CONCEJSTKATION QUENCHING 773 



also if fluorescence were competing, not only with the bimolecular reaction 

 (23.7), but also A\-ith one (or several) mononiolecular (or pseudomonomolec- 

 ular) transformations of the excited molecule, such as energy dissipation by 

 internal conversion, or tautomerization, or a reaction with the solvent. 

 In this case, the constant k in (23.5), instead of meaning (23.6), would have 

 the meaning (23.10): 



(23.10) k = kc/ikf + kd) 



where ka is the mononiolecular rate constant of the competing energy- 

 dissipating process (or processes), (corresponding to the sum fc,- -{■ kt, 

 internal conversion plus tautomerization, in equation 19.5 in Vol. I, page 

 546). 



Furthermore, in this case, the constant C would not be equal to Fo (the 

 fluorescence intensity with quantum yield 1), as assumed by Weiss and 

 Weil-Malherbe, but would have the meaning: 



(23.11) C = FoA7/(A7 + kd) 



With the assumption C = Fo, the data of Weiss and Weil-Malherbe indi- 

 cate a yield of fluorescence (<p = F/Fo = F/C) of 4% at 1 X 10"^ mole/1, 

 and 21% at 2 X 10"* mole/1, (and, of course, 100% at infinite dilution); 

 but since no check was made by an experimental determination of Fo, the 

 true value of Fo may have been > C, i. e., the quantum yield of fluorescence 

 may have been correspondingly lower (not reaching 100% at infinite dilu- 

 tion). 



Comparison of (23.10) with (23.6) shows that by correcting the deriva- 

 tions of Weiss and Weil-Malherbe for the possibility of internal conversion 

 or other mononiolecular deactivation processes, one would obtain, from 

 their value of A", a value of k^ even larger than the one given in (23.9) : 



(23.12) Ac > 2 X 10'2 



The extraordinarily large value of this bimolecular rate constant makes one 

 skeptical about the correctness of Weiss and Weil-Malherbe's experiments, 

 or, at least, of their interpretation. Assuming that Chi* is deactivated by 

 the first encounter with Chi — which is not implausible — the above value 

 of kc gives for the average interval between two encounters (at [Chi] = 1 

 niole/1.) : 



(23.13) i = 5 X 10-3 sec. 



This is at least one whole order of magnitude less than can be estimated 

 from the formula for the frequency of collisions in gases, and two or three 

 orders of magnitude less than the estimate based on the rate of diffusion 

 of dyestuff molecules in solution. 



The rates of those reactions in solution that occur by the first (or one of the first) 

 molecular collision are determined by the rate of diffusion (which brings the molecules 



