Amobarbital
Amobarbital is a drug, a barbiturate derivative. It has sedative-hypnotic properties, it is a white crystalline powder with no odor and a bitter taste. It was first synthesized in Germany in 1923, it is considered an intermediate acting barbiturate. If amobarbital is taken for extended periods of time and psychological dependence can develop. Amobarbital withdrawal may be life-threatening. Amobarbital was once manufactured by Eli Lilly and Company in the US under the brand name Amytal in bright blue bullet shaped capsule form containing either 50 or 100 mg of the drug, it was abused, known as "blue heavens" on the streets, was discontinued by Eli Lilly in the early 1980s. In an in vitro study in fat thalamic slices amobarbital worked by activating GABAA receptors, which decreased input resistance, depressed burst and tonic firing in ventrobasal and intralaminar neurons, while at the same time increasing burst duration and mean conductance at individual chloride channels. Amobarbital has been used in a study to inhibit mitochondrial electron transport in the rat heart in an attempt to preserve mitochondrial function following reperfusion.
A 1988 study found that amobarbital increases benzodiazepine receptor binding in vivo with less potency than secobarbital and pentobarbital, but greater than phenobarbital and barbital. It has an LD50 in mice of 212 mg/kg s.c. Amobarbital undergoes both hydroxylation to form 3'-hydroxyamobarbital, N-glucosidation to form 1-amobarbital. Anxiety Epilepsy Insomnia Wada test When given by an intravenous route, sodium amobarbital has a reputation for acting as a so-called truth serum. Under the influence, a person will divulge information that under normal circumstances they would block; this was most due to loss of inhibition. As such, the drug was first employed clinically by Dr. William Bleckwenn at the University of Wisconsin to circumvent inhibitions in psychiatric patients; the use of amobarbital as a truth serum has lost credibility due to the discovery that a subject can be coerced into having a "false memory" of the event. The drug may be used intravenously to interview patients with catatonic mutism, sometimes combined with caffeine to prevent sleep.
It was used by the United States armed forces during World War II in an attempt to treat shell shock and return soldiers to the front-line duties. This use has since been discontinued as the powerful sedation, cognitive impairment, dis-coordination induced by the drug reduced soldiers' usefulness in the field. Amobarbital was once manufactured in the US by Eli Lilly Pharmaceuticals under the brand name Amytal in capsule form, it was discontinued in the early 80's replaced by the benzodiazepine family of drugs. Amobarbital was widely abused, known on the streets as "blue heavens" because of their blue capsule; the following drugs should be avoided when taking amobarbital: Antiarrhythmics, such as verapamil and digoxin Antiepileptics, such as phenobarbital or carbamazepine Antihistamines, such as doxylamine and clemastine Antihypertensives, such as atenolol and propranolol EthanolAlcohol https://www.drugs.com/food-interactions/amobarbital.html Benzodiazepines, such as diazepam, nitrazepam,alprazolam,or lorazepam Chloramphenicol Chlorpromazine Cyclophosphamide Ciclosporin Digitoxin Doxorubicin Doxycycline Methoxyflurane Metronidazole Narcotic analgesics, such as morphine and oxycodone Quinine Steroids, such as prednisone and cortisone Theophylline Warfarin Amobarbital has been known to decrease the effects of hormonal birth control, sometimes to the point of uselessness.
Being chemically related to phenobarbital, it might do the same thing to digitoxin, a cardiac glycoside. Some side effects of overdose include confusion. Amobarbital, like all barbiturates, is synthesized by reacting malonic acid derivatives with urea derivatives. In particular, in order to make amobarbital, α-ethyl-α-isoamylmalonic ester is reacted with urea, it has been used to convict alleged murderers such as Andres English-Howard, who strangled his girlfriend to death but claimed innocence. He was surreptitiously administered the drug by his lawyer, under the influence of it he revealed why he strangled her and under what circumstances. On the night of August 28, 1951, the housekeeper of actor Robert Walker found him to be in an emotional state, she called Walker's psychiatrist who administered amobarbital for sedation. Walker was drinking prior to his emotional outburst, it is believed the combination of amobarbital and alcohol resulted in a severe reaction; as a result, he passed out and stopped breathing, all efforts to resuscitate him failed.
