In molecular geometry, bond length or bond distance is the average distance between nuclei of two bonded atoms in a molecule. It is a transferable property of a bond between atoms of fixed types independent of the rest of the molecule. Bond length is related to bond order: when more electrons participate in bond formation the bond is shorter. Bond length is inversely related to bond strength and the bond dissociation energy: all other factors being equal, a stronger bond will be shorter. In a bond between two identical atoms, half the bond distance is equal to the covalent radius. Bond lengths are measured in the solid phase by means of X-ray diffraction, or approximated in the gas phase by microwave spectroscopy. A bond between a given pair of atoms may vary between different molecules. For example, the carbon to hydrogen bonds in methane are different from those in methyl chloride, it is however possible to make generalizations. A table with experimental single bonds for carbon to other elements is given below.
Bond lengths are given in picometers. By approximation the bond distance between two different atoms is the sum of the individual covalent radii; as a general trend, bond distances decrease across the row in the periodic table and increase down a group. This trend is identical to that of the atomic radius; the bond length between two atoms in a molecule depends not only on the atoms but on such factors as the orbital hybridization and the electronic and steric nature of the substituents. The carbon–carbon bond length in diamond is 154 pm, the largest bond length that exists for ordinary carbon covalent bonds. Since one atomic unit of length is 52.9177 pm, the C–C bond length is 2.91 atomic units, or three Bohr radii long. Unusually long bond lengths do exist. In one compound, tricyclobutabenzene, a bond length of 160 pm is reported; the current record holder is another cyclobutabenzene with length 174 pm based on X-ray crystallography. In this type of compound the cyclobutane ring would force 90° angles on the carbon atoms connected to the benzene ring where they ordinarily have angles of 120°.
The existence of a long C–C bond length of up to 290 pm is claimed in a dimer of two tetracyanoethylene dianions, although this concerns a 2-electron-4-center bond. This type of bonding has been observed in neutral phenalenyl dimers; the bond lengths of these so-called "pancake bonds" are up to 305 pm. Shorter than average C–C bond distances are possible: alkenes and alkynes have bond lengths of 133 and 120 pm due to increased s-character of the sigma bond. In benzene all bonds have the same length: 139 pm. Carbon–carbon single bonds increased s-character is notable in the central bond of diacetylene and that of a certain tetrahedrane dimer. In propionitrile the cyano group withdraws electrons resulting in a reduced bond length. Squeezing a C–C bond is possible by application of strain. An unusual organic compound exists called In-methylcyclophane with a short bond distance of 147 pm for the methyl group being squeezed between a triptycene and a phenyl group. In an in silico experiment a bond distance of 136 pm was estimated for neopentane locked up in fullerene.
The smallest theoretical C–C single bond obtained in this study is 131 pm for a hypothetical tetrahedrane derivative. The same study estimated that stretching or squeezing the C–C bond in an ethane molecule by 5 pm required 2.8 or 3.5 kJ/mol, respectively. Stretching or squeezing the same bond by 15 pm required an estimated 21.9 or 37.7 kJ/mol. Bond length tutorial
Critical point (thermodynamics)
In thermodynamics, a critical point is the end point of a phase equilibrium curve. The most prominent example is the liquid-vapor critical point, the end point of the pressure-temperature curve that designates conditions under which a liquid and its vapor can coexist. At higher temperatures, the gas cannot be liquefied by pressure alone. At the critical point, defined by a critical temperature Tc and a critical pressure pc, phase boundaries vanish. Other examples include the liquid–liquid critical points in mixtures. For simplicity and clarity, the generic notion of critical point is best introduced by discussing a specific example, the liquid-vapor critical point; this was the first critical point to be discovered, it is still the best known and most studied one. The figure to the right shows the schematic PT diagram of a pure substance; the known phases solid and vapor are separated by phase boundaries, i.e. pressure-temperature combinations where two phases can coexist. At the triple point, all three phases can coexist.
However, the liquid-vapor boundary terminates in an endpoint at some critical temperature Tc and critical pressure pc. This is the critical point. In water, the critical point occurs at 22.064 MPa. In the vicinity of the critical point, the physical properties of the liquid and the vapor change with both phases becoming more similar. For instance, liquid water under normal conditions is nearly incompressible, has a low thermal expansion coefficient, has a high dielectric constant, is an excellent solvent for electrolytes. Near the critical point, all these properties change into the exact opposite: water becomes compressible, expandable, a poor dielectric, a bad solvent for electrolytes, prefers to mix with nonpolar gases and organic molecules. At the critical point, only one phase exists; the heat of vaporization is zero. There is a stationary inflection point in the constant-temperature line on a PV diagram; this means that at the critical point: T = 0 T = 0 Above the critical point there exists a state of matter, continuously connected with both the liquid and the gaseous state.
