1.
Siwa Oasis
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The Siwa Oasis is an oasis in Egypt, between the Qattara Depression and the Egyptian Sand Sea in the Western Desert, nearly 50 km east of the Libyan border, and 560 km from Cairo. Its fame lies primarily in its ancient role as the home to an oracle of Ammon, historically, it is part of Ancient Libya. The Siwa oasis is in a depression that reaches below sea level. To the west the Jaghbub oasis lies in a similar depression, the oasis was called Ammonium in ancient times. Early Arab geographers termed it Santariyyah and its modern name Siwa, first attested in the 15th century, is of uncertain origin. Although the oasis is known to have settled since at least the 10th millennium BC, the earliest evidence of connection with ancient Egypt is the 26th Dynasty. During the Ptolemaid period of Egypt its ancient Egyptian name was sḫ. t-ỉm3w, Greek settlers at Cyrene made contact with the oasis around the same time, and the oracle temple of Amun, who, Herodotus was told, took the image here of a ram. Herodotus knew of a fountain of the Sun that ran coldest in the noontide heat, during his campaign to conquer the Persian Empire, Alexander the Great reached the oasis, supposedly by following birds across the desert. Evidence of Christianity at Siwa is uncertain, but in 708 the Siwans resisted an Islamic army, a local manuscript mentions only seven families totaling 40 men living at the oasis in 1203. In the 12th century Al-Idrisi mentions it as being inhabited mainly by Berbers, with an Arab minority, the Egyptian historian Al-Maqrizi travelled to Siwa in the 15th century and described how the language spoken there is similar to the language of the Zenata. The first European to visit since Roman times was the English traveler William George Browne, the oasis was officially added to Egypt by Muhammad Ali of Egypt in 1819. In the Spring of 1893, German explorer and photographer, Hermann Burchardt, took photographs of the architecture of the town of Siwa, consequently, Arab rule from distant Cairo was at first tenuous and marked by several revolts. Siwa was also the site of fighting during World War I. The British Armys Long Range Desert Group was based here, German soldiers went skinny dipping in the lake of the oracle, contrary to local customs which prohibit public nudity. In 1942 while the Italian 136th Infantry Division Giovani Fascisti occupied the oasis, the oasis makes a brief appearance as a base of the LRDG in the 1958 war film Ice Cold in Alex. The ancient fortress of Siwa, known as the Shali Ghadi, was built on rock and made of kershif. Only one building in the Shali complex has been repaired and is in use, gradually eroded by infrequent rains and slowly collapsing, the Shali remains a prominent feature, towering five stories above the modern town and lit at night by floodlights. It is most easily approached from its southwest side, south of the end of the road which curves around from the north side of the Shali
2.
Hydrogen
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Hydrogen is a chemical element with chemical symbol H and atomic number 1. With a standard weight of circa 1.008, hydrogen is the lightest element on the periodic table. Its monatomic form is the most abundant chemical substance in the Universe, non-remnant stars are mainly composed of hydrogen in the plasma state. The most common isotope of hydrogen, termed protium, has one proton, the universal emergence of atomic hydrogen first occurred during the recombination epoch. At standard temperature and pressure, hydrogen is a colorless, odorless, tasteless, non-toxic, nonmetallic, since hydrogen readily forms covalent compounds with most nonmetallic elements, most of the hydrogen on Earth exists in molecular forms such as water or organic compounds. Hydrogen plays an important role in acid–base reactions because most acid-base reactions involve the exchange of protons between soluble molecules. In ionic compounds, hydrogen can take the form of a charge when it is known as a hydride. The hydrogen cation is written as though composed of a bare proton, Hydrogen gas was first artificially produced in the early 16th century by the reaction of acids on metals. Industrial production is mainly from steam reforming natural gas, and less often from more energy-intensive methods such as the electrolysis of water. Most hydrogen is used near the site of its production, the two largest uses being fossil fuel processing and ammonia production, mostly for the fertilizer market, Hydrogen is a concern in metallurgy as it can embrittle many metals, complicating the design of pipelines and storage tanks. Hydrogen gas is flammable and will burn in air at a very wide range of concentrations between 4% and 75% by volume. The enthalpy of combustion is −286 kJ/mol,2 H2 + O2 →2 H2O +572 kJ Hydrogen gas forms explosive mixtures with air in concentrations from 4–74%, the explosive reactions may be triggered by spark, heat, or sunlight. The hydrogen autoignition temperature, the temperature of spontaneous ignition in air, is 500 °C, the detection of a burning hydrogen leak may require a flame detector, such leaks can be very dangerous. Hydrogen flames in other conditions are blue, resembling blue natural gas flames, the destruction of the Hindenburg airship was a notorious example of hydrogen combustion and the cause is still debated. The visible orange flames in that incident were the result of a mixture of hydrogen to oxygen combined with carbon compounds from the airship skin. H2 reacts with every oxidizing element, the ground state energy level of the electron in a hydrogen atom is −13.6 eV, which is equivalent to an ultraviolet photon of roughly 91 nm wavelength. The energy levels of hydrogen can be calculated fairly accurately using the Bohr model of the atom, however, the atomic electron and proton are held together by electromagnetic force, while planets and celestial objects are held by gravity. The most complicated treatments allow for the effects of special relativity
3.
