924 CONCENTRATION FACTORS CHAP. 27 



slope of this curve will be reduced by 10%.) This example of the "advance 

 effect" exercised by a "limiting factor" according to the general laws of 

 reaction kinetics has already been quoted in chapter 26. 



(c) Slow Carboxylation 



This case is contained in the aboA'c-derived general equations (27.16- 

 27.19), if one makes the assumption: 



(27.27) k^Ao<^kj 

 This implies another inequality : 



(27.28) /crf [CO2 ]»/(-.' [ACOol 



(since A-,.-lo[CO,] > AvUiCO,], > A-JA]lC"().], = /.{[AC'O,] + A*, the last 

 equation being the steady state condition for the complex ACO2). 

 Conditions (27.27 and 27.28) reduce (27.13) to: 



(27.29) [COaJa = [CO2] 



as it should be when the diffusion supply is ample. Consequently, (27.14) 

 and (27.15) are replaced by: 



(27.30) [ACO2] = A-.,[C02]Ao/(A:: + k* + A:, [CO-,]) 



and (27.16), by the much simpler equation: 



(27.31) P = nkM[CO,]k*/ik: + k* + k^iCO,]) 

 This equation can be written as: 



(27.32) P/(Pn>ax. - P) = k,[CO,]/{k: + kt) 

 These hyperbolae reach half saturation at: 



(27.33) ./JCOd = ^ (1 + I) 



(as could be derived also directly from equation 27. 17) . Their initial slopes 

 are (c/. 27.18): 



(27.34) {dP/d[C02])a = nk^k^*/{K + k*) 

 All curves (27.31) are confined under the "roof": 



(27.35) Pli:n. = nfcaAo[C02] 



an equation that can also be derived from (27.19), and obviously represents 

 the maximum possible rate of carboxylation. By reasoning similar to that 

 employed just above, it can be sho^vn that a "primary" carbon dioxide 

 curve with an initial slope ak^A^in will have its slope reduced, in consequence 

 of slow carboxylation, to a/ {a + l)/Cai4on. In other words, in this case, too, 