Walker died at 32 years old. Eli Lilly manufactured Amobarbital under the brand name Amytal, it was discontinued in the 1980's replaced by the benzodiazepine family of drugs. Amytal was widely abused. Street names for Amobarbital include "blues", "blue angels", "blue birds", "blue devils", "blue heavens" due to their blue capsule. Blue 88 Depressant Tuinal
Jmol
Jmol is computer software for molecular modelling chemical structures in 3-dimensions. Jmol returns a 3D representation of a molecule that may be used as a teaching tool, or for research e.g. in chemistry and biochemistry. It is written in the programming language Java, so it can run on the operating systems Windows, macOS, Unix, if Java is installed, it is free and open-source software released under a GNU Lesser General Public License version 2.0. A standalone application and a software development kit exist that can be integrated into other Java applications, such as Bioclipse and Taverna. A popular feature is an applet that can be integrated into web pages to display molecules in a variety of ways. For example, molecules can be displayed as ball-and-stick models, space-filling models, ribbon diagrams, etc. Jmol supports a wide range of chemical file formats, including Protein Data Bank, Crystallographic Information File, MDL Molfile, Chemical Markup Language. There is a JavaScript-only version, JSmol, that can be used on computers with no Java.
The Jmol applet, among other abilities, offers an alternative to the Chime plug-in, no longer under active development. While Jmol has many features that Chime lacks, it does not claim to reproduce all Chime functions, most notably, the Sculpt mode. Chime requires plug-in installation and Internet Explorer 6.0 or Firefox 2.0 on Microsoft Windows, or Netscape Communicator 4.8 on Mac OS 9. Jmol operates on a wide variety of platforms. For example, Jmol is functional in Mozilla Firefox, Internet Explorer, Google Chrome, Safari. Chemistry Development Kit Comparison of software for molecular mechanics modeling Jmol extension for MediaWiki List of molecular graphics systems Molecular graphics Molecule editor Proteopedia PyMOL SAMSON Official website Wiki with listings of websites and moodles Willighagen, Egon. "Fast and Scriptable Molecular Graphics in Web Browsers without Java3D". Doi:10.1038/npre.2007.50.1
Acetaldehyde
Acetaldehyde is an organic chemical compound with the formula CH3CHO, sometimes abbreviated by chemists as MeCHO. It is one of the most important aldehydes, occurring in nature and being produced on a large scale in industry. Acetaldehyde occurs in coffee and ripe fruit, is produced by plants, it is produced by the partial oxidation of ethanol by the liver enzyme alcohol dehydrogenase and is a contributing cause of hangover after alcohol consumption. Pathways of exposure include air, land, or groundwater, as well as drink and smoke. Consumption of disulfiram inhibits acetaldehyde dehydrogenase, the enzyme responsible for the metabolism of acetaldehyde, thereby causing it to build up in the body; the International Agency for Research on Cancer has listed acetaldehyde as a Group 1 carcinogen. Acetaldehyde is "one of the most found air toxins with cancer risk greater than one in a million". Acetaldehyde was first observed by the Swedish pharmacist/chemist Carl Wilhelm Scheele. In 1835, Liebig named it "aldehyde".
In 2003, global production was about 1 million tonnes. Before 1962, ethanol and acetylene were the major sources of acetaldehyde. Since ethylene is the dominant feedstock; the main method of production is the oxidation of ethylene by the Wacker process, which involves oxidation of ethylene using a homogeneous palladium/copper system: 2 CH2=CH2 + O2 → 2 CH3CHOIn the 1970s, the world capacity of the Wacker-Hoechst direct oxidation process exceeded 2 million tonnes annually. Smaller quantities can be prepared by the partial oxidation of ethanol in an exothermic reaction; this process is conducted over a silver catalyst at about 500–650 °C. CH3CH2OH + 1⁄2 O2 → CH3CHO + H2OThis method is one of the oldest routes for the industrial preparation of acetaldehyde. Prior to the Wacker process and the availability of cheap ethylene, acetaldehyde was produced by the hydration of acetylene; this reaction is catalyzed by mercury salts: C2H2 + Hg2+ + H2O → CH3CHO + HgThe mechanism involves the intermediacy of vinyl alcohol, which tautomerizes to acetaldehyde.
