NOTES
3290 The final result obtained after introducing the Einstein-Stokes relation between diffusion and viscosity is
+
2RT (RA RB)' 300017 RARB
#I$=-
in l./mol sec, where RA and RB are the radii of the reacting species. A plot of the measured rate us. T/q should give a straight line, and this is indeed the case, as is shown in Figure 9. From the ratio of the slopes of the V and ir bands, one ~ derived ~ ~ above. Also obtains E ~ ~ ~ ~1/3 / as E was from the results a t 1000 mp, one gets EIOOO
=
4.1
x
103(n
+
where n is the ratio RA/RB. A value of n = 1 gives el000 = 1.6 X lo4 l./mol cm in fair agreement with the value obtained for other cases of solvated electrons.16 Since the lines obtained in Figure 9 are fairly straight and their slopes give reasonable values for the extinction coefficients, we may consider it as an argument in favor of a diffusion-controlled mechanism.
When the reacting species are ions, one should multiply the right-hand side of the above equation by the factor" 6 e' - 1 where ZAZBe2 6 = D ~ T ( R A RB)
+
ZA, Zg are the charges of the reacting ions, RA,Ru are their radii, and D is the dielectric constant. Taking D = 12.5 and reasonable assumptions for the radii, the value for the correction term will be just. -6, ie., e2/D(RA R B ) ~ ( ~ / ifT we ) assume the reaction to be eX a + + Xa. This would result in a straight-line plot of k / e us. 1/17. Since our measurements were done over a narrow range of temperature (200-300"1
