{"id":823,"date":"2019-09-27T15:09:36","date_gmt":"2019-09-27T15:09:36","guid":{"rendered":"http:\/\/chemdictionary.org\/?p=823"},"modified":"2019-09-27T15:09:38","modified_gmt":"2019-09-27T15:09:38","slug":"beer-lambert-law","status":"publish","type":"post","link":"https:\/\/chemdictionary.org\/beer-lambert-law\/","title":{"rendered":"Beer-Lambert Law"},"content":{"rendered":"\n

<\/p>\n\n\n\n

History<\/strong><\/h2>\n\n\n\n

The beer \u2013lambert law is also known as Beer\u2019s law, the Lambert-Beer law\nor the Beer-Lambert-Bouguer Law. The reason for so many names is because more\nthan one law is involved in it.  In 1729\nPierre Bouger discovered the law and published it in Essai d\u2019optique sur la\ngradation de la lumiere. In 1760 Lambert quoted the Bouger\u2019s discovery in his\nPhotometria which states that the absorbance of a sample is directly\nproportional to the path length of light. Lambert did not claim any discovery,\nbut he was often credited with it. In 1852, August Beer discovered that\nabsorbance is proportional to the sample concentration. Generally, beers law\nrelates only to concentration while Beer-Lambert law relates absorbance to both\nconcentration and thickness of a sample.<\/p>\n\n\n\n

Definition<\/strong><\/h2>\n\n\n\n

Beer Lamberts Law states a relationship between the attenuation of light\nthrough a substance and the properties of that substance. It is defined as:<\/p>\n\n\n\n

\u201cThe path length and concentration of a\nchemical are directly proportional to its absorption of light.\u201d<\/em><\/p>\n\n\n\n

The premise is that as a beam of light is passed through a chemical\nsolution that beam of light becomes weaker. The attenuation of light occurs\neither as a result of distance through a solution or by increasing\nconcentration.<\/p>\n\n\n\n

The equation for Beer’s Law<\/strong><\/p>\n\n\n\n

Beers law may be written as:<\/p>\n\n\n\n

A= <\/strong>\u03b5<\/strong>bc<\/strong><\/strong><\/p>\n\n\n\n

Where <\/strong><\/p>\n\n\n\n

A= absorbance (no units)<\/strong><\/p>\n\n\n\n

\u03b5 = A Greek Letter Epsilon, the\nmolar absorption coefficient with units of <\/strong><\/p>\n\n\n\n

       Mol-1<\/sup> cm-1<\/sup><\/strong><\/p>\n\n\n\n

b = the path length of a sample\nusually expressed in cm<\/strong><\/p>\n\n\n\n

c= the concentration of the\ncompound in solution, expressed in M<\/strong><\/p>\n\n\n\n

while calculating the absorbance of a sample by using this equation, it\ndepends on two assumptions:<\/strong><\/p>\n\n\n\n

  1. the absorbance is directly proportional to the path length of the sample.<\/strong><\/li>
  2. The absorbance is directly\nproportional to the concentration of the sample.<\/strong><\/strong><\/li><\/ol>\n\n\n\n

    How to use Beer\u2019s Law?<\/strong><\/p>\n\n\n\n

    Many modern instruments perform beers law calculations\nby comparing a blank cuvette with a sample. A graph can easily be prepared by\nusing standard solutions to determine the concentration of a specimen. The\ngraphing method assumes a straight-line relationship between concentration and\nabsorbance, which is valid for dilute solutions.<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n

    Figure 1.1<\/p>\n\n\n\n

    In above Figure 1.1 graph shows that the\nconcentration is directly proportional to absorbance. Let the concentration =C\nand the absorbance =A. As C increases, A increases proportionally. Hence<\/p>\n\n\n\n

    A \u03b1 C<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n

    Figure 1.2<\/p>\n\n\n\n

    This second Figure 1.2 graph tells us that as the path length is allowed\nto travel through the width of the cuvette, increases, the absorbance increases\nproportionally. The path line is represented by a symbol d.<\/p>\n\n\n\n

    A \u03b1 d<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n

    Figure 1.3<\/p>\n\n\n\n

    Some molecules that absorb a lot of light even at low concentrations are\nvery brightly colored while others are not so good at absorbing light. The\nmolar absorbance coefficient \u20ac, which is known as Epsilon is a characteristic\nfor each type of molecule.<\/p>\n\n\n\n

    A= \u20acCd<\/p>\n\n\n\n

    This is known as Beer-Lambert Law.<\/p>\n\n\n\n

    A steep slope is achieved if \u20ac has a large value and it reflects a\nstrong absorbance.<\/p>\n\n\n\n

    In figure 1.3, A is plotted on the y-axis and C on the x-axis, and the\nslope achieved is \u20acd =A\/C.<\/p>\n\n\n\n