PH
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In chemistry, pH is a numeric scale used to specify the acidity or basicity of an aqueous solution. It is approximately the negative of the base 10 logarithm of the concentration, measured in units of moles per liter. More precisely it is the negative of the logarithm to base 10 of the activity of the hydrogen ion, solutions with a pH less than 7 are acidic and solutions with a pH greater than 7 are basic. Pure water is neutral, at pH7, being neither an acid nor a base, contrary to popular belief, the pH value can be less than 0 or greater than 14 for very strong acids and bases respectively. The pH scale is traceable to a set of standard solutions whose pH is established by international agreement, the pH of aqueous solutions can be measured with a glass electrode and a pH meter, or an indicator. In the first papers, the notation had the H as a subscript to the p, as so. The exact meaning of the p in pH is disputed, but according to the Carlsberg Foundation and it has also been suggested that the p stands for the German Potenz, others refer to French puissance. Another suggestion is that the p stands for the Latin terms pondus hydrogenii, potentia hydrogenii and it is also suggested that Sørensen used the letters p and q simply to label the test solution and the reference solution. Currently in chemistry, the p stands for decimal cologarithm of, PH is defined as the decimal logarithm of the reciprocal of the hydrogen ion activity, aH+, in a solution. P H = − log 10 = log 10 For example and this definition was adopted because ion-selective electrodes, which are used to measure pH, respond to activity. For H+ number of electrons transferred is one and it follows that electrode potential is proportional to pH when pH is defined in terms of activity. The reference electrode may be a silver chloride electrode or a calomel electrode, the hydrogen-ion selective electrode is a standard hydrogen electrode. Reference electrode | concentrated solution of KCl || test solution | H2 | Pt Firstly, the cell is filled with a solution of hydrogen ion activity. Then the emf, EX, of the cell containing the solution of unknown pH is measured. PH = pH + E S − E X z The difference between the two measured emf values is proportional to pH and this method of calibration avoids the need to know the standard electrode potential. The proportionality constant, 1/z is ideally equal to 12.303 R T / F the Nernstian slope, to apply this process in practice, a glass electrode is used rather than the cumbersome hydrogen electrode. A combined glass electrode has a reference electrode. It is calibrated against buffer solutions of hydrogen ion activity
4.
Solid
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Solid is one of the four fundamental states of matter. It is characterized by structural rigidity and resistance to changes of shape or volume, unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a gas does. The atoms in a solid are tightly bound to other, either in a regular geometric lattice or irregularly. The branch of physics deals with solids is called solid-state physics. Materials science is concerned with the physical and chemical properties of solids. Solid-state chemistry is concerned with the synthesis of novel materials, as well as the science of identification. The atoms, molecules or ions which make up solids may be arranged in a repeating pattern. Materials whose constituents are arranged in a regular pattern are known as crystals, in some cases, the regular ordering can continue unbroken over a large scale, for example diamonds, where each diamond is a single crystal. Almost all common metals, and many ceramics, are polycrystalline, in other materials, there is no long-range order in the position of the atoms. These solids are known as amorphous solids, examples include polystyrene, whether a solid is crystalline or amorphous depends on the material involved, and the conditions in which it was formed. Solids which are formed by slow cooling will tend to be crystalline, likewise, the specific crystal structure adopted by a crystalline solid depends on the material involved and on how it was formed. While many common objects, such as an ice cube or a coin, are chemically identical throughout, for example, a typical rock is an aggregate of several different minerals and mineraloids, with no specific chemical composition. Wood is an organic material consisting primarily of cellulose fibers embedded in a matrix of organic lignin. In materials science, composites of more than one constituent material can be designed to have desired properties, the forces between the atoms in a solid can take a variety of forms. For example, a crystal of sodium chloride is made up of sodium and chlorine. In diamond or silicon, the atoms share electrons and form covalent bonds, in metals, electrons are shared in metallic bonding. Some solids, particularly most organic compounds, are together with van der Waals forces resulting from the polarization of the electronic charge cloud on each molecule. The dissimilarities between the types of solid result from the differences between their bonding, metals typically are strong, dense, and good conductors of both electricity and heat
5.
