Quantitative analysis molar absorptivity

This equation forms the basis of quantitative analysis by absorption photometry. When is 1 cm and c is expressed in moles per liter, the symbol e is substituted for the constant a. The value for c is a constant for a given compound at a given wavelength under prescribed conditions of solvent, temperature, pH, etc., and is called the molar absorptivity. The nomenclature of spectrophotometry is summarized in Table 3-2. Values for e are useful to characterize compounds, establish their purity, and compare sensitivities of measurements obtained on derivatives. Pure bilirubin, for example, when dissolved in chloroform at 25 °C, has a molar absorptivity of 60,700+1600 at 453 nm. The molecular weight of bilirubin is 584. Hence a solution containing 5mg/L (0.005 g/L) should have an absorbance of... 

EDTA forms colored complexes with a variety of metal ions that may serve as the basis for a quantitative spectrophotometric method of analysis. The molar absorptivities of the EDTA complexes of Cu +, Co +, and Ni + at three wavelengths are summarized in the following table (all values of e are in cm )... 

If we are dealing with compounds for which the wavelengths and the molar intensities of the absorption bands are known, then we can use the degree of absorption for quantitative analysis with the aid of the Beer-Lambert law (see Table 9-3 for definitions) ... 

Model-based nonlinear least-squares fitting is not the only method for the analysis of multiwavelength kinetics. Such data sets can be analyzed by so-called model-free or soft-modeling methods. These methods do not rely on a chemical model, but only on simple physical restrictions such as positiveness for concentrations and molar absorptivities. Soft-modeling methods are discussed in detail in Chapter 11 of this book. They can be a powerful alternative to hard-modeling methods described in this chapter. In particular, this is the case where there is no functional relationship that can describe the data quantitatively. These methods can also be invaluable aids in the development of the correct kinetic model that should be used to analyze the data by hard-modeling techniques. 

By carrying out one experiment, changes of monomer and polymer and also of the initiator (azobisisobutyronitrile) are reflected in the NIR and the IR, respectively. Quantitative analysis is largely facilitated by the appearance of characteristic non-overlapping bands. On the other hand, computer programs for band separation are available. In addition, the integration of molar absorption coefficients to yield concentrations need not extend over entire bands, but may be performed over half bands or even over suitable band sections. 

U nlike ir spectroscopy, ultraviolet spectroscopy lends itself to precise quantitative analysis of substances. The intensity of an absorption band is usually given by the molar extinction coefficient e, which, according to the Beer-Lambert Law, is equal to the absorbance A, divided by the product of the molar concentration c, and the path length /, in centimeters. 

In the /"region, the molar extinction coefficients range from 2 to 12. In the intermediate coupling treatments, which have had considerable success in the quantitative analysis of the spectra (see, e.g., 32), J remains a good quantum number, and the absorption bands correspond to excitations from the ground state (formally a I9/2 state) to other J values. But each J state suffers a small splitting into a number of... 

The molar absorptivity of a species at an absorption maximum is characteristic of that species. Peak molar absorp-tivities for many organic compounds range from 10 or less to 10,000 or more. Some transition metal complexes have molar absorptivities of 10.000 to 50.000. High molar absorptivities are desirable for quantitative analysis because they lead to high analytical sensitivity. 

Beer s law, as expressed in Equations 24-6 and 24-8, can be used in several ways. We can calculate molar absorptivities of species if the concentration is known, as shown in Example 24-3. We can use the measured value of absorbance to obtain concentration if absorptivity and path length are known. Absorptivities, however, are functions of such variables as solvent, solution composition, and temperature. Because of variations in absorptivity with conditions, it is never wise to depend on literature values for quantitative work. Hence, a standard solution of the analyte in the same solvent and at a similar temperature is used to obtain the absorptivity at the time of the analysis. Most often, we use a series of standard solutions of the analyte to construct a calibration curve, or working curve, of A versus c (see Chapter 26, Figure 23-6) or to obtain a linear regression equation (see Chapter 8). It may also be necessary to duplicate closely the overall composition of the analyte solution to compensate for matrix effects. Alternatively, the method of standard additions (see Sections 8C-3 and 26A-4) is used for the same purpose. 

Spreadsheet Summary In the first exercise in Chapter 12 of Applications of Microsoft Excel in Analytical Chemistry, a spreadsheet is developed to calculate the molar absorptivity of permanganate ion. A plot of absorbance versus permanganate concentration is constructed, and least-squares analysis of the linear plot is carried out. The data are analyzed statistically to determine the uncertainty of the molar absorptivity. In addition, other spreadsheets are presented for calibration in quantitative spectrophotometric experiments and for calculation of concentrations of unknown solutions. 

The detector signal is much more dependent on specific compound properties in liquid chromatography than it is in gas chromatography. For example, the UV signal is a function of the molar absorptivity, which varies between 0 and 10 0001 mol cm depending on the compound used. The molar absorptivity and absorbance maximum also vary between homologues. Hence at least one calibration chromatogram must be obtained for each quantitative analysis. ... 

The relationship between the concentration of analyte and the intensity of light absorbed is the basis of quantitative applications of spectrophotometry. In addition, features of absorption spectra such as the molar absorptivity, spectral position, and shape and breadth of the absorption band are related to molecular structure and environment and therefore can be used for qualitative analysis. 

Infrared spectrometry is used for quantitative analysis in many applications, such as industrial hygiene and air quality monitoring. When you have your car emission tested (most or all states require this), an infrared probe is inserted in the exhaust tailpipe to measure CO, CO2, and hydrocarbons (based on an average molar absorptivity for hydrocarbons). 

Quantitative analysis of a sample is essentially performed by determining its absorbance and comparing this with the infrared absorptivity a or the molar absorptivity e (see Table 7.2 and Sec. 7.3) of pure compounds. 

The quantitative analysis of a component in solution can be successfully carried out given that there is a suitable band in the spectrum of the component of interest. The band chosen for analysis should have a high molar absorptivity, not overlap with other peaks from other components in the mixture or the solvent, be symmetrical, and give a linear calibration plot of absorbance versus concentration. 

According to the above-mentioned effect of polarization, in principle each molecule exhibits absorption at different wavelengths and intensity distributions. Bouguer, Lambert, and Beer realized many years ago a correlation between the number of particles, their properties, and the optical pathlength through a cell. It is described by a linear dependency between the attenuation and the concentration, whereby the molar decadic absorption coefficient e is derived as the proportionality constant speciflc to the molecular properties of the molecules analyzed [2,12,13]. This so-called Lambert-Beer law allows quantitative analysis of gaseous, liquid, or solid samples by absorption spectrometry. 

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