possible because he was studying gases in relatively low pressure situations where they behaved in an "ideal" manner. These ideal relationships apply to safety calculations for a variety of flight conditions on the materials in use. However, the high technology equipment in use today was designed to help us safely explore the more exotic operating environments where the gases no longer behave in an "ideal" manner. As gases are subjected to extreme conditions, tools to interpret them become more complex, from the Euler equations for inviscid flow to the Navier–Stokes equations that fully account for viscous effects. This advanced math, including statistics and multivariable calculus, adapted to the conditions of the gas system in question, makes it possible to solve such complex dynamic situations as space vehicle reentry. An example is the analysis of the space shuttle reentry pictured to ensure the material properties under this loading condition are appropriate. In this flight situation, the gas is no longer behaving ideally.

Pressure

The symbol used to represent pressure in equations is "p" or "P" with SI units of pascals.

When describing a container of gas, the term pressure (or absolute pressure) refers to the average force per unit area that the gas exerts on the surface of the container. Within this volume, it is sometimes easier to visualize the gas particles moving in straight lines until they collide with the container (see diagram at top). The force imparted by a gas particle into the container during this collision is the change in momentum of the particle. During a collision only the normal component of velocity changes. A particle traveling parallel to the wall does not change its momentum. Therefore, the average force on a surface must be the average change in linear momentum from all of these gas particle collisions.

Pressure is the sum of all the normal components of force exerted by the particles impacting the walls of the container divided by the surface area of the wall.

Temperature

The symbol used to represent temperature in equations is T with SI units of kelvins.

The speed of a gas particle is proportional to its absolute temperature. The volume of the balloon in the video shrinks when the trapped gas particles slow down with the addition of extremely cold nitrogen. The temperature of any physical system is related to the motions of the particles (molecules and atoms) which make up the [gas] system. In statistical mechanics, temperature is the measure of the average kinetic energy stored in a molecule (also known as the thermal energy). The methods of storing this energy are dictated by the degrees of freedom of the molecule itself (energy modes). Thermal (kinetic) energy added to a gas or liquid (an endothermic process) produces translational, rotational, and vibrational motion. In contrast, a solid can only increase its internal energy by exciting additional vibrational modes, as the crystal lattice structure prevents both translational and rotational motion. These heated gas molecules have a greater speed range (wider distribution of speeds) with a higher average or mean speed. The variance of this distribution is due to the speeds of individual particles constantly varying, due to repeated collisions with other particles. The speed range can be described by the Maxwell–Boltzmann distribution. Use of this distribution implies ideal gases near thermodynamic equilibrium for the system of particles being considered.

Specific volume

The symbol used to represent specific volume in equations is "v" with SI units of cubic meters per kilogram.

The symbol used to represent volume in equations is "V" with SI units of cubic meters.

When performing a thermodynamic analysis, it is typical to speak of intensive and extensive properties. Properties which depend on the amount of gas (either by mass or volume) are called extensive properties, while properties that do not depend on the amount of gas are called intensive properties. Specific volume is an example of an intensive property because it is the ratio of volume occupied by a unit of mass of a gas that is identical throughout a system at equilibrium. 1000 atoms a gas occupy the same space as any other 1000 atoms for any given temperature and pressure. This concept is easier to visualize for solids such as iron which are incompressible compared to gases. However, volume itself --- not specific --- is an extensive property.

Density

The symbol used to represent density in equations is ρ (rho) with SI units of kilograms per cubic meter. This term is the reciprocal of specific volume.

Since gas molecules can move freely within a container, their mass is normally characterized by density. Density is the amount of mass per unit volume of a substance, or the inverse of specific volume. For gases, the density can vary over a wide range because the particles are free to move closer together when constrained by pressure or volume. This variation of density is referred to as compressibility. Like pressure and temperature, density is a state variable of a gas and the change in density during any process is governed by the laws of thermodynamics. For a static gas, the density is the same throughout the entire container. Density is therefore a scalar quantity. It can be shown by kinetic theory that the density is inversely proportional to the size of the container in which a fixed mass of gas is confined. In this case of a fixed mass, the density decreases as the volume increases.

Microscopic view of gases

If one could observe a gas under a powerful microscope, one would see a collection of particles without any definite shape or volume that are in more or less random motion. These gas particles only change direction when they collide with another particle or with the sides of the container. This microscopic view of gas is well-described by statistical mechanics, but it can be described by many different theories. The kinetic theory of gases, which makes the assumption that these collisions are perfectly elastic, does not account for intermolecular forces of attraction and repulsion.

