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    Theory of Colorimetry


    Before we can discuss the technique of colorimetry it is important to understand and to differentiate this technique and others which involve measuring electromagnetic radiation from various parts of the spectrum.

    The following table should clarify the types of radiation that constitute the electromagnetic spectrum.

    For those who are unfamiliar with the definition of wavelength and its units here is a brief guide:

    Radiation may be considered as a wave. The wavelength is the distance between two successive peaks of that wave.

    The wavelengths in the table are expressed in nanometers (nm) these are related to metres thus:

    1 nanometer = 10-9 metre

    Colorimetry is just one of the types of photometric analysis techniques i.e. it is a light measuring analytical procedure.

    Colorimetric measurements are made using a white light source which is passed through a colour filter or alternative wavelength selection device. This incident light then passes through a cuvette containing a chemical compound in solution. The intensity of the light leaving the sample will be less than the light entering the cuvette. The loss of light or absorption is proportional to the concentration of the compound.

    Colorimetry however only applies to measurements made in the visible region of the electromagnetic spectrum e.g. (380 - 780 nm). The extent to which light is absorbed by a sample is dependant upon many factors. The main general contributors are the wavelength of the incident light and the colour of the solution.

    Each compound in solution has a typical (and usually unique) absorption spectrum, an example is shown in fig. 4.

    The spectrum is a pattern of the amount of light absorbed by the substance in the solution plotted against the wavelength of the light

    In most cases the spectrum will have a peak i.e. a wavelength at which absorption is at a maximum. This is often referred to as the max for the compound in question.

    If the absorption is being quantified it is essential that it is measured as close as possible to the max. Sensitivity is reduced at any other wavelength.

    From the example our sample has a max at about 460 nm in the blue part of the spectrum. So what colour will it appear to be?

    Well the answer is yellow!

    Confused? Well here is the explanation:

    Inert materials whether solid or liquid appear coloured due to the way they modify light illuminating the object. Thus different objects absorb some wavelengths and reflect others. If white light passes through a yellow solution, it absorbs all colours except yellow. Similarly, a book cover appears red since it absorbs all colours except red.

    If a solution is clear and colourless it has not absorbed any visible radiation and therefore all the white light is transmitted ie. it is transparent.

    See the example of the spectral distribution curve solution in figure 5. The solution absorbs blue light strong a max at 460nm and therefore appears yellow.

    If the concentration of the yellow solution is reduced by half the two solutions will give curves shown. Therefore for greatest sensitivity and linearity it is essential to limit the measuring wavelength to the area of highest absorption. Figure 5 shows that the correct wavelength at which to measure a solution is the one which gives greatest absorption.

    The wavelength or colour filter that will produce the maximum absorbance can be selected in two ways:

      1. Take readings throughout the spectrum on a typical standard solution of the substance under investigation and establish the peak wavelength
      2. Choose a filter of the complementary colour to the standard solution. Figure 6 shows the basic relationship between colours


    There are several options open to the manufacturer of a colorimeter when deciding how to select the wavelength i.e. produce monchromatic radiation (one wavelength band) from polychromatic radiation (white light). These basic options are-

      a. Gelatin filters
      b. Interference filters
      c. Grating monochromators
      d. Prisms
    Gelatin Filters

    These are low cost selection devices which produce or transmit a wide band of radiation usually 20 nm. Fortunately most colorimetric analyses have a wide absorption band which allows excellent results to be obtained from a simple colorimeter. The most common type of gelatin filter is constructed by sandwiching a thin layer of dyed gelatin of the desired colour between two thin glass plates.

    There are two drawbacks which can be encountered using gelatin filters:

    1. They have a wide bandpass, see Fig 15, which can lead to non linearity in standard curves

    2. They absorb approximately 30-40% of all incident radiation thereby reducing energy throughput to the detector.

    However these filters are eminently suitable for most general applications.

    (Glass Filters Coloured glass filters are now more or less historical selection devices in colorimeters and have very wide bandposses often up to 150nm. Specific wavelengths can however be achieved by using a combination of glass filters.)

    To ensure all wavelengths in the visible spectrum are catered for approximately 8 Gelatin filters are required. A typical range of filters will have the following transmission curves.

    Interference Filters

    These are used to select wavelengths more accurately by providing a narrow bandpass typically of around 10nm. The interference filter also only absorbs approximately 10% of the incident radiation over the whole spectrum thereby allowing light of higher intensity to reach the detector.

    The theory of operation of an interference filter is fairly complicated but has been simplified below.

    An interference filter comprises of several highly reflecting but partially transmitting films of silver separated by thin layers of transparent dielectric material (often magnesium fluoride (MgF2) This is also referred to as an MD or metallic dielectric filter). When white (polychromatic) light passes through the dielectric layers multiple reflections appear between the semi-transparent mirrors. However some energy from the light beams passes straight through the filter. It is this wavelength which is desired for analysis. If the dielectric layer thickness is altered slightly the resultant wavelength is changed.


    Before the analyst attempts to perform quantitative colorimetric analysis it is important to understand the theoretical aspects of the technique.

    The relationship between concentration and the light absorbed is the basis of the following theoretical consideration;

    The seemingly obvious way of taking readings on a colorimeter is to measure % transmission and adjust the 'blank" to 100%.

    For example, consider a situation where a blank is measured followed by three standard solutions having concentrations of 1, 2 and 3 units respectively. Ideally, a colorimeter should be giving concentration readings directly, but consider the above solutions when analysed.

    The solution with a concentration of 1 unit reduces the light to 50% therefore, the solution with a concentration of 2 units will reduce the light to 25% and the solution with a concentration of 3 units will reduce the light to 12.5%.

    Therefore if the colorimeter is calibrated using a transmission scale, the following graph is produced.

    The calibration in %T has the drawbacks of being non- linear and readings decreasing with increasing concentration. Bonguer first investigated this type of relationship for changes in thickness of solid materials. His work was followed by Lambert and Beer in 1852, who extended the studies to solutions. All three investigators contributed what is universally known as The Beer Lambert Law.

    This states that:
    The light transmitted through a solution changes in an inverse logarithmic relationship to the sample concentration.

    In order to take measurements both directly and linearly in terms of concentration, %T readings must be converted into an inverse logarithmic form which are called optical density units (OD) or absorbance (A).

    The formula is: = OD = log10100/%T

    Therefore, for the given example, the relationship of OD to concentration is shown in the table below.

    Concentration %T OD
    0 100 0
    1 50 0.3
    2 25 0.6
    3 12.5 0.9

    A calibration curve of OD against concentration linear and directly proportional.

    Optical density (absorbance) is used for colorimetric analysis so that readings relate directly to concentration.

    Similarly, optical density changes directly with sample path length. Thus we arrive at.

    Abs = E x c x l

    Abs = Absorbance

    E = Extinction coefficient or molar absorbtivity
    c = Concentration
    l = Path length

    l is fixed by the pathlength of the cuvette (usually 10mm) and E is a constant for each chemical species hence Abs C