The determination of an analyte’s concentration based on its absorption of ultravi- olet or visible radiation is one of the most frequently encountered quantitative ana- lytical methods. One reason for its popularity is that many organic and inorganic compounds have strong absorption bands in the UV/Vis region of the electromag- netic 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 Pb2+ 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 analyses based on the absorption of infrared radiation, although important, are less frequently encountered than those for UV/Vis absorption. One reason is the greater tendency for instrumental deviations from Beer’s law when using infrared radiation. Since infrared absorption bands are relatively narrow, de- viations due to the lack of monochromatic radiation are more pronounced. In addi- tion, infrared sources are less intense than sources of UV/Vis radiation, making stray radiation more of a problem. Differences in pathlength for samples and stan- dards when using thin liquid films or KBr pellets are a problem, although an inter- nal standard can be used to correct for any difference in pathlength. Finally, estab- lishing a 100% T (A = 0) baseline is often difficult since the optical properties of NaCl sample cells may change significantly with wavelength due to contamination and degradation. This problem can be minimized by determining absorbance rela- tive to a baseline established for the absorption band. Figure 10.32 shows how this is accomplished.
The applications of Beer’s law for the quantitative analysis of samples in envi- ronmental chemistry, clinical chemistry, industrial chemistry and forensic chem- istry are numerous. Examples from each of these fields follow.
Methods for the analysis of waters and wastewaters relying on the absorption of UV/Vis radiation are among some of the most fre- quently employed analytical methods. Many of these methods are outlined in Table 10.6, and a few are described later in more detail.
Although the quantitative analysis of metals in water and wastewater is ac- complished primarily by atomic absorption or atomic emission spectroscopy, many metals also can be analyzed following the formation of a colored metal– ligand complex. One advantage to these spectroscopic methods is that they are easily adapted to the field analysis of samples using a filter photometer. One lig- and used in the analysis of several metals is diphenylthiocarbazone, also known as dithizone. Dithizone is insoluble in water, but when a solution of dithizone in CHCl3 is shaken with an aqueous solution containing an appropriate metal ion, a colored metal–dithizonate complex forms that is soluble in CHCl3. The selectivity of dithizone is controlled by adjusting the pH of the aqueous sample. For exam- ple, Cd2+ is extracted from solutions that are made strongly basic with NaOH, Pb2+ from solutions that are made basic with an ammoniacal buffer, and Hg2+ from solutions that are slightly acidic.
When chlorine is added to water that portion available for disinfection is called the chlorine residual. Two forms of the chlorine residual are recognized. The free chlorine residual includes Cl2, HOCl, and OCl–. The combined chlorine residual, which forms from the reaction of NH3 with HOCl, consists of monochloroamine, NH2Cl, dichlororamine, NHCl2, and trichloroamine, NCl3. Since the free chlorine residual is more efficient at disinfection, analytical methods have been developed to determine the concentration of both forms of residual chlorine. One such method is the leuco crystal violet method. Free residual chlorine is determined by adding leuco crystal violet to the sample, which instantaneously oxidizes giving a bluish color that is monitored at 592 nm. Completing the analysis in less than 5 min pre- vents a possible interference from the combined chlorine residual. The total chlo- rine residual (free + combined) is determined by reacting a separate sample with io- dide, which reacts with both chlorine residuals to form HOI. When the reaction is complete, leuco crystal violet is added and oxidized by HOI, giving the same bluish colored product. The combined chlorine residual is determined by difference.
Spectroscopic methods also are used in determining organic constituents in water. For example, the combined concentrations of phenol, and ortho- and meta- substituted phenols are determined by using steam distillation to separate the phe- nols from nonvolatile impurities. The distillate is reacted with 4-aminoantipyrine at pH 7.9 ± 0.1 in the presence of K3Fe(CN)6, forming a colored antipyrine dye. The dye is extracted into CHCl3, and the absorbance is monitored at 460 nm. A calibration curve is prepared using only the unsubstituted phenol, C6H5OH. Be- cause the molar absorptivities of substituted phenols are generally less than that for phenol, the reported concentration represents the minimum concentration of phe- nolic compounds.
