Spectrophotometric determination of the reaction progress

Sensitive tests for the uniformity of a reaction can be done by global analysis of the complete set of spectra recorded during photolysis. These methods, described in Section 3.7.5, provide the best evaluation of the minimum number of spectral components required to reproduce a sequence of spectra within experimental accuracy and the time-dependent species concentrations thus obtained accurately define the reaction progress. Simpler versions use absorbance differences observed at a few selected wavelengths where the changes are largest. Uniform reactions give linear plots of Aversus AA(/,2, ). For two sequential photoreactions, absorbance difference plots are curved, but plots of absorbance difference quotients, AA(21,7)/AA(/l24) versus AA(21,7)/AA(/l3,7), are linear. Isosbestic points provide the simplest criterion 

We now derive several equations for the spectrophotometric quantum yield determination of unidirectional photoreactions A — B. Reversible photoreactions will be treated in Section 3.9.3. The reader should not be deterred by the complex appearance of some of these equations. They are easy to use and give highly reproducible results, because absorbance measurements are precise. The photoreaction is induced by continuous irradiation with a monochromatic light source that exposes the sample 

In order to determine the quantum yield A = — dnA/dnp by absorption measurements, the molar absorption coefficients of the starting material A and of the product (mixture) B must be known. The differential amount of light absorbed by the reactant, dnp, during an exposure interval, dt, is then given by Equation 3.18. Replacing the partial absorbance by the reactant A at time t, A Ah by s AnA(t)l/V, where / is the optical pathlength, we obtain 

We insert Equations 3.19 and 3.21 into P a = dnA/d p and replace 0 a a by 20 ) to obtain Equation 3.22, the general differential equation used for the spectrophotometric determination of quantum yields the reason for introducing the so-called pseudo quantum yield Q = P-asa will become evident in Section 3.9.4. 

Equation 3.22 Differential equation for the spectrophotometric determination of quantum yields. 

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