Bouguer-Lambert-Beer’s law

This is a generalised form of Bouguer-Lambert-Beer s law. Inserting eq. (1.35) in eq. (1.34) gives the moles of light quanta which are absorbed by reactant A, at a distance z from the entrance window per second and per litre ... 

According to Bouguer-Lambert-Beer s law (see Section 3.3.2, eq. (3.57)) the absorbance in decadic units at any wavelength is measured as a sum of the partial absorbances of all the absorbing components ... 

In Chapter 3 Napierian units were used for absorption coefficients and absorbance. The reason was a simpler handling of the equations. Since instrumentation reads decadic units, they are used in most equations in this chapter. The decadic molar spectral absorption coefficient e of the compounds (i) varies with wavelength A. For this reason Bouguer-Lambert-Beer s law is restricted to monochromatic radiation. This restriction and the interactions between molecules in concentrated solutions cause two problems in applying the law to quantitative evaluation ... 

The Beer-Lambert law (also called the Beer-Lambert-Bouguer law or simply Beer s law) is the linear relationship between absorbance and concentration of an absorber of electromagnetic radiation. The general Beer-Lambert law is usually written as ... 

Beer s Law, 23 107. See also Beer-Lambert expression/law Lambert-Beer-Bouguer law quantitative analysis based on, 23 140-141... 

Lambda-cyhalothrin, in microcapsule formulations, 7 564t Lambda-derived cloning vectors, 12 504-506 Lambda sensor, 10 56 Lambent, commercial defoamer, 3 24 It Lambert-Beer-Bouguer law, 23 126. See also Beer s Law... 

Beer s law (Beer 1852), which, because it builds on earlier observations by Bouguer and Lambert, is also known as the Beer Lambert law. 

The main advantage of multivariate calibration based on CLS with respect to univariate calibration is that CLS does not require selective measurements. Selectivity is obtained mathematically by solving a system of equations, without the requirement for chemical or instrumental separations that are so often needed in univariate calibration. In addition, the model can use a large number of sensors to obtain a signal-averaging effect [4], which is beneficial for the precision of the predicted concentration, making it less susceptible to the noise in the data. Finally, for the case of spectroscopic data, the Lambert Bouguer Beer s law provides a sound foundation for the predictive model. 

The multivariate quantitative spectroscopic analysis of samples with complex matrices can be performed using inverse calibration methods, such as ILS, PCR and PLS. The term "inverse" means that the concentration of the analyte of interest is modelled as a function of the instrumental measurements, using an empirical relationship with no theoretical foundation (as the Lambert Bouguer-Beer s law was for the methods explained in the paragraphs above). Therefore, we can formulate our calibration like eqn (3.3) and, in contrast to the CLS model, it can be calculated without knowing the concentrations of all the constituents in the calibration set. The calibration step requires only the instrumental response and the reference value of the property of interest e.g. concentration) in the calibration samples. An important advantage of this approach is that unknown interferents may be present in the calibration samples. For this reason, inverse models are more suited than CLS for complex samples. 

A Historical Sketch, J. Chem. Ed 1961,38, 129. The equation that we call Beer s law embodies contributions by R Bouguer (1698-1758), J. H. Lambert (1728-1777), and A. Beer (1825-1863). Beer published his work in 1852, and similar conclusions were independently reached and published within a few months by F. Bernard. 

Transparent materials interact with light only by absorption. This interaction is formulated quantitatively in the Bouguer-Lambert and Beer s Laws (c.f. i). In paper, however, surface reflection is the dominating type of interaction. This results in very desirable properties like high brightness and opacity, but complicates the interpretation of optical tests with regard to absorption data. The Kubelka-Munk theory attempts to separate the two types of... 

Light beam of intensity /(v) and the Bouguer-Lambert-Beer law, or Beer s law. 

As with other types of absorption spectroscopy e.g., UV-visible spectroscopy), the basis of quantitative analysis in infrared spectroscopy is the Bouguer-Beer-Lambert law or Beer s law (equation (13)) ... 

Equation (2.9), which summarizes the relationship between absorbance, concentration of the species measured, sample path length, and the absorptivity of the species is known as the Beer-Lambert-Bouguer Law or, more commonly, as Beer s Law. 

The relationship between absorbance and concentration is known as Beer s law (also referred to by other names such as the Beer-Lambert law and the Bouguer-Lambert-Beer law) and is defined by the equation ... 

This fundamental equation for spectrometric quantitative analysis is known as Beer-Lambert-Bouguer law, sometimes shortened to Beer s law or Beer-Lambert law. 

It is often found, within certain concentration limits, that the intensity of the absorption is proportional to both the concentration, c (mole per liter), and the thickness, / (centimeter), of the sample in the beam that is, the absorbance = tic, where e is defined as the molar extinction coeffident. This relationship is referred to as Beer s law or the Beer Lambert law. The law is named after August Beer (1825-1863), a lecturer in Bonn who studied optics, and Johann H. Lambert (1728-1777), a Swiss mathematician. It has been suggested that Beer s law was initially discovered by the French mathematician Pierre Bouguer (1698-1758). Lambert made reference (with attribution) to it and, much later, Beer extended it to its present form. 

The first assumption in spectroscopic measurements is that Beer s law relationship applies between a change in spectrometer response and the concentration of analyte material present in a sample specimen. The Bouguer, Lambert, and Beer relationship assumes that the transmission of a sample within an incident beam is equivalent to 10 exponent the negative product of the molar extinction coefficient (in L mol" cm ), multiplied by the concentration of a molecule in solution (in mol L times the path-length (in cm) of the sample in solution. There are some obvious (and not so obvious) problems with this assumption. The main difficulty in the assumed relationship is that the molecules often interact, and the extinction coefficient (absorptivity) may vary due to changes in the molecular configuration of the sample. The obvious temperature, pressure, and interference issues also create a less than ideal situation for the analyst. However, for many (if not most) analytical problems the relationship holds well enough. 

The following are properties of the Bouguer, Lambert, and Beer (Beer s law) relationship ... 

The term Bouguer-Lambert law is not familiar to many spectroscopists. The term Beer-Lambert law or merely Beer s law is frequently used in its place. Technically, Beer s law refers to the observation that the contribution of an absorber to the absorbance of a sample is proportional to the concentration of the absorber. The symbol k is referred to by some spectroscopists as the Beer-Lambert absorption coejficient. Because of the possibility of decadic or napierian absorbance and the various units by which concentration can be expressed, several different quantities are all Beer-Lambert absorption coefficients. The term absorptivity is commonly used in equations for decadic absorbance and can include concentration in any rmits. The term linear absorption coefficient is the usual name for the linear napierian absorption coefficient of a pure material. 

Quantitative infrared analysis is based upon Beer s law, often called the Bouguer-Beer law or the Lambert-Beer law. The simplest form of Beer s law is... 

Beer s law, also referred to as the Beer-Lambert law, or the Beer-Lambert-Bouguer law, expresses the relationship of the absorption of radiation by the sample to the concentration of the desired component and to the path length of the sample. One of the forms in which the law is written follows ... 

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