Molecular absorption also can be used for the analysis of environmentally sig- nificant airborne pollutants. In many cases the analysis is carried out by collecting the sample in water, converting the analyte to an aqueous form that can be analyzed by methods such as those described in Table 10.6. For example, the concentration of NO2 can be determined by oxidizing NO2 to NO3–. The concentration of NO3– is then determined by reducing to NO3– with Cd and reacting the NO3– with sulfanil- amide and N-(1-naphthyl)-ethylenediamine to form a brightly colored azo dye. An- other important application is the determination of SO2, which is determined by collecting the sample in an aqueous solution of HgCl42– where it reacts to form Hg(SO ) 2–. Addition of p-rosaniline and formaldehyde results in the formation of a bright purple complex that is monitored at 569 nm. Infrared absorption has proved useful for the analysis of organic vapors, including HCN, SO2, nitrobenzene, methyl mercaptan, and vinyl chloride. Frequently, these analyses are accomplished using portable, dedicated infrared photometers.
UV/Vis molecular absorption is one of the most commonly employed techniques for the analysis of clinical samples, several examples of which are listed in Table 10.7.
The analysis of clinical samples is often complicated by the complexity of the sample matrix, which may contribute a significant background absorption at the desired wavelength. The determination of serum barbiturates provides one example of how this problem is overcome. The barbiturates are extracted from a sample of serum with CHCl3, and extracted from the CHCl3 into 0.45 M NaOH (pH ~ 13). The absorbance of the aqueous extract is measured at 260 nm and includes contri- butions from the barbiturates as well as other components extracted from the serum sample. The pH of the sample is then lowered to approximately 10 by adding NH4Cl, and the absorbance remeasured. Since the barbiturates do not absorb at this pH, the absorbance at pH 10 is used to correct the absorbance at pH 13; thus
UV/Vis molecular absorption is used for the analysis of a di- verse array of industrial samples, including pharmaceuticals, food, paint, glass, and metals. In many cases the methods are similar to those described in Tables 10.6 and 10.7. For example, the iron content of food can be determined by bringing the iron into solution and analyzing using the o-phenanthroline method listed in Table 10.6.
Many pharmaceutical compounds contain chromophores that make them suit- able for analysis by UV/Vis absorption. Products that have been analyzed in this fashion include antibiotics, hormones, vitamins, and analgesics. One example of the use of UV absorption is in determining the purity of aspirin tablets, for which the active ingredient is acetylsalicylic acid. Salicylic acid, which is produced by the hy- drolysis of acetylsalicylic acid, is an undesirable impurity in aspirin tablets, and should not be present at more than 0.01% w/w. Samples can be screened for unac- ceptable levels of salicylic acid by monitoring the absorbance at a wavelength of 312 nm. Acetylsalicylic acid absorbs at 280 nm, but absorbs poorly at 312 nm. Con- ditions for preparing the sample are chosen such that an absorbance of greater than 0.02 signifies an unacceptable level of salicylic acid.
UV/Vis molecular absorption is routinely used in the analy- sis of narcotics and for drug testing. One interesting forensic application is the de- termination of blood alcohol using the Breathalyzer test. In this test a 52.5-mL breath sample is bubbled through an acidified solution of K2Cr2O7. Any ethanol present in the breath sample is oxidized by the dichromate, producing acetic acid and Cr3+ as products. The concentration of ethanol in the breath sample is deter- mined from the decrease in absorbance at 440 nm where the dichromate ion ab- sorbs. A blood alcohol content of 0.10%, which is the legal limit in most states, cor- responds to 0.025 mg of ethanol in the breath sample.
