A chemical reaction is a process that leads to the transformation of one set of chemical substances to another.Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, often coming about only after the input of some type of energy, viz. heat, light or electricity. Classically, chemical reactions encompass changes that strictly involve the motion of electrons in the forming and breaking of chemical bonds, although the general concept of a chemical reaction, in particular the notion of a chemical equation, is applicable to transformations of elementary particles, as well as nuclear reactions.The substance/substances initially involved in a chemical reaction are called reactants. Chemical reactions are usually characterized by a chemical change, and they yield one or more products, which usually have properties different from the reactants.Different chemical reactions are used in combination in chemical synthesis in order to get a desired product. In biochemistry, series of chemical reactions catalyzed by enzymes form metabolic pathways, by which syntheses and decompositions impossible under ordinary conditions are performed within a cell.

Reaction typesSome common kinds of reactions are listed below. Note that it is perfectly possible for a single reaction to fall under more than one category:Isomerisation, in which a chemical compound undergoes a structural rearrangement without any change in its net atomic composition;

Direct combination or synthesis, in which 2 or more chemical elements or compounds unite to form a more complex product:N2 + 3 H2 → 2 NH3

Chemical decomposition or analysis, in which a compound is decomposed into smaller compounds or elements:2 H2O → 2 H2 + O2

Single displacement or substitution, characterized by an element being displaced out of a compound by a more reactive element:2 Na(s) + 2 HCl (aq) → 2 NaCl(aq) + H2(g)

Metathesis or double displacement reaction, in which two compounds exchange ions or bonds to form different compounds:NaCl(aq) + AgNO3(aq) → NaNO3(aq) + AgCl(s)

Acid-base reactions, broadly characterized as reactions between an acid and a base, can have different definitions depending on the acid-base concept employed. Some of the most common are: Arrhenius definition: Acids dissociate in water releasing H3O+ ions; bases dissociate in water releasing OH- ions.Brønsted-Lowry definition: Acids are proton (H+) donors; bases are proton acceptors. Includes the Arrhenius definition.Lewis definition: Acids are electron-pair acceptors; bases are electron-pair donors. Includes the Brønsted-Lowry definition.Redox reactions , in which changes in oxidation numbers of atoms in involved species occur. Those reactions can often be interpreted as transferences of electrons between different molecular sites or species. An example of a redox reaction is:2 S2O3

2−(aq) + I2(aq) → S4O62−(aq) + 2 I−(aq)

In which I2 is reduced to I- and S2O32- (thiosulfate anion) is oxidized to S4O6

2-.Combustion, a kind of redox reaction in which any combustible substance combines with an oxidizing element, usually oxygen, to generate heat and form oxidized products. The term combustion is usually used for only large-scale oxidation of whole molecules, i.e. a controlled oxidation of a single functional group is not combustion.C10H8+ 12 O2 → 10 CO2 + 4 H2OCH2S + 6 F2 → CF4 + 2 HF + SF6

Disproportionation a redox reaction in which one reactant forming two distinct products varying in oxidation state.2 Sn2+ → Sn + Sn4+

Organic reaction s encompass a wide assortment of reactions involving compounds which have carbon as the main element in their molecular structure. The reactions in which an organic compound may take part are largely defined by its functional groups.

Chemical kinetics The rate of a chemical reaction is a measure of how the concentration or pressure of the involved substances changes with time. Analysis of reaction rates is important for several applications, such as in chemical engineering or in chemical equilibrium study. Rates of reaction depends basically on:Reactant concentrations, which usually make the reaction happen at a faster rate if raised through increased collisions per unit time,Surface area available for contact between the reactants, in particular solid ones in heterogeneous systems. Larger surface area leads to higher reaction rates.Pressure, by increasing the pressure, you decrease the volume between molecules. This will increase the frequency of collisions of molecules.Activation energy, which is defined as the amount of energy required to make the reaction start and carry on spontaneously. Higher activation energy implies that the reactants need more energy to start than a reaction with a lower activation energy.Temperature, which hastens reactions if raised, since higher temperature increases the energy of the molecules, creating more collisions per unit time,The presence or absence of a catalyst. Catalysts are substances which change the pathway (mechanism) of a reaction which in turn increases the speed of a reaction by lowering the activation energy needed for the reaction to take place. A catalyst is not destroyed or changed during a reaction, so it can be used again.For some reactions, the presence of electromagnetic radiation, most notably ultraviolet, is needed to promote the breaking of bonds to start the reaction. This is particularly true for reactions involving radicals.Reaction rates are related to the concentrations of substances involved in reactions, as quantified by the rate law of each reaction. Note that some reactions have rates that are independent of reactant concentrations. These are called zero order reactions.

Reactions and EnergyChemical energy is part of all chemical reactions. Energy is needed to break chemical bonds in the starting substances. As new bonds form in the final substances, energy is released. By comparing the chemical energy of the original substances with the chemical energy of the final substances, you can decide if energy is released or absorbed in the overall reaction.

Exothermic ReactionsA chemical reaction in which energy is released is called an exothermic reaction. Exo means "go out" or "exit." Thermic means "heat" or "energy." Exothermic reactions can give off energy in several forms. If heat is released in an exothermic reaction, the nearby matter will become warmer. The nearby matter absorbs the heat released by the reaction. The reaction between gasoline and oxygen in a car's engine is an exothermic reaction.

Stoichiometry (stoi·chi·om·e·try - stoi'kē-ŏm'ĭ-trē) is a branch of chemistry that deals with the quantitative relationships that exist among the reactants and products in chemical reactions. In a balanced chemical reaction, the relations among quantities of reactants and products typically form a ratio of whole numbers. For example, in a reaction that forms ammonia (NH3), exactly one molecule of nitrogen (N2) reacts with three molecules of hydrogen (H2) to produce two molecules of NH3:N2 + 3H2 → 2NH3

Reaction stoichiometry describes the quantitative relationships among substances as they participate in chemical reactions. In the example above, reaction stoichiometry describes the 1:3:2 ratio of molecules of nitrogen, hydrogen, and ammonia.

Composition stoichiometry describes the quantitative (mass) relationships among elements in compounds. For example, composition stoichiometry describes the nitrogen to hydrogen (mass) relationship in the compound ammonia.Stoichiometry can be used to calculate quantities such as the amount of products that can be produced with given reactants and percent yield (the percentage of the given reactant that is made into the product).

A stoichiometric amount or stoichiometric ratio of a reagent is the amount or ratio where, assuming that the reaction proceeds to completion:all reagent is consumed,there is no shortfall of reagent, andno residues remain.

Gas stoichiometry deals with reactions involving gases, where the gases are at a known temperature, pressure, and volume, and can be assumed to be ideal gasses. For gases, the volume ratio is ideally the same by the ideal gas law, but the mass ratio of a single reaction has to be calculated from the molecular masses of the reactants and products. In practice, due to the existence of isotopes, molar masses are used instead when calculating the mass ratio.While almost all reactions have integer-ratio stoichiometry in amount of matter units (moles, number of particles), some nonstoichiometric compounds are known.Stoichiometry is based on the law of conservation of mass. The mass of the reactants equals the mass of the products.

Different stoichiometries in competing reactionsOften, more than one reaction is possible given the same starting materials. The reactions may differ in their stoichiometry. For example, the methylation of benzene (C6H6), through a Friedel-Crafts reaction using AlCl3 as catalyst, may produce singly-methylated (C6H5CH3), doubly-methylated (C6H4(CH3)2), or still more highly-methylated

products, as shown in the following example,

In this example, which reaction takes place is controlled in part by the relative concentrations of the reactants.

Stoichiometric coefficientIn layman's terms, the stoichiometric coefficient of any given component is the number of molecules which participate in the reaction as written.For example, in the reaction CH4 + 2 O2 → CO2 + 2 H2O, the stoichiometric coefficient of CH4 would be 1 and the stoichiometric coefficient of O2 would be 2.In more technically-precise terms, the stoichiometric coefficient in a chemical reaction system of the i–th component is defined as

or

where Ni is the number of molecules of i, and ξ is the progress variable or extent of reaction (Prigogine & Defay, p. 18; Prigogine, pp. 4–7; Guggenheim, p. 37 & 62).The extent of reaction ξ can be regarded as a real (or hypothetical) product, one molecule of which is produced each time the reaction event occurs. It is the extensive quantity describing the progress of a chemical reaction equal to the number of chemical transformations, as indicated by the reaction equation on a molecular scale, divided by the Avogadro constant (it is essentially the amount of chemical transformations). The change in the extent of reaction is given by dξ = dnB/nB, where nB is the stoichiometric number of any reaction entity B (reactant or product) an dnB is the corresponding amount.[1]

The stoichiometric coefficient νi represents the degree to which a chemical species participates in a reaction. The convention is to assign negative coefficients to reactants (which are consumed) and positive ones to products. However, any reaction may be viewed as "going" in the reverse direction, and all the coefficients then change sign (as does the free energy). Whether a reaction actually will go in the arbitrarily-selected forward direction or not depends on the amounts of the substances present at any given time, which determines the kinetics and thermodynamics, i.e., whether equilibrium lies to the right or the left.If one contemplates actual reaction mechanisms, stoichiometric coefficients will always be integers, since elementary reactions always involve whole molecules. If one uses a composite representation of an "overall" reaction, some may be rational fractions. There are often chemical species present that do not participate in a reaction; their stoichiometric coefficients are therefore zero. Any chemical species that is regenerated, such as a catalyst, also has a stoichiometric coefficient of zero.The simplest possible case is an isomerism

in which νB = 1 since one molecule of B is produced each time the reaction occurs, while νA = −1 since one molecule of A is necessarily consumed. In any chemical reaction, not only is the total mass conserved, but also the numbers of atoms of each kind are conserved, and this imposes a corresponding number of constraints on possible values for the stoichiometric coefficients. Of course, only a small subset of the possible atomic rearrangements will occur.There are usually multiple reactions proceeding simultaneously in any natural reaction system, including those in biology. Since any chemical component can participate in several reactions simultaneously, the stoichiometric coefficient of the i–th component in the k–th reaction is defined as

so that the total (differential) change in the amount of the i–th component is

.Extents of reaction provide the clearest and most explicit way of representing compositional change, although they are not yet widely used.

