Concentration, Beer’s law

In a sensitive and specific colorimetric method 1,1,1-trichloro-2,2-bis(p-methoxyphenyl)-ethane is extracted from plant or animal tissue, using benzene or petroleum ether as the solvent. The solvent is evaporated at room temperature by a current of air and the residue dehydroha log ena ted with 2% alcoholic potassium hydroxide. By petroleum ether extraction the resulting 1,1-dichloro-2,2-bis(p-methoxyphenyl)-ethylene is removed from the reaction mixture. After the solvent is removed by air evaporation the dehydroha log ena ted methoxychlor is isolated from the nonsaponifiable portion of the fats and waxes by dissolving the residue in hot acetone, chilling, and filtering. After the acetone is removed by air evaporation, the residue is treated with 85% sulfuric acid. This produces a red solution with an absorption maximum at 555 m/z, the intensity of which can be read on a colorimeter and is a function of the methoxychlor concentration. Beer s law is obeyed over the range of 1 to 50 micrograms. 

When the absorbing substance is present in solution, the absorption of light also depends upon the concentration Beer s law states that the rate of decrease in intensity of radiation absorbed is proportional to the intensity of radiation and to the concentration of the solute. Mathematically... 

T oluene diisocyanate in particular can be obtained in a range of mixtures of the 2,4- and the 2,6-isomers. The proportion of the two isomers present can be determined by infrared spectrophotometry. The method is based on the quantitative intensity measurement of absorption bands at 12-35//m and 12-80/im for the 2,4- and 2,6-isomers, respectively. As the heights of the absorption bands do not vary linearly with concentration (Beer s law) it is necessary to construct calibration curves. 

At higher concentrations Beer s law is not valid and heteropolynuclear complexes have been assumed to be formed a. 

The concept of absorbance units at 260 nm, A bo (aIso known as optical density units. ODU) often causes confusion for students. By definition, one unit is the amount of sample that gives a UV absorbance at X = 250 nm of 1.0 if the sample is dissolved in 1 ml volume and measured in a l-cm pathlength cuvette. Since aborbance is proportional to concentration (Beer s Law) and the volume is 1 ml, the number of Ajsq units of a sample is proportional to the number of moles of strands. Knowledge of the number of A260 units is important for planning UV melting experiments to optimize sensitivity. 

It is very difficult to obtain quantitative data with infrared spectrophotometry. This is again a problem related to the solvent. There isn t possibly a solvent that is completely transparent to infrared. In order to minimize absorption due to any solvent that is used, scientists use very small pathlengths. This too is not desirable as far as quantitative results are concerned because short pathlength would require higher solute concentration. At high concentration. Beer s law may not be obeyed. 

Beer s Law The equation that relates the absorbance of a sample to its concentration. Beer s Law is used in FTIR quantitative analysis to perform calibrations and to predict unknown concentrations. 

Relationships between the intensity of incident light, sample thickness, concentration and intensity of transmitted light are embodied in Beer s law and Lambert s law. ... 

Beer s law This states that the proportion of light absorbed depends on the thickness d) of the absorbing layer, and on the molecular concentration (c) of the absorbing substance in the layer. It is an extension of Lambert s law, and may be written in the form... 

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 ... 

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. 

According to Beer s law, a calibration curve of absorbance versus the concentration of analyte in a series of standard solutions should be a straight line with an intercept of 0 and a slope of ab or eb. In many cases, however, calibration curves are found to be nonlinear (Figure 10.22). Deviations from linearity are divided into three categories fundamental, chemical, and instrumental. 

Fundamental Limitations to Beers Law Beer s law is a limiting law that is valid only for low concentrations of analyte. There are two contributions to this fundamental limitation to Beer s law. At higher concentrations the individual particles of analyte no longer behave independently of one another. The resulting interaction between particles of analyte may change the value of 8. A second contribution is that the absorptivity, a, and molar absorptivity, 8, depend on the sample s refractive index. Since the refractive index varies with the analyte s concentration, the values of a and 8 will change. For sufficiently low concentrations of analyte, the refractive index remains essentially constant, and the calibration curve is linear. 

Chemical Limitations to Beer s Law Chemical deviations from Beer s law can occur when the absorbing species is involved in an equilibrium reaction. Consider, as an example, an analysis for the weak acid, HA. To construct a Beer s law calibration curve, several standards containing known total concentrations of HA, Cmt, are prepared and the absorbance of each is measured at the same wavelength. Since HA is a weak acid, it exists in equilibrium with its conjugate weak base, A ... 

Because values of ttuA nray depend on the concentration of HA, equation 10.10 may not be linear. A Beer s law calibration curve of A versus Qot will be linear if one of two conditions is met. If the wavelength is chosen such that 8ha and 8a are equal, then equation 10.10 simplifies to... 

For small concentrations of analyte, Pstray is significantly smaller than Pq and Py, and the absorbance is unaffected by the stray radiation. At higher concentrations of analyte, however, Pstray is no longer significantly smaller than Py and the absorbance is smaller than expected. The result is a negative deviation from Beer s law. 

The determination of an analyte s concentration based on its absorption of ultraviolet or visible radiation is one of the most frequently encountered quantitative analytical methods. One reason for its popularity is that many organic and inorganic compounds have strong absorption bands in the UV/Vis region of the electromagnetic spectrum. In addition, analytes that do not absorb UV/Vis radiation, or that absorb such radiation only weakly, frequently can be chemically coupled to a species that does. For example, nonabsorbing solutions of Pb + can be reacted with dithizone to form the red Pb-dithizonate complex. An additional advantage to UV/Vis absorption is that in most cases it is relatively easy to adjust experimental and instrumental conditions so that Beer s law is obeyed. 

Quantitative Analysis for a Single Analyte The concentration of a single analyte is determined by measuring the absorbance of the sample and applying Beer s law (equation 10.5) using any of the standardization methods described in Chapter 5. The most common methods are the normal calibration curve and the method of standard additions. Single-point standardizations also can be used, provided that the validity of Beer s law has been demonstrated. 

The relationship between transmittance and the concentration of the scattering particles is similar to that given by Beer s law... 

Spectroscopic measurements may also involve the scattering of light by a particulate form of the analyte, fn turbidimetry, the decrease in the radiation s transmittance through the sample is measured and related to the analyte s concentration through Beer s law. fn nephelometry we measure the intensity of scattered radiation, which varies linearly with the analyte s concentration. 

Fixed-time integral methods are advantageous for systems in which the signal is a linear function of concentration. In this case it is not necessary to determine the concentration of the analyte or product at times ti or f2, because the relevant concentration terms can be replaced by the appropriate signal. For example, when a pseudo-first-order reaction is followed spectrophotometrically, when Beer s law... 

When D and H3O+ are present in excess, the kinetics of the reaction are pseudo-first-order in H2O2, and can be used to determine the concentration of H2O2 by following the production of I2 with time. In one analysis the absorbance of the solution was measured after 240 s at 348 nm (where Beer s law holds for I2). When a set of standard solutions of H2O2 was analyzed, the following results were obtained... 

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... 

It increases with the concentration of scattering centers, which is equivalent to Beer s law. 

A study of the effect of substitution patterns in oxadiazoles and isoxazoles and their effect on the UV spectra in the lO -lO M concentration range was performed. Hypso-chromic effects and deviations from Beer s law were observed and were believed to be associated with antiparallel, sandwich-type self-association via dipole-dipole interactions. Beer s law is followed when the molecular dipole moments are small or when self-association is sterically hindered. 

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