Kinetic theory of gases

Kinetic theory provides insight into the macroscopic properties of gases by considering their molecular composition and motion. Starting with the definitions of momentum and kinetic energy, one can use the conservation of momentum and geometric relationships of a cube to relate macroscopic system properties of temperature and pressure to the microscopic property of kinetic energy per molecule. The theory provides averaged values for these two properties.

The kinetic theory of gases can help explain how the system (the collection of gas particles being considered) responds to changes in temperature, with a corresponding change in kinetic energy.

For example: Imagine you have a sealed container of a fixed-size (a constant volume), containing a fixed-number of gas particles; starting from absolute zero (the theoretical temperature at which atoms or molecules have no thermal energy, i.e. are not moving or vibrating), you begin to add energy to the system by heating the container, so that energy transfers to the particles inside. Once their internal energy is above zero-point energy, meaning their kinetic energy (also known as thermal energy) is non-zero, the gas particles will begin to move around the container. As the box is further heated (as more energy is added), the individual particles increase their average speed as the system's total internal energy increases. The higher average-speed of all the particles leads to a greater rate at which collisions happen (i.e. greater number of collisions per unit of time), between particles and the container, as well as between the particles themselves.

The macroscopic, measurable quantity of pressure, is the direct result of these microscopic particle collisions with the surface, over which, individual molecules exert a small force, each contributing to the total force applied within a specific area. (Read § Pressure.)

Likewise, the macroscopically measurable quantity of temperature, is a quantification of the overall amount of motion, or kinetic energy that the particles exhibit. (Read § Temperature.)

Thermal motion and statistical mechanics

In the kinetic theory of gases, kinetic energy is assumed to purely consist of linear translations according to a speed distribution of particles in the system. However, in real gases and other real substances, the motions which define the kinetic energy of a system (which collectively determine the temperature), are much more complex than simple linear translation due to the more complex structure of molecules, compared to single atoms which act similarly to point-masses. In real thermodynamic systems, quantum phenomena play a large role in determining thermal motions. The random, thermal motions (kinetic energy) in molecules is a combination of a finite set of possible motions including translation, rotation, and vibration. This finite range of possible motions, along with the finite set of molecules in the system, leads to a finite number of microstates within the system; we call the set of all microstates an ensemble. Specific to atomic or molecular systems, we could potentially have three different kinds of ensemble, depending on the situation: microcanonical ensemble, canonical ensemble, or grand canonical ensemble. Specific combinations of microstates within an ensemble are how we truly define macrostate of the system (temperature, pressure, energy, etc.). In order to do that, we must first count all microstates though use of a partition function. The use of statistical mechanics and the partition function is an important tool throughout all of physical chemistry, because it is the key to connection between the microscopic states of a system and the macroscopic variables which we can measure, such as temperature, pressure, heat capacity, internal energy, enthalpy, and entropy, just to name a few. (Read: Partition function Meaning and significance)

Using the partition function to find the energy of a molecule, or system of molecules, can sometimes be approximated by the Equipartition theorem, which greatly-simplifies calculation. However, this method assumes all molecular degrees of freedom are equally populated, and therefore equally utilized for storing energy within the molecule. It would imply that internal energy changes linearly with temperature, which is not the case. This ignores the fact that heat capacity changes with temperature, due to certain degrees of freedom being unreachable (a.k.a. "frozen out") at lower temperatures. As internal energy of molecules increases, so does the ability to store energy within additional degrees of freedom. As more degrees of freedom become available to hold energy, this causes the molar heat capacity of the substance to increase.

Brownian motion

Brownian motion is the mathematical model used to describe the random movement of particles suspended in a fluid. The gas particle animation, using pink and green particles, illustrates how this behavior results in the spreading out of gases (entropy). These events are also described by particle theory.

Since it is at the limit of (or beyond) current technology to observe individual gas particles (atoms or molecules), only theoretical calculations give suggestions about how they move, but their motion is different from Brownian motion because Brownian motion involves a smooth drag due to the frictional force of many gas molecules, punctuated by violent collisions of an individual (or several) gas molecule(s) with the particle. The particle (generally consisting of millions or billions of atoms) thus moves in a jagged course, yet not so jagged as would be expected if an individual gas molecule were examined.

Intermolecular forces - the primary difference between Real and Ideal gases

Forces between two or more molecules or atoms, either attractive or repulsive, are called intermolecular forces. Intermolecular forces are experienced by molecules when they are within physical proximity of one another. These forces are very important for properly modeling molecular systems, as to accurately predict the microscopic behavior of molecules in any system, and therefore, are necessary for accurately predicting the physical properties of gases (and liquids) across wide variations in physical conditions.