The reaction is conducted at 90–95 °C, the acetaldehyde formed is separated from water and mercury and cooled to 25–30 °C. In the wet oxidation process, iron sulfate is used to reoxidize the mercury back to the mercury salt; the resulting iron sulfate is oxidized in a separate reactor with nitric acid. Traditionally, acetaldehyde was produced by the partial dehydrogenation of ethanol: CH3CH2OH → CH3CHO + H2In this endothermic process, ethanol vapor is passed at 260–290 °C over a copper-based catalyst; the process was once attractive because of the value of the hydrogen coproduct, but in modern times is not economically viable. The hydroformylation of methanol with catalysts like cobalt, nickel, or iron salts produces acetaldehyde, although this process is of no industrial importance. Noncompetitive, acetaldehyde arises from synthesis gas with modest selectivity. Like many other carbonyl compounds, acetaldehyde tautomerizes to give an enol: CH3CH=O ⇌ CH2=CHOH ∆H298,g = +42.7 kJ/molThe equilibrium constant is 6×10−7 at room temperature, thus that the relative amount of the enol form in a sample of acetaldehyde is small.
At room temperature, acetaldehyde is more stable than vinyl alcohol by 42.7 kJ/mol: Overall the keto-enol tautomerization occurs but is catalyzed by acids. Photo-induced keto-enol tautomerization is viable under stratospheric conditions; this photo-tautomerization is relevant to the earth's atmosphere, because vinyl alcohol is thought to be a precursor to carboxylic acids in the atmosphere. Acetaldehyde is a common electrophile in organic synthesis. In condensation reactions, acetaldehyde is prochiral, it is used as a source of the "CH3C+H" synthon in aldol and related condensation reactions. Grignard reagents and organolithium compounds react with MeCHO to give hydroxyethyl derivatives. In one of the more spectacular condensation reactions, three equivalents of formaldehyde add to MeCHO to give pentaerythritol, C4. In a Strecker reaction, acetaldehyde condenses with cyanide and ammonia to give, after hydrolysis, the amino acid alanine. Acetaldehyde can condense with amines to yield imines; these imines can be used to direct subsequent reactions like an aldol condensation.
It is a building block in the synthesis of heterocyclic compounds. In one example, it converts, to 5-ethyl-2-methylpyridine. Three molecules of acetaldehyde condense to form "paraldehyde", a cyclic trimer containing C-O single bonds. Condensation of four molecules of acetaldehyde give the cyclic molecule metaldehyde. Paraldehyde can be produced in good yields. Metaldehyde is only obtained in a few percent yield and with cooling using HBr rather than H2SO4 as the catalyst. At -40 °C in the presence of acid catalysts, polyacetaldehyde is produced. Acetaldehyde forms a stable acetal upon reaction with ethanol under conditions that favor dehydration; the product, CH3CH2, is formally named 1,1-diethoxyethane but is referred to as "acetal". This can cause confusion as "acetal" is more used to describe compounds with the functional groups RCH2 or RR'C2 rather than referring to
Dimer (chemistry)
A dimer is an oligomer consisting of two monomers joined by bonds that can be either strong or weak, covalent or intermolecular. The term homodimer is used when the two molecules are heterodimer when they are not; the reverse of dimerisation is called dissociation. When two oppositely charged ions associate into dimers, they are referred to as Bjerrum pairs. Carboxylic acids form dimers by hydrogen bonding of the acidic hydrogen and the carbonyl oxygen when anhydrous. For example, acetic acid forms a dimer in the gas phase, where the monomer units are held together by hydrogen bonds. Under special conditions, most OH-containing molecules form dimers. Borane occurs as the dimer diborane, due to the high Lewis acidity of the boron center. Excimers and exciplexes are excited structures with a short lifetime. For example, noble gases do not form stable dimers, but do form the excimers Ar2*, Kr2* and Xe2* under high pressure and electrical stimulation. Molecular dimers are formed by the reaction of two identical compounds e.g.: 2A → A-A.