With complex reaction systems, it is often useful to consider both the representation of a reaction system in terms of the amounts of the chemicals present { Ni } (state variables), and the representation in terms of the actual compositional degrees of freedom, as expressed by the extents of reaction { ξk }. The transformation from a vector expressing the extents to a vector expressing the amounts uses a rectangular matrix whose elements are the stoichiometric coefficients [ νi k ].The maximum and minimum for any ξk occur whenever the first of the reactants is depleted for the forward reaction; or the first of the "products" is depleted if the reaction as viewed as being pushed in the reverse direction. This is a purely kinematic restriction on the reaction simplex, a hyperplane in composition space, or N-space, whose dimensionality equals the number of linearly-independent chemical reactions. This is necessarily less than the number of chemical components, since each reaction manifests a relation between at least two chemicals. The accessible region of the hyperplane depends on the amounts of each chemical species actually present, a contingent fact. Different such amounts can even generate different hyperplanes, all of which share the same algebraic stoichiometry.In accord with the principles of chemical kinetics and thermodynamic equilibrium, every chemical reaction is reversible, at least to some degree, so that each equilibrium point must be an interior point of the simplex. As a consequence, extrema for the ξ's will not occur unless an experimental system is prepared with zero initial amounts of some products.The number of physically-independent reactions can be even greater than the number of chemical components, and depends on the various reaction mechanisms. For example, there may be two (or more) reaction paths for the isomerism above. The reaction may occur by itself, but faster and with different intermediates, in the presence of a catalyst.The (dimensionless) "units" may be taken to be molecules or moles. Moles are most commonly used, but it is more suggestive to picture incremental chemical reactions in terms of molecules. The N's and ξ's are reduced to molar units by dividing by Avogadro's number. While dimensional mass units may be used, the comments about integers are then no longer applicable.

Stoichiometry matrixIn complex reactions, stoichiometries are often represented in a more compact form called the stoichiometry matrix. The stoichiometry matrix is denoted by the symbol,

.If a reaction network has n reactions and m participating molecular species then the stoichiometry matrix will have corresponding n columns and m rows.For example, consider the system of reactions shown below:S1 → S2

5S3 + S2 → 4S3 + 2S2

S3 → S4

S4 → S5.This systems comprises four reactions and five different molecular species. The stoichiometry matrix for this system can be written as:

where the rows correspond to S1, S2, S3, S4 and S5, respectively. Note that the process of converting a reaction scheme into a stoichiometry matrix can be a lossy transformation, for example, the stoichiometries in the second reaction simplify when included in the matrix. This means that it is not always possible to recover the original reaction scheme from a stoichiometry matrix.Often the stoichiometry matrix is combined with the rate vector, v to form a compact equation describing the rates of change of the molecular species:

Gas stoichiometryGas stoichiometry is the quantitative relationship (ratio) between reactants and products in a chemical reaction with reactions that produce gases. Gas stoichiometry applies when the gases produced are assumed to be ideal, and the temperature, pressure, and volume of the gases are all known. The ideal gas law is used for these calculations. Often, but not always, the standard temperature and pressure (STP) are taken as 0°C and 1 bar and used as the conditions for gas stoichiometric calculations.Gas stoichiometry calculations solve for the unknown volume or mass of a gaseous product or reactant. For example, if we wanted to calculate the volume of gaseous NO2 produced from the combustion of 100 g of NH3, by the reaction:4NH3 (g) + 7O2 (g) → 4NO2 (g) + 6H2O (l)we would carry out the following calculations:

There is a 1:1 molar ratio of NH3 to NO2 in the above balanced combustion reaction, so 5.871 mol of NO2 will be formed. We will employ the ideal gas law to solve for the volume at 0 °C (273.15 K) and 1 atmosphere using the gas law constant of R = 0.08206 L · atm · K−1 · mol−1 :

PV = nRT

V

Gas stoichiometry often involves having to know the molar mass of a gas, given the density of that gas. The ideal gas law can be re-arranged to obtain a relation between the density and the molar mass of an ideal gas:

and and thus:

where:

P = absolute gas pressure

V = gas volume

n = number of moles

R = universal ideal gas law constant

T = absolute gas temperature

ρ = gas density at T and P

m = mass of gas

M = molar mass of gas Stoichiometric air-fuel ratios of common fuelsFuel By mass By volume [2] Percent fuel by massGasoline 14.7 : 1 — 6.8%Natural gas 17.2 : 1 9.7 : 1 5.8%Propane (LP) 15.5 : 1 23.9 : 1 6.45%Ethanol 9 : 1 — 11.1%Methanol 6.4 : 1 — 15.6%Hydrogen 34 : 1 2.39 : 1 2.9%Diesel 14.6 : 1 0.094 : 1 6.8%Gasoline engines are run at stoichiometric air-to-fuel ratio, because gasoline is so volatile that mixes properly with the air. Diesel engines, in contrast, run lean, with more air available than simple stoichiometry would require. Diesel fuel is heavier and does not burn immediately to give gaseous products. Thus, it would form soot (black smoke) at stoichiometric ratio.

Atomic weight (symbol: Ar) is a dimensionless physical quantity, the ratio of the average mass of atoms of an element (from a given source) to 1/12 of the mass of an atom of carbon-12 (known as the unified atomic mass unit).[1][2] The term is usually used, without further qualification, to refer to the standard atomic weights published at regular intervals by the International Union of Pure and Applied Chemistry (IUPAC)[3][4] and which are intended to be applicable to normal laboratory materials. These standard atomic weights are reprinted in a wide variety of textbooks, commercial catalogues, wallcharts etc, and in the table below. The fact "relative atomic mass of the element" may also be used to describe this physical quantity, and indeed the continued use of the term "atomic weight" has attracted considerable controversy since at least the 1960s[5] (see below).Atomic weights, unlike atomic masses (the masses of individual atoms), are not physical constants and vary from sample to sample. Nevertheless, they are sufficiently constant in "normal" samples to be of fundamental importance in chemistry.

Determination of atomic weight

Modern atomic weights are calculated from measured values of atomic mass (for each nuclide) and isotopic composition. Highly accurate atomic masses are available[9][10] for virtually all non-radioactive nuclides, but isotopic compositions are both harder to measure to high precision and more subject to variation between samples. [11][12] For this reason, the atomic weights of the twenty-two mononuclidic elements are known to especially high accuracy – an uncertainty of only one part in 38 million in the case of fluorine, a precision which is greater than the current best value for the Avogadro constant (one part in 20 million).

The calculation is exemplified for silicon, whose atomic weight is especially important in metrology. Silicon exists in nature as a mixture of three isotopes: 28Si, 29Si and 30Si. The atomic masses of these nuclides are known to a precision of one part in 14 billion for 28Si and about one part in one billion for the others. However the range of natural abundance for the isotopes is such that the standard abundance can only be given to about ±0.001% (see table). The calculation is

Ar(Si) = (27.97693 × 0.922297) + (28.97649 × 0.046832) + (29.97377 × 0.030872) = 28.0854

The estimation of the uncertainty is complicated[13], especially as the sample distribution is not necessarily symmetrical: the IUPAC standard atomic weights are quoted with estimated symmetrical uncertainties,[14] and the value for silicon is 28.0855(3). The relative standard uncertainty in this value is 1 × 10–5 or 10 ppm.

Definition

There are varying interpretations of this definition. Many chemists use molecular mass as a synonym of molar mass,[3] differing only in units (see average molecular mass below). A stricter interpretation does not equate the two, as the mass of a single molecule is not the same as the average of an ensemble. Because a mole of molecules may contain a variety of molecular masses due to natural isotopes, the average mass is usually not identical to the mass of any single molecule. The actual numerical difference can be very small when considering small molecules and the molecular mass of the most common isotopomer in which case the error only matters to physicists and a small subset of highly specialized chemists; however it is always more correct, accurate and consistent to use molar mass in any bulk stoichiometric calculations. The size of this error becomes much larger when considering larger molecules or less abundant isotopomers. The molecular mass of a molecule which happens to contain heavier isotopes than the average molecule in the sample can differ from the molar mass by several mass units. Also the molar mass comes into comparison with the number of particles contained within the structure by multiplying the number of moles by Avogadro's constant: NA=6.022 141 79(30)ˑ1023 mol−1.

Average mass

The average molecular mass (sometimes abbreviated as average mass) is another variation on the use of the term molecular mass. The average molecular mass is the abundance weighted mean (average) of the molecular masses in a sample. This is often closer to what is meant when "molecular mass" and "molar mass" are used synonymously and may have derived from shortening of this term. The average molecular mass and the molar mass of a particular substance in a particular sample are in

Isotope Atomic mass[10] Abundance[11]

Standard Range28Si 27.976 926 532 46(194) 92.2297(7)% 92.21–92.25%29Si 28.976 494 700(22) 4.6832(5)% 4.69–4.67%30Si 29.973 770 171(32) 3.0872(5)% 3.10–3.08%

fact numerically identical and may be interconverted by Avogadro's constant. It should be noted, however, that the molar mass is almost always a computed figure derived from the standard atomic weights, whereas the average molecular mass, in fields that need the term, is often a measured figure specific to a sample. Therefore, they often vary since one is theoretical and the other is experimental. Specific samples may vary significantly from the expected isotopic composition due to real deviations from earth's average isotopic abundances.

Computation

The molecular mass can be calculated as the sum of the individual isotopic masses (as found in a table of isotopes) of all the atoms in any molecule. This is possible because molecules are created by chemical reactions which, unlike nuclear reactions, have very small binding energies compared to the rest mass of the atoms ( < 10−9) and therefore create a negligible mass defect. The use of average atomic masses derived from the standard atomic weights found on a standard periodic table will result in an average molecular mass, whereas the use of isotopic masses will result in a molecular mass consistent with the strict interpretation of the definition, i.e. that of a single molecule. However, any given molecule may contain any given combination of isotopes, so there may be multiple molecular masses for each chemical compound.

Measurement

The molecular mass can also be measured directly using mass spectrometry. In mass spectrometry, the molecular mass of a small molecule is usually reported as the monoisotopic mass, that is, the mass of the molecule containing only the most common isotope of each element. Note that this also differs subtly from the molecular mass in that the choice of isotopes is defined and thus is a single specific molecular mass of the many possible. The masses used to compute the monoisotopic molecular mass are found on a table of isotopic masses and are not found on a typical periodic table. The average molecular mass is often used for larger molecules since molecules with many atoms are unlikely to be composed exclusively of the most abundant isotope of each element. A theoretical average molecular mass can be calculated using the standard atomic weights found on a typical periodic table, since there is likely to be a statistical distribution of atoms representing the isotopes throughout the molecule. This however may differ from the true average molecular mass of the sample due to natural (or artificial) variations in the isotopic distributions.

The basis for determination of molecular weight according to the Staudinger method (since replaced by the more general Mark-Houwink equation[4]) is the fact that relative viscosity of suspensions depends on volumetric proportion of solid particles.

Unit type variation

The molar mass of a substance is the mass of 1 mol (the SI unit for the basis SI quantity amount of substance, having the symbol n) of the substance. This has a numerical value which is the average molecular mass of the molecules in the substance multiplied by Avogadro's constant approximately 6.022*1023. The most common units of molar mass are g/mol because in those units the numerical value equals the average molecular mass in units of u.