Arising from the study of physical chemistry, one of the most prominent intermolecular forces throughout physics, are van der Waals forces. Van der Waals forces play a key role in determining nearly all physical properties of fluids such as viscosity, flow rate, and gas dynamics (see physical characteristics section). The van der Waals interactions between gas molecules, is the reason why modeling a "real gas" is more mathematically difficult than an "ideal gas". Ignoring these proximity-dependent forces allows a real gas to be treated like an ideal gas, which greatly simplifies calculation.

The intermolecular attractions and repulsions between two gas molecules depend on the distance between them. The combined attractions and repulsions are well-modelled by the Lennard-Jones potential, which is one of the most extensively studied of all interatomic potentials describing the potential energy of molecular systems. Due to the general applicability and importance, the Lennard-Jones model system is often referred to as 'Lennard-Jonesium'.The Lennard-Jones potential between molecules can be broken down into two separate components: a long-distance attraction due to the London dispersion force, and a short-range repulsion due to electron-electron exchange interaction (which is related to the Pauli exclusion principle).

When two molecules are relatively distant (meaning they have a high potential energy), they experience a weak attracting force, causing them to move toward each other, lowering their potential energy. However, if the molecules are too far away, then they would not experience attractive force of any significance. Additionally, if the molecules get too close then they will collide, and experience a very high repulsive force (modelled by Hard spheres) which is a much stronger force than the attractions, so that any attraction due to proximity is disregarded.

As two molecules approach each other, from a distance that is neither too-far, nor too-close, their attraction increases as the magnitude of their potential energy increases (becoming more negative), and lowers their total internal energy. The attraction causing the molecules to get closer, can only happen if the molecules remain in proximity for the duration of time it takes to physically move closer. Therefore, the attractive forces are strongest when the molecules move at low speeds. This means that the attraction between molecules is significant when gas temperatures is low. However, if you were to isothermally compress this cold gas into a small volume, forcing the molecules into close proximity, and raising the pressure, the repulsions will begin to dominate over the attractions, as the rate at which collisions are happening will increase significantly. Therefore, at low temperatures, and low pressures, attraction is the dominant intermolecular interaction.

If two molecules are moving at high speeds, in arbitrary directions, along non-intersecting paths, then they will not spend enough time in proximity to be affected by the attractive London-dispersion force. If the two molecules collide, they are moving too fast and their kinetic energy will be much greater than any attractive potential energy, so they will only experience repulsion upon colliding. Thus, attractions between molecules can be neglected at high temperatures due to high speeds. At high temperatures, and high pressures, repulsion is the dominant intermolecular interaction.

Accounting for the above stated effects which cause these attractions and repulsions, real gases, delineate from the ideal gas model by the following generalization:

At low temperatures, and low pressures, the volume occupied by a real gas, is less than the volume predicted by the ideal gas law.
At high temperatures, and high pressures, the volume occupied by a real gas, is greater than the volume predicted by the ideal gas law.

Mathematical models

An equation of state (for gases) is a mathematical model used to roughly describe or predict the state properties of a gas. At present, there is no single equation of state that accurately predicts the properties of all gases under all conditions. Therefore, a number of much more accurate equations of state have been developed for gases in specific temperature and pressure ranges. The "gas models" that are most widely discussed are "perfect gas", "ideal gas" and "real gas". Each of these models has its own set of assumptions to facilitate the analysis of a given thermodynamic system. Each successive model expands the temperature range of coverage to which it applies.

Ideal and perfect gas

The equation of state for an ideal or perfect gas is the ideal gas law and reads

P V = n R T,

where P is the pressure, V is the volume, n is amount of gas (in mol units), R is the universal gas constant, 8.314 J/(mol K), and T is the temperature. Written this way, it is sometimes called the "chemist's version", since it emphasizes the number of molecules n. It can also be written as

P = ρ R_{s} T,

where $R_{s}$ is the specific gas constant for a particular gas, in units J/(kg K), and ρ = m/V is density. This notation is the "gas dynamicist's" version, which is more practical in modeling of gas flows involving acceleration without chemical reactions.

The ideal gas law does not make an assumption about the heat capacity of a gas. In the most general case, the specific heat is a function of both temperature and pressure. If the pressure-dependence is neglected (and possibly the temperature-dependence as well) in a particular application, sometimes the gas is said to be a perfect gas, although the exact assumptions may vary depending on the author and/or field of science.