It is called supercritical fluid. The common textbook knowledge that all distinction between liquid and vapor disappears beyond the critical point has been challenged by Fisher and Widom who identified a p,T-line that separates states with different asymptotic statistical properties; the existence of a critical point was first discovered by Charles Cagniard de la Tour in 1822 and named by Dmitri Mendeleev in 1860 and Thomas Andrews in 1869. Cagniard showed that CO2 could be liquefied at 31 °C at a pressure of 73 atm, but not at a higher temperature under pressures as high as 3,000 atm. Solving the above condition T = 0 for the van der Waals equation, one can compute the critical point as T c = 8 a 27 R b, V c = 3 n b, p c = a 27 b 2. However, the van der Waals equation, based on a mean field theory, does not hold near the critical point. In particular, it predicts wrong scaling laws. To analyse properties of fluids near the critical point, reduced state variables are sometimes defined relative to the critical properties T r = T T c, p r = p p c, V r = V R T c / p c.
The principle of corresponding states indicates that substances at equal reduced pressures and temperatures have equal reduced volumes. This relationship is true for many substances, but becomes inaccurate for large values of pr. For some gases, there is an additional correction factor, called Newton's correction, added to the critical temperature and critical pressure calculated in this manner; these vary with the pressure range of interest. The liquid–liquid critical point of a solution, which occurs at the critical solution temperature, occurs at the limit of the two-phase region of the phase diagram. In other words, it is the point at which an infinitesimal change in some thermodynamic variable will lead to separation of the mixture into two distinct liquid phases, as shown in the polymer–solvent phase diagram to the right. Two types of liquid–liquid critical points are the upper critical solution temperature, t
In optics, the refractive index or index of refraction of a material is a dimensionless number that describes how fast light propagates through the material. It is defined as n = c v, where c is the speed of light in vacuum and v is the phase velocity of light in the medium. For example, the refractive index of water is 1.333, meaning that light travels 1.333 times as fast in vacuum as in water. The refractive index determines how much the path of light is bent, or refracted, when entering a material; this is described by Snell's law of refraction, n1 sinθ1 = n2 sinθ2, where θ1 and θ2 are the angles of incidence and refraction of a ray crossing the interface between two media with refractive indices n1 and n2. The refractive indices determine the amount of light, reflected when reaching the interface, as well as the critical angle for total internal reflection and Brewster's angle; the refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, the wavelength in that medium is λ = λ0/n, where λ0 is the wavelength of that light in vacuum.
This implies that vacuum has a refractive index of 1, that the frequency of the wave is not affected by the refractive index. As a result, the energy of the photon, therefore the perceived color of the refracted light to a human eye which depends on photon energy, is not affected by the refraction or the refractive index of the medium. While the refractive index affects wavelength, it depends on photon frequency and energy so the resulting difference in the bending angle causes white light to split into its constituent colors; this is called dispersion. It can be observed in prisms and rainbows, chromatic aberration in lenses. Light propagation in absorbing materials can be described using a complex-valued refractive index; the imaginary part handles the attenuation, while the real part accounts for refraction. The concept of refractive index applies within the full electromagnetic spectrum, from X-rays to radio waves, it can be applied to wave phenomena such as sound. In this case the speed of sound is used instead of that of light, a reference medium other than vacuum must be chosen.
The refractive index n of an optical medium is defined as the ratio of the speed of light in vacuum, c = 299792458 m/s, the phase velocity v of light in the medium, n = c v. The phase velocity is the speed at which the crests or the phase of the wave moves, which may be different from the group velocity, the speed at which the pulse of light or the envelope of the wave moves; the definition above is sometimes referred to as the absolute refractive index or the absolute index of refraction to distinguish it from definitions where the speed of light in other reference media than vacuum is used. Air at a standardized pressure and temperature has been common as a reference medium. Thomas Young was the person who first used, invented, the name "index of refraction", in 1807. At the same time he changed this value of refractive power into a single number, instead of the traditional ratio of two numbers; the ratio had the disadvantage of different appearances. Newton, who called it the "proportion of the sines of incidence and refraction", wrote it as a ratio of two numbers, like "529 to 396".
