B.V. Absorption photometry B. V. a.1. Electromagnetic radiations The most important types of electromagnetic radiation are illustrated in Figure 30. Radiant energy is characterized by its wavelength. For absorption photometry the wavelength range between 200 nm and 2000 nm is especially important. Radiation between 400 and 760 nm is visible to the human eye as colored light. Adjacent to visible light at the long-wavelength end is the infrared. It is invisible, but its intensity can indeed be measured with the appropriate photocells. Of shorter wavelength than visible light are the ultraviolet rays which are also invisible to the human eye but can be measured with suitable photocells. The great majority of all materials have the ability to absorb selectively radiant energy of definite wavelengths with the concomitant generation of heat. This observation is the basis for a large numberof analytical methods. The human eye is relatively insensitive in distinguishing different colors and intensities of light. Therefore, absorption is usually measured with the aid of photocells. This field of analytical technique is known as absorption photometry. I1'""0 .< 10' 10' 1 km 10' 10' 1m 10'" 10-' 10.... 1 mm 11, m 1P 10-' 1 nm 1 mp 1 pm 1/11' 10~' 10-" I I I Infra red Ultraviolet I _ Visible light "ot,,, roy, ~ro" 10-" Figure 30. Electromagnetic spectrum. 107 Hertzian rays • Cosrriic rays Downloaded by: Université René Descartes Paris 5 188.8.131.52 - 10/28/2017 2:06:28 PM B.V.a. Physical principles The term "colorimetry" should be avoided because the colorless ultraviolet and infrared regions are just as useful in photometric procedures as visible light. B.V.a.2. Visible light Electromagnetic oscillations with a wavelength between 400 and 760 nm are visible to the human eye as light. White or "colorless" light is a mixture of many different colored light rays, i. e. light rays with different wavelengths. It is described as being polychromatic. If such white light is passed through a prism or a diffraction grating lig ht rays of different wavelengths are refracted or diffracted through different angles. Projection of the emitted rays on to a screen produces the well-known spectrum with violet at the short wavelength end and red at the long wavelength end. The wavelengths of the individual color regions are given in Table 20. When a solution appears colored to the human eye it is because the solution absorbs all the incident light with the exception of the wavelengths perceived by the eye. Thus, a blue solution appears blue because the long wavelength red rays are absorbed. A red solution, on the contrary, absorbs the short wavelength blue light and transmits only the red light rays. This relationship is schematically represented in Figure 31. B.V. a. 3. The law of Bouguer and Lambert It is easierto understand the important physical relationships of light when it is considered not as waves but as rays. Let us provisionally assume that the light be of a single wavelength only, i. e. monochromatic light. I.R.l-- II II II Visible • - ----1 U•V• - Characteristic color white yellow orange red purple 700 red 600 500 orange yellow green green 400 nm blue spectrum color Figure 31. Characteristic colors and spectrum colors. 108 Downloaded by: Université René Descartes Paris 5 184.108.40.206 - 10/28/2017 2:06:28 PM blue Table 20. Wavelength range of colors in visible light Color Wavelength range Violet Blue Green Yellow Orange Red 400-450 nm 450-500 nm 500-570 nm 570-590 nm 590-620 nm 620-760 nm When monochromatic light, with a definite initial intensity (10) passes through an optically homogeneous medium or layer, the intensity ofthe emergent light (11) is less than that of the incident light (10): i. e. some of the light is absorbed. The quotient 1,/1 0 is known as the transmittance, abbreviation T. If 10 is equal to 100% the intensity of the emergent light may be measured as a percentage %T = T x 100 In 1729 Bouguer investigated the relationship between a decrease of light intensity and the thickness of the absorbing medium (d). He observed that optically homogenous layers of equal thickness, lying one behind the other, all absorb a constant proportion of the incident light. The principle of this law of Bouguer and Lambert is shown schematically in Figure 32. Incident light (10) traverses three identical layers of thickness 1. The first layer absorbs 25% of 10 and therefore transmits 75%. Layer 2 again absorbs 25% of the incident light, i. e. 25% of 75% and accordingly transmits 56.2%. Layer 3 absorbs 25% of the remaining 56.2% and thus only 42.2% of the original light intensity emerges from layer 3. The corresponding percentage transmissions are 75% after layer 1,56.2% after layer 2, and 42.2% after layer 3. In Figure 33a the relationship between the percentage transmission and the number of optical layers is plotted on ordinary millirn9ter paper. Obviously I "-1, I, Light ray 2 I Light intensity (T) 100% 3 ..