Amalgam (chemistry)
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An amalgam is an alloy of mercury with another metal. Almost all metals can form amalgams with mercury, the exceptions being iron, platinum, tungsten. Silver-mercury amalgams are important in dentistry, and gold-mercury amalgam is used in the extraction of gold from ore, zinc amalgam finds use in organic synthesis, e. g. for the Clemmensen Reduction. It is the agent in the Jones reductor, used in analytical chemistry. For the alkali metals, amalgamation is exothermic, and distinct chemical forms can be identified, such as KHg, KHg is a gold-coloured compound with a melting point of 178 °C, and KHg2 a silver-coloured compound with a melting point of 278 °C. These amalgams are very sensitive to air and water, but can be worked with under dry nitrogen, the Hg-Hg distance is around 300 picometres, Hg-K around 358 pm. Phases K5Hg7 and KHg11 are also known, rubidium, strontium and barium undecamercurides are known, sodium amalgam is produced as a by product of the chloralkali process and used as an important reducing agent in organic and inorganic chemistry. With water it decomposes into concentrated sodium hydroxide solution, hydrogen and mercury, if absolutely water-free alcohol is used instead of water, an alkoxide of sodium is produced instead of the alkali solution. Aluminium can form an amalgam through a reaction with mercury, aluminium amalgam may be prepared by either grinding aluminium pellets or wire in mercury, or by allowing aluminium wire or foil to react with a solution of mercuric chloride. This amalgam is used as a reagent to reduce compounds, such as the reduction of imines to amines, the aluminium is the ultimate electron donor, and the mercury serves to mediate the electron transfer. The reaction itself and the waste from it contain mercury, so safety precautions. As an environmentally friendlier alternative, hydrides or other reducing agents can often be used to accomplish the same synthetic result, another environmentally friendly alternative is an alloy of aluminium and gallium which similarly renders the aluminium more reactive by preventing it from forming an oxide layer. Tin amalgam was used in the middle of the 19th century as a mirror coating. A variety of amalgams are known that are of interest mainly in the research context, ammonium amalgam is a grey, soft, spongy mass discovered in 1808 by Humphry Davy and Jöns Jakob Berzelius. Dentistry has used alloys of mercury with metals such as silver, copper, indium, tin, Amalgam is an excellent and versatile restorative material and is used in dentistry for a number of reasons. It is inexpensive and relatively easy to use and manipulate during placement, it remains soft for a time so it can be packed to fill any irregular volume. Amalgam possesses greater longevity compared to other direct restorative materials. However, this difference has decreased with continual development of composite resins, Amalgam is typically compared to resin-based composites because many applications are similar and many physical properties and costs are comparable
6.