Conversion factor of average molecular mass to molar mass:

molar mass = average molecular mass * ((1/6.022)*10-23g/u)*(6.022*1023/mol)ormolar mass in g/mol= average molecular mass in u

(Note that these relations are true for theoretical and experimental values, but not between experimental and theoretical values. Molar mass is most often theoretical and average molecular mass is most often experimental)

The average atomic mass of natural hydrogen is 1.00794 u and that of natural oxygen is 15.9994 u; therefore, the molecular mass of natural water with formula H2O is (2 × 1.00794 u) + 15.9994 u = 18.01528 u. Therefore, one mole of water has a mass of 18.01528 grams. However, the exact mass of hydrogen-1 (the most common hydrogen isotope) is 1.00783, and the exact mass of oxygen-16 (the most common oxygen isotope) is 15.9949, so the mass of the most common molecule of water is 18.01056 u. The difference of 0.00472 u or 0.03% comes from the fact that natural water contain traces of water molecules containing, oxygen-17, oxygen-18 or hydrogen-2 (Deuterium) atoms. Although this difference is trivial in bulk chemistry calculations, it can result in complete failure in situations where the behavior of individual molecules matters, such as in mass spectrometry and particle physics (where the mixture of isotopes does not act as an average).

There are also situations where the isotopic distributions are not typical such as with heavy water used in some nuclear reactors which is artificially enriched with Deuterium. In these cases the computed values of molar mass and average molecular mass, which are ultimately derived from the standard atomic weights, will not be the same as the actual molar mass or average molecular mass of the sample. In this case the mass of deuterium is 2.0136 u and the average molecular mass of this water (assuming 100% deuterium enrichment) is (2 × 2.0136 u) + 15.9994 u = 20.0266 u. This is a very large difference of ~11% error from the expected average molecular mass based on the standard atomic weights. Furthermore the most abundant molecular mass is actually slightly less than the average molecular mass since oxygen-16 is still the most common. (2 × 2.0136 u) + 15.9949 u = 20.0221 u. Although this is an extreme artificial example, natural variation in isotopic distributions do occur and are measurable. For example, the atomic weight of lithium as found by isotopic analysis of 39 lithium reagents from several manufacturers varied from 6.939 to 6.996. [5]

A chemical bond is an attraction between atoms or molecules and allows the formation of chemical compounds, which contain two or more atoms. A chemical bond is the attraction caused by the electromagnetic force between opposing charges, either between electrons and nuclei, or as the result of a dipole attraction. The strength of bonds varies considerably; there are "strong bonds" such as covalent or ionic bonds and "weak bonds" such as dipole-dipole interactions, the London dispersion force and hydrogen bonding.Since opposite charges attract via a simple electromagnetic force, the negatively charged electrons orbiting the nucleus and the positively charged protons in the nucleus attract each other. Also, an electron positioned between two nuclei will be attracted to both of them. Thus, the most stable configuration of nuclei and electrons is one in which the electrons spend more time between nuclei, than anywhere else in space. These electrons cause the nuclei to be attracted to each other, and this attraction results in the bond. However, this assembly cannot collapse to a size dictated by the volumes of these individual particles. Due to the matter wave nature of electrons and their smaller mass, they occupy a very much larger amount of volume compared with the nuclei, and this volume occupied by the electrons keeps the atomic nuclei relatively far apart, as compared with the size of the nuclei themselves.In general, strong chemical bonding is associated with the sharing or transfer of electrons between the participating atoms. Molecules, crystals, and diatomic gases— indeed most of the physical environment around us— are held together by chemical bonds, which dictate the structure of matter.

In the simplest view of a so-called covalent bond , one or more electrons (often a pair of electrons) are drawn into the space between the two atomic nuclei. Here the negatively charged electrons are attracted to the positive charges of both nuclei, instead of just their own. This overcomes the repulsion between the two positively charged nuclei of the two atoms, and so this overwhelming attraction holds the two nuclei in a fixed configuration of equilibrium, even though they will still vibrate at equilibrium position. In summary, covalent bonding involves sharing of electrons in which the positively charged nuclei of two or more atoms simultaneously attract the negatively charged electrons that are being shared. In a polar covalent bond, one or more electrons are unequally shared between two nuclei.In a simplified view of an ionic bond , the bonding electron is not shared at all, but transferred. In this type of bond, the outer atomic orbital of one atom has a vacancy which allows addition of one or more electrons. These newly added electrons potentially occupy a lower energy-state (effectively closer to more nuclear charge) than they experience in a different atom. Thus, one nucleus offers a more tightly bound position to an electron than does another nucleus, with the result that one atom may transfer an electron to the other. This transfer causes one atom to assume a net positive charge, and the other to assume a net negative charge. The bond then results from electrostatic attraction between atoms, and the atoms become positive or negatively charged ions.All bonds can be explained by quantum theory, but, in practice, simplification rules allow chemists to predict the strength, directionality, and polarity of bonds. The octet rule and VSEPR theory are two examples. More sophisticated theories are valence bond theory which includes orbital hybridization and resonance, and the linear combination of atomic orbitals molecular orbital method which includes ligand field theory. Electrostatics are used to describe bond polarities and the effects they have on chemical substances.

HistoryEarly speculations into the nature of the chemical bond, from as early as the 12th century, supposed that certain types of chemical species were joined by a type of chemical affinity. In 1704, Isaac Newton famously outlined his atomic bonding theory, in "Query 31" of his Opticks, whereby atoms attach to each other by some "force". Specifically, after acknowledging the various popular theories in vogue at the time, of how atoms were reasoned to attach to each other, i.e. "hooked atoms", "glued together by rest", or "stuck together by conspiring motions", Newton states that he would rather infer from their cohesion, that "particles attract one another by some force, which in immediate contact is exceedingly strong, at small distances performs the chemical operations, and reaches not far from the particles with any sensible effect."In 1819, on the heels of the invention of the voltaic pile, Jöns Jakob Berzelius developed a theory of chemical combination stressing the electronegative and electropositive character of the combining atoms. By the mid 19th century, Edward Frankland, F.A. Kekule, A.S. Couper, A.M. Butlerov, and Hermann Kolbe, building on the theory of radicals, developed the theory of valency, originally called "combining power", in which compounds were joined owing to an attraction of positive and negative poles. In 1916, chemist Gilbert N. Lewis developed the concept of the electron-pair bond, in which two atoms may share one to six electrons, thus forming the single electron bond, a single bond, a double bond, or a triple bond; in Lewis's own words, "An electron may form a part of the shell of two different atoms and cannot be said to belong to either one exclusively."[1]

That same year, Walther Kossel put forward a theory similar to Lewis' only his model assumed complete transfers of electrons between atoms, and was thus a model of ionic bonds. Both Lewis and Kossel structured their bonding models on that of Abegg's rule (1904).In 1927, the first mathematically complete quantum description of a simple chemical bond, i.e. that produced by one electron in the hydrogen molecular ion, H2

+, was derived by the Danish physicist Oyvind Burrau.[2] This work showed that the quantum approach to chemical bonds could be fundamentally and quantitatively correct, but the mathematical methods used could not be extended to molecules containing more than one electron. A more practical, albeit less quantitative, approach was put forward in the same year by Walter Heitler and Fritz London. The Heitler-London method forms the basis of what is now called valence bond theory. In 1929, the linear combination of atomic orbitals molecular orbital method (LCAO) approximation was introduced by Sir John Lennard-Jones, who also suggested methods to derive electronic structures of molecules of F2 (fluorine) and O2 (oxygen) molecules, from basic quantum principles. This molecular orbital theory represented a covalent bond as an orbital formed by combining the quantum mechanical Schrödinger atomic orbitals which had been hypothesized for electrons in single atoms. The equations for bonding electrons in multi-electron atoms could not be solved to mathematical perfection (i.e., analytically), but approximations for them still gave many good qualitative predictions and results. Most quantitative calculations in modern quantum chemistry use either valence bond or molecular orbital theory as a starting point, although a third approach, Density Functional Theory, has become increasingly popular in recent years.In 1935, H. H. James and A. S. Coolidge carried out a calculation on the dihydrogen molecule that, unlike all previous calculation which used functions only of the distance of the electron from the atomic nucleus, used functions which also explicitly added the distance between the two electrons.[3] With up to 13 adjustable parameters they obtained a result very close to the experimental result for the dissociation energy. Later extensions have used up to 54 parameters and give excellent agreement with experiment. This calculation convinced the scientific community that quantum theory could give agreement with experiment. However this approach has none of the physical pictures of the valence bond and molecular orbital theories and is difficult to extend to larger molecules.

Valence bond theoryIn 1927, valence bond theory was formulated and argued that a chemical bond forms when two valence electrons, in their respective atomic orbitals, work or function to hold two nuclei together, by virtue of system energy lowering effects. Building on this theory, chemist Linus Pauling published in 1931 what some consider one of the most important papers in the history of chemistry: "On the Nature of the Chemical Bond". In this paper, elaborating on the works of Lewis, and the valence bond theory (VB) of Heitler and London, and his own earlier work, he presented six rules for the shared electron bond, the first three of which were already generally known:

1. The electron-pair bond forms through the interaction of an unpaired electron on each of two atoms.2. The spins of the electrons have to be opposed.3. Once paired, the two electrons cannot take part in additional bonds.His last three rules were new:4. The electron-exchange terms for the bond involves only one wave function from each atom.5. The available electrons in the lowest energy level form the strongest bonds.6. Of two orbitals in an atom, the one that can overlap the most with an orbital from another atom will form the strongest bond, and this bond will tend to lie in the direction of the concentrated orbital.Building on this article, Pauling's 1939 textbook: On the Nature of the Chemical Bond would become what some have called the "bible" of modern chemistry. This book helped experimental chemists to understand the impact of quantum theory on chemistry. However, the later edition in 1959 failed to address adequately the problems that appeared to be better understood by molecular orbital theory. The impact of valence theory declined during the 1960s and 1970s as molecular orbital theory grew in popularity and was implemented in many large computer programs. Since the 1980s, the more difficult problems of implementing valence bond theory into computer programs have been largely solved and valence bond theory has seen a resurgence.

Comparison of valence bond and molecular orbital theoryIn some respects valence bond theory is superior to molecular orbital theory. When applied to the simplest two-electron molecule, H2, valence bond theory, even at the simplest Heitler-London approach, gives a much closer approximation to the bond energy, and it provides a much more accurate representation of the behavior of the electrons as chemical bonds are formed and broken. In contrast simple molecular orbital theory predicts that the hydrogen molecule dissociates into a linear superposition of hydrogen atoms and positive and negative hydrogen ions, a completely unphysical result. This explains in part why the curve of total energy against interatomic distance for the valence bond method lies above the curve for the molecular orbital method at all distances and most particularly so for large distances. This situation arises for all homonuclear diatomic molecules and is particularly a problem for F2, where the minimum energy of the curve with molecular orbital theory is still higher in energy than the energy of two F atoms.