-I I I ..-1, I, I 75% 75%01 75% 75%01 56.2% Transmission in % 100% 75% 56.2% 42.2% log (%T) 2.0 1.875 1.750 1.625 I 0.125 Differences 2.0-log (%T) i ~ E 0 Figure 32. Law of Bouguer and Lambert. 109 II I II I 0.125 0.125 0.125 I 0.250 0.375 Downloaded by: Université René Descartes Paris 5 220.127.116.11 - 10/28/2017 2:06:28 PM 2 Optical layers there is not a linear relationship between layer thickness and transmission. However, if the values are plotted on semi-logarithmic paper as in Figure 33b, the observed points lie on a straight line. In other words, there is a linear relationshi p between the layer thickness and the logarithm of the percentage transmission, as shown in Figure 33c. Therefore, if we plotthe logarithm ofthe percentage transmission against the layer thickness on ordinary millimeter paper, a straight line results as is shown in Figure 33c.lf, instead ofthe number of optical layers, the layer thickness b is employed, a direct proportionality between layer thickness and the logarithm of the transmission is observed in accordance with the Bouguer-Lambert law: -log T = bxk This may be expressed: The transmission of light decreases logarithmically with linear increase in the layer thickness. B.V. a. 4. Transmittance and absorbance In photometric measurements we are not directly interested in how much light is transmitted by a solution but in how much it absorbs. Obviously there must be a relationship between transmittance and absorption. The measure of absorption is the absorbance. abbreviated A (also called the optical density, 0.0., or extinction). This is equal tothe negative logarithm of the transmission: A = - log T = -log I, as % of 10 100 and likewise A = 2-log %T. If we recalculate the experimental data given in Figure 32 and in Figure 33 employing the absorbance A, a direct relationship between the number of optical layers and the extinction can be demonstrated. The greater the layer thickness (b) the higher is the extinction. Accordingly the Bouguer-Lambert law can also be written as follows: A = bk The human eye finds it easier to read the equal subdivisions of a percentage transmittance scale and consequently the readings are somewhat more exact, especially at higher absorbance values. It is sometimes advisable to read the results as percentage transmittance readings and to convert these mathematically to absorbance. However, if the photometer has a fairly large scale, the increased work entailed by this procedure is scarcely justified by the increase in exactness of the readings. 110 Downloaded by: Université René Descartes Paris 5 18.104.22.168 - 10/28/2017 2:06:28 PM It is important to emphasize that all of the curves given in Figure 33 describe the same experiment. It is obviously clearer to express the result as absorbance than as transmittance. We recommend therefore that all results should be read and calculated as absorbance. Transmittance readings can readily be converted into absorbance and back again with a slide rule and the equation A = 2-log %T,or more simply by means of a table (Appendix IV, page 506). % transmission (%T) 100 a ~ \ 80 1 1. '\. .'" "- '\l '" 20 ~ ,. 2 3 4 5 6 '\. \~ 20 10 o ~. 40 l~ 40 log (%T) c \. 2.0 "- 60 \ b I\. 80 60 o % transmission (%T) 100 )~ o 2 3 4 5 6 Absorbance (A) = 2-log (%T) d 1.0 ~\ 1.8 0.8 "'~ ".'\ 1.6 1.4 0.6 I\. 7 0.4 \. )' ,,~ 1.2 " o 0.2 o 1.0 2 3 4 5 6 / tV )~ / o tV )r 2 3 4 5 6 Figure 33. Relationship between layer thickness or concentration of a solution (abscissa) and transmittance or absorbance of the solution (ordinate). B.V. a. 5. Beer's law If the number of dissolved molecules in the absorbance layer, i.e. the concentration (C) is substituted for the layer thickness, the equation becomes = Cxk. In other words, absorbance is proportional to concentration. This physical relation, usually known as the Beer-Lambert law, is the fundamental basis of photometry with modern apparatus (b= constant). 111 Downloaded by: Université René Descartes Paris 5 22.214.171.124 - 10/28/2017 2:06:28 PM A B.V. b.1. Absorbing molecules Attempts to determine substances after a color-producing reaction are based upon an old analytical principle which has many useful applications: a) The substance to be measured may exhibit characteristic absorption in visible light (hemoglobin, carotenes), in the ultraviolet (protein, nucleic acid) or in the infrared (steroids). b) The substanceto be measured may form a colored compound with an added reagent (cholesterol, ammonia). c) The substance investigated may release a colored compound from an added reagent (chloride). d) The substance may decolorise an added colored compound. In any of these methods the following conditions must be fulfilled: 1. The concentration of the colored compound must be exclusively dependent on the concentration of the measured substance (specificity). 