In developing a quan- titative analytical procedure, the conditions under which Beer’s law is obeyed must be established. First, the most appropriate wavelength for the analysis is determined from an absorption spectrum. In most cases the best wavelength corresponds to an absorption maximum because it provides greater sensitivity and is less susceptible to instrumental limitations to Beer’s law due to the lack of monochromatic radia- tion. Second, if an instrument with adjustable slits is being used, then an appropri- ate slit width needs to be chosen. The absorption spectrum also aids in selecting a slit width. Generally the slit width should be as wide as possible to increase the throughput of radiation from the source, while being narrow enough to avoid in- strumental limitations to Beer’s law. Finally, a calibration curve is constructed to determine the range of concentrations for which Beer’s law is valid. Additional con- siderations that are important in any quantitative method are the effect of potential interferents and establishing an appropriate blank.
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. 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 analysis of two or more components in the same sample is straightforward if there are regions in the sample’s spectrum in which each component is the only absorbing species. In this case each component can be analyzed as if it were the only species in solution. Unfortunately, UV/Vis ab- sorption bands are so broad that it frequently is impossible to find appropriate wavelengths at which each component of a mixture absorbs separately. Earlier we learned that Beer’s law is additive (equation 10.6); thus, for a two-component mix- ture of X and Y, the mixture’s absorbance, Am, is
(Am)λ1 = (εX)λ1bCX + (εY)λ1bCY ……….10.11
where λ1 is the wavelength at which the absorbance is measured. Since equation 10.11 includes terms for both the concentrations of X and Y, the absorbance at one wave- length does not provide sufficient information to determine either CX or CY. If we measure the absorbance at a second wavelength, λ2,
(Am)λ2 = (εX)λ2bCX + (εY)λ2bCY ……….10.12
then CX and CY can be determined by solving equations 10.11 and 10.12. Of course, it is necessary to determine values for ε for each component at both wavelengths. In general, for a mixture of n components, the absorbance must be measured at n dif- ferent wavelengths.
To obtain results with good accuracy and precision the two wavelengths should be selected so that εX > εY at one wavelength and εY < εX at the other wavelength. The optimum precision is obtained when the difference in molar absorptivities is as large as possible. One method for locating the optimum wavelengths, therefore, is to plot εX/εY as a function of wavelength and determine the wavelengths at which εX/εY reaches maximum and minimum values.
Two additional methods for determining the composition of a mixture deserve mention. In multiwavelength linear regression analysis (MLRA) the absorbance of a mixture is compared with that of standard solutions at several wavelengths. If ASX and ASY are the absorbances of standard solutions of components X and Y at any wavelength, then
where CSX and CSY are the known concentrations of X and Y in the standard solu- tions. Solving equations 10.13 and 10.14 for εX and εY, substituting into equation (the wavelength designation can be dropped), and rearranging gives
To determine CX and CY, the mixture’s absorbance and the absorbances of the stan- dard solutions are measured at several wavelengths. Plotting Am/ASX versus ASY/ASX gives a straight line with a slope of CY/CSY and a y-intercept of CX/CSX.
The generalized standard addition method (GSAM) extends the analysis of mixtures to situations in which matrix effects prevent the determination of εX andεY using external standards. When adding a known concentration of analyte to a solution containing an unknown concentration of analyte, the concentrations usu- ally are not additive. Conservation of mass, however, is always obeyed. Equation 10.11 can be written in terms of moles, n, by using the relationship
where V is the total solution volume. Substituting equation 10.15 into 10.11 and gives
where Q is the volume-corrected absorbance. If a standard is added to the sample, the moles of X and Y increase by the amount ∆nX and ∆nY, and the new volume- corrected absorbances are
Values for (εX)λ1, (εY)λ1, (εX)λ2, and (εY)λ2 are obtained by plotting ∆Qλ1 versus ∆nX, ∆Qλ1 versus ∆nY, ∆Qλ2 versus ∆nX, and ∆Qλ2 versus ∆nY and determining the slopes. Equations 10.16 and 10.17 can then be solved to determine nX and nY.
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