Nitrogen
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Nitrogen is a chemical element with symbol N and atomic number 7. It was first discovered and isolated by Scottish physician Daniel Rutherford in 1772, although Carl Wilhelm Scheele and Henry Cavendish had independently done so at about the same time, Rutherford is generally accorded the credit because his work was published first. Nitrogen is the lightest member of group 15 of the periodic table, the name comes from the Greek πνίγειν to choke, directly referencing nitrogens asphyxiating properties. It is an element in the universe, estimated at about seventh in total abundance in the Milky Way. At standard temperature and pressure, two atoms of the element bind to form dinitrogen, a colourless and odorless diatomic gas with the formula N2, dinitrogen forms about 78% of Earths atmosphere, making it the most abundant uncombined element. Nitrogen occurs in all organisms, primarily in amino acids, in the nucleic acids, the human body contains about 3% nitrogen by mass, the fourth most abundant element in the body after oxygen, carbon, and hydrogen. The nitrogen cycle describes movement of the element from the air, into the biosphere and organic compounds, many industrially important compounds, such as ammonia, nitric acid, organic nitrates, and cyanides, contain nitrogen. The extremely strong bond in elemental nitrogen, the second strongest bond in any diatomic molecule. Synthetically produced ammonia and nitrates are key industrial fertilisers, and fertiliser nitrates are key pollutants in the eutrophication of water systems. Apart from its use in fertilisers and energy-stores, nitrogen is a constituent of organic compounds as diverse as Kevlar used in high-strength fabric, Nitrogen is a constituent of every major pharmacological drug class, including antibiotics. Many notable nitrogen-containing drugs, such as the caffeine and morphine or the synthetic amphetamines. Nitrogen compounds have a long history, ammonium chloride having been known to Herodotus. They were well known by the Middle Ages, alchemists knew nitric acid as aqua fortis, as well as other nitrogen compounds such as ammonium salts and nitrate salts. The mixture of nitric and hydrochloric acids was known as aqua regia, celebrated for its ability to dissolve gold, the discovery of nitrogen is attributed to the Scottish physician Daniel Rutherford in 1772, who called it noxious air. Though he did not recognise it as a different chemical substance, he clearly distinguished it from Joseph Blacks fixed air. The fact that there was a component of air that does not support combustion was clear to Rutherford, Nitrogen was also studied at about the same time by Carl Wilhelm Scheele, Henry Cavendish, and Joseph Priestley, who referred to it as burnt air or phlogisticated air. Nitrogen gas was inert enough that Antoine Lavoisier referred to it as air or azote, from the Greek word άζωτικός. In an atmosphere of nitrogen, animals died and flames were extinguished
7.
Caesium
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Caesium or cesium is a chemical element with symbol Cs and atomic number 55. It is a soft, silvery-gold alkali metal with a point of 28.5 °C. Caesium is a metal and has physical and chemical properties similar to those of rubidium and potassium. The metal is extremely reactive and pyrophoric, reacting with water even at −116 °C, Caesium is one of the most reactive elements of all, even more reactive than fluorine, the most reactive nonmetal. It is the least electronegative element, with a value of 0.79 on the Pauling scale and it has only one stable isotope, caesium-133. Caesium is mined mostly from pollucite, while the radioisotopes, especially caesium-137, the German chemist Robert Bunsen and physicist Gustav Kirchhoff discovered caesium in 1860 by the newly developed method of flame spectroscopy. The first small-scale applications for caesium were as a getter in vacuum tubes, since then, caesium has been widely used in highly accurate atomic clocks. The radioactive isotope caesium-137 has a half-life of about 30 years and is used in applications, industrial gauges. Although the element is only toxic, the metal is a hazardous material. It is a ductile, pale metal, which darkens in the presence of trace amounts of oxygen. When in the presence of oil, it loses its metallic lustre and takes on a duller. It has a point of 28.4 °C, making it one of the few elemental metals that are liquid near room temperature. Mercury is the elemental metal with a known melting point lower than caesium. In addition, the metal has a low boiling point,641 °C. Its compounds burn with a blue or violet colour, Caesium forms alloys with the other alkali metals, gold, and mercury. At temperatures below 650 °C, it does not alloy with cobalt, iron, molybdenum, nickel, platinum, tantalum and it forms well-defined intermetallic compounds with antimony, gallium, indium, and thorium, which are photosensitive. It mixes with all the alkali metals, the alloy with a molar distribution of 41% caesium, 47% potassium. A few amalgams have been studied, CsHg 2 is black with a metallic lustre, while CsHg is golden-coloured
8.