The concepts of hybridization are so versatile, and the variability in bonding in most organic compounds is so modest, that valence bond theory remains an integral part of the vocabulary of organic chemistry. However, the work of Friedrich Hund, Robert Mulliken, and Gerhard Herzberg showed that molecular orbital theory provided a more appropriate description of the spectroscopic, ionization and magnetic properties of molecules. The deficiencies of valence bond theory became apparent when hypervalent molecules (e.g. PF5) were explained without the use of d orbitals that were crucial to the bonding hybridisation scheme proposed for such molecules by Pauling. Metal complexes and electron deficient compounds (e.g. diborane) also appeared to be well described by molecular orbital theory, although valence bond descriptions have been made.In the 1930s the two methods strongly competed until it was realised that they are both approximations to a better theory. If we take the simple valence bond structure and mix in all possible covalent and ionic structures arising from a particular set of atomic orbitals, we reach what is called the full configuration interaction wave function. If we take the simple molecular orbital description of the ground state and combine that function with the functions describing all possible excited states using unoccupied orbitals arising from the same set of atomic orbitals, we also reach the full configuration interaction wavefunction. It can be then seen that the simple molecular orbital approach gives too much weight to the ionic structures, while the simple valence bond approach gives too little. This can also be described as saying that the molecular orbital approach is too delocalised, while the valence bond approach is too localised.The two approaches are now regarded as complementary, each providing its own insights into the problem of chemical bonding. Modern calculations in quantum chemistry usually start from (but ultimately go far beyond) a molecular orbital rather than a valence bond approach, not because of any intrinsic superiority in the former but rather because the MO approach is more readily adapted to numerical computations. However better valence bond programs are now available.[edit] Bonds in chemical formulaThe 3-dimensionality of atoms and molecules makes it difficult to use a single technique for indicating orbitals and bonds. In molecular formulae the chemical bonds (binding orbitals) between atoms are indicated by various different methods according to the type of discussion. Sometimes, they are completely neglected. For example, in organic chemistry chemists are sometimes concerned only with the functional groups of the molecule. Thus, the molecular formula of ethanol (a compound in alcoholic beverages) may be written in a paper in conformational, 3-dimensional, full 2-dimensional (indicating every bond with no 3-dimensional directions), compressed 2-dimensional (CH3–CH2–OH), separating the functional group from another part of the molecule (C2H5OH), or by its atomic constituents (C2H6O), according to what is discussed. Sometimes, even the non-bonding valence shell electrons (with the 2-dimensional approximate directions) are marked, i.e. for elemental carbon .

'C'. Some chemists may also mark the respective orbitals, i.e. the hypothetical ethene−4 anion (\

/C=C/\ −4) indicating the possibility of bond formation.

Strong chemical bondsTypical bond lengths in pmand bond energies in kJ/mol.Bond lengths can be converted to Åby division by 100 (1 Å = 100 pm).Data taken from [1].

Bond Length(pm)

Energy(kJ/mol)

H — HydrogenH–H 74 436H–O 96 366H–F 92 568H–Cl 127 432C — CarbonC–H 109 413C–C 154 348C=C 134 614C≡C 120 839C–N 147 308C–O 143 360C–F 134 488C–Cl 177 330N — NitrogenN–H 101 391N–N 145 170N≡N 110 945O — OxygenO–O 148 145O=O 121 498F, Cl, Br, I — HalogensF–F 142 158Cl–Cl 199 243Br–H 141 366Br–Br 228 193I–H 161 298I–I 267 151

Strong chemical bonds are the intramolecular forces which hold atoms together in molecules. A strong chemical bond is formed from the transfer or sharing of electrons between atomic centers and relies on the electrostatic attraction between the protons in nuclei and the electrons in the orbitals. Although these bonds typically involve the transfer of integer numbers of electrons (this is the bond order), some systems can have intermediate numbers. An example of this is the organic molecule benzene, where the bond order is 1.5 for each carbon atom.The types of strong bond differ due to the difference in electronegativity of the constituent elements. A large difference in electronegativity leads to more polar (ionic) character in the bond.] Covalent bondCovalent bonding is a common type of bonding, in which the electronegativity difference between the bonded atoms is small or nonexistent. Bonds within most organic compounds are described as covalent. See sigma bonds and pi bonds for LCAO-description of such bonding.

A polar covalent bond is a covalent bond with a significant ionic character. This means that the electrons are closer to one of the atoms than the other, creating an imbalance of charge. They occur as a bond between two atoms with moderately different electronegativities, and give rise to dipole-dipole interactions. The electronegativity of these bonds is 0.3 - 1.7 .A coordinate covalent bond is one where both bonding electrons are from one of the atoms involved in the bond. These bonds give rise to Lewis acids and bases. The electrons are shared roughly equally between the atoms in contrast to ionic bonding. Such bonding occurs in molecules such as the ammonium ion (NH4

+) and are shown by an arrow pointing to the Lewis acid. Also known as non-polar covalent bond, the electronegativity of these bonds range < 0.3 .Molecules which are formed primarily from non-polar covalent bonds are often immiscible in water or other polar solvents, but much more soluble in non-polar solvents such as hexane.

Ionic bondIonic bonding is a type of electrostatic interaction between atoms which have a large electronegativity difference. There is no precise value that distinguishes ionic from covalent bonding but a difference of electronegativity of over 1.7 is likely to be ionic and a difference of less than 1.7 is likely to be covalent. [4] Ionic bonding leads to separate positive and negative ions. Ionic charges are commonly between −3e to +3e. Ionic bonding commonly occurs in metal salts such as sodium chloride (table salt). A typical feature of ionic bonds is that the species form into ionic cystals, in which no ion is specifically paired with any single other ion, in a specific directional bond. Rather, each species of ion is surrounded by ions of the opposite charge, and the spacing between it and each of the oppositely charged ions near it, is the same for all surrounding atoms of the same type. It is thus no longer possible to associate an ion with any specific other single ionized atom near it, as it is in covalent crystals.Ionic crystals may contain a mixture of covalent and ionic species, as for example salts of complex acids, such as sodium cyanide. Many minerals are also of this type. In such crystals, the bonds between sodium and the anions cyanide (CN-) are ionic, with no sodium associated with a particular cyanide. However, the bonds between C and N atoms in cyanide are of the covalent type, making each of the carbon and nitrogen associated with just one of its opposite type, to which it is physically closer than the other carbons or nitrogens. When such salts dissolve into water, the ionic bonds are typically broken by the interaction with water, but the covalent bonds continue to hold.

One- and three-electron bondsBonds with one or three electrons can be found in radical species, which have an odd number of electrons. The simplest example of a 1-electron bond is found in the hydrogen molecular cation, H2

+. One-electron bonds often have about half the bond energy of a 2-electron bond, and are therefore called "half bonds". However, there are exceptions: in the case of dilithium, the bond is actually stronger for the 1-electron Li2

+ than for the 2-electron Li2. This exception can be explained in terms of hybridization and inner-shell effects.[5]

The simplest example of three-electron bonding can be found in the helium dimer cation, He2+, and can also be considered a "half bond" because, in molecular orbital

terms, the third electron is in an anti-bonding orbital which cancels out half of the bond formed by the other two electrons. Another example of a molecule containing a 3-electron bond, in addition to two 2-electron bonds, is nitric oxide, NO. The oxygen molecule, O2 can also be regarded as having two 3-electron bonds and one 2-electron bond, which accounts for its paramagnetism and its formal bond order of 2.[6]

Molecules with odd-electron bonds are usually highly reactive. These types of bond are only stable between atoms with similar electronegativities. [6]

Bent bondsBent bonds, also known as banana bonds, are bonds in strained or otherwise sterically hindered molecules whose binding orbitals are forced into a banana-like form. Bent bonds are often more susceptible to reactions than ordinary bonds.

3c-2e and 3c-4e bondsIn three-center two-electron bonds ("3c-2e") three atoms share two electrons in bonding. This type of bonding occurs in electron deficient compounds like diborane. Each such bond (2 per molecule in diborane) contains a pair of electrons which connect the boron atoms to each other in a banana shape, with a proton (nucleus of a hydrogen atom) in the middle of the bond, sharing electrons with both boron atoms.Three-center four-electron bonds ("3c-4e") also exist which explain the bonding in hypervalent molecules. In certain cluster compounds, so-called four-center two-electron bonds also have been postulated.In certain conjugated π (pi) systems, such as benzene and other aromatic compounds (see below), and in conjugated network solids such as graphite, the electrons in the conjugated system of π-bonds are spread over as many nuclear centers as exist in the molecule or the network.

Aromatic bond

In organic chemistry, certain configurations of electrons and orbitals infer extra stability to a molecule. This occurs when π orbitals overlap and combine with others on different atomic centres, forming a long range bond. For a molecule to be aromatic, it must obey Hückel's rule, where the number of π electrons fit the formula 4n + 2, where n is an integer. The bonds involved in the aromaticity are all planar.In benzene, the prototypical aromatic compound, 18 (n = 4) bonding electrons bind 6 carbon atoms together to form a planar ring structure. The bond "order" (average number of bonds) between the different carbon atoms may be said to be (18/6)/2=1.5, but in this case the bonds are all identical from the chemical point of view. They may sometimes be written as single bonds alternating with double bonds, but the view of all ring bonds as being equivalently about 1.5 bonds in strength, is much closer to truth.In the case of heterocyclic aromatics and substituted benzenes, the electronegativity differences between different parts of the ring may dominate the chemical behaviour of aromatic ring bonds, which otherwise are equivalent.

Metallic bondIn a metallic bond, bonding electrons are delocalized over a lattice of atoms. By contrast, in ionic compounds, the locations of the binding electrons and their charges are static. Because of delocalization or the free moving of electrons, it leads to the metallic properties such as conductivity, ductility and hardness.Intermolecular bondingThere are four basic types of bonds that can be formed between two or more (otherwise non-associated) molecules, ions or atoms. Intermolecular forces cause molecules to be attracted or repulsed by each other. Often, these define some of the physical characteristics (such as the melting point) of a substance.A large difference in electronegativity between two bonded atoms will cause dipole-dipole interactions. The bonding electrons will, on the whole, be closer to the more electronegative atom more frequently than the less electronegative one, giving rise to partial charges on each atomic center, and causing electrostatic forces between molecules.A hydrogen bond is effectively a strong example of a permanent dipole. The large difference in electronegativities between hydrogen and any of fluorine, nitrogen and oxygen, coupled with their lone pairs of electrons cause strong electrostatic forces between molecules. Hydrogen bonds are responsible for the high boiling points of water and ammonia with respect to their heavier analogues.The London dispersion force arises due to instantaneous dipoles in neighbouring atoms. As the negative charge of the electron is not uniform around the whole atom, there is always a charge imbalance. This small charge will induce a corresponding dipole in a nearby molecule; causing an attraction between the two. The electron then moves to another part of the electron cloud and the attraction is broken.A cation-pi interaction occurs between the negative charges of pi bonds above and below an aromatic ring and a cation.