Hauksbee, who called it the "ratio of refraction", wrote it as a ratio with a fixed numerator, like "10000 to 7451.9". Hutton wrote it as a ratio with a fixed denominator, like 1.3358 to 1. Young did not use a symbol for the index of refraction, in 1807. In the next years, others started using different symbols: n, m, µ; the symbol n prevailed. For visible light most transparent media have refractive indices between 1 and 2. A few examples are given in the adjacent table; these values are measured at the yellow doublet D-line of sodium, with a wavelength of 589 nanometers, as is conventionally done. Gases at atmospheric pressure have refractive indices close to 1 because of their low density. All solids and liquids have refractive indices above 1.3, with aerogel as the clear exception. Aerogel is a low density solid that can be produced with refractive index in the range from 1.002 to 1.265. Moissanite lies at the other end of the range with a refractive index as high as 2.65. Most plastics have refractive indices in the range from 1.3 to 1.7, but some high-refractive-index polymers can have values as high as 1.76.
For infrared light refractive indices can be higher. Germanium is transparent in the wavelength region from 2 to 14 µm and has a refractive index of about 4. A type of new materials, called topological insulator, was found holding higher refractive index of up to 6 in near to mid infrared frequency range. Moreover, topological insulator material are transparent; these excellent properties make them a type of significant materials for infrared optics. According to the theory of relativity, no information can travel faster than the speed of light in vacuum, but this does not mean that the refractive index cannot be lower than 1; the refractive index measures the phase velocity of light. The phase velocity is the speed at which the crests of the wave move and can be faster than the speed of light in vacuum, thereby give a refractive index below 1; this can occur close to resonance frequencies, for absorbing media, in plasmas, for X-rays. In the X-ray regime the refractive indices are
Enthalpy of vaporization
The enthalpy of vaporization known as the heat of vaporization or heat of evaporation, is the amount of energy that must be added to a liquid substance, to transform a quantity of that substance into a gas. The enthalpy of vaporization is a function of the pressure; the enthalpy of vaporization is quoted for the normal boiling temperature of the substance. The heat of vaporization is temperature-dependent, though a constant heat of vaporization can be assumed for small temperature ranges and for reduced temperature T r ≪ 1; the heat of vaporization diminishes with increasing temperature and it vanishes at a certain point called the critical temperature. Above the critical temperature, the liquid and vapor phases are indistinguishable, the substance is called a supercritical fluid. Values are quoted in J/mol or kJ/mol, although kJ/kg or J/g, older units like kcal/mol, cal/g and Btu/lb are sometimes still used, among others; the enthalpy of condensation is by definition equal to the enthalpy of vaporization with the opposite sign: enthalpy changes of vaporization are always positive, whereas enthalpy changes of condensation are always negative.
The enthalpy of vaporization can be written as Δ H v a p = Δ U v a p + p Δ V It is equal to the increased internal energy of the vapor phase compared with the liquid phase, plus the work done against ambient pressure. The increase in the internal energy can be viewed as the energy required to overcome the intermolecular interactions in the liquid. Hence helium has a low enthalpy of vaporization, 0.0845 kJ/mol, as the van der Waals forces between helium atoms are weak. On the other hand, the molecules in liquid water are held together by strong hydrogen bonds, its enthalpy of vaporization, 40.65 kJ/mol, is more than five times the energy required to heat the same quantity of water from 0 °C to 100 °C. Care must be taken, when using enthalpies of vaporization to measure the strength of intermolecular forces, as these forces may persist to an extent in the gas phase, so the calculated value of the bond strength will be too low; this is true of metals, which form covalently bonded molecules in the gas phase: in these cases, the enthalpy of atomization must be used to obtain a true value of the bond energy.
An alternative description is to view the enthalpy of condensation as the heat which must be released to the surroundings to compensate for the drop in entropy when a gas condenses to a liquid. As the liquid and gas are in equilibrium at the boiling point, ΔvG = 0, which leads to: Δ v S = S g a s − S l i q u i d = Δ v H / T b As neither entropy nor enthalpy vary with temperature, it is normal to use the tabulated standard values without any correction for the difference in temperature from 298 K. A correction must be made if the pressure is different from 100 kPa, as the entropy of a gas is proportional to its pressure: the entropies of liquids vary little with pressure, as the compressibility of a liquid is small; these two definitions are equivalent: the boiling point is the temperature at which the increased entropy of the gas phase overcomes the intermolecular forces. As a given quantity of matter always has a higher entropy in the gas phase than in a condensed phase, from Δ G = Δ H − T Δ S,the Gibbs free energy change falls with increasing temperature: gases are favored at higher temperatures, as is observed in practice.