2. The color must be stable. 3. Color development must be nearly independent of the environmental conditions (temperature, light). 4. The colored compound must follow the Beer-Lambert law. Before any steps can be taken to measure a colored compound the spectral properties of the compound must be fully investigated. B.V. b. 2. Absorption spectrophotometry Instead of inspecting the entire spectrum by eye we may use an absorption spectrophotometer which enables the entire wavelength range to be surveyed. The absorbance is first measured with monochromatic light at a wavelength of 400 nm, then with monochromatic light of wavelength of410 nm and so on until the entire spectrum is measured. The concentration of the solution is maintained constant throughout. Thus, a picture of the relative absorption of the compound at different wavelengths is obtained. Examples of such absorption spectrums are given in Figure 45 (page 137) and Figure 70 (page 330). B.V. b.3. The absorptivity The absorption spectrum is a stable and reproduci ble property of a great many compounds. It is useful not only for the identification of a given compound but also enables its concentration to be determined by measuring the absorbance with monochromatic light. The following are the conditions necessary for using molar absorptivity in measuring the concentration: 1. Absolute calibrated pipets must be used for preparing the necessary dilutions. 2. A photometer, which gives absolute measurements and which is stabilized against electrical transients in the power supply, must be used. 3. Monochromatic light is essential. 4. Cuvets with plane parallel sides, usually of 1 cm light path must be used. 5. Measurement must be made at constant temperature. If even a single one of these conditions is not fulfilled, calculation of the concentration using the molar absorptivity is no longer reliable. It is clear that this 112 Downloaded by: Université René Descartes Paris 5 126.96.36.199 - 10/28/2017 2:06:28 PM B.V.b. Optical properties of molecules principle applies not only for the measurement of components with characteristic colors, but also for the determination of all colored reaction products with stable spectral properties. As a rule readings are taken at the wavelength of the absorption maximum. This is, however, not an unconditional requirement. It is more important that the wavelength should always be exactly reproducible. The most exact results are thus obtained with photometers which use isolated monochromatic lines (e.g. the mercury lamp+a filter). A value often employed is the percentage absorptivity, a, which is defined as a A c% x b in which A c b is the measured absorbance, is the concentration of the solution in g/100 ml, and is the thickness of the absorbing layer (in most cuvets b = 1 cm). After the percentage absorptivity has first been empirically determined concentrations can subsequently be calculated from single measurements at the defined wavelength. Accordingly A ab c% If the molecular weight of a substance is known the percentage absorptivity is replaced by the molar absorptivity. This is defined as e A cM x b where A cM b is the measured absorbance, is the concentration in moles/1000 ml, and is the thickness of the absorbing layer in cm. Also in this case the molar concentration can easily be evaluated from the known coefficients by measurement of the absorbance: A exb Occasionally it will be more practical to use the millimolar or micromolar absorptivity instead of the molar coefficient. In German-speaking areas the absorptivity is occasionally referred to the units of moles!ml (instead of moles! liter). Care must be taken not to confuse these two values which differ by a factor of 1000. 113 Downloaded by: Université René Descartes Paris 5 188.8.131.52 - 10/28/2017 2:06:28 PM cM Unfortunately the scientific literature [1-5] employs the concept of the absorptivity in a surprising variety of ways. We have therefore collected the most important definitions and abbreviations in the following table: Definitions and abbreviations of photometric concepts Definition Nomenclature Abbreviation -log T Absorbance, extinction [2,3,4,5], optical density A,OD Alb Absorptivity , absorbance index , extinction coefficient K A c% x b Absorptivity [3,4,5], absorbancy index, specific extinction coefficient % ) a ( A 11c~xA cM x b Molar absorptivity [3, 4, 5], molar absorbancy index , molar extinction coefficient The absorptivity is therefore of special value when the standard is difficult to obtain orto keep, e.g. in the estimation of protein with the biuret reagent, or in the determination of bilirubin as azobilirubin. Butthe absorptivity is used in many other determinations. Occasionally it is necessary to calcUlate the percentage absorptivity from the molar absorptivity or vice versa: e = a x MW 10 or a = eX 10 MW Literature 1. Lothian, G. F.: Analyst 