Chemical Limitations to Beer’s Law

 Dilution of solution (than more of reagent excess, it is less deviation from the law);

 рН of medium: state of metal ion

stability of complex ions

 competitive reactions (for ligand)

 competitive reactions (complexing agent)

 polymerization and dissociation reactions

 ox-red reactions

Chemical deviations from Beer’s law can occur when the absorbing species is involved in an equilibrium reaction. Consider, as an example, an analysis for the weak acid, HA. To construct a Beer’s law calibration curve, several standards containing known total concentrations of HA, C _tot, are prepared and the absorbance of each is measured at the same wavelength. Since HA is a weak acid, it exists in equilibrium with its conjugate weak base, A^–

If both HA and A^– absorb at the selected wavelength, then Beers law is written as

where C _HA and C _A are the equilibrium concentrations of HA and A^–. Since the weak acid’s total concentration, C _tot, is

the concentrations of HA and A^– can be written as

where a_HA is the fraction of weak acid present as HA. Substituting equations gives

Because values of aHA may depend on the concentration of HA, equation may not be linear. A Beer’s law calibration curve of A versus C _tot will be linear if one of two conditions is met. If the wavelength is chosen such that e_HA and e_A are equal, then equation simplifies to

and a linear Beer’s law calibration curve is realized. Alternatively, if a_HA is held constant for all standards, then equation will be a straight line at all wavelengths.

Because HA is a weak acid, values of a_HA change with pH. To maintain a constant value for a_HA, therefore, we need to buffer each standard solution to the same pH.

Depending on the relative values of e_HA and e_A, the calibration curve will show a positive or negative deviation from Beer’s law if the standards are not buffered to the same pH.