For an ideal gas, the ideal gas law applies without restrictions on the specific heat. An ideal gas is a simplified "real gas" with the assumption that the compressibility factor Z is set to 1 meaning that this pneumatic ratio remains constant. A compressibility factor of one also requires the four state variables to follow the ideal gas law.

This approximation is more suitable for applications in engineering although simpler models can be used to produce a "ball-park" range as to where the real solution should lie. An example where the "ideal gas approximation" would be suitable would be inside a combustion chamber of a jet engine. It may also be useful to keep the elementary reactions and chemical dissociations for calculating emissions.

Real gas

Each one of the assumptions listed below adds to the complexity of the problem's solution. As the density of a gas increases with rising pressure, the intermolecular forces play a more substantial role in gas behavior which results in the ideal gas law no longer providing "reasonable" results. At the upper end of the engine temperature ranges (e.g. combustor sections – 1300 K), the complex fuel particles absorb internal energy by means of rotations and vibrations that cause their specific heats to vary from those of diatomic molecules and noble gases. At more than double that temperature, electronic excitation and dissociation of the gas particles begins to occur causing the pressure to adjust to a greater number of particles (transition from gas to plasma). Finally, all of the thermodynamic processes were presumed to describe uniform gases whose velocities varied according to a fixed distribution. Using a non-equilibrium situation implies the flow field must be characterized in some manner to enable a solution. One of the first attempts to expand the boundaries of the ideal gas law was to include coverage for different thermodynamic processes by adjusting the equation to read pVⁿ = constant and then varying the n through different values such as the specific heat ratio, γ.

Real gas effects include those adjustments made to account for a greater range of gas behavior:

Compressibility effects (Z allowed to vary from 1.0)
Variable heat capacity (specific heats vary with temperature)
Van der Waals forces (related to compressibility, can substitute other equations of state)
Non-equilibrium thermodynamic effects
Issues with molecular dissociation and elementary reactions with variable composition.

For most applications, such a detailed analysis is excessive. Examples where real gas effects would have a significant impact would be on the Space Shuttle re-entry where extremely high temperatures and pressures were present or the gases produced during geological events as in the image of the 1990 eruption of Mount Redoubt.

Permanent gas

Permanent gas is a term used for a gas which has a critical temperature below the range of normal human-habitable temperatures and therefore cannot be liquefied by pressure within this range. Historically such gases were thought to be impossible to liquefy and would therefore permanently remain in the gaseous state. The term is relevant to ambient temperature storage and transport of gases at high pressure.

Historical research

Boyle's law

Boyle's law was perhaps the first expression of an equation of state. In 1662 Robert Boyle performed a series of experiments employing a J-shaped glass tube, which was sealed on one end. Mercury was added to the tube, trapping a fixed quantity of air in the short, sealed end of the tube. Then the volume of gas was carefully measured as additional mercury was added to the tube. The pressure of the gas could be determined by the difference between the mercury level in the short end of the tube and that in the long, open end. The image of Boyle's equipment shows some of the exotic tools used by Boyle during his study of gases.

Through these experiments, Boyle noted that the pressure exerted by a gas held at a constant temperature varies inversely with the volume of the gas. For example, if the volume is halved, the pressure is doubled; and if the volume is doubled, the pressure is halved. Given the inverse relationship between pressure and volume, the product of pressure (P) and volume (V) is a constant (k) for a given mass of confined gas as long as the temperature is constant. Stated as a formula, thus is:

P V = k

Because the before and after volumes and pressures of the fixed amount of gas, where the before and after temperatures are the same both equal the constant k, they can be related by the equation:

$P_{1} V_{1} = P_{2} V_{2} .$

Charles's law

In 1787, the French physicist and balloon pioneer, Jacques Charles, found that oxygen, nitrogen, hydrogen, carbon dioxide, and air expand to the same extent over the same 80 kelvin interval. He noted that, for an ideal gas at constant pressure, the volume is directly proportional to its temperature:

\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}

Gay-Lussac's law

In 1802, Joseph Louis Gay-Lussac published results of similar, though more extensive experiments. Gay-Lussac credited Charles' earlier work by naming the law in his honor. Gay-Lussac himself is credited with the law describing pressure, which he found in 1809. It states that the pressure exerted on a container's sides by an ideal gas is proportional to its temperature.