In this example, monomer "A" is said to dimerise to give the dimer "A-A". An example is a diaminocarbene, which dimerise to give a tetraaminoethylene: 2 C2 → 2C=C2Carbenes are reactive and form bonds. Dicyclopentadiene is an asymmetrical dimer of two cyclopentadiene molecules that have reacted in a Diels-Alder reaction to give the product. Upon heating, it "cracks" to give identical monomers: C10H12 → 2 C5H6Many nonmetallic elements occur as dimers: hydrogen, oxygen, the halogens, i.e. fluorine, chlorine and iodine. Noble gases can form dimers linked for example dihelium or diargon. Mercury occurs as a mercury cation, formally a dimeric ion. Other metals may form a proportion of dimers in their vapour. Known metallic dimers include Li2, Na2, K2, Rb2 and Cs2. Many small organic molecules, most notably formaldehyde form dimers; the dimer of formaldehyde is dioxetane. In the context of polymers, "dimer" refers to the degree of polymerization 2, regardless of the stoichiometry or condensation reactions.
This is applicable to disaccharides. For example, cellobiose is a dimer of glucose though the formation reaction produces water: 2C6H12O6 → C12H22O11 + H2OHere, the dimer has a stoichiometry different from the pair of monomers. Amino acids can form dimers, which are called dipeptides. An example is glycylglycine. Other examples are carnosine. Pyrimidine dimers are formed by a photochemical reaction from pyrimidine DNA bases; this cross-linking causes DNA mutations, causing skin cancers. Monomer Trimer Polymer Protein dimer "IUPAC "Gold Book" definition". Retrieved 2009-04-30
Boiling point
The boiling point of a substance is the temperature at which the vapor pressure of a liquid equals the pressure surrounding the liquid and the liquid changes into a vapor. The boiling point of a liquid varies depending upon the surrounding environmental pressure. A liquid in a partial vacuum has a lower boiling point than when that liquid is at atmospheric pressure. A liquid at high pressure has a higher boiling point than when that liquid is at atmospheric pressure. For example, water at 93.4 °C at 1,905 metres altitude. For a given pressure, different liquids will boil at different temperatures; the normal boiling point of a liquid is the special case in which the vapor pressure of the liquid equals the defined atmospheric pressure at sea level, 1 atmosphere. At that temperature, the vapor pressure of the liquid becomes sufficient to overcome atmospheric pressure and allow bubbles of vapor to form inside the bulk of the liquid; the standard boiling point has been defined by IUPAC since 1982 as the temperature at which boiling occurs under a pressure of 1 bar.
The heat of vaporization is the energy required to transform a given quantity of a substance from a liquid into a gas at a given pressure. Liquids may change to a vapor at temperatures below their boiling points through the process of evaporation. Evaporation is a surface phenomenon in which molecules located near the liquid's edge, not contained by enough liquid pressure on that side, escape into the surroundings as vapor. On the other hand, boiling is a process in which molecules anywhere in the liquid escape, resulting in the formation of vapor bubbles within the liquid. A saturated liquid contains as much thermal energy. Saturation temperature means boiling point; the saturation temperature is the temperature for a corresponding saturation pressure at which a liquid boils into its vapor phase. The liquid can be said to be saturated with thermal energy. Any addition of thermal energy results in a phase transition. If the pressure in a system remains constant, a vapor at saturation temperature will begin to condense into its liquid phase as thermal energy is removed.
A liquid at saturation temperature and pressure will boil into its vapor phase as additional thermal energy is applied. The boiling point corresponds to the temperature at which the vapor pressure of the liquid equals the surrounding environmental pressure. Thus, the boiling point is dependent on the pressure. Boiling points may be published with respect to the NIST, USA standard pressure of 101.325 kPa, or the IUPAC standard pressure of 100.000 kPa. At higher elevations, where the atmospheric pressure is much lower, the boiling point is lower; the boiling point increases with increased pressure up to the critical point, where the gas and liquid properties become identical. The boiling point cannot be increased beyond the critical point; the boiling point decreases with decreasing pressure until the triple point is reached. The boiling point cannot be reduced below the triple point. If the heat of vaporization and the vapor pressure of a liquid at a certain temperature are known, the boiling point can be calculated by using the Clausius–Clapeyron equation, thus: T B = − 1, where: T B is the boiling point at the pressure of interest, R is the ideal gas constant, P is the vapour pressure of the liquid at the pressure of interest, P 0 is some pressure where the corresponding T 0 is known, Δ H vap is the heat of vaporization of the liquid, T 0 is the boiling temperature, ln is the natural logarithm.