    Importance\nof Beers law:<\/strong><\/p>\n\n\n\n

    Beers law plays an important role in the\nfields of chemistry, physics, and meteorology. In chemistry Beers law is used\nto measure the concentration of chemical solutions, oxidation analysis and to\nmeasure the degradation of the polymer. Beer’s law also describes the attenuation\nof radiation through the Earth\u2019s atmosphere. On the other hand, if applied to\nlight, this law helps scientists to understand the attenuation of particle\nbeams, such as neutrons. In theoretical Physics, the beer lambert law is a\nsolution to the Bhatnagar-Gross-Krook (BKG) operator, which is used in the\nBoltzmann equation for computational fluid dynamics.<\/p>\n\n\n\n

    Beer\u2019s\nLaw Example Calculation:<\/strong><\/h3>\n\n\n\n

    A sample having a maximum absorbance value of\n275nm. It has a molar absorptivity of 8400M-1cm-1. 1cm is the width of a cuvette.\nA spectrophotometer value detected A=0.70. calculate the concentration of the\nsample.<\/p>\n\n\n\n

    By using Beer\u2019s law, we will calculate the\nconcentration of the sample.<\/p>\n\n\n\n

                            A=\n\u03b5bc<\/p>\n\n\n\n

                            0.70\n= (8400 M-1cm-1) (1cm) (c)<\/p>\n\n\n\n

    By dividing both sides of the equation by [(8400\nM-1cm-1) (1cm)]<\/p>\n\n\n\n

                            c=\n8.33 x 10-5 mol\/L<\/p>\n\n\n\n

    Transmittance\nand absorbance of light using Beers law:<\/strong><\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n

                                                                Figure\n1.4<\/p>\n\n\n\n

    The transmittance and absorbance of light by\na substance was first introduced followed by an explanation of the Beer-Lambert\nLaw.<\/p>\n\n\n\n

    Consider a solution and a monochromatic light\nis allowed to pass through it; having an incident intensity of I0<\/sub>\nand a transmitted intensity of I (Figure 1.4)<\/p>\n\n\n\n

    The transmittance, T, of the solution is defined as the ratio of the transmitted intensity, I, divided by the incident intensity, Io<\/sub>.<\/p>\n\n\n\n

    T=I\/Io<\/sub><\/p>\n\n\n\n

    It takes the values between 0 and 1. Generally, it is commonly expressed as a percentage transmittance:<\/p>\n\n\n\n

    T (%)= 100 I\/Io<\/sub><\/p>\n\n\n\n

    The absorbance A, of the solution, is related to the transmittance and incident and transmitted intensities by the following relations:<\/p>\n\n\n\n

    A = log10 Io<\/sub>\/I<\/p>\n\n\n\n

    A = -log10 T<\/p>\n\n\n\n

    There is a logarithmic relationship between\nthe absorbance to the transmittance. The 0 absorbance corresponds to a\ntransmittance of 100% while an absorbance of 1 corresponds to a transmittance\nof 10%. The table given below tells us the values of transmittance and\nabsorbance.<\/p>\n\n\n\n
    \n Absorbance<\/strong>\n <\/td>\n Transmittance<\/strong>\n <\/td><\/tr>
    \n 0\n <\/td>\n 100%\n <\/td><\/tr>
    \n 1\n <\/td>\n 10%\n <\/td><\/tr>
    \n 2\n <\/td>\n 1%\n <\/td><\/tr>
    \n 3\n <\/td>\n 0.1%\n <\/td><\/tr>
    \n 4\n <\/td>\n 0.01%\n <\/td><\/tr>
    \n 5\n <\/td>\n 0.001%\n <\/td><\/tr><\/tbody><\/table>\n\n\n\n
    \"\"<\/figure>\n\n\n\n

    Attenuation\nof 510nm laser through three solutions of Rhodamine 6G having different\nabsorbance values at 510nm. A bright yellow glow is the fluorescence emission\nat ~<\/sub>560nm.<\/em><\/p>\n\n\n\n

    Limitation and Deviation of Beer-Lambert Law:<\/strong><\/p>\n\n\n\n

    Beer-Lambert law is unable to maintain a\nlinear relationship between attenuation and the concentration of an analyte.\nThese deviations have been classified into three categories: <\/p>\n\n\n\n

    • Real:\nthis deviation is due to the limitation of the law itself.<\/li>
    • Chemical:\nthis deviation is observed due to specific chemical species of the sample being\nanalyzed.<\/li>
    • Instrument:\nthis deviation occurs due to how the attenuation measurements are made.<\/li><\/ul>\n\n\n\n