Vapor
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A vapor is different from an aerosol. An aerosol is a suspension of particles of liquid, solid. For example, water has a temperature of 647 K. In the atmosphere at ordinary temperatures, therefore, gaseous water will condense into a liquid if its pressure is increased sufficiently. A vapor may co-exist with a liquid, when this is true, the two phases will be in equilibrium, and the gas-partial pressure will be equal to the equilibrium vapor pressure of the liquid. Vapor refers to a gas phase at a temperature where the substance can also exist in the liquid or solid state. If the vapor is in contact with a liquid or solid phase, the term gas refers to a compressible fluid phase. Fixed gases are gases for which no liquid or solid can form at the temperature of the gas, a liquid or solid does not have to boil to release a vapor. Vapor is responsible for the processes of cloud formation and condensation. It is commonly employed to carry out the processes of distillation. The constituent molecules of a vapor possess vibrational, rotational, and these motions are considered in the kinetic theory of gases. The vapor pressure is the pressure from a liquid or a solid at a specific temperature. The equilibrium vapor pressure of a liquid or solid is not affected by the amount of contact with the liquid or solid interface, the normal boiling point of a liquid is the temperature at which the vapor pressure is equal to normal atmospheric pressure. For two-phase systems, the pressure of the individual phases are equal. The total vapor pressure is the sum of the component partial pressures, perfumes contain chemicals that vaporize at different temperatures and at different rate in scent accords known as notes. Atmospheric water vapor is found near the surface, and may condense into small liquid droplets and form meteorological phenomena such as fog, mist. Mercury-vapor lamps and sodium vapor lamps produce light from atoms in excited states, flammable liquids do not burn when ignited. It is the cloud above the liquid that will burn if the vapors concentration is between the lower flammable limit and upper flammable limit of the flammable liquid
9.
Conjugate acid
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A conjugate acid, within the Brønsted–Lowry acid–base theory, is a species formed by the reception of a proton by a base—in other words, it is a base with a hydrogen ion added to it. On the other hand, a base is merely what is left after an acid has donated a proton in a chemical reaction. Hence, a base is a species formed by the removal of a proton from an acid. A proton is a particle with a unit positive electrical charge, it is represented by the symbol H+ because it constitutes the nucleus of a hydrogen atom, that is. A cation can be an acid, and an anion can be a conjugate base, depending on which substance is involved. In an acid-base reaction, an acid plus a base reacts to form a conjugate base plus a conjugate acid, refer to the following figure, We say that the water molecule is the conjugate acid of the hydroxide ion after the latter received the hydrogen proton donated by ammonium. On the other hand, ammonia is the base for the acid ammonium after ammonium has donated a hydrogen ion towards the production of the water molecule. The strength of an acid is directly proportional to its dissociation constant. If a conjugate acid is strong, its dissociation will have an equilibrium constant. The strength of a base can be seen as the tendency of the species to pull hydrogen protons towards itself. If a conjugate base is classified as strong, it will hold on to the hydrogen proton when in solution, if a chemical species is classified as a weak acid, its conjugate base will be strong in nature. This can be observed in ammonias reaction with water, the reaction proceeds until most of the ammonia has been transformed to ammonium. This shift to the right in the equilibrium of the reaction means that ammonium does not dissociate easily in water. On the other hand, if a species is classified as a strong acid, an example of this case would be the dissociation of Hydrochloric acid HCl in water. Since HCl is an acid, its conjugate base will be a weak conjugate base. Therefore, in system, most H+ will be in the form of a Hydronium ion H 3O+ instead of attached to a Cl anion. To summarize, the stronger the acid or base, the weaker the conjugate, the acid and conjugate base as well as the base and conjugate acid are known as conjugate pairs. When finding a conjugate acid or base, it is important to look at the reactants of the chemical equation, to identify the conjugate acid, look for the pair of compounds that are related
10.
Salt (chemistry)
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In chemistry, a salt is an ionic compound that results from the neutralization reaction of an acid and a base. Salts are composed of related numbers of cations and anions so that the product is electrically neutral and these component ions can be inorganic, such as chloride, or organic, such as acetate, and can be monatomic, such as fluoride, or polyatomic, such as sulfate. There are several varieties of salts, salts that hydrolyze to produce hydroxide ions when dissolved in water are alkali salts, whilst those that hydrolyze to produce hydronium ions in water are acidic salts. Neutral salts are those salts that are neither acidic nor basic, zwitterions contain an anionic centre and a cationic centre in the same molecule, but are not considered to be salts. Examples of zwitterions include amino acids, many metabolites, peptides, usually, non-dissolved salts at standard conditions for temperature and pressure are solid, but there are exceptions. Molten salts and solutions containing dissolved salts are called electrolytes, as they are able to conduct electricity. As observed in the cytoplasm of cells, in blood, urine, plant saps and mineral waters, therefore, their salt content is given for the respective ions. Salts can appear to be clear and transparent, opaque, and even metallic, in many cases, the apparent opacity or transparency are only related to the difference in size of the individual monocrystals. Since light reflects from the boundaries, larger crystals tend to be transparent. The color of the salt is due to the electronic structure in the d-orbitals of transition elements or in the conjugated organic dye framework. Different salts can elicit all five basic tastes, e. g. salty, sweet, sour, bitter, and umami or savory. Salts of strong acids and strong bases are non-volatile and odorless and that slow, partial decomposition is usually accelerated by the presence of water, since hydrolysis is the other half of the reversible reaction equation of formation of weak salts. Many ionic compounds can be dissolved in water or other similar solvents, the exact combination of ions involved makes each compound have a unique solubility in any solvent. The solubility is dependent on how well each ion interacts with the solvent, for example, all salts of sodium, potassium and ammonium are soluble in water, as are all nitrates and many sulfates – barium sulfate, calcium sulfate and lead sulfate are examples of exceptions. However, ions that bind tightly to each other and form highly stable lattices are less soluble, for example, most carbonate salts are not soluble in water, such as lead carbonate and barium carbonate. Some soluble carbonate salts are, sodium carbonate, potassium carbonate, solid salts do not conduct electricity. Moreover, solutions of salts also conduct electricity, the name of a salt starts with the name of the cation followed by the name of the anion. Salts are often referred to only by the name of the cation or by the name of the anion. g
11.