Electrons in chemical bondsIn the (unrealistic) limit of "pure" ionic bonding, electrons are perfectly localized on one of the two atoms in the bond. Such bonds can be understood by classical physics. The forces between the atoms are characterized by isotropic continuum electrostatic potentials. Their magnitude is in simple proportion to the charge difference.Covalent bonds are better understood by valence bond theory or molecular orbital theory. The properties of the atoms involved can be understood using concepts such as oxidation number. The electron density within a bond is not assigned to individual atoms, but is instead delocalized between atoms. In valence bond theory, the two electrons on the two atoms are coupled together with the bond strength depending on the overlap between them. In molecular orbital theory, the linear combination of atomic orbitals (LCAO) helps describe the delocalized molecular orbital structures and energies based on the atomic orbitals of the atoms they came from. Unlike pure ionic bonds, covalent bonds may have directed anisotropic properties. These may have their own names, such as Sigma and Pi bond.In the general case, atoms form bonds that are intermediates between ionic and covalent, depending on the relative electronegativity of the atoms involved. This type of bond is sometimes called polar covalent.

Lewis structures (also known as Lewis dot diagrams, electron dot diagrams, and electron dot structures) are diagrams that show the bonding between atoms of a molecule, and the lone pairs of electrons that may exist in the molecule.[1][2][3] A Lewis structure can be drawn for any covalently-bonded molecule, as well as coordination compounds. The Lewis structure was named after Gilbert N. Lewis, who introduced it in his 1916 article The Atom and the Molecule.[4] They are similar to electron dot diagrams in that the valence electrons in lone pairs are represented as dots, but they also contain lines to represent shared pairs in a chemical bond (single, double, triple, etc.).Lewis structures show each atom and its position in the structure of the molecule using its chemical symbol. Lines are drawn between atoms that are bonded to one another (pairs of dots can be used instead of lines). Excess electrons that form lone pairs are represented as pairs of dots, and are placed next to the atoms.Although many of the elements react by gaining, losing or sharing electrons until they have achieved a valence shell electron configuration with a full octet (8) of electrons, there are many noteworthy exceptions to the 'octet rule'. One example is hydrogen (H), which has only a single valence electron and tends to react to attain either 0 or 2 valence electrons. When H has two electrons in its valence shell, it could be said to obey a 'duet rule', and achieves a valence shell electron configuration equivalent to helium (He).

ConstructionCounting electronsThe total number of electrons represented in a Lewis structure is equal to the sum of the numbers of valence electrons on each individual atom. Non-valence electrons are not represented in Lewis structures.The octet rule states atoms with eight electrons in their valence shell will be stable, regardless of whether these electrons are bonding or nonbonding. The rule applies well to acidic compounds. The 18-Electron rule is operative on atoms from period 4, which have to achieve 18 electrons to their orbitals and achieve a stable configuration which has the same electron configuration as a Noble gas. Similarly from period 6, the atoms have to achieve 32 electrons to fill their orbitals.[edit] Placing electrons

Lewis structures for oxygen, fluorine, the hydrogen sulfate anion, and formamideOnce the total number of available electrons has been determined, electrons must be placed into the structure. They should be placed initially as lone pairs: one pair of dots for each pair of electrons available. Lone pairs should initially be placed on outer atoms (other than hydrogen) until each outer atom has eight electrons in bonding pairs and lone pairs; extra lone pairs may then be placed on the central atom. When in doubt, lone pairs should be placed on more electronegative atoms first.Once all lone pairs are placed, atoms, especially the central atoms, may not have an octet of electrons. In this case, the atoms must form a double bond; a lone pair of electrons is moved to form a second bond between the two atoms. As the bonding pair is shared between the two atoms, the atom that originally had the lone pair still has an octet; the other atom now has two more electrons in its valence shell.they are very hard

Aside from organic compounds, only a minority of compounds have an octet of electrons. Incomplete octets are common for compounds of groups 2 and 13 such as beryllium, boron, and aluminium. Compounds with more than eight electrons in the Lewis representation of the valence shell of an atom are called hypervalent, and are common for elements of groups 15 to 18, such as phosphorus, sulfur, iodine, and xenon.Lewis structures for polyatomic ions may be drawn by the same method. When counting electrons, negative ions should have extra electrons placed in their Lewis structures; positive ions should have fewer electrons than an uncharged molecule.When the Lewis structure of an ion is written, the entire structure is placed in brackets, and the charge is written as a superscript on the upper right, outside the brackets.A simpler method has been proposed for constructing Lewis structures eliminating the need for electron counting: the atoms are drawn showing the valence electrons, bonds are then formed by pairing up valence electrons of the atoms involved in the bond-making process and anions and cations are formed by adding or removing electrons to/from the appropriate atoms.[5]

A trick is to count up valence electrons, then count up the number of electrons needed to complete the octet rule (or with Hydrogen just 2 electrons), then take the difference of these two numbers and your answer is the number of electrons that make up the bonds. The rest of the electrons just go and fill all the other atoms' octets.

Formal chargeIn terms of Lewis structures, formal charge is used in the description, comparison and assessment of likely topological and resonance structures[6] by determining the apparent electronic charge of each atom within, based upon its electron dot structure assuming exclusive covalency or non-polar bonding. It has uses in determining possible electron re-configuration when referring to reaction mechanisms, and often results in the same sign as the partial charge of the atom, with exceptions. In general, the formal charge of an atom can be calculated using the following formula, assuming non-standard definitions for the markup used:

where:Cf is the Formal charge.Nv represents the number of valence electrons in a free atom of the element.

Ue represents the number of unshared electrons on the atom.Bn represents the total number of bonds the atom has with another.The formal charge of an atom is computed as the difference between the number of valence electrons that a neutral atom would have and the number of electrons that belong to it in the Lewis structure. Electrons in covalent bonds are split equally between the atoms involved in the bond. The total of the formal charges on an ion should be equal to the charge on the ion, and the total of the formal charges on a neutral molecule should be equal to zero.

ResonanceFor some molecules and ions, it is difficult to determine which lone pairs should be moved to form double or triple bonds. This is sometimes the case when multiple atoms of the same type surround the central atom, and is especially common for polyatomic ions.When this situation occurs, the molecule's Lewis structure is said to be a resonance structure, and the molecule exists as a resonance hybrid. Each of the different possibilities is superimposed on the others, and the molecule is considered to have a Lewis structure equivalent to an average of these states.The nitrate ion (NO3

-), for instance, must form a double bond between nitrogen and one of the oxygens to satisfy the octet rule for nitrogen. However, because the molecule is symmetrical, it does not matter which of the oxygens forms the double bond. In this case, there are three possible resonance structures. Expressing resonance when drawing Lewis structures may be done either by drawing each of the possible resonance forms and placing double-headed arrows between them or by using dashed lines to represent the partial bonds.When comparing resonance structures for the same molecule, usually those with the fewest formal charges contribute more to the overall resonance hybrid. When formal charges are necessary, resonance structures that have negative charges on the more electronegative elements and positive charges on the less electronegative elements are favored.The resonance structure should not be interpreted to indicate that the molecule switches between forms, but that the molecule acts as the average of multiple forms.

Example: Lewis structure of the nitrite ionThe formula of the nitrite ion is NO2

−.Step one: Nitrogen is the least electronegative atom, so it is the central atom by multiple criteria.Step two: Count valence electrons. Nitrogen has 5 valence electrons; each oxygen has 6, for a total of (6 × 2) + 5 = 17. The ion has a charge of −1, which indicates an extra electron, so the total number of electrons is 18.Step three: Place ion pairs. Each oxygen must be bonded to the nitrogen, which uses four electrons — two in each bond. The 14 remaining electrons should initially be placed as 7 lone pairs. Each oxygen may take a maximum of 3 lone pairs, giving each oxygen 8 electrons including the bonding pair. The seventh lone pair must be placed on the nitrogen atom.Step four: Satisfy the octet rule. Both oxygen atoms currently have 8 electrons assigned to them. The nitrogen atom has only 6 electrons assigned to it. One of the lone pairs on an oxygen atom must form a double bond, but either atom will work equally well. We therefore must have a resonance structure.Step five: Tie up loose ends. Two Lewis structures must be drawn: one with each oxygen atom double-bonded to the nitrogen atom. The second oxygen atom in each structure will be single-bonded to the nitrogen atom. Place brackets around each structure, and add the charge (−) to the upper right outside the brackets. Draw a double-headed arrow between the two resonance forms.

Alternative formats

Two varieties of condensed structural formula, both showing butane

A skeletal diagram of butane

A space filling diagram for butane.Chemical structures may be written in more compact forms, particularly when showing organic molecules. In condensed structural formulas, many or even all of the covalent bonds may be left out, with subscripts indicating the number of identical groups attached to a particular atom. Another shorthand structural diagram is the

skeletal formula (also known as a bond-line formula or carbon skeleton diagram). In skeletal formulae, carbon atoms are not signified by the symbol C but by the vertices of the lines. Hydrogen atoms bonded to carbon are not shown — they can be inferred by counting the number of bonds to a particular carbon atom — each carbon is assumed to have four bonds in total, so any bonds not shown are, by implication, to hydrogen atoms.

Other diagrams may be more complex than Lewis structures, showing bonds in 3D using various forms such as space filling diagrams.

