Absorbance-concentration relationship

It should be noted that the calculation is based upon an assumption of a linear absorbance/concentration relationship and this may only apply over short concentration ranges. 

The method is capable of detecting as little as 5 pig protein and a calibration curve is necessary because of the variations between different proteins and the non-linearity of the absorbance-concentration relationship. 

The sensitivity should be such that the desired or optimum absorbance concentration relationship is achieved and sustained from determination to determination. 

In addition to the quantitative analysis of mixtures, measurement of the intensity of an IR band can be used to determine reaction rates of slow to moderate reactions. The reactant or product has to have a clean absorption band and the absorbance concentration relationship must be determined from calibration standards. The reaction cannot be extremely fast because the band has to be scanned and even FTIR spectrometers are not instantaneous. FTIR spectrometers have permitted the determination of the kinetics of reactions much more rapid than could be handled by dispersive instruments. 

In the case of samples that produce scatter in transmission or diffuse reflectance spectra, a number of factors corrupt the linearity of the Beer-Lambert absorbance concentration relationship. Sample scattering of radiation results in an alteration of the proportion of absorbed and reflected radiation so that pathlength becomes another unknown in the Beer-Lambert relationship. Particle size, particle shape, crystalline form, bulk, density, and the nature of the pore space (filled with air, water, or oil) are all variables that dictate the effective pathlength of the radiation. Sample surfaces also reflect specular energy that has not interacted with molecular structures. This form of energy has an overall effect on spectra, contributing primarily to the curvilinearity of the spectral baseline. 

Recall that large peaks frequently do not subtract completely because they may have a nonlinear absorbance/concentration relationship. These peaks are present in subtraction results and are a form of subtraction artifact. Comparison of the reference spectrum and result can help spot these artifacts any features common to both are unsubtracted reference peaks. This type of comparison is illustrated in Figure 3.5 where an unsubtracted reference peak from liquid water was spotted by comparing the reference to the result. There is nothing we can do to force a particular peak to follow Beer s Law. Hence there is nothing that can be done about unsubtracted reference bands except to learn to recognize them and ignore them. 

The left-hand-side quantity is the absorbance, A, and the linear relationship between absorbance, concentration and path length is known as the Beer-Lambert law ... 

Ingestion of yage in healthy volunteers yields plasma concentrations of 10 to 250 ng/mL for harmine and 1.0 to 25.0 ng/mL of harmaline (Callaway et al. 1996). The dose-concentration relationships are linear in this range. DMT shows linear dose-concentration relationships for plasma concentrations between 5 and 1000 ng/mL. Systemically administered j8-carbolines penetrate brain tissue, with relatively even distribution (Moncrieff 1989). DMT taken alone is not absorbed well orally. It may be taken as a snuff or smoked, or mixed with other plants to improve absorption. 

Wallace [34] demonstrated that a Hnear absorbance-to-concentration relationship is adequate to correct for the interaction. The absorbance for sample n can be related to its true concentration by Eq. 2.2... 

This relationships cannot hold at higher concentrations when it approaches l, indicating that at high concentrations all of the light is absorbed independent of absorber concentrations. 

The functions now realized by microprocessors include the control of the optical system (lamp and analytical wavelength selection), selection of the kind of data collected (e.g., absorbance, concentration), zero-adjustment, autocalibration and control of measurement parameters [21]. The microprocessor determines the equation of the regression curve and provides statistical processing of the results. It can also be programmed to measure the absorbance, the % transmittance at a selected wavelength, or the concentration based on the relationship (linear or non-linear) established between the measured absorbance and the concentration. 

It is not surprising that simple kinetics do not model browning accurately, since measuring browning is determining the concentration of a product after a series of reactions. Polynomial equation have been used to characterize these absorbance-time relationships. These are developed from idea that a reactant is produced during the reaction and are based on a consecutive 3-step mechanism... 

The discussion of luminescence has, up to the present, been based on the properties of dilute solutions in which the analyte molecules were presumed not to interact with one another. It has already been established that at high absorbance at the wavelength of excitation, deviations from linearity of the fluorescence in-tensity-versus-concentration relationship may occur because of the exponential variation of luminescence intensity with concentration. However, over a wide range of solute concentrations, solute-solute interactions may also account for loss of luminescence intensity with increasing solute concentration. 

Linearity of the absorbance/concentration function can also be impaired by some reactions, e.g., dissociation and association reactions, or interaction of the solvent with the monitored chemical species. A classical example is potassium dichromate (K2CT2O7) solutions, which contain Cr2042, HCrOj and C O2- ions and other Cr(VI) species [15]. As these ions have different absorption spectra and their relative proportions depend on the total chromium concentration and pH of the solution, a perfectly linear relationship between absorbance and Cr(VI) concentration is not attainable. Moreover, a simple dilution may alter the species distribution. For spectrophotometric measurements, pH buffering is therefore required. 

Although the equation that relates absorbance, concentration, and light path bears the names of Beer and Lambert, it is believed that Pierre Bouguer (1698-1758), a French mathematician, first formulated the relationship in 1729. 

Determining the Relationship between Absorbance and Concentration 1 he method of external standards (sec Section ID-2) is most often used to establish the absorbance versus concentration relationship. After deciding on the conditions for the analysis, the calibration curve is prepared from a series of standard solutions that bracket the concentration range expected for the samples. Seldom, if ever, is it safe to assume adherence to Beer s law and use only a single standard to determine the molar ab,soq)tivity. It is never a good idea to base the results of an analysis on a literature value for the molar absorptivity. 

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. 

In the (9) relation, Co i C o represents molar concentration of pure solvent in the two cells (placed in reference route and in the sample route respectively), and C is the molar concentration of solute in the cells placed in the route sample. It is obvious that C o < Co because in the sample cells is in addition to solvent, a quantity of solution. The signal recorded by spectrometry, AA( v), to the number of wave (v), is the difference between the both absorbance of relationship (9)... 

The relationship between absorbance, concentration, and length of the sample cell (cuvette) is known as the Beer-Lambert Law, A = scl where A is absorbance, s is the molar absorptivity (also called extinction coefficient) of the molecules in the sample having the units per moles per liter per centimeter (M" cm ), c is concentration in moles per liter (Ad), and / is the length of the cuvette in centimeters (cm). 

Most substances obey Beer s Law at low to moderate concentrations that still permit transmission of the IR beam. Higher percentages of IR transmitted through the sample produce lower absorbance values. Once the absorbance versns concentration relationship has been established by a calibration curve through the plotting of absorbance values measured for standard samples at different concentrations, the unknown sample concentration can be determined when its IR absorbance is measured. Sample concentration can be calculated as... 

The Beer-Lambert law is the relationship between absorbance, concentration, length of the light path, and molar absorptivity A = cle. 

Figure 5 shows the relationship between the sample thickness and the absorber concentration. Since the infrared absorber is blended into the lower substrate, the entire lower substrate will act as a heat sink and will absorb and dissipate the laser eneigy as heat. The depth... 

The iimnodified temi absorbance usually means this quantity, though some authors use the Napierian absorbance B = -hiT. The absorbance is so iisefiil because it nomially increases linearly with path length, /, tlirough the sample and with the concentration, c, of the absorbing species within the sample. The relationship is usually called Beer s law ... 

The relationship between a sample s absorbance and the concentration of the absorbing species (A = zbC). 

Equations 10.4 and 10.5, which establish the linear relationship between absorbance and concentration, are known as the Beer-Lambert law, or more commonly, as Beer s law. Calibration curves based on Beer s law are used routinely in quantitative analysis. 

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