88: 678, 1963. - 2. Cooper, B.S., A. E.Gillam, G. F. Lothian and R.A. Morton: Analyst 67: 164, 1942. - 3. Brode, W. R.: J.opt.Soc. Amer. 39: 1022, 1949. - 4. Hughes, H. K.: Anal. Chem. 24: 1349, 1952. - 5. U.S. National Bureau of Standards, Circular No.484, Washington D.C. 1949. B.V.c. Apparatus for photometry B.V. c.1. Principle of the photometer The photometer is used to measure the absorbance of unknown solutions at a predetermined wavelength in absolute and reproducible terms . A diagram of such an apparatus is shown in Figure 34. Every instrument employs a light source. If an incandescent lamp, which produces white light, is used then potentially every wavelength in the visible region can be isolated. When gas discharge tubes are used as the light source, then monochromatic light of only the specific wavelengths generated by the lamp can be obtained. The lines generated by a mercury lamp are tabulated in Table 21. The optics of the instrument serve to concentrate the light rays. For the resolution of the light into the desired wavelengths several different systems can be employed. First the wavelength range of white light can be narrowed by the use of filters. The band-width of a simple filter photometer is, however, too wide to be spoken of as monochromatic. The ideal small band-width of 1 nm can be obtained, however, by combination of a special filter with a mercury lamp as light source. This type of apparatus is known as a spectral line photometer. There remains the possibility of splitting the incident light beam into approximately mono114 Downloaded by: Université René Descartes Paris 5 184.108.40.206 - 10/28/2017 2:06:28 PM where MW is the molecular weight of the compound sought. I Light source III Optical system II Diaphragm IV Light decomposition V VI Analytical Photocell sample VII Measuring apparatus (galvanometer) I I I II'~~~I Figure 34. Schematic diagram of a photometer. chromatic rays with a prism or diffraction grating and then to center the isolated ray by the appropriate optics. This apparatus is called the spectrophotometer. When the light ray is rendered as monochromatic as possible it is passed through the solution to be analyzed. Plane parallel cuvets of 1 cm optical thickness are much to be preferred to round test tubes. The intensity of light passing through the cuvet is then measured by the photocell which produces a signal capable of being read on a galvanometer scale. 1. Kortum, G.: Kolorimetrie, Photometrie und Spektrometrie. Springer, Berlin-Giittingen-Heidelberg. 4. Auf!. 1962. Table21. The lines of mercury and cadmium lamps (nm) which can be isolated by a filter. Hg Cd 313 326 334 366 404/407 435/436 468 480 492 509 546 577/579 623 644 691 772 1014 B.V. c. 2. Types of photometer At the present time some 50 different types of photometer are commercially available. The prices of these instruments range from 70 to 11,000 U.S. dollars. 115 Downloaded by: Université René Descartes Paris 5 220.127.116.11 - 10/28/2017 2:06:28 PM Literature The quality ofthe apparatus is largely proportional tothe price. The photometer is today the central and most important piece of equipment in the clinical chemistry laboratory, and consequently only highly stable apparatus should be purchased. It should provide approximately monochromatic light, i.e. a band-width of less than 5 nm. Only two basic types of apparatus have practical significance: 1. Spectral-line photometers. As light source these use a mercury or cadmium lamp which emit a discontinuous spectrum. The wavelengths of the lines obtainable are listed in Table 21. With the aid of appropriate filters the Ii nes can be isolated to produce predominantly monochromatic light having a bandwidth of about 1 nm. These instruments are especially useful for routine work as well as forthe measurement of absolute absorbances. 2. Spectrophotometers. In this equipment any wavelength is selected and isolated with a prism or diffraction grating. The band-width differs from one apparatus to another but in the highest quality instruments it reaches approximately the band-width of the spectral-line photometer. Commercially available instruments can be roughly divided into two groups: (a) with outstanding performance and a price above 2,500 U.S. dollars and (b) with fairly good performance and price approximately 1,000 U.S. dollars. There is still another group of less expensive instruments whose performance, however, does not reach sufficiently high standards. The following points are of particular importance in choosing a photometer: 1. Its wavelength range should extend down to 340 nm for enzyme determinations. 2. The apparatus should employ cuvets and if possible it should also be provided with semi-micro cuvets with a light path of 1.0 cm and volume of 0.5 ml. If possible flow cuvets should also be available. 3. The scale of the photometer must be adequate for a wide range of absorbance. 