Valence shell electron pair repulsion (VSEPR) theory is a model in chemistry used to predict the shape of individual molecules based upon the extent of electron-pair electrostatic repulsion.[1] It is also named Gillespie-Nyholm theory after its two main developers. The acronym "VSEPR" is sometimes pronounced "vesper" for ease of pronunciation.[2]

The premise of VSEPR is that the valence electron pairs surrounding an atom mutually repel each other, and will therefore adopt an arrangement that minimizes this repulsion, thus determining the molecular geometry. The number of electron pairs surrounding an atom, both bonding and nonbonding, is called its steric number.VSEPR theory is usually compared and contrasted with valence bond theory, which addresses molecular shape through orbitals that are energetically accessible for bonding. Valence bond theory concerns itself with the formation of sigma and pi bonds. Molecular orbital theory is another model for understanding how atoms and electrons are assembled into molecules and polyatomic ions.VSEPR theory has long been criticized for not being quantitative, and therefore limited to the generation of "crude", even though structurally accurate, molecular geometries of covalent molecules. However, molecular mechanics force fields based on VSEPR have also been developed.[3]

DescriptionVSEPR theory mainly involves predicting the layout of electron pairs surrounding one or more central atoms in a molecule, which are bonded to two or more other atoms. The geometry of these central atoms in turn determines the geometry of the larger whole.The number of electron pairs in the valence shell of a central atom is determined by drawing the Lewis structure of the molecule, expanded to show all lone pairs of electrons, alongside protruding and projecting bonds. Where two or more resonance structures can depict a molecule, the VSEPR model is applicable to any such structure. For the purposes of VSEPR theory, the multiple electron pairs in a multiple bond are treated as though they were a single "pair".These electron pairs are assumed to lie on the surface of a sphere centered on the central atom, and since they are negatively charged, tend to occupy positions that minimizes their mutual electrostatic repulsions by maximising the distance between them. The number of electron pairs therefore determine the overall geometry that they will adopt.For example, when there are two electron pairs surrounding the central atom, their mutual repulsion is minimal when they lie at opposite poles of the sphere. Therefore, the central atom is predicted to adopt a linear geometry. If there are 3 electron pairs surrounding the central atom, their repulsion is minimized by placing them at the vertices of a triangle centered on the atom. Therefore, the predicted geometry is trigonal. Similarly, for 4 electron pairs, the optimal arrangement is tetrahedral.This overall geometry is further refined by distinguishing between bonding and nonbonding electron pairs. A bonding electron pair is involved in a sigma bond with an adjacent atom, and, being shared with that other atom, lies farther away from the central atom than does a nonbonding pair (lone pair), which is held close to the central atom by its positively-charged nucleus. Therefore, the repulsion caused by the lone pair is greater than the repulsion caused by the bonding pair. As such, when the overall geometry has two sets of positions that experience different degrees of repulsion, the lone pair(s) will tend to occupy the positions that experience less repulsion. In other words, the lone pair-lone pair (lp-lp) repulsion is considered to be stronger than the lone pair-bonding pair (lp-bp) repulsion, which in turn is stronger than the bonding pair-bonding pair (bp-bp) repulsion. Hence, the weaker bp-bp repulsion is preferred over the lp-lp or lp-bp repulsion.This distinction becomes important when the overall geometry has two or more non-equivalent positions. For example, when there are 5 electron pairs surrounding the central atom, the optimal arrangement is a trigonal bipyramid. In this geometry, two positions lie at 180° angles to each other and 90° angles to the other 3 adjacent positions, whereas the other 3 positions lie at 120° to each other and at 90° to the first two positions. The first two positions therefore experience more repulsion than the last three positions. Hence, when there are one or more lone pairs, the lone pairs will tend to occupy the last three positions first.The difference between lone pairs and bonding pairs may also be used to rationalize deviations from idealized geometries. For example, the H2O molecule has four electron pairs in its valence shell: two lone pairs and two bond pairs. The four electron pairs are spread so as to point roughly towards the apices of a tetrahedron. However, the bond angle between the two O-H bonds is only 104.5°, rather than the 109.5° of a regular tetrahedron, because the two lone pairs (whose density or probability envelopes lie closer to the oxygen nucleus) exert a greater mutual repulsion than the two bond pairs.

AXE MethodThe "AXE method" of electron counting is commonly used when applying the VSEPR theory. The A represents the central atom and always has an implied subscript one. The X represents the number of sigma bonds between the central atoms and outside atoms. Multiple covalent bonds (double, triple, etc) count as one X. The E represents the number of lone electron pairs surrounding the central atom. The sum of X and E, known as the steric number, is also associated with the total number of hybridized orbitals used by valence bond theory.Based on the steric number and distribution of X's and E's, VSEPR theory makes the predictions in the following tables. Note that the geometries are named according to the atomic positions only and not the electron arrangement. For example the description of AX2E1 as bent means that AX2 is a bent molecule without reference to the lone pair, although the lone pair helps to determine the geometry.

StericNo.

Basic Geometry0 lone pair

1 lone pair 2 lone pairs 3 lone pairs

2Linear

3

Trigonal planar

Bent

4

Tetrahedral Trigonal pyramidBent

5

Trigonal bipyramid Seesaw T-shaped Linear

6

Octahedral Square pyramid Square planar

7

Pentagonal bipyramid Pentagonal pyramid

8Square antiprismatic

Molecule Type Shape Electron arrangement† Geometry‡ Examples

AX1En Diatomic HF, O2

AX2E0 Linear BeCl2, HgCl2, CO2

AX2E1 Bent NO2−, SO2, O3

AX2E2 Bent H2O, OF2

AX2E3 Linear XeF2, I3−

AX3E0 Trigonal planar BF3, CO32−, NO3

−, SO3

AX3E1 Trigonal pyramidal NH3, PCl3

AX3E2 T-shaped ClF3, BrF3

AX4E0 Tetrahedral CH4, PO43−, SO4

2−, ClO4−

AX4E1 Seesaw SF4

AX4E2 Square planar XeF4

AX5E0 Trigonal bipyramidal PCl5

AX5E1 Square pyramidal ClF5, BrF5

AX6E0 Octahedral SF6

AX6E1 Pentagonal pyramidal XeOF5−, IOF5

2− [7]

AX7E0 Pentagonal bipyramidal IF7

AX8E0 Square antiprismatic XeF2−8† Electron arrangement including lone pairs, shown in pale yellow‡ Observed geometry (excluding lone pairs)When the substituent (X) atoms are not all the same, the geometry is still approximately valid, but the bond angles may be slightly different from the ones where all the outside atoms are the same. For example, the double-bond carbons in alkenes like C2H4 are AX3E0, but the bond angles are not all exactly 120°. Similarly, SOCl2 is AX3E1, but because the X substituents are not identical, the XAX angles are not all equal.

ExamplesThe methane molecule (CH4) is tetrahedral because there are four pairs of electrons. The four hydrogen atoms are positioned at the vertices of a tetrahedron, and the bond angle is cos-1(-1/3) ≈ 109°28'. This is referred to as an AX4 type of molecule. As mentioned above, A represents the central atom and X represents all of the outer atoms.The ammonia molecule (NH3) has three pairs of electrons involved in bonding, but there is a lone pair of electrons on the nitrogen atom. It is not bonded with another atom; however, it influences the overall shape through repulsions. As in methane above, there are four regions of electron density. Therefore, the overall orientation of the regions of electron density is tetrahedral. On the other hand, there are only three outer atoms. This is referred to as an AX3E type molecule because the lone pair is represented by an E. The observed shape of the molecule is a trigonal pyramid, because the lone pair is not "visible" in experimental methods used to determine molecular geometry. The shape of a molecule is found from the relationship of the atoms even though it can be influenced by lone pairs of electrons.A steric number of seven is possible, but it occurs in uncommon compounds such as iodine heptafluoride. The base geometry for this is pentagonal bipyramidal.The most common geometry for a steric number of eight is a square antiprismatic geometry.[8] Examples of this include the octafluoroxenate ion (XeF2−8) in nitrosonium octafluoroxenate(VI),[9][10] octacyanomolybdate (Mo(CN)4−8), and octafluorozirconate (ZrF4−8).[8]

ExceptionsThere are groups of compounds where VSEPR fails to predict the correct geometry.Transition metal compoundsMany transition metal compounds do not have geometries explained by VSEPR which can be ascribed to there being no lone pairs in the valence shell and the interaction of core d electrons with the ligands.[11] The structure of some of these compounds, including metal hydrides and alkyl complexes such as hexamethyltungsten, can be predicted correctly using the VALBOND theory, which is based on sd hybrid orbitals and the 3-center-4-electron bonding model.[12][13] Crystal field theory is another theory that can often predict the geometry of coordination complexes.Group 2 halidesThe gas phase structures of the triatomic halides of the heavier members of group 2, (i.e. calcium, strontium and barium halides, MX2), are not linear as predicted but are bent, (approximate X-M-X angles: CaF2, 145°; SrF2, 120°; BaF2, 108°; SrCl2, 130°; BaCl2, 115°; BaBr2, 115°; BaI2, 105°).[14] It has been proposed by Gillespie that this is caused by interaction of the ligands with the electron core of the metal atom, polarising it so that the inner shell is not spherically symmetric, thus influencing the molecular geometry. [11][15]

Some AX2E2 moleculesOne example is molecular lithium oxide, Li2O, which is linear rather than being bent, and this has been ascribed to the bonding being essentially ionic leading to strong repulsion between the lithium atoms.[16]

Another example is O(SiH3)2 with an Si-O-Si angle of 144.1° which compares to the angles in Cl2O (110.9°), (CH3)2O (111.7°)and N(CH3)3 (110.9°). Gillespie's rationalisation is that the localisation of the lone pairs, and therefore their ability to repel other electron pairs, is greatest when the ligand has an electronegativity similar to, or greater than, the central atom.[11] When the central atom is more electronegative, as in O(SiH3)2, the lone pairs are less well localised, have a weaker repulsive effect and this combined with the stronger ligand-ligand repulsion (-SiH3 is a relatively large ligand compared to the examples above) gives the larger than expected Si-O-Si bond angle.[11]

Some AX6E1moleculesSome AX6E1 molecules, e.g. the Te(IV) and Bi(III) anions, TeCl6

2−, TeBr62−, BiCl6

3−, BiBr63− and BiI6

3−, are regular octahedra and the lone pair does not affect the geometry.[17] One rationalization is that steric crowding of the ligands allows no room for the non-bonding lone pair;[11] another rationalization is the inert pair effect.[18]

Molecular geometry or molecular structure 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 influence of thermal excitationSince the motions of the atoms in a molecule are determined by quantum mechanics, one must define “motion” in a quantum mechanical way. The overall (external) quantum mechanical motions translation and rotation hardly change the geometry of the molecule. (To some extent rotation influences the geometry via Coriolis forces and centrifugal distortion, but this is negligible for the present discussion.) A third type of motion is vibration, which is the internal motion of the atoms in a molecule. The molecular vibrations are harmonic (at least to good approximation), which means that the atoms oscillate about their equilibrium, even at the absolute zero of temperature. At absolute zero all atoms are in their vibrational ground state and show zero point quantum mechanical motion, that is, the wavefunction of a single vibrational mode is not a sharp peak, but an exponential of finite width. At higher temperatures the vibrational modes may be thermally excited (in a classical interpretation one expresses this by stating that “the molecules will vibrate faster”), but they oscillate still around the recognizable geometry of the molecule.