Estimation of the enthalpy of vaporization of electrolyte solutions can be carried out using equations based on the chemical thermodynamic models, such as Pitzer model or TCPC model. The vaporization of metals is a key step in metal vapor synthesis, which exploits the increased reactivity of metal atoms or small particles relative to the bulk elements. Enthalpies of vaporization of common substances, measured at their respective standard boiling points: Enthalpy of fusion Enthalpy of sublimation Joback method CODATA Key Values for Thermodynamics Gmelin, Leopold. Gmelin-Handbuch der anorganischen Chemie / 08 a. Berlin: Springer. Pp. 116–117. ISBN 978-3-540-93516-2. NIST Chemistry WebBook Young, Francis W. Sears, Mark W. Zemansky, Hugh D.. University physics. Read
Aluminium oxide or aluminum oxide is a chemical compound of aluminium and oxygen with the chemical formula Al2O3. It is the most occurring of several aluminium oxides, identified as aluminium oxide, it is called alumina and may be called aloxide, aloxite, or alundum depending on particular forms or applications. It occurs in its crystalline polymorphic phase α-Al2O3 as the mineral corundum, varieties of which form the precious gemstones ruby and sapphire. Al2O3 is significant in its use to produce aluminium metal, as an abrasive owing to its hardness, as a refractory material owing to its high melting point. Corundum is the most common occurring crystalline form of aluminium oxide. Rubies and sapphires are gem-quality forms of corundum, which owe their characteristic colors to trace impurities. Rubies are given their characteristic deep red color and their laser qualities by traces of chromium. Sapphires come in different colors given by various other impurities, such as titanium. Al2O3 is an electrical insulator but has a high thermal conductivity for a ceramic material.
Aluminium oxide is insoluble in water. In its most occurring crystalline form, called corundum or α-aluminium oxide, its hardness makes it suitable for use as an abrasive and as a component in cutting tools. Aluminium oxide is responsible for the resistance of metallic aluminium to weathering. Metallic aluminium is reactive with atmospheric oxygen, a thin passivation layer of aluminium oxide forms on any exposed aluminium surface; this layer protects the metal from further oxidation. The thickness and properties of this oxide layer can be enhanced using a process called anodising. A number of alloys, such as aluminium bronzes, exploit this property by including a proportion of aluminium in the alloy to enhance corrosion resistance; the aluminium oxide generated by anodising is amorphous, but discharge assisted oxidation processes such as plasma electrolytic oxidation result in a significant proportion of crystalline aluminium oxide in the coating, enhancing its hardness. Aluminium oxide was taken off the United States Environmental Protection Agency's chemicals lists in 1988.
Aluminium oxide is on the EPA's Toxics Release Inventory list. Aluminium oxide is an amphoteric substance, meaning it can react with both acids and bases, such as hydrofluoric acid and sodium hydroxide, acting as an acid with a base and a base with an acid, neutralising the other and producing a salt. Al2O3 + 6 HF → 2 AlF3 + 3 H2O Al2O3 + 2 NaOH + 3 H2O → 2 NaAl4 The most common form of crystalline aluminium oxide is known as corundum, the thermodynamically stable form; the oxygen ions form a nearly hexagonal close-packed structure with the aluminium ions filling two-thirds of the octahedral interstices. Each Al3+ center is octahedral. In terms of its crystallography, corundum adopts a trigonal Bravais lattice with a space group of R3c; the primitive cell contains two formula units of aluminium oxide. Aluminium oxide exists in other, phases, including the cubic γ and η phases, the monoclinic θ phase, the hexagonal χ phase, the orthorhombic κ phase and the δ phase that can be tetragonal or orthorhombic.
Each has properties. Cubic γ-Al2O3 has important technical applications; the so-called β-Al2O3 proved to be NaAl11O17. Molten aluminium oxide near the melting temperature is 2/3 tetrahedral, 1/3 5-coordinated, with little octahedral Al-O present. Around 80% of the oxygen atoms are shared among three or more Al-O polyhedra, the majority of inter-polyhedral connections are corner-sharing, with the remaining 10–20% being edge-sharing; the breakdown of octahedra upon melting is accompanied by a large volume increase, the density of the liquid close to its melting point is 2.93 g/cm3. The structure of molten alumina is temperature dependent and the fraction of 5- and 6-fold aluminium increases during cooling, at the expense of tetrahedral AlO4 units, approaching the local structural arrangements found in amorphous alumina. Aluminium hydroxide minerals are the main component of the principal ore of aluminium. A mixture of the minerals comprise bauxite ore, including gibbsite and diaspore, along with impurities of iron oxides and hydroxides and clay minerals.
