The relationship between absorbance and concentration

In general absorbance varies during a photochemical reaction. Therefore within the rate laws either the concentrations have to be substituted by the absorbances or the absorbance at the wavelength of irradiation by the concentrations to be able to calculate the integrals, eqs. (3.43) and (3.44), respectively. In principle the relationship between absorbance and concentration is given by the Bouguer-Lambert-Beer law as derived in Section 1.4.3 by Fig. 1.2. For uniform reactions, absorbance at the wavelength of irradiation is defined in Section 1.4.4 by eq. (1.38) to 

The solutions of this equation with respect to the degree of advancement 

At the end of the reaction the degree of advancement and the absorption will amount to 

A combination of eqs. (1.9) and (3.61) allows rearrangement with respect to concentrations 

In this last equation E has been defined according to 

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Linear regression of the calibration standards gives the relationship between absorbance and concentration as... 

Determination of the Relationship between Absorbance and Concentration The calibration standards for a photometric or a spectrophotometric analysis should approximate as closely as possible the overall composition of the actual samples, and should encompass a reasonable range of analyte concentrations. It is seldom safe to assume that Beer s law holds and to use only a single standard to determine the molar absorptivity. It is almost never a good idea to base the results of an analysis solely on a literature value for the molar absorptivity. 

Let us have a look now at the atomization process. The measured absorbance in atomic absorption spectrometry is proportional to the concentration of free atoms in the gas phase. By introducing a constant kp for the relationship between absorbance and concentration, the absorbance Aj at temperature T would be... 

Selecting a title - it is a common fault to use titles that are grammatically incorrect a widely applicable format is to state the relationship between the independent and dependent variables within the title, e.g. The relationship between absorbance and concentration . 

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 ... 

To simplify the previous equation into its more standard form showing absorbance as a logarithmic term, used to linearize the relationship between spectrophotometer response and concentration, gives the following expression as the relationship between absorbance and concentration ... 

The following statements hold true for what is most often termed Beer s law (1) The relationship between transmittance and concentration is nonlinear, and (2) the relationship between absorbance and concentration is linear. Beer s law is the common basis for quantitative analysis. Knowledge of Beer s law allows us to calculate the maximum theoretical dynamic range for an instrument using a few simple mathematical relationships. 

Like many physical laws this is an idealised formulation of a natural process. In fact, however, the relationship between absorbance and concentration is linear only to about 1-1.5 absorbance units (depending on the chemical component). An absorbance of 1.5 means that only 3 % of the incident light passes through the cuvette. 

Application of UVA IS for the purpose of quantitative analysis requires compliance with Beer s law over the concentration range of interest. Whenever the linear dynamic range of the instrument is exceeded, and the relationship between absorbance and concentration becomes non-linear, the easiest solution is to dilute the sample to an absorbance level within the linear dynamic range. With solid samples, however, this is not possible. An alternative is to select one or more wavelengths on the side of the absorbance band, where absorptivity is lower. 

One of the major advances in quantitative analysis has been an integration of spectrometry and multivariate, or chemometric, techniques. This integration has led to a number of ways that data can be extracted from spectra. Not all the information that is extracted is immediately recognized as quantitative information, but it is always related back to spectral properties that are quantitative responses. The relationship between absorbance and concentration is well known as Beer s law (see Chapter 1). When reliance is made upon Beer s law, precautions must be taken to assure that there is indeed a linear relationship between the absorbance that is measured by the spectrometer and concentration. Infrared spectrometry has been used for quantitative analysis since its early development, but it is only since the early 1980s that extensive use of infrared spectrometry for the analysis of multiple components has been made. The analysis of multiple components is the primary focus of this chapter. 

There is one serious shortcoming to CLS The set of equations must be calibrated for every component in the mixture. This is a direct consequence of the relationship between absorbance and concentration. Absorbance is the sum of the concentrations of all the components in the mixture, and if one or more components are ignored, the equations are invalid. The corollary to this is that if an unknown or uncalibrated component appears in an unknown mixture, the model will be unable to predict any of the components correctly. 

Strategy Using either a graphing calculator or an Excel spreadsheet, we graph the tabulated data to verify that the relationship between absorbance and concentration is linear and that the line goes through the origin. We then use the line and the measured absorbance to determine the concentration of the unknown solution. 

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