To get a feeling for the probability that the vibration of molecule may be thermally excited, we inspect the Boltzmann factor , where ΔE is the excitation energy of the vibrational mode, k the Boltzmann constant and T the absolute temperature. At 298K (25 °C), typical values for the Boltzmann factor are: 0.089 for ΔE = 500 cm-1 ; ΔE = 0.008 for 1000 cm-1 ; 7 10-4 for ΔE = 1500 cm-1. That is, if the excitation energy is 500 cm-1, then about 9 percent of the molecules are thermally excited at room temperature. The lowest excitation vibrational energy in water is the bending mode (about 1600 cm-1). 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 (as compared to vibration) low temperatures. From a classical point of view it can be stated that more molecules rotate faster at higher temperatures, i.e., they have larger angular velocity and angular momentum. In quantum mechanically 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.The results of many spectroscopic experiments are broadened because they involve an averaging over rotational states. It is often difficult to extract geometries from spectra at high temperatures, because the number of rotational states probed in the experimental averaging increases with increasing temperature. Thus, many spectroscopic observations can only be expected to yield reliable molecular geometries at temperatures close to absolute zero, because at higher temperatures too many higher rotational states are thermally populated.

BondingMolecules, by definition, are most often held together with covalent bonds involving single, double, and/or triple bonds, where a "bond" is a shared pair of electrons (the other method of bonding between atoms is called ionic bonding and involves a positive cation and a negative anion).Molecular geometries can be specified in terms of bond lengths, bond angles and torsional angles. The bond length is defined to be the average distance between the centers of two atoms bonded together in any given molecule. A bond angle is the angle formed between three atoms across at least two bonds. For four atoms bonded together in a chain, the torsional angle is the angle between the plane formed by the first three atoms and the plane formed by the last three atoms.Molecular geometry is determined by the quantum mechanical behavior of the electrons. Using the valence bond approximation this can be understood by the type of bonds between the atoms that make up the molecule. When atoms interact to form a chemical bond, the atomic orbitals are said to mix in a process called orbital hybridisation. The two most common types of bonds are Sigma bonds and Pi bonds. The geometry can also be understood by molecular orbital theory where the electrons are delocalised.An understanding of the wavelike behavior of electrons in atoms and molecules is the subject of quantum chemistry.

IsomersIsomers are types of molecules that share a chemical formula but have different geometries, resulting in very different properties:A pure substance is composed of only one type of isomer of a molecule (all have the same geometrical structure).Structural isomers have the same chemical formula but different physical arrangements, often forming alternate molecular geometries with very different properties. The atoms are not bonded (connected) together in the same orders. Functional isomers are special kinds of structural isomers, where certain groups of atoms exhibit a special kind of behavior, such as an ether or an alcohol.Stereoisomers may have many similar physicochemical properties (melting point, boiling point) and at the same time very different biochemical activities. This is because they exhibit a handedness that is commonly found in living systems. One manifestation of this chirality or handedness is that they have the ability to rotate polarized light in different directions.Protein folding concerns the complex geometries and different isomers that proteins can take.

Types of molecular structureThere are six basic shape types for moleculesLinear: In a linear model, atoms are connected in a straight line. The bond angles are set at 180°. A bond angle is very simply the geometric angle between two adjacent bonds. For example, carbon dioxide has a linear molecular shape.Trigonal planar: Just from its name, it can easily be said that molecules with the trigonal planar shape are somewhat triangular and in one plane (meaning a flat surface). Consequently, the bond angles are set at 120°. An example of this is boron trifluoride.Tetrahedral: Tetra- signifies four, and -hedral relates to a surface, so tetrahedral almost literally means "four surfaces." This is when there are four bonds all on one central atom, with no extra unshared electron pairs. In accordance with the VSEPR (valence-shell electron pair repulsion theory), the bond angles between the electron bonds are arccos(−1/3) = 109.5°. An example of a tetrahedral molecule is methane (CH4).Octahedral: Octa- signifies eight, and -hedral relates to a surface, so octahedral almost literally means "eight surfaces." The bond angle is 90 degrees. An example of an octahedral molecule is sulfur hexafluoride (SF6).Pyramidal: Pyramidal-shaped molecules have pyramid-like shapes. Unlike the linear and trigonal planar shapes but similar to the tetrahedral orientation, pyramidal shapes requires three dimensions in order to fully separate the electrons. Here, there are only three pairs of bonded electrons, leaving one unshared lone pair. Lone pair - bond pair repulsions change the angle from the tetrahedral angle to a slightly lower value. An example is NH3 (ammonia).Bent: The final basic shape of a molecule is the non-linear shape, also known as bent or angular. One of the most unquestionably important molecules any chemist studies is water, or H2O. A water molecule has a non-linear shape because it has two pairs of bonded electrons and two unshared lone pairs. Like in the other arrangements, electrons must be spaced as far as possible. Lone pair - bond pair repulsions push the angle from the tetrahedral angle down to around 106°.[edit] VSEPR TableThe bond angles in the table below are ideal angles from the simple VSEPR theory, followed by the actual angle for the example given in the following column where this differs. For many cases, such as trigonal pyramidal and bent, the actual angle for the example differs from the ideal angle, but all examples differ by different amounts. For example, the angle in H2S (92°) differs from the tetrahedral angle by much more than the angle for H2O (104.5°) does.

Bonding Electron PairsLone Pairs Electron Domains Shape Ideal Bond Angle (example's bond angle) Example Image

2 0 2 linear 180° BeCl2

3 0 3 trigonal planar 120° BF3

2 1 3 bent 120° (119°) SO2

4 0 4 tetrahedral 109.5° CH4

3 1 4 trigonal pyramidal 109.5° (107.5°) NH3

2 2 4 bent 109.5° (104.5°) H2O

5 0 5 trigonal bipyramidal 90°, 120° PCl5

4 1 5 seesaw 180°, 120° (173.1°, 101.6°) SF4

3 2 5 T-shaped 90°, 180° (87.5°, < 180°) ClF3

2 3 5 linear 180° XeF2

6 0 6 octahedral 90° SF6

5 1 6 square pyramidal 90° (84.8°) BrF5

4 2 6 square planar 90° XeF4

7 0 7 pentagonal bipyramidal 90°, 72° IF7

3D RepresentationsLine or stick - atomic nuclei are not represented, just the bonds as sticks or lines. As in 2D molecular structures of this type, atoms are implied at each vertex.

Electron density plot - shows the electron density determined either crystallographically or using quantum mechanics rather than distinct atoms or bonds

Ball and stick - atomic nuclei are represented by spheres (balls) and the bonds as sticks

Spacefilling models or CPK models (also an atomic coloring scheme in representations) - the molecule is represented by overlapping spheres representing the atoms

Cartoon - a representation used for proteins where loops, beta sheets, alpha helices are represented diagrammatically and no atoms or bonds are represented explicitly just the protein backbone as a smooth pipe

Gas Laws

Boyle's LawBoyle's Law shows that, at constant temperature, the product of an ideal gas's pressure and volume is always constant. It was published in 1622. It can be determined experimentally using a pressure gauge and a variable volume container. It can also be found logically; if a container with a fixed amount of molecules inside it is reduced in volume, more molecules will hit the sides of the container per unit time causing a greater pressure.As a mathematical equation, Boyle's law is:

Where P is the pressure (Pa), V the volume (m3) of a gas, and k1 (measured in joules) is the constant from this equation—it is not the same as the constants from the other equations below.

Charles's LawCharles's Law, or the law of volumes, was found in 1787. It says that, for an ideal gas at constant pressure, the volume is proportional to the absolute temperature (in kelvins). This can be found using the kinetic theory of gases or a heated container with a variable volume (such as a conical flask with a balloon).

Where T is the absolute temperature of the gas (in kelvins) and k2 (in m3·K−1) is the constant produced.

Gay-Lussac's LawThe pressure (or Gay-Lussac's) law was found by Joseph Louis Gay-Lussac in 1809. It states that the pressure exerted on a container's sides by an ideal gas is proportional to the absolute temperature of the gas. This follows from the kinetic theory—by increasing the temperature of the gas, the molecules' speeds increase meaning an increased amount of collisions with the container walls.As a mathematical formula, this is:

Avogadro's LawAvogadro's Law states that the volume occupied by an ideal gas is proportional to the amount of moles (or molecules) present in the container. This gives rise to the molar volume of a gas, which at STP is 22.4 dm3 (or liters).

Where n is equal to the number of moles of gas (the number of molecules divided by Avogadro's Number).

Combined and ideal gas lawsThe combined gas law or general gas equation is formed by the combination of the three laws, and shows the relationship between the pressure, volume and temperature for a fixed mass of gas:

With the addition of Avogadro's law, the combined gas law develops into the ideal gas law:

Where the constant, now named R, is the gas constant with a value of 8.314472(15) J·K−1·mol−1

An equivalent formulation of this law is:

wherek is the Boltzmann constant (1.381×10−23J·K−1 in SI units)N is the number of molecules.

These equations are exact only for an ideal gas, which neglects various intermolecular effects (see real gas). However, the ideal gas law is a good approximation for most gases under moderate pressure and temperature.This law has the following important consequences:If temperature and pressure are kept constant, then the volume of the gas is directly proportional to the number of molecules of gas.If the temperature and volume remain constant, then the pressure of the gas changes is directly proportional to the number of molecules of gas present.If the number of gas molecules and the temperature remain constant, then the pressure is inversely proportional to the volume.If the temperature changes and the number of gas molecules are kept constant, then either pressure or volume (or both) will change in direct proportion to the temperature.Other gas lawsGraham's law states that the rate at which gas molecules diffuse is inversely proportional to the square root of its density. Combined with Avogadro's law (i.e. since equal volumes have equal number of molecules) this is the same as being inversely proportional to the root of the molecular weight.Dalton's law of partial pressures states that the pressure of a mixture of gases simply is the sum of the partial pressures of the individual components. Dalton's Law is as follows:

,OR

,Where PTotal is the total pressure of the atmosphere, PGas is the pressure of the gas mixture in the atmosphere, and PH2O is the water pressure at that temperature.Henry's law states that:At a constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid.

Gas is one of three classical states of matter.[1] Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point (see phase change), boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons are so energized that they leave their parent atoms from within the gas. A pure gas may be made up of individual atoms (e.g. a noble gas or atomic 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 would contain a variety of pure gases much like the air. What distinguishes a gas 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 interaction of gas particles in the presence of electric and gravitational fields are considered negligible as indicated by the constant velocity vectors in the image.The gaseous state of matter is found between the liquid and plasma states,[2] the latter of which provides the upper temperature boundary for gases. Bounding the lower end of the temperature scale lie degenerative quantum gases[3] which are gaining increased attention these days.[4] High-density atomic gases super cooled to incredibly low temperatures are classified by their statistical behavior as either a Bose gas or a Fermi gas. For a comprehensive listing of these exotic states of matter see list of states of matter.

