CAKBOK DIOXIDE DIFFUSION 921 



as the "primary" carbon dioxide curves, and treat the empirical curves as 

 if they were basically such curves, deformed by superimposed kinetic in- 

 fluences. In the region of low carbon dioxide concentrations (or in the 

 presence of poisons such as hydrogen cyanide), these additional influences 

 comprise supply reactions of limited efficiency — slow carbon dioxide dif- 

 fusion and slow carhoxylation. These two processes of limited, but [CO2]- 

 proportional, maximum rate tend to impose a slanting "roof" on the 

 P — /[CO2] curves and thus to convert Bose's several divergent hyperbolae 

 into Blackman's single and almost straight line. In the region of high CO2 

 concentrations, the additional kinetic influences must be due to [CO2]- 

 independent factors, such as catalyst deficiencies, which tend to impose a 

 horizontal "ceiling" on the over-all rate, i. e., to produce "carbon dioxide 

 saturation" of photosjiithesis even before the acceptor A has become sat- 

 urated with carbon dioxide. 



(6) Diffusion Factors 



When diffusion and carboxylation are slow processes (more exactly, 

 when their maximum rate under the given conditions is not rapid compared 

 with the actual rate of photosjoithesis, P) the concentration [C02]a of the 

 carbon dioxide molecules in the immediate neighborhood of the acceptor 

 may decline during photosynthesis considerably below the concentration of 

 the same species in the medium, [CO2]; while the concentration of the 

 carboxylated acceptor, [ACO2], may decline markedly below the value 

 corresponding to the thermodynamic equilibrium, as determined by equa- 

 tion (27.3). The stationary concentrations, [C02]a and [ACO2], estab- 

 lished under such conditions, can be calculated by the application of the 

 law of mass action to the reactions (27.1) and (27.2): 



(27.13) [CO^la = (fcdlCOo] + A-;[AC02])/(A:aAo - A^JACO,] + k,) 



and: 



(27.14) [ACO2] = (A-a[COo]aAo)/(A;* +K + k^CO^U) 



Combined, these two equations give a quadratic equation for [ACO2] 

 (and thus also for P) as a function of [CO2]. Its one physically significant 

 solution is: 



k^k* Ao + Kkd + k*kd + A;,fc4COo] 



(27.15) [AGO,] = — - — ■ ' — 



' kJc^Ao + <A;j + kfk,i + k^kj[C02]\ AoAvlCOo] 



2 kfk^ J k* 