Jmol
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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 and it is written in the programming language Java, so it can run on the operating systems Windows, macOS, Linux, and 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 range of chemical file formats, including Protein Data Bank, Crystallographic Information File, MDL Molfile. There is also 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, which is no longer under active development. While Jmol has many features that Chime lacks, it does not claim to reproduce all Chime functions, most notably, Chime requires plug-in installation and Internet Explorer 6.0 or Firefox 2.0 on Microsoft Windows, or Netscape Communicator 4.8 on Mac OS9. Jmol requires Java installation and operates on a variety of platforms. For example, Jmol is fully functional in Mozilla Firefox, Internet Explorer, Opera, Google Chrome, fast and Scriptable Molecular Graphics in Web Browsers without Java3D
12.
Molecular geometry
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Molecular geometry is the three-dimensional arrangement of the atoms that constitute a molecule. It determines several properties of a substance including its reactivity, polarity, phase of matter, color, magnetism and biological activity. The angles between bonds that an atom forms depend only weakly on the rest of molecule, i. e. they can be understood as approximately local, the molecular geometry can be determined by various spectroscopic methods and diffraction methods. IR, microwave and Raman spectroscopy can give information about the molecule geometry from the details of the vibrational and rotational absorbance detected by these techniques. X-ray crystallography, neutron diffraction and electron diffraction can give molecular structure for crystalline solids based on the distance between nuclei and concentration of electron density, gas electron diffraction can be used for small molecules in the gas phase. NMR and FRET methods can be used to determine complementary information including relative distances, dihedral angles, angles, molecular geometries are best determined at low temperature because at higher temperatures the molecular structure is averaged over more accessible geometries. Larger molecules often exist in multiple stable geometries that are close in energy on the energy surface. Geometries can also be computed by ab initio quantum chemistry methods to high accuracy, the molecular geometry can be different as a solid, in solution, and as a gas. The position of each atom is determined by the nature of the bonds by which it is connected to its neighboring atoms. Since the motions of the atoms in a molecule are determined by quantum mechanics, the overall quantum mechanical motions translation and rotation hardly change the geometry of the molecule. In addition to translation and rotation, a type of motion is molecular vibration. The molecular vibrations are harmonic, and the atoms oscillate about their equilibrium positions, at higher temperatures the vibrational modes may be thermally excited, but they oscillate still around the recognizable geometry of the molecule. At 298 K, typical values for the Boltzmann factor β are, β =0.089 for ΔE =500 cm−1, β =0.008 for ΔE =1000 cm−1, β = 7×10−4 for ΔE =1500 cm−1. When an excitation energy is 500 cm−1, then about 8.9 percent of the molecules are excited at room temperature. To put this in perspective, the lowest excitation vibrational energy in water is the bending mode, thus, at room temperature less than 0.07 percent of all the molecules of a given amount of water will vibrate faster than at absolute zero. As stated above, rotation hardly influences the molecular geometry, but, as a quantum mechanical motion, it is thermally excited at relatively low temperatures. From a classical point of view it can be stated that at temperatures more molecules will rotate faster. In quantum mechanical language, more eigenstates of higher angular momentum become thermally populated with rising temperatures, typical rotational excitation energies are on the order of a few cm−1