      Beer law and lambert law are only able to\ndescribe the absorption behavior of the solutions that contain relatively low\namounts of solutes dissolved in it i.e. <10mm. the analyte starts behaving\ndifferently when the concentration of the analyte in the solution is high i.e.\n>10mm. this is due to the interaction of the analyte with the solvent and\nother solute molecules and sometimes even due to hydrogen bonding interactions.<\/p>\n\n\n\n

      1. At higher\nconcentrations, solute molecules can cause different charge distributions on\ntheir neighboring species in the solution. If the concentration of the solution\nis more than 10-2M (0.01M) in that case the achieved relation is not linear while\nplotting a graph between Absorbance V\/s concentration. This means that\nBeer-Lambert’s law deviates. <\/li><\/ol>\n\n\n\n
        \"\"<\/figure>\n\n\n\n
        • The molar\nextinction coefficient \u03b5 depends on the\nrefractive index of the absorbing medium. If the initial concentration of the\nabsorbing medium is greater than 10-2M then refractive index changes and hence\nthe \u03b5 changes. The refractive index does\nnot change if the concentration is less than 0.01M and hence the \u03b5 does not change and the law holds true.<\/li>
        • The\nBeer-Lambert law also fails, if the absorbing species react with the solvent\ni.e. either association or dissociation takes place. For example, the\ndichromate ions react with water producing chromate ions which are yellow in\ncolor. <\/li><\/ul>\n\n\n\n
          \"\"<\/figure>\n\n\n\n
          • The law\nalso deviates if non-monochromatic light is used.<\/li>
          • The\nchange in temperature also leads to the deviation of Beer-lamberts’ law.<\/li>
          • The\ndeviation may also occur if the width of the instrument is not proper.<\/li>
          • In\ninstruments where filters are used also leads towards deviation because we do\nnot get monochromatic light through filters.<\/li><\/ul>\n\n\n\n

            The Beer-Lambert law is also not compatible\nwith Maxwell’s equation. It only describes the propagation within the medium\nbut doesn’t tell us the transmittance through a medium. It can be able to be compatible\nwith Maxwell\u2019s equation if the transmittance of a sample with a solute is\nradioed against the transmittance of the pure solvent that describes why it\nworks well in spectrophotometry. <\/p>\n\n\n\n

            Presently, the Beer lambert law is declared\nas a limiting law because the absorbance is only nearly linear depending on the\nconcentration. This is the reason that the attenuation coefficient also depends\non concentration and density even if there are no interactions. However, these\nchanges are negligible except for high concentrations and large oscillator\nstrength.<\/p>\n\n\n\n

            Beer-Lambert Law in the atmosphere:<\/strong><\/p>\n\n\n\n

            The attenuation of solar or stellar radiation\nis also described with the help of this law as it travels through the\natmosphere. In this case, there is a scattering of radiation as well as\nabsorption. The beer-lambert law for the atmosphere is written as:<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            the optical depth for a slant path is \u03c4\u2032\n= m\u03c4, where T refers to a vertical path, m represents the relative air\nmass and a plane parallel atmosphere is given as m=sec \u03b8 where \u03b8 represents the\nzenith angle corresponds to the given path.<\/p>\n\n\n\n

             Each Tx<\/sub>\ndescribes the optical depth where the subscripts tell us the source of\nscattering or absorption <\/em><\/p>\n\n\n\n

            • a represents the aerosols that absorb or\nscatter<\/li>
            • g represents the uniform mixed gases i.e.\ncarbon dioxide CO2<\/sub> and molecular oxygen O2<\/sub> that only\nabsorb<\/li>
            • NO2<\/sub> is the nitrogen dioxide due to\nurban pollution (absorption only)<\/li>
            • RS tells us the effects due to Raman\nscattering in the atmosphere<\/li>
            • W refers to the absorption of water vapor<\/li>
            • O3<\/sub> refers to ozone (absorption\nonly) <\/li>
            • r is known as Rayleigh scattering from\nmolecular oxygen and nitrogen which are responsible for the blue color of the\nsky. <\/li>
            • The\nattenuators selection which needed to be considered depends on the wavelength\nrange and can include many other compounds i.e. HONO, formaldehyde, tetra\noxygen, glyoxal, and many other halogen radicals<\/li><\/ul>\n\n\n\n

              m refers to optical mass or air mass factor\nwhereas \u03b8 represents the observed object\u2019s zenith angle. This equation is used\nfor the correction of satellite images by Ta<\/sub>, the aerosol optical\nthickness and is also used in predicting the role of aerosols in climate.<\/p>\n\n\n\n

              References:<\/strong><\/p>\n\n\n\n

              \nhttps:\/\/chem.libretexts.org\/Bookshelves\/Physical_and_Theoretical_Chemistry_Textbook_Maps\/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)\/Spectroscopy\/Electronic_Spectroscopy\/Electronic_Spectroscopy_Basics\/The_Beer-Lambert_Law\n<\/div><\/figure>\n\n\n\n
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