EXTERNAL SUPPLY AND EXHAUSTION EFFECTS 907 



of dehydration being about 10 sec.-^ at 18° C; (c/. Table 8.III). The 

 rate of dehydration of HCOa" ions was not given there, but we can esti- 

 mate it from the rate of addition of OH" to CO2, determined experimen- 

 tally by Brinkman, Margaria and Roughton (1933) : 



CO2 + OH- , HCO3- 



k' 

 k = 2.05 X 103 (18° C.) 



To obtain k', first calculate the equilibrium constant of the above reaction 

 from the known constants of dissociation of water (1.04 X 10~"), ionic 

 dissociation of H2CO3 into H+ and HCO3- (1.8 X 10""), and hydration of 

 CO2 (2.2 X 10-^), and obtain: 



K = k/k' = 4.4 X 10' 



This, together with the above value for k, gives (for 18° C.) : 

 A;' = (2.05 X 103)7(4.4 X 10') = 0.47 X 10"* 



This indicates that an HCOa" ion lives, on the average, at 18° C, as long 

 as 2.7 X 10^ sec. before being dissociated into OH ~ and GO2. A bicarbonate 

 buffer containing y mole HCOs^/l. can therefore supply a maximum of 4.7 

 X 10 ~^ y mole C02/l./sec. by this dehydration process. At pH < 10, 

 dehydration via H2CO3 must be added; at pH 9 it can double the rate 

 of conversion of HCOs" to CO2 (assuming the association of HCOs" and 

 H+ to H2CO3 to be practically instantaneous). A solution containing 

 y = 0.02 mole/1. HCO3- (Warburg's il//10 buffer No. 2, pH ^ 10.7) 

 is thus able to supply a maximum of 9 X 10"'' mole CO2/I. sec. The cor- 

 responding figure for buffer No. 9 (0.085 M HCO3-, pH ^ 9.4) is 5 X 

 10 ~^ mole CO2/I. sec. Comparing these figures with the above-estimated 

 maximum rates of photosynthesis in strong light (from 2 X 10~Ho 2 X 

 10-^ mole CO2/I. min., or from 3.3 X 10 ^^ to 3.3 X 10 "^ mole CO2/I. sec. 

 for suspensions containing from 0.1% to 1% cells by volume), we note that 

 the maximum supply exceeds maximum consumption in the 0.1% suspen- 

 sion by a factor of about three in buffer No. 2 and by a factor of about fifteen 

 in buffer No. 9. In 1% suspension, the supply is quite insufficient in buf- 

 fer No. 2 and barely sufficient in buffer No. 9. Considering the roughness 

 of the calculation (e. g., the use of concentrations instead of activities), the 

 margin is by no means secure even in the dilute suspension. Assuming the 

 calculation to be exact, a supply process with a maximum rate equal to 

 only 3 times the noninhibited rate of reaction is bound to cause a marked 

 inhibition (c/. chapter 26). It is therefore an open question whether the 

 limited rate of reproduction of CO2 molecules from HCOs^ ions can play a 

 role in the determination of the rate of photosynthesis of dilute suspensions 

 in strong light, at least in the more alkaline carbonate buffers. This 



