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Study Notes: AAS Deviations from Beer’s Law

Departures from linearity occur and one should never use a particular standard and assume Beer’s Law is being followed. There is a need to measure absorbance of at least one standard every time an analysis is performed and, if required, apply a correction if there is any deviation from the calibration curve.

It is often assumed that Beer’s Law is always a linear plot describing the relationship between absorbance and concentration. Deviations do occur however to cause non-linearity. This can be attributed to a range of chemical and instrumental factors, some of which are briefly considered below.

Beer’s Law successfully describes the behaviour of dilute samples only. At high concentrations (i.e. greater than 10-2 M) there may be interaction between analyte atoms of interest and other atomic species in the sample such that the absorption characteristics of the analyte are affected. Such variables in the production of the atomic vapour are uncontrollable and hence the requirement for close scrutiny of standards and calibration curves to ensure that linearity has been obtained. Any deviation of the standard from its original calibration value can be used as a correction factor to the analytical results. One such method is the Standard-Addition Method.

Instrumental factors including stray light, noise and effects due to polychromatic radiation (monochromator efficiency, wavelength selected etc.) also cause spectrophotometers to suffer from non-linearity.

The net outcome of all of these influences is that Beer’s Law loses linearity at the high and low concentration ends of the relationship. As a consequence the best results (minimum overall error) are obtained for flame AAS when absorbance is in the range 0.1 to 0.8. For absorbances below 0.1 and above 0.8 considerable errors may be expected (but this will be dependent upon the performance characteristics of the individual spectrophotometer). A midpoint absorbance of ~0.44 is often used for convenience.

The manufacturer of the AAS usually indicates the characteristic concentration that can be expected for each element in aqueous solution. The characteristic concentration is defined as the concentration in solution, of the element which will produce a change, compared to the blank of 0.0044 absorbance units (i.e. 1% absorption).

A calibration curve (concentration versus absorbance) where at high concentration/absorbence the curve becomes non-linear.

It is always important for the analyst to check or know that the concentration range being worked on is indeed linear and not just simply apply Beer’s Law assuming linearity when in fact substantial errors are being introduced. The preparation of a calibration curve with standards bracketing the concentration of the samples to be analysed will highlight non-linearity. Where there is non-linearity the calibration curve should be used for quantitation rather than the Beer’s Law equation or the samples pre-diluted to return the calibration curve to linearity. The working range may also be adjusted by alteration of the instrument sensitivity. This is achieved by selecting a less sensitive incident wavelength, rotating the burner across the optical path or both. Such adjustments have been covered in Study Notes: Analytical Wavelength and Solvents.

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