Saturation pressure is the pressure for a corresponding saturation temperature at which a liquid boils into its vapor phase. Saturation pressure and saturation temperature have a direct relationship: as saturation pressure is increased, so is saturation temperature. If the temperature in a system remains constant, vapor at saturation pressure and temperature will begin to condense into its liquid phase as the system pressure is increased. A liquid at saturation pressure and temperature will tend to flash into its vapor phase as system pressure is decreased. There are two conventions regarding the standard boiling point of water: The normal boiling point is 99.97 °C at a pressure of 1 atm. The IUPAC recommended standard boiling point of water at a standard pressure of 100 kPa is 99.61 °C. For comparison, on top of Mount Everest, at 8,848 m elevation, the pressure is about 34 kPa and the boiling point of water is 71 °C; the Celsius temperature scale was defined until 1954 by two points: 0 °C being defined by the wate
Glycolaldehyde
Glycolaldehyde is the organic compound with the formula HOCH2-CHO. It is the smallest possible molecule that contains both a hydroxyl group, it is a reactive molecule that occurs both in the biosphere and in the interstellar medium. It is supplied as a white solid. Although it conforms to the general formula for carbohydrates, Cnn, it is not considered to be a saccharide. Glycolaldehyde exists; as a solid and molten liquid, it exists as a dimer. In aqueous solution, it exists as a mixture of at least four species, which interconvert, it is the only possible diose, a 2-carbon monosaccharide, although a diose is not a saccharide. While not a true sugar, it is the simplest sugar-related molecule, it is reported to taste sweet. Glycolaldehyde is the second most abundant compound formed. Glycolaldehyde can be synthesized by the oxidation of ethylene glycol using hydrogen peroxide in the presence of Iron sulphate, it can form by action of ketolase on fructose 1,6-bisphosphate in an alternate glycolysis pathway.
This compound is transferred by thiamine pyrophosphate during the pentose phosphate shunt. In purine catabolism, xanthine is first converted to urate; this is converted to 5-hydroxyisourate, which decarboxylates to allantoic acid. After hydrolyzing one urea, this leaves glycolureate. After hydrolyzing the second urea, glycolaldehyde is left. Two glycolaldehydes condense to form erythrose 4-phosphate, which goes to the pentose phosphate shunt again. Glycolaldehyde is an intermediate in the formose reaction. In the formose reaction, two formaldehyde molecules condense to make glycolaldehyde. Glycolaldehyde is converted to glyceraldehyde; the presence of this glycolaldehyde in this reaction demonstrates how it might play an important role in the formation of the chemical building blocks of life. Nucleotides, for example, rely on the formose reaction to attain its sugar unit. Nucleotides are essential for life, because they compose the genetic information and coding for life, it is invoked in theories of abiogenesis.
In the laboratory, it can be converted to amino acids and short dipeptides may have facilitated the formation of complex sugars. For example, L-valyl-L-valine was used as a catalyst to form tetroses from glycolaldehyde. Theoretical calculations have additionally shown the feasibility of dipeptide-catalyzed synthesis of pentoses; this formation showed stereospecific, catalytic synthesis of D-ribose, the only occurring enantiomer of ribose. Since the detection of this organic compound, many theories have been developed related various chemical routes to explain its formation in stellar systems, it was found that UV-irradiation of methanol ices containing CO yielded organic compounds such as glycolaldehyde and methyl formate, the more abundant isomer of glycolaldehyde. The abundances of the products disagree with the observed values found in IRAS 16293-2422, but this can be accounted for by temperature changes. Ethylene Glycol and glycolaldehyde require temperatures above 30 K; the general consensus among the astrochemistry research community is in favor of the grain surface reaction hypothesis.