4. Provision of an automatic recording attachment offers great advantage. The different types of cuvet are compared in Table 22. It is advisable to work only with plane parallel cuvets. If round measuring test tubes must be used these must first be calibrated because the optical properties vary according to the position of rotation of the tube. Valuable comparative investigations of the quality of commonly available photometers have been carried out by Pohl [1-5]. 1. Pohl, H.: Chemiker ltg. 79: 401, 471, 551, 629, 1955. - 2. Pohl, H.: Chemiker ltg. 80: 819, 855, 1956. 3. Pohl, H.: Chemiker ltg. 81: 785, 1957. - 4. Pohl, H.: Chemiker ltg. 83: 513, 1959. - 5. Pohl, H.: Chemiker ltg. 85: 12, 1961. Table 22. Usable types of cuvet (light path d = 1 cm) Type Normal Material Plateglass Quartz Optical glass (OS) Transmission limit Width of light beam Fluid volume required for 1 cm sample path length Filling height 350 nm 10 mm 200 nm 10 mm 300 nm 10 mm 4mm 2.5 ml 25 mm 2.5 ml 25 mm 2.5 ml 25 mm 0.5 ml 0.1 ml 12.5 mm 5mm 116 Normal Normal Semi micro Micro 2mm Downloaded by: Université René Descartes Paris 5 18.104.22.168 - 10/28/2017 2:06:28 PM Literature B.V. c.3. The significance of monochromatic light The great significance of monochromatic light in making exact measurements is apparent from consideration of Figures 35a and band 36. When a solution with the absorption spectrum indicated is measured monochromatically at 492 nm, monochromatically at 546 nm and with a polychromatic light of half band width 20 nm and a maximum of 520 nm, the resulting standard curves are given in Figure 35 b. When monochromatic light is used, a straight line is obtained which is independent of whether the maximal absorbance of the solution (J. max.) is used or whether a wavelength on either shoulder is used. There is no absolute requirement to use the absorption maximum when making exact measurements. On the other hand, measuring with polychromatic light produces a standard curve which deviates from a straight line at increasing concentrations and therefore deviates from Beer's law. Measurement is therefore made more difficult since many standards must be determined and hence absolute measurements are impossible. a E b E 3.0 2.0 1.0 400 500 600 nm c B.V.d. Evaluation of the results B.V. d.1. The standard curve For every new method the validity of Beer's law must be thoroughly tested. This is most quickly done by the preparation of a standard or calibration curve. A series of dilutions of the analytical solution in arithmetic (i.e. not in a geometric) progression is prepared and the absorbance is measured using the reagent blank. The results are plotted on millimeter paper and a straight line is drawn through the points. The equation of the curve is deduced from the regression equation and the standard deviation and the correlation coefficient are calculated. From the equation a straight line is calculated and constructed. The graphical and the mathematical results are compared. The first question to be decided is whether the calibration line passes through the point of origin. If this is not the case it is advisable to check the blank value. 117 Downloaded by: Université René Descartes Paris 5 22.214.171.124 - 10/28/2017 2:06:28 PM Figure 35. Calibration curves for the use of measurement wavelengths of different band widths: 1. Monochromatic light at 492 nm; 2. Polychromatic light from a filter with a maximum at 520 nm and a half band width of 20 nm; 3. Monochromatic light of 546 nm. It may perhaps be possible to make the calibration curve pass through the point of origin by alteration of the order of addition of the reagents. Those methods in which it is not possible to obtain a coincidence of the absorbance zero with the concentration zero are difficult to employ for routine analysis as they introduce unavoidable complications in the method of calculation. Secondly, the question ofthe validity of the laws of Bouguer-Lambert and Beer must be considered, i.e. is there a direct proportionality between the absorbance and the concentration? If this is in fact the case and if the correlation coefficient exceeds 0.98, the method is suitable for clinical chemistry. Ifthe cali bration curve does not show a linear relationship between absorbance and concentration, one speaks of a deviation from Beer's law. Such deviations can be grouped in one or the other of the following categories: 1. Chemical basis: The so-called true deviations are due to the effects of the solvent medium, e.g. the salt and protein errors of indicators. More frequently, however, they may be caused by the fact thatthe chromogenic color reaction is not strictly stoichiometric. Examples of this type are ammonia determination with Nessler's reagent and the determination of protein by the Folin reaction (page 243). 