Bauxites are found in laterites. Bauxite is purified by the Bayer process: Al2O3 + H2O + NaOH → NaAl4 Al3 + NaOH → NaAl4Except for SiO2, the other components of bauxite do not dissolve in base. Upon filtering the basic mixture, Fe2O3 is removed; when the Bayer liquor is cooled, Al3 precipitates. NaAl4 → NaOH + Al3The solid Al3 Gibbsite is calcined to give aluminium oxide: 2 Al3 → Al2O3 + 3 H2OThe product aluminium oxide tends to be multi-phase, i.e. consisting of several phases of aluminium oxide rather than corundum. The production process can therefore be optimized to produce a tailored product; the type of phases present affects, for example, the solubility and pore structure of the aluminium oxide product which, in turn, affects the cost of aluminium production and pollution control. Known as alundum or aloxite in the mining and materials science communities, aluminium oxide finds wide use. Annual world production of aluminium oxide in 2015 was 115 million tonnes, over 90% of, used in the manufacture of aluminium metal.
The major uses of speciali
Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent; the birefringence is quantified as the maximum difference between refractive indices exhibited by the material. Crystals with non-cubic crystal structures are birefringent, as are plastics under mechanical stress. Birefringence is responsible for the phenomenon of double refraction whereby a ray of light, when incident upon a birefringent material, is split by polarization into two rays taking different paths; this effect was first described by the Danish scientist Rasmus Bartholin in 1669, who observed it in calcite, a crystal having one of the strongest birefringences. However it was not until the 19th century that Augustin-Jean Fresnel described the phenomenon in terms of polarization, understanding light as a wave with field components in transverse polarizations. A mathematical description of wave propagation in a birefringent medium is presented below.
Following is a qualitative explanation of the phenomenon. The simplest type of birefringence is described as uniaxial, meaning that there is a single direction governing the optical anisotropy whereas all directions perpendicular to it are optically equivalent, thus rotating the material around this axis does not change its optical behavior. This special direction is known as the optic axis of the material. Light propagating parallel to the optic axis is governed by a refractive index no. Light whose polarization is in the direction of the optic axis sees an optical index ne. For any ray direction there is a linear polarization direction perpendicular to the optic axis, this is called an ordinary ray. However, for ray directions not parallel to the optic axis, the polarization direction perpendicular to the ordinary ray's polarization will be in the direction of the optic axis, this is called an extraordinary ray. I.e. when unpolarized light enters an uniaxial birefringent material it is split into two beams travelling different directions.
The ordinary ray will always experience a refractive index of no, whereas the refractive index of the extraordinary ray will be in between no and ne, depending on the ray direction as described by the index ellipsoid. The magnitude of the difference is quantified by the birefringence: Δ n = n e − n o; the propagation of the ordinary ray is described by no as if there were no birefringence involved. However the extraordinary ray, as its name suggests, propagates unlike any wave in a homogenous optical material, its refraction at a surface can be understood using the effective refractive index. However it is in fact an inhomogeneous wave whose power flow is not in the direction of the wave vector; this causes an additional shift in that beam when launched at normal incidence, as is popularly observed using a crystal of calcite as photographed above. Rotating the calcite crystal will cause one of the two images, that of the extraordinary ray, to rotate around that of the ordinary ray, which remains fixed.
When the light propagates either along or orthogonal to the optic axis, such a lateral shift does not occur. In the first case, both polarizations see the same effective refractive index, so there is no extraordinary ray. In the second case the extraordinary ray propagates at a different phase velocity but is not an inhomogeneous wave. A crystal with its optic axis in this orientation, parallel to the optical surface, may be used to create a waveplate, in which there is no distortion of the image but an intentional modification of the state of polarization of the incident wave. For instance, a quarter-wave plate is used to create circular polarization from a linearly polarized source; the case of so-called biaxial crystals is more complex. These are characterized by three refractive indices corresponding to three principal axes of the crystal. For most ray directions, both polarizations would be classified as extraordinary rays but with different effective refractive indices. Being extraordinary waves, the direction of power flow is not identical to the direction of the wave vector in either case.
