Absorbance, A

Cobalt(II) compounds are often incorporated in the gel. When the gel has absorbed a fair amount of moisture it will turn pink but will revert to blue on heating. 

If the sample is placed in the path of the infrared beam, usually between the source and the monochromator, it will absorb a part of the photon energy having the same frequency as the vibrations of the sample molecule s atoms. The comparison of the source s emission spectrum with that obtained by transmission through the sample is the sample s transmittance spectrum. 

The total energy absorbed, A , is the integral of tire power over time. Keeping just the lowest order tenns we find... 

There are two fimdamental types of spectroscopic studies absorption and emission. In absorption spectroscopy an atom or molecule in a low-lying electronic state, usually the ground state, absorbs a photon to go to a higher state. In emission spectroscopy the atom or molecule is produced in a higher electronic state by some excitation process, and emits a photon in going to a lower state. In this section we will consider the traditional instrumentation for studying the resulting spectra. They define the quantities measured and set the standard for experimental data to be considered. 

It is usually convenient to work with the decadic absorbance. A, defined by... 

X-ray photoelectron spectroscopy (XPS) is among the most frequently used surface chemical characterization teclmiques. Several excellent books on XPS are available [1, 2, 3, 4, 5, 6 and 7], XPS is based on the photoelectric effect an atom absorbs a photon of energy hv from an x-ray source next, a core or valence electron with bindmg energy is ejected with kinetic energy (figure Bl.25.1) ... 

For two Bom-Oppenlieimer surfaces (the ground state and a single electronic excited state), the total photodissociation cross section for the system to absorb a photon of energy ai, given that it is initially at a state x) with energy can be shown, by simple application of second-order perturbation theory, to be [89]... 

An illustrative example generates a 2 x 2 calibration matrix from which we can determine the concentrations xi and X2 of dichromate and permanganate ions simultaneously by making spectrophotometric measurements yi and j2 at different wavelengths on an aqueous mixture of the unknowns. The advantage of this simple two-component analytical problem in 3-space is that one can envision the plane representing absorbance A as a linear function of two concentration variables A =f xuX2). 

The absorbance A is proportional to 1 through Beer s law (see Computer Projeet 2-1). The analytical problem is to solve the matrix equation... 

Thermal neutron absorption cross section. Simply designated cross section, it represents the ease with which a given nuclide can absorb a thermal neutron (energy less than or equal to 0.025 eV) and become a different nuclide. The cross section is given here in units of barns (1 barn = 10 cm ). If the mode of reaction is other than ( ,y), it is so indicated. 

A more important source of UV/Vis absorption for inorganic metal-ligand complexes is charge transfer, in which absorbing a photon produces an excited state species that can be described in terms of the transfer of an electron from the metal, M, to the ligand, L. 

An alternative method for expressing the attenuation of electromagnetic radiation is absorbance. A, which is defined as... 

The absorptivity and molar absorptivity give, in effect, the probability that the analyte will absorb a photon of given energy. As a result, values for both a and 8 depend on the wavelength of electromagnetic radiation. 

Beer s law can be extended to samples containing several absorbing components provided that there are no interactions between the components. Individual absorbances, A , are additive. For a two-component mixture of X and Y, the total absorbance, Atot, is... 

The concentration of fluoride in drinking water may be determined indirectly by its ability to form a complex with zirconium. In the presence of the dye SPADNS, solutions of zirconium form a reddish colored compound, called a lake, that absorbs at 570 nm. When fluoride is added, the formation of the stable ZrFe complex causes a portion of the lake to dissociate, decreasing the absorbance. A plot of absorbance versus the concentration of fluoride, therefore, has a negative slope. 

Quantitative Analysis of Mixtures The analysis of two or more components in the same sample is straightforward if there are regions in the sample s spectrum in which each component is the only absorbing species. In this case each component can be analyzed as if it were the only species in solution. Unfortunately, UV/Vis absorption bands are so broad that it frequently is impossible to find appropriate wavelengths at which each component of a mixture absorbs separately. Earlier we learned that Beer s law is additive (equation 10.6) thus, for a two-component mixture of X and Y, the mixture s absorbance, A, is... 

Using equation 10.25, the value of can be determined in one of two ways. The simplest approach is to prepare three solutions, each of which contains the same amount, C, of indicator. The pH of one solution is made acidic enough that [HIn] [In-]. The absorbance of this solution gives Anin- The value of Ain is determined by adjusting the pH of the second solution such that [In-] [HIn]. Finally, the pH of the third solution is adjusted to an intermediate value, and the pH and absorbance, A, are recorded. The value of can then be calculated by making appropriate substitutions into equation 10.25. 

Selectivity Selectivity is rarely a problem in molecular absorption spectrophotometry. In many cases it is possible to find a wavelength at which only the analyte absorbs or to use chemical reactions in a manner such that the analyte is the only species that absorbs at the chosen wavelength. When two or more species contribute to the measured absorbance, a multicomponent analysis is still possible, as shown in Example 10.6. 

Theoretical Models of the Response Surface Mathematical models for response surfaces are divided into two categories those based on theory and those that are empirical. Theoretical models are derived from known chemical and physical relationships between the response and the factors. In spectrophotometry, for example, Beer s law is a theoretical model relating a substance s absorbance. A, to its concentration, Ca... 

If all spins ( 1/2) in an atom or molecule are paired (equal numbers of spin +1/2 and -1/2), the total spin must be zero, and that state is described as a singlet (total spin, S = 0 and the state is described by the term 2S + 1 = 1). When a singlet ground-state atom or molecule absorbs a photon, a valence electron of spin 1/2 moves to a higher energy level but maintains the same... 

If the target at which a laser beam is directed can absorb light of the laser wavelength, then the target will absorb a large amount of energy in a very small space in a very short time. 

Induced absorption, in which the molecular (or atom) M absorbs a quantum of radiation and is excited from m to n ... 

If radiation of a particular wavelength I, or wavenumber v, of intensity /q enters a cell of length I, containing an absorbing sample, and emerges from the cell with reduced intensity /, the absorbance A is given by ... 

The above discussion was based on the premise of a single internal reflection. An increase in sensitivity can be realized through the use of multiple internal reflections. In the case of multiple reflections, the absorbance A becomes... 

Fig. 1. Absorption column arrangement with a gas absorber A and a stripper S to recover solvent.

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