However, some scientists believe the reaction occurs within colder parts of the core. The dense core will not allow for irradiation; this change will alter the reaction forming glycolaldehyde. The different conditions studied indicate how problematic it could be to study chemical systems that are light-years away; the conditions for the formation of glycolaldehyde are still unclear. At this time, the most consistent formation reactions seems to be on the surface of ice in cosmic dust. Glycolaldehyde has been identified in gas and dust near the center of the Milky Way galaxy, in a star-forming region 26000 light-years from Earth, around a protostellar binary star, IRAS 16293-2422, 400 light years from Earth. Observation of in-falling glycolaldehyde spectra 60 AU from IRAS 16293-2422 suggests that complex organic molecules may form in stellar systems prior to the formation of planets arriving on young planets early in their formation; the interior region of a dust cloud is known to be cold. With temperatures as cold as 4 Kelvin the gases within the cloud will freeze and fasten themselves to the dust, which provides the reaction conditions conducive for the formation of complex molecules such as glycolaldehyde.
When a star has formed from the dust cloud, the temperature within the core will increase. This will cause the molecules on the dust to be released; the molecule will emit radio waves that can be analyzed. The Atacama Large Millimeter/submilliter Array first detected glycolaldehyde. ALMA consists of 66 antennas. On October 23, 2015, researchers at the Paris Observatory announced the discovery of glycolaldehyde and ethyl alcohol on Comet Lovejoy, the first such identification of these substances in a comet. "Cold Sugar in Space Provides Clue to the Molecular Origin of Life". National Radio Astronomy Observatory. September 20, 2004. Retrieved December 20, 2006
Density
The density, or more the volumetric mass density, of a substance is its mass per unit volume. The symbol most used for density is ρ, although the Latin letter D can be used. Mathematically, density is defined as mass divided by volume: ρ = m V where ρ is the density, m is the mass, V is the volume. In some cases, density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more called specific weight. For a pure substance the density has the same numerical value as its mass concentration. Different materials have different densities, density may be relevant to buoyancy and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser. To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative density" or "specific gravity", i.e. the ratio of the density of the material to that of a standard material water.
Thus a relative density less than one means. The density of a material varies with pressure; this variation is small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density. Increasing the temperature of a substance decreases its density by increasing its volume. In most materials, heating the bottom of a fluid results in convection of the heat from the bottom to the top, due to the decrease in the density of the heated fluid; this causes it to rise relative to more dense unheated material. The reciprocal of the density of a substance is called its specific volume, a term sometimes used in thermodynamics. Density is an intensive property in that increasing the amount of a substance does not increase its density. In a well-known but apocryphal tale, Archimedes was given the task of determining whether King Hiero's goldsmith was embezzling gold during the manufacture of a golden wreath dedicated to the gods and replacing it with another, cheaper alloy.
Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated and compared with the mass. Baffled, Archimedes is said to have taken an immersion bath and observed from the rise of the water upon entering that he could calculate the volume of the gold wreath through the displacement of the water. Upon this discovery, he leapt from his bath and ran naked through the streets shouting, "Eureka! Eureka!". As a result, the term "eureka" entered common parlance and is used today to indicate a moment of enlightenment; the story first appeared in written form in Vitruvius' books of architecture, two centuries after it took place. Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time. From the equation for density, mass density has units of mass divided by volume; as there are many units of mass and volume covering many different magnitudes there are a large number of units for mass density in use.
The SI unit of kilogram per cubic metre and the cgs unit of gram per cubic centimetre are the most used units for density. One g/cm3 is equal to one thousand kg/m3. One cubic centimetre is equal to one millilitre. In industry, other larger or smaller units of mass and or volume are more practical and US customary units may be used. See below for a list of some of the most common units of density. A number of techniques as well as standards exist for the measurement of density of materials; such techniques include the use of a hydrometer, Hydrostatic balance, immersed body method, air comparison pycnometer, oscillating densitometer, as well as pour and tap. However, each individual method or technique measures different types of density, therefore it is necessary to have an understanding of the type of density being measured as well as the type of material in question; the density at all points of a homogeneous object equals its total mass divided by its total volume. The mass is measured with a scale or balance.
To determine the density of a liquid or a gas, a hydrometer, a dasymeter or a Coriolis flow meter may be used, respectively. Hydrostatic weighing uses the displacement of water due to a submerged object to determine the density of the object. If the body is not homogeneous its density varies between different regions of the object. In that case the density around any given location is determined by calculating the density of a small volume around that location. In the limit of an infinitesimal volume the density of an inhomogeneous object at a point becomes: ρ = d m / d V, where d V is an elementary volume at position r; the mass of the body t
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