SOME GENKRAL KINETIC CONSIDERATIONS RHO 



refers, or by some other parameter, Fg, F4 . . . For example, in a set of 

 curves, P = /[CO.], for various values of light intensity, I, the saturation 

 levels will be well separated (as in figs. 26.2 and 26.3) if saturation is im- 

 posed by the rate of light supply, but will coincide (as in fig. 26.4) if satura- 

 tion is due to the limited rate of a dark, catalytic reaction. 



Coincidence or divergence of the initial slopes depends on the qualitative 

 and quantitative relationships between the variables Fi and F2. If both 

 these variables affect the rate of the same reaction step, the rate will gener- 

 ally depend on both of them. For example, if Fi is the concentration, 

 [CO2], and F2 is temperature, and if the slope of the ascending part of the 

 curves P = f [CO2] is determined by the velocity of carbon dioxide m\)p\y 

 by diffusion, this slope will depend on temperature. If, on the other hand 

 (a) the factors Fi and F2 affect different steps in the "catenary series" 

 (e. g., if Fi is light intensity and F2 is temperature) and (6) the relative 

 values of Fi and F2 are such that the process affected by F2 is far below its 

 maximum rate when that affected by Fi approaches its maximum rate- 

 then (and only then) the reaction rate will be a function of Fi alone, and 

 practically independent of F2. 



The second condition (b) is important. Contrary to the way in which 

 the concept of "limiting factors" or "rate-determining reaction steps" often 

 is used, the existence of a reaction step of limited maximum efficiency af- 

 fects the rate of the over-all reaction long before the rate actually "hits 

 the ceiling." Therefore, if several reaction steps have maximum rates 

 which are not too different in their order of magnitude, the rate of the over- 

 all reaction must be affected by all these "potential bottlenecks" and not 

 only by the "narrowest" one. 



This fact was recognized in the alterations of Liebig's "law of the mini- 

 mum," which we have mentioned on page 862, and some quantitative illus- 

 trations of it will be given later in our analytical discussions. To make it 

 plausible, we may use a mechanical analogy; the flow of water through 

 a system of pipes with several strictions depends on the diameter and length 

 of all of them, and not only on the one that has the greatest flow resistance. 



In the plot of P against Fi, for different values of F2, we can expect all 

 cui-ves to be to the right of, and below, two "limiting" lines: one a slant- 

 ing "roof" imposed by the maximmn rate of the "slowest" reaction step 

 the rate of which is proportional to Fi (or, more generally, is a function of 

 Fi) ; and the second a horizontal "ceiling" imposed by the maximum rate 

 of the slowest reaction step the maximum rate of which is independent of 

 Fi. For example, in the case of curves P = f [CO2], for different tempera- 

 tures, the two limiting curves may be determined by the maximum rate of 

 diffusion of carbon dioxide and the rate of light absorption, respectively 

 (cf. fig. 26.6). These two limiting lines together form a typical "Blackman 