\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}

Avogadro's law

In 1811, Amedeo Avogadro verified that equal volumes of pure gases contain the same number of particles. His theory was not generally accepted until 1858 when another Italian chemist Stanislao Cannizzaro was able to explain non-ideal exceptions. For his work with gases a century prior, the physical constant that bears his name (the Avogadro constant) is the number of atoms per mole of elemental carbon-12 (6.022×10²³ mol⁻¹). This specific number of gas particles, at standard temperature and pressure (ideal gas law) occupies 22.40 liters, which is referred to as the molar volume.

Avogadro's law states that the volume occupied by an ideal gas is proportional to the amount of substance in the volume. This gives rise to the molar volume of a gas, which at STP is 22.4 dm³/mol (liters per mole). The relation is given by $\frac{V_{1}}{n_{1}} = \frac{V_{2}}{n_{2}},$ where n is the amount of substance of gas (the number of molecules divided by the Avogadro constant).

Dalton's law

In 1801, John Dalton published the law of partial pressures from his work with ideal gas law relationship: The pressure of a mixture of non reactive gases is equal to the sum of the pressures of all of the constituent gases alone. Mathematically, this can be represented for n species as:

Pressure_total = Pressure₁ + Pressure₂ + ... + Pressure_n

The image of Dalton's journal depicts symbology he used as shorthand to record the path he followed. Among his key journal observations upon mixing unreactive "elastic fluids" (gases) were the following:

Unlike liquids, heavier gases did not drift to the bottom upon mixing.
Gas particle identity played no role in determining final pressure (they behaved as if their size was negligible).

Special topics

Compressibility

Thermodynamicists use this factor (Z) to alter the ideal gas equation to account for compressibility effects of real gases. This factor represents the ratio of actual to ideal specific volumes. It is sometimes referred to as a "fudge-factor" or correction to expand the useful range of the ideal gas law for design purposes. Usually this Z value is very close to unity. The compressibility factor image illustrates how Z varies over a range of very cold temperatures.

Boundary layer

Particles will, in effect, "stick" to the surface of an object moving through it. This layer of particles is called the boundary layer. At the surface of the object, it is essentially static due to the friction of the surface. The object, with its boundary layer is effectively the new shape of the object that the rest of the molecules "see" as the object approaches. This boundary layer can separate from the surface, essentially creating a new surface and completely changing the flow path. The classical example of this is a stalling airfoil. The delta wing image clearly shows the boundary layer thickening as the gas flows from right to left along the leading edge.

Turbulence

Satellite view of weather pattern in vicinity of Robinson Crusoe Islands on 15 September 1999, shows a turbulent cloud pattern called a Kármán vortex street

In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic, stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time. The satellite view of weather around Robinson Crusoe Islands illustrates one example.

Viscosity

Viscosity, a physical property, is a measure of how well adjacent molecules stick to one another. A solid can withstand a shearing force due to the strength of these sticky intermolecular forces. A fluid will continuously deform when subjected to a similar load. While a gas has a lower value of viscosity than a liquid, it is still an observable property. If gases had no viscosity, then they would not stick to the surface of a wing and form a boundary layer. A study of the delta wing in the Schlieren image reveals that the gas particles stick to one another (see Boundary layer section).

Reynolds number

In fluid mechanics, the Reynolds number is the ratio of inertial forces (v_sρ) which dominate a turbulent flow, to viscous forces (μ/L) which is proportional to viscosity. It is one of the most important dimensionless numbers in fluid dynamics and is used, usually along with other dimensionless numbers, to provide a criterion for determining dynamic similitude. As such, the Reynolds number provides the link between modeling results (design) and the full-scale actual conditions. It can also be used to characterize the flow.

Maximum entropy principle

As the total number of degrees of freedom approaches infinity, the system will be found in the macrostate that corresponds to the highest multiplicity. In order to illustrate this principle, observe the skin temperature of a frozen metal bar. Using a thermal image of the skin temperature, note the temperature distribution on the surface. This initial observation of temperature represents a "microstate". At some future time, a second observation of the skin temperature produces a second microstate. By continuing this observation process, it is possible to produce a series of microstates that illustrate the thermal history of the bar's surface. Characterization of this historical series of microstates is possible by choosing the macrostate that successfully classifies them all into a single grouping.

Thermodynamic equilibrium

When energy transfer ceases from a system, this condition is referred to as thermodynamic equilibrium. Usually, this condition implies the system and surroundings are at the same temperature so that heat no longer transfers between them. It also implies that external forces are balanced (volume does not change), and all chemical reactions within the system are complete. The timeline varies for these events depending on the system in question. A container of ice allowed to melt at room temperature takes hours, while in semiconductors the heat transfer that occurs in the device transition from an on to off state could be on the order of a few nanoseconds.

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