The two refractive indices can be determined using the index ellipsoids for given directions of the polarization. Note that for biaxial crystals the index ellipsoid will not be an ellipsoid of revolution but is described by three unequal principle refractive indices nα, nβ and nγ, thus there is no axis. Although there is no axis of symmetry, there are two optical axes or binormals which are defined as directions along which light may propagate without birefringence, i.e. directions along which the wavelength is independent of polarization. For this reason, birefringent materials with three distinct refractive indices are called biaxial. Additionally, there are two distinct axes known as optical ray axes or biradials along which the group velocity of the light is independent of polarization; when an arbitrary beam of light strikes the surface of a b
Ultraviolet–visible spectroscopy or ultraviolet–visible spectrophotometry refers to absorption spectroscopy or reflectance spectroscopy in part of the ultraviolet and the full, adjacent visible spectral regions. This means it uses light in the adjacent ranges; the absorption or reflectance in the visible range directly affects the perceived color of the chemicals involved. In this region of the electromagnetic spectrum and molecules undergo electronic transitions. Absorption spectroscopy is complementary to fluorescence spectroscopy, in that fluorescence deals with transitions from the excited state to the ground state, while absorption measures transitions from the ground state to the excited state. Molecules containing bonding and non-bonding electrons can absorb energy in the form of ultraviolet or visible light to excite these electrons to higher anti-bonding molecular orbitals; the more excited the electrons, the longer the wavelength of light it can absorb. There are four possible types of transitions, they can be ordered as follows: σ–σ* > n–σ* > π–π* > n–π*.
UV/Vis spectroscopy is used in analytical chemistry for the quantitative determination of different analytes, such as transition metal ions conjugated organic compounds, biological macromolecules. Spectroscopic analysis is carried out in solutions but solids and gases may be studied. Solutions of transition metal ions can be colored because d electrons within the metal atoms can be excited from one electronic state to another; the colour of metal ion solutions is affected by the presence of other species, such as certain anions or ligands. For instance, the colour of a dilute solution of copper sulfate is a light blue. Organic compounds those with a high degree of conjugation absorb light in the UV or visible regions of the electromagnetic spectrum; the solvents for these determinations are water for water-soluble compounds, or ethanol for organic-soluble compounds. Solvent polarity and pH can affect the absorption spectrum of an organic compound. Tyrosine, for example, increases in absorption maxima and molar extinction coefficient when pH increases from 6 to 13 or when solvent polarity decreases.
While charge transfer complexes give rise to colours, the colours are too intense to be used for quantitative measurement. The Beer–Lambert law states that the absorbance of a solution is directly proportional to the concentration of the absorbing species in the solution and the path length. Thus, for a fixed path length, UV/Vis spectroscopy can be used to determine the concentration of the absorber in a solution, it is necessary to know how the absorbance changes with concentration. This can be taken from references, or more determined from a calibration curve. A UV/Vis spectrophotometer may be used as a detector for HPLC; the presence of an analyte gives. For accurate results, the instrument's response to the analyte in the unknown should be compared with the response to a standard; the response for a particular concentration is known as the response factor. The wavelengths of absorption peaks can be correlated with the types of bonds in a given molecule and are valuable in determining the functional groups within a molecule.
The Woodward–Fieser rules, for instance, are a set of empirical observations used to predict λmax, the wavelength of the most intense UV/Vis absorption, for conjugated organic compounds such as dienes and ketones. The spectrum alone is not, however, a specific test for any given sample; the nature of the solvent, the pH of the solution, high electrolyte concentrations, the presence of interfering substances can influence the absorption spectrum. Experimental variations such as the slit width of the spectrophotometer will alter the spectrum. To apply UV/Vis spectroscopy to analysis, these variables must be controlled or accounted for in order to identify the substances present; the method is most used in a quantitative way to determine concentrations of an absorbing species in solution, using the Beer–Lambert law: A = log 10 = ε c L,where A is the measured absorbance, I 0 is the intensity of the incident light at a given wavelength, I is the transmitted intensity, L the path length through the sample, c the concentration of the absorbing species.
For each species and wavelength, ε is a constant known as the molar absorptivity or extinction coefficient. This constant is a fundamental molecular property in a given solvent, at a particular temperature and pressure, has units of 1 / M ∗ c m; the absorbance and extinction ε are sometimes defined in terms of the natural logarithm instead of the base-10 logarithm. The Beer–Lambert Law is useful for characterizing many compounds but does not hold as a universal relationship for the concentration and absorption of all s