Physical characteristicsDrifting smoke particles provide clues to the movement of the surrounding gas.As most gases are difficult to observe directly with our senses, they are described through the use of four physical properties or macroscopic characteristics: the gas’s pressure, volume, number of particles (chemists group them by moles), and temperature. These four characteristics were repeatedly observed by men such as Robert Boyle, Jacques Charles, John Dalton, Joseph Gay-Lussac and Amedeo Avogadro for a variety of gases in a great many settings. Their detailed studies ultimately led to a mathematical relationship among these properties expressed by the ideal gas law (see simplified models section below).Gas particles are widely separated from one another, and as such do not influence adjacent particles to the same degree as liquids or solids. This influence (intermolecular forces) results from the magnetic charges that these gas particles carry. Like charges repel, while oppositely charged particles attract one another. Gases made from ions carry permanent charges, as do compounds with their polar covalent bonds. These polar covalent bonds produce permanent charge concentrations within the molecule while the compound's net charge remains neutral. Transient charges exist in covalent bonds of molecules and 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.[5][6] A quick comparison of boiling points for compounds formed by ionic and covalent bonds leads us to this conclusion[7]. The drifting smoke particles in the image provides some insight into low pressure gas behavior.Compared to the other states of matter, gases have an incredibly 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.

MacroscopicShuttle imagery of re-entry phase.When observing a 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. By way of contrast, a smaller length scale corresponds to a microscopic or particle point of view.From this global vantage point, the gas characteristics measured are either in terms of the gas particles themselves (velocity, pressure, or temperature) or their surroundings (volume). By way of 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 locking the number of particles and temperature. He observed that when the pressure was increased on the gas, by adding more mercury to the column, the trapped gas volume decreased. Mathematicians describe this situation as an inverse relationship. Furthermore, when Boyle multiplied the pressure and volume of each observation, the product (math) was always the same, a constant. This relationship held true for every gas that Boyle observed leading to the law, (PV=k), named to honor his work in this field of study.There are many math tools to choose from when analyzing gas properties. As gases are subjected to extreme conditions, the math tools become a bit more complex, from the Euler equations (inviscid flow) to the Navier-Stokes equations [8] that fully account for viscous effects. These equations are tailored to meet the unique conditions of the gas system in question. Boyle's lab equipment allowed the use of algebra 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 enable safety calculations for a variety of flight conditions on the materials in use. 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. This advanced math, to include statistics and multivariable calculus, makes possible the solution to such complex dynamic situations as space vehicle reentry. One such example might be the analysis of the image depicting space shuttle reentry to ensure the material properties under this loading condition are not exceeded. It is safe to say that in this flight regime, the gas is no longer behaving ideally.

PressurePressurized gases.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 the gas exerts on the surface area 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 of the article). The force imparted by a gas particle into the container during this collision is the change in momentum of the particle. As a reminder from classical mechanics, momentum, by definition, is the product of mass and velocity.[9] Notice that during a collision only the normal component of velocity changes. A particle traveling parallel to the wall never changes its momentum. So the average force on a surface must be the average change in linear momentum from all of these gas particle collisions. To be more precise, 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. The image "Pressurized gases" depicts gas pressure and temperature spikes used in the entertainment industry.

TemperatureAir balloon shrinks after submerging into liquid nitrogenMain article: Thermodynamic temperatureThe 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.[10] In statistical mechanics, temperature is the measure of the average kinetic energy stored in a particle. The methods of storing this energy are dictated by the degrees of freedom of the particle itself (energy modes). Kinetic energy added (endothermic process) to gas particles by way of collisions produces linear, rotational, and vibrational motion as well. By contrast, a molecule in a solid can only increase its vibration modes with the addition of heat as the lattice crystal structure prevents both linear and rotational motions. These heated gas molecules have a greater speed range which constantly varies due to constant 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 volumeExpanding gases link to changes in specific volume.: Specific volumeThe symbol used to represent specific volume in equations is "v" with SI units of cubic meters per kilogram.Gas volumeThe 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.[11] 1000 atoms of protactinium as 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. When the seat ejection is initiated in the rocket sled image the specific volume increases with the expanding gases, while mass is conserved. Since a gas fills any container in which it is placed, volume is an extensive property.

DensityThe symbol used to represent density in equations is ρ (pronounced 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 mass per volume of a substance or simply, 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 or both. 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 is a simple physical quantity that has a magnitude but no direction associated with it. 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.

MicroscopicIf one could observe a gas under a powerful microscope, one would see a collection of particles (molecules, atoms, ions, electrons, etc.) without any definite shape or volume that are in more or less random motion. These neutral gas particles only change direction when they collide with another particle or the sides of the container. By stipulating that these collisions are perfectly elastic, this substance is transformed from a real to an ideal gas. This particle or microscopic view of a gas is described by the Kinetic-molecular theory. All of the assumptions behind this theory can be found in the postulates section of Kinetic Theory.

Kinetic theoryKinetic 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 [12] , one can use the conservation of momentum and geometric relationships of a cube to relate macro 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 theory also explains how the gas system responds to change. For example, as a gas is heated from absolute zero, when it is (in theory) perfectly still, its internal energy (temperature) is increased. As a gas is heated, the particles speed up and its temperature rise. This results in greater numbers of collisions with the container sides each second due to the higher particle speeds associated with elevated temperatures. As the number of collisions (per unit time) increase on the surface area of the container, the pressure increases in a proportional manner.

Brownian motionBrownian 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 as to how they move, but their motion is different from Brownian Motion. The reason is that 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 was examined.

Intermolecular forces

When gases are compressed, intermolecular forces like those shown here start to play a more active role.Main articles: van der Waals force and Intermolecular forceAs discussed earlier, momentary attractions (or repulsions) between particles have an effect on gas dynamics. In physical chemistry, the name given to these intermolecular forces is van der Waals force. These forces play a key role in determining physical properties of a gas such as viscosity and flow rate (see physical characteristics section). Ignoring these forces in certain conditions (see Kinetic-molecular theory) allows a real gas to be treated like an ideal gas. This assumption allows the use of ideal gas laws which greatly simplifies the path to a solution.Proper use of these gas relationships requires us to take one more look at the Kinetic-molecular theory (KMT). When these gas particles possess a magnetic charge or Intermolecular force they gradually influence one another as the spacing between them is reduced (the hydrogen bond model illustrates one example). In the absence of any charge, at some point when the spacing between gas particles is greatly reduced they can no longer avoid collisions between themselves at normal gas temperatures found in a lab. Another case for increased collisions among gas particles would include a fixed volume of gas, which upon heating would contain very fast particles. What this means to us is that these ideal equations provide reasonable results except for extremely high pressure [compressible] or high temperature [ionized] conditions. Notice that all of these excepted conditions allow energy transfer to take place within the gas system. The absence of these internal transfers is what is referred to as ideal conditions (perfect - or well behaved) in which the energy exchange occurs only at the boundaries of the system. Real gases experience some of these collisions and intermolecular forces. When these collisions are statistically negligible [incompressible], results from these ideal equations are still valid. At the other end of the spectrum, when the gas particles are compressed into close proximity they behave more like a liquid, and hence another connection to fluid dynamics.

Simplified modelsAn 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[13]. Each successive model expands the temperature range of coverage to which it applies. The image of first powered flight at Kitty Hawk, North Carolina illustrates one example on the successful application of these relationships in 1903. More recent examples include the 2009 maiden flights of the first solar powered aircraft, the Solar Impulse, and the first commercial airliner to be constructed primarily from composite materials, the Dreamliner.

Perfect gasBy definition, a perfect gas is one in which intermolecular forces are negligible due to the separation of the molecules and any particle collisions are elastic.Perfect gas equation of stateThe symbol n represents the number of particles grouped by moles of a substance. All other symbols in these equations use notation described earlier in the Macroscopic Section. These relationships are valid only when used with absolute temperatures and pressures.Chemist's version – PV = nRTThe gas constant, R, in this expression has different units than the Gas Dynamicist's version. The Chemist's version emphasizes numbers of particles (n), while the latter emphasizes the particle mass in the density term ρ.Gas Dynamicist's version- P = ρRTThere are two subclassifications to a perfect gas although various textbooks either omit or combine the following simplifications into a general "perfect gas" definition. For sake of clarity, these simplifications are defined separately in the following two subsections.

Calorically perfectThe Calorically perfect gas model is the most restrictive from a temperature perspective[14], as it adds the following condition:Constant specific heats (valid for most gases below 1000 K)u = CvT, h = CpTHere u represents internal energy, h represents enthalpy, and the C terms represent the specific heat capacity at either constant volume or constant pressure, respectively.Although this may be the most restrictive model from a temperature perspective, it is accurate enough to make reasonable predictions within the limits specified. A comparison of calculations for one compression stage of an axial compressor (one with variable Cp, and one with constant Cp) produces a deviation small enough to support this approach. As it turns out, other factors come into play and dominate during this compression cycle. These other effects would have a greater impact on the final calculated result than whether or not Cp was held constant. (examples of these real gas effects include compressor tip-clearance, separation, and boundary layer/frictional losses, etc.)

Thermally perfectA thermally perfect gas is:in thermodynamic equilibriumnot chemically reacting (chemical equilibrium)cp - cv = R (still valid even though specific heats vary with temperature)Internal energy, enthalpy, and specific heats are functions of temperature only.u = u(T), h = h(T), du = CvdT, dh = CpdT

This type of approximation is useful for modeling, for example, a turbine where temperature fluctuations are usually not large enough to cause any significant deviations from the thermally perfect gas model. Heat capacity is still allowed to vary, though only with temperature and the molecules are not permitted to dissociate. [15]

Ideal gasAn "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 [16] . It may also be useful to keep the elementary reactions and chemical dissociations for calculating emissions.

Real gasEach one of the assumptions listed below adds to the complexity of the problem's solution. As the density of a gas increases with pressure rises, 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).[17] 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 effectsIssues 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 are present or the gases produced during geological events as in the image of the 1990 eruption of Mount Redoubt.

Compressibility factors for air.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.[edit] Reynolds NumberMain article: Reynolds numberIn fluid mechanics, the Reynolds number is the ratio of inertial forces (vsρ) to viscous forces (μ/L). 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 Reynold's number provides the link between modeling results (design) and the full scale actual conditions. It can also be used to characterize the flow.

ViscositySatellite view of weather pattern in vicinity of Robinson Crusoe Islands on 15 September 1999, shows a unique turbulent cloud pattern called a Kármán vortex streetMain article: ViscosityViscosity, 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).

TurbulenceDelta wing in wind tunnel. The shadows form as the indices of refraction change within the gas as it compresses on the leading edge of this wing.Main article: TurbulenceIn 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 just one example.

Boundary layerParticles 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.

Maximum entropy principleAs 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 equilibriumWhen 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.