52 PROBLEMS IN PHOTOSYNTHESIS 



When 



and 



we find from equation 19 



(HCO3-) = ^(NaHCOa) 



(CO32-) = /^(NaoCOa) 



_ a^(NaHCO:i)^ 

 /3(Na.C03)(C02) 



or 



(NaHCOa)^ - ^ ^ - A- r?m 



(Na,C03)(C0j - ^^^- ^ ™ 



Equation 20 has been verified for dilute solutions. The value of K' remains 

 constant if the total Na concentration is kept constant. At 25 ° C the fol- 

 lowing empirical equation has been found 



K' = 8739 - 1671 log Cn^ (21) 



The equation is valid for values between 100 and 1000 millimole of the total 

 Na concentration C^^. The constant K' is dependent upon the temperature, 

 but may be calculated approximately from the reaction heat of bicarbonate 

 dissociation. 



In this type of experiment a mixture of the following composition is used : 

 85 ml 0.1 molar NaHCOg + 15 ml 0.1 molar NaaCOg.* In this solution 

 C'Na = 85 + 2 X 15 = 115 millimole per liter, so that, according to equation 

 21, 'the value of A'' at 25 ° C is 5300. When (NaHCOg) = 0.085 mole/liter 

 and (NagCOa) = 0.015 mole/liter, we obtain, according to equation 20, 



(CO2) = 91 X 10-« mole/liter 



During the experiment the equilibrium between the salts is disturbed by 

 CO2 assimilation. However, when the CO2 uptake is small by comparison 

 with the salt concentration, the changes in the concentration may be ignored 

 because the carbonate-bicarbonate mixture acts as a buffer. This is shown 

 by the following example. The volume of the cell suspension is 10 ml. We 

 remove 200 /.il CO2, i.e., 0.2/22400 = 9 X 10-« mole/liter. The CO2 

 concentration, which was 91 X lO"'' mole/liter, will thus be decreased by 

 10%. The CO2 partial pressure of the carbonate buffer used is 0.20 X IO-2 

 atm = 20 mm manometer fluid. The removal of 200 m1 CO2 therefore means 

 a change of only about 2 mm manometer fluid in the CO2 partial pressure. 



The pH of the carbonate buffer can be calculated from the Henderson- 

 Hasselbalch equation 



^. , , (NaHCOa) ,., , 1 0-085 .. 



pH = pK. + log ^-^cO^ = ^-^^ + ^°^ 91 X 10- « = ^-2 



* The mixture of 95 ml 0.2 moles NaHCOa + 5 ml 0.2 molar NaiCOj is preferred today. Its 

 pH is 8.8 and the COj partial pressure at 20°C about 2 atm % (see § 29). 



