1 26 COLORIMETRY-SPECTROPHOTOMETRY 



One of the assumptions involved in the development of spectropho- 

 tometry was that the amount of light absorbed by a colored material 

 would be independent of the presence of other materials. Each molecule 

 would behave as an individual and would not be influenced by other 

 molecules. Because of the apparent validity of this assumption, it is 

 sometimes possible to measure the concentrations of two components in 

 the solution by making measurements at two wavelengths. As an ex- 

 ample, consider the pair of hypothetical solutions in Fig. 9-10. Pigment 

 P absorbs strongly at 600 mfJi, while pigment Q absorbs strongly at 650 

 m//.. The absorption by pigment P is low at 650 mjtt, as is that of pigment 

 Q at 600 m/A. The dotted curve in this graph shows the absorption 

 spectrum that would be found in the case of a mixed solution containing 

 equal concentrations of these two pigments. At wavelength 600 m/n, a 

 large portion of the absorption results from pigment P. Pigment Q con- 

 tributes only a small amount to the total absorption. At 650 m//-, the re- 

 lationships are reversed. If we know the absorption coefficients, it is pos- 

 sible to calculate the concentration of both components in this mixture 

 by the following set of transformations. Once the calculations have been 

 made the final pair of equations can be used directly in analyses. 



Agoo ^= Measured absorbancy at 600 m/u.. 

 K^eoo = Absorption coefficient for pigment P at 600 mfi. 



[P] = Concentration of pigment P. 

 Other symbols follow the same system. 



Aeoo = K^eoo h [P] + K%oo h [Q] (9-5) 



Ae6o = K^65o h [P] + K%,o h [Q] (9-6) 



Solving for [P], from equation 9-5, 



iV 600 t) 



Substituting in equation 9-6 and solving for [Q], 



r^l 1 / K 600 /l650 K 650^600 \ .^ q^ 



b \K 600 K'^650 K 650 K^GOO/ 



Substituting [Q] in equation 9-7 and simplifying, 



rpT 1 / K^650 AeOO K'^600 A650 \ ^q qn 



b \K 600 K^650 K. 6.50 K^GOoJ 



When the numerical values for the various constants are known, these 

 equations can be simplified. 



