The Beer-Lambert Relationship

To assess the photochemical potential of a reaction system it is essential to know its absorbance spectrum. The strength of the absorption of UV/VlS radiation as a function of the wavelength X is given by the well known Beer-Lambert law of absorbing molecules in solution (Eq. 3-4) or of absorbing gas phase components (Eq. 3-6). The relationship A = f(X) is called the absorbance spectrum. 

Aio is the (decadic) absorbance of a beam of collimated monochromatic radiation in a homogeneous isotropic medium (Verhoeven, 1996) is the incident spectral radiant power  

I is the thickness of the solution traversed by the UV/VIS radiation (also called pathlength of irradiation). 

The transmittance T is the ratio of transmitted spectral radiant power to 

For the sake of simpHcity, in many cases it is adequate to express Px as 100%. For example, absorption of 99% of an incident beam means that the absorbance becomes Aio = log p =-logT= log 1 =2. 

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THE BEER-LAMBERT RELATIONSHIP IN QUANTITATIVE INFRARED SPECTROPHOTOMETRY... 

Infrared spectra are recorded using either or both absorbance and percentage transmission just as they are in visible/ultraviolet electronic spectra, and the Beer Lambert relationship ... 

The Beer-Lambert relationship in quantitative infrared spectrophotometry 752... 

Figure 2.13 Validity of the Beer-Lambert relationship for different monochromating systems. The absorbance of varying concentrations of cyanmethaemoglobin was measured at 540 nm using a spectrophotometer (A) and a simple photometer (B) with a glass filter.

Alterations that may occur in the molecular nature of the sample due to changes in concentration may also result in deviation from the Beer-Lambert relationship. Molecules may tend to associate with one another when the concentration is high or, conversely, complexes may tend to dissociate in low concentrations. Both types of change may possibly affect the absorption characteristics of the compound and result in non-linear graphs. 

Concentrations in the region of 0.1 mol 1 1 are often convenient but it obviously depends upon such factors as the amount of substance available, the cost, the solubility, etc. From this stock solution, a series of accurate dilutions are prepared using volumetric glassware and the absorbance of each dilution measured in a 1-cm cuvette at the wavelength of maximum absorbance for the compound. A plot of absorbance against concentration will give an indication of the validity of the Beer-Lambert relationship for the compound and a value for the molar absorption coefficient may be calculated from these individual measurements or from the slope of the linear portion of the graph ... 

The graph indicates that for the instrument used, the Beer-Lambert relationship for NADH is only valid up to a concentration ot 0.3 mmol l-1 fan absorbance value of 1.75). 

The use of a single standard in this way assumes that the Beer-Lambert relationship is valid over the absorbance range measured and again it is necessary to confirm the relationship before using the method. 

The analysis of a range of known concentrations of the test substance is necessary to validate the Beer-Lambert relationship. If the plot of absorbance values against concentration results in a straight line then either of the two previously outlined methods may be used. If, however, the resulting graph shows a curve instead of a straight line then the implication is that the actual value for the molar absorption coefficient is dependent to some extent upon the concentration of the compound and as a result invalidates both methods. In such circumstances a graphical plot (calibration curve) will be needed. 

Stray light may cause deviations from the Beer-Lambert relationship BECAUSE... 

The ability to produce monochromatic radiation is a very desirable feature of photometric instruments because the Beer-Lambert relationship is only strictly true for monochromatic radiation. A good spectrophotometer may provide radiation of a specified wavelength with a range or bandwidth of as little as 0.1 nm, but it can be appreciated that even this is still not monochromatic when it is considered that the bandwidth of the sodium emission line is about 1 X 10-5 nm. This fact provides one of the major problems in the design of photometric instrumentation, namely the production of so-called monochromatic radiation. 

In which of the following techniques is the Beer-Lambert relationship of significance ... 

The method is extremely robust and reliable and obeys the Beer-Lambert relationship to a final protein concentration of about 2 g 1 1 (a sample concentration of about 20 g l-1) with a lower limit of about 100 fig of protein (sample concentration of 1.0 g l-1). The colour reaches maximum intensity in about 15 min and is stable for at least several hours. The method is simple and reliable and readily lends itself to automation but its lack of sensitivity is its greatest drawback. All proteins react in a similar manner and results show very little difference for different proteins. 

From the charge passed, 10 mol of charge forms 10 mol of bronze. Then, by taking c = 10 mol dm , e = 5200 cm mol dm is obtained from the Beer-Lambert relationship (equation (8.3)). 

The Beer-Lambert relationship is additive (/.e., the absorption of light by one chemical species is unaffected... 

A difficulty encountered in measuring the concentration of an unknown absorbing species in solution is deviation from the Beer-Lambert law. For reasons stated earlier in this chapter, some absorbing species do not demonstrate an increase in absorbance that is proportional to an increase in concentration. (In reality, most compounds follow the Beer-Lambert relationship over a relatively small concentration range.) When measuring solution concentration, adherence to the Beer-Lambert law must always be tested in the concentration range under study. 

The UV-VIS absorption spectrum of a protein is a characteristic property of that specific protein and can aid in the identification of an unknown. The a-lactalbumin fraction will first be characterized by measurement of the spectrum from 240 to 340 nm. From this, the absorption coefficient is calculated using the Beer-Lambert relationship. Finally, the AZi0/A290 ratio is calculated this may be used as an indicator of the purity of the isolated a-lactalbumin. 

Use the Beer-Lambert relationship (Equation 4.3) to calculate the absorption coefficient in terms of 0/ at 280 nm. 

When a light beam passes through a suspension, the dispersed particles scatter light away from the forward direction, thus reducing the intensity of the transmitted beam. Turbidity, the reduction in light intensity due to such scattering, is directly analogous to the Beer-Lambert relationship used in absorption spectrophotometry,4445... 

These two principles are combined in the Beer-Lambert relationship, which is usually expressed in terms of the intensity of the incident light (/q) and the emergent light (/) ... 

For most practical purposes, the Beer-Lambert relationship will apply and you should use the absorbance scale. 

A single (purified) substance in solution can be quantified using the Beer-Lambert relationship (eqn [26.5]), provided its absorptivity is known at a particular wavelength (usually at the absorption maximum for the substance, since this will give the greatest sensitivity). The molar absorptivity is the absorbance given by a solution with a concentration of lmolL ... 

Standard solutions of known concentration of analyte to provide absorbances between 0.2 and 0.8 are prepared by serial dilutions of a stock solution of an authentic standard. Each standard solution is aspirated into the flame and the observed absorbance is recorded. A calibration curve is then prepared by plotting absorbance versus concentration of analyte. As predicted by the Beer - Lambert relationship, the resulting plot wiU be linear or have a slight curvature (towards the concentration axis) at higher concentrations. The absorbance of an unknown, measured under identical operating conditions, is then related to analyte concentration in the unknown using the cahbration curve (i.e., a process of linear interpolation is used). A prerequisite to successfully using the method of external standards is that the sample and standard solutions behave identically in the flame no measurable... 

Analyse your samples replace the appropriate reference blank with a test sample, allow the absorbance reading to stabilize (5-10s) and read the absorbance value from the meter/readout device. For absorbance readings greater than one (i.e. < 10% transmission), the signal-to-noise ratio is too low for accurate results. Your analysis may require a calibration curve or you may be able to use the Beer-Lambert relationship (eqn [26.51) to determine the concentration of test substance in your samples. 

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