Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

4 SPECTRAL LINE-BROADENING 151This reaction is of the second order with rate coefficient k, and it may be shown70that(cf. in the NMR treatment, above), thus k = l/cNzN-. This may be expressed interms of the line-width at half height, but it is a much simpler matter experimentallyto measure the difference in field between the points of extreme slope (AH, inFig. 17) than the half-height width.Thus k is more simply derived from k = 1.6 x lo7AH&,, where the numerical constant contains the Land6 g-factor, the Bohr mag-neton and Planck’s constant.This is one of several reactions of this type in which an organic negative radicalionand its parent molecule react in the presence of an alkali metal. It is found,rather interestingly, that the rate coefficients depend on the nature of the metal.To account for this, it has been postulated that the metal is involved in a bridgingrole in the activated complex, e.g., dipy . . K+ . . dipy- for the case of 2,2’-dipyridyl(dipy)”. A more extreme case of this association between the radical-ion andthe ion of the alkali metal used to form it occurs in the reaction of benzophenonewith its negative ion. The spectrum of (bemophenone)- in DMB has many hyperhelines caused by the interaction of the free electron with the ‘H and, when themetal is sodium, the 23Na nuclei. When benzophenone is added, the structure, dueto the proton interaction, disappears and only the lines associated with the sodiuminteraction remain. To account for this, it has been suggested that the odd electronmoves rapidly over all the proton positions (too fast for the lines characteristic ofthe electron in the different proton environments to be seen), but relatively slowlyfrom one sodium nucleus to another. Seen another way, this means that the transferof an electron from molecule to molecule is associated with the transfer of thecation72.Before leaving ESR techniques a couple of methods will be mentioned which measurethe rate of decay of radicals during a matter of milliseconds. Normally ESRcannot be used to follow decay rates in this time range because of the largeoutput time constants of the spectrometer. In what was effectively a combinationof pulse radiolysis and ESR, ethyl radicals were produced in liquid ethane by pulsesof electrons and two techniques were used to follow their rate of di~appearance~~.The first of these was a rotating sector of the type which has been used in photosynthesisexperiments (cf. Section 1); the average radical concentration was measureddirectly from the height of the recorded ESR signal at a fixed field, correspondingto maximum absorption. The time function was varied by altering the speed ofrotation of the disc. The second technique used sampling. As discussed in Section 1,the signal/noise ratio of a signal can be increased by averaging many measurementsof the same quantity. The intensity of maximum absorption was measured manytimes at a fixed time-interval after irradiation and averaged; this procedure wasReferences pp. 176-1 79