2. Physical basis: False deviations from Beer's law are almost always due to the fact that the light used for the measurement was not monochromatic. A deviation from Beer's law does not by any means indicate that the method cannot be used. Its use, however, is subject to one of the following limitations: 1. Frequently the relationship is linear up to a certain concentration and deviates only at higher concentrations. Accordingly, the analytical sample should be diluted so that the absorbance falls in the linear range. 0.6 Eppendorf b = j em A. = 405 nm 0.5 0.4 0.3 0.2 (Coleman( b = 19 mm 0 A. = 405 nm 0.1 ~----r----r----T---~----40 80 120 160 I.U. Figure 36. Calibration curve for the estimation of alkaline phosphatase. Measurement with monochromatic light (Eppendorf photometer) and with polychromatic light (Coleman photometer). 118 Downloaded by: Université René Descartes Paris 5 126.96.36.199 - 10/28/2017 2:06:28 PM o 2. In many cases it is possible to adjust reagent concentrations so as to avoid deviation from a straight line at higher concentrations. 3. Reactions which do not follow Beer's law never give absolute measurements. If the two possibilities previously mentioned do not improve the procedure the sole remain· ing possibility is to include at least five standards in every series of determinations and to prepare a standard curve each time. The results are more reliable the closer the concentration of the standard is to the concentration of the unknown. B. V. d. 2. Calculation of results using standards The result may be calculated either from the reading for a closely related standard or directly from the extinction coefficient. The following illustrates calculation with a standard. The method is based on four determinations for each analysis: T TB RB S the test analysis containing all reagents and the analytical sample, the analysis blank containing only the analytical sample and serving as correc· tion for intrinsic optical absorption, the reagent blank containing the reagents without the analytical sample and giving the correction for the intrinsic absorption of the reagents, the standard containing the standard solution and all reagents. In some methods one or more of these controls may be superfluous. For exam· pie, in the determination of hemoglobin the analytical blank is not needed. All readings should be taken with water in the reference cuvet. The RB value provides a control of the quality of the reagents. The TB value is important for measuring the serum blank. From the following readings: A(To) A(TBo) A(RBo) A(So) the observed the observed the observed the observed absorbance of the test mixture, absorbance of the test blank, absorbance of the reagent blank, absorbance of the standard solution, the corrected absorbance ofthe standard and ofthe test sample are calculated: A(Tc) A(Sc) = A(To)-A(TBo)-A(RBo), = A(So)-A(RBo). The values are next corrected forthe difference of the volumes of T and S from the nominal volumes of the method. If T and S are pipeUed with the same pipet and the same volume no correction is necessary. If different pipets are employed the pure and volume·corrected value is calculated as follows: A(T) = A(Tc) x A(S) = A(Sc) x desired volume desired volume pipet volume pipet volume c(T) = 119 A(T) A(S) x c(S) Downloaded by: Université René Descartes Paris 5 188.8.131.52 - 10/28/2017 2:06:28 PM By this procedure the absorbance of the standard and the test sample are corrected for the blank values and to the standard volume. The basic formula for all further calculations, derived from the Beer-Lambert law, is as follows: in which c(A) c(S) is the concentration of the analytical sample, and is the concentration of the standard. A collection of photometric formulas is given on the front cover of this book. B.V. d. 3. Calculation ofthe results using the molar absorptivity When the following conditions apply the use of a standard is unnecessary: 1. The substance to be determined is itself colored or the colored product is formed in a reproducible stoichiometric relationship to the substance to be determined. 2. Beer's law is valid over the whole range of concentrations. 3. Pipets with absolute calibrations are used. 4. Plane parallel cuvets with known light-paths are used. In such a case it is sufficient to determine the analytical value only. When the percentage absorptivity is known the following formula holds: c(T) = A(T ) (dilution factor) ax b The result is given in g/100 ml. In a similar manner the molar absorptivity can be employed: c(T) = A(T ) (dilution factor) eX b From this equation the result is obtained in moles/liter. 120 Downloaded by: Université René Descartes Paris 5 184.108.40.206 - 10/28/2017 2:06:28 PM In our laboratory we use molar absorptivities as much as possible. Nevertheless, we carry a standard through the analytical procedure which, however, serves only as a primary control. The calculation is made from the molar absorptivity.