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Chapter: Modern Analytical Chemistry: Spectroscopic Methods of Analysis

Evaluation - Ultraviolet-Visible and Infrared Spectrophotometry

Scale of Operation : Molecular UV/Vis absorption is routinely used for the analysis of trace analytes in macro and meso samples.


Scale of Operation 

Molecular UV/Vis absorption is routinely used for the analysis of trace analytes in macro and meso samples. Major and minor analytes can be de- termined by diluting samples before analysis, and concentrating a sample may allow for the analysis of ultratrace analytes. The scale of operations for infrared absorp- tion is generally poorer than that for UV/Vis absorption.


Under normal conditions relative errors of 1–5% are easily obtained with UV/Vis absorption. Accuracy is usually limited by the quality of the blank. Examples of the type of problems that may be encountered include the presence of particulates in a sample that scatter radiation and interferents that react with analytical reagents. In the latter case the interferant may react to form an absorbing species, giving rise to a positive determinate error. Interferents also may prevent the analyte from reacting, leading to a negative determinate error. With care, it may be possible to improve the accuracy of an analysis by as much as an order of magnitude.


In absorption spectroscopy, precision is limited by indeterminate er- rors, or instrumental “noise,” introduced when measuring absorbance. Precision is generally worse with very low absorbances due to the uncertainty of distin- guishing a small difference between P0 and PT, and for very high absorbances when PT approaches 0. We might expect, therefore, that precision will vary with transmittance.

We can derive an expression between precision and transmittance by applying the propagation of uncertainty. To do so we write Beer’s law as


Using Table 4.9, the absolute uncertainty in the concentration, sC, is given as


where sT is the absolute uncertainty for the transmittance. Dividing equation 10.27 by equation 10.26 gives the relative uncertainty in concentration, sC/C, as

Thus, if sT is known, the relative uncertainty in concentration can be determined for any transmittance.

Calculating the relative uncertainty in concentration is complicated by the fact that sT may be a function of the transmittance. Three categories of indeterminate instrumental error have been observed.17 Table 10.8 provides a summary of these categories. A constant sT is observed for the uncertainty associated with the reading %T from a meter’s analog or digital scale. Typical values are ±0.2–0.3% (k1 of 0.002–0.003) for an analog scale, and ±0.001% (k1 of ±0.00001) for a digital scale. A constant sT also is observed for the thermal transducers used in infrared spec- trophotometers. The effect of a constant sT on the relative uncertainty in concen- tration is shown by curve A in Figure 10.35. Note that the relative uncertainty is very large for both high and low absorbances, reaching a minimum when the ab- sorbance is 0.434. This source of indeterminate error is important for infrared spectrophotometers and for inexpensive UV/Vis spectrophotometers. To obtain a relative uncertainty in concentration of ±1–2%, the absorbance must be kept be- tween 0.1 and 1.

Values of sT are a complex function of transmittance when indeterminate er- rors are dominated by the noise associated with photon transducers. Curve B in Figure 10.35 shows that the relative uncertainty in concentration is very large for low absorbances, but is less affected by higher absorbances. Although the relative uncertainty reaches a minimum when the absorbance is 0.96, there is little change in the relative uncertainty for absorbances between 0.5 and 2. This source of indeterminate error generally limits the precision of high-quality UV/Vis spectropho- tometers for mid-to-high absorbances.

Finally, values of sT are directly proportional to transmittance for indetermi- nate errors due to fluctuations in source intensity and for uncertainty in positioning the sample cell within the spectrometer. The latter is of particular importance since the optical properties of any sample cell are not uniform. As a result, repositioning the sample cell may lead to a change in the intensity of transmitted radiation. As shown by curve C in Figure 10.35, the effect of this source of indeterminate error is only important at low absorbances. This source of indeterminate errors is usually the limiting factor for high-quality UV/Vis spectrophotometers when the ab- sorbance is relatively small.

When the relative uncertainty in concentration is limited by the %T readout res- olution, the precision of the analysis can be improved by redefining the standards used to define 100% T and 0% T. Normally 100% T is established using a blank, and 0% T is established while using a shutter to prevent source radiation from reaching the detector. When the absorbance is too high, precision can be improved by reset- ting 100% T using a standard solution of analyte whose concentration is less than that of the sample (Figure 10.36a). For a sample whose absorbance is too low, preci- sion can be improved by redefining 0% T, using a standard solution of analyte whose concentration is greater than that of the analyte (Figure 10.36b). In this case a cali- bration curve is required because a linear relationship between absorbance and con- centration no longer exists. Precision can be further increased by combining these two methods (Figure 10.36c). Again, a calibration curve is necessary because the rela- tionship between absorbance and concentration is no longer linear.


The sensitivity of a molecular absorption analysis is equivalent to the slope of a Beer’s-law calibration curve and is determined by the product of the an- alyte’s absorptivity and the pathlength of the sample cell. Sensitivity is improved by selecting a wavelength when absorbance is at a maximum or by increasing the pathlength.


Selectivity is rarely a problem in molecular absorption spectrophotom- etry. In many cases it is possible to find a wavelength at which only the analyte ab- sorbs or to use chemical reactions in a manner such that the analyte is the only species that absorbs at the chosen wavelength. When two or more species con- tribute to the measured absorbance, a multicomponent analysis is still possible, as shown in Example 10.6.

Time, Cost, and Equipment 

The analysis of a sample by molecular absorption spec- troscopy is relatively rapid, although additional time may be required when it is nec- essary to use a chemical reaction to transform a nonabsorbing analyte into an ab- sorbing form. The cost of UV/Vis instrumentation ranges from several hundred dollars for a simple, manually operated, single-beam instrument equipped with an inexpensive grating, to as much as $50,000 for a computer-controlled, high-resolu- tion, double-beam instrument equipped with variable slits and operating over an ex- tended range of wavelengths. Fourier transform infrared spectrometers can be ob- tained for as little as $15,000–$20,000, although more expensive models are available.


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