THEORETICAL REMARKS 1249 



bola 1/T = f{T) can be approximated by a straight line, and the two 

 functions (31.4) and (31.8) are therefore not too different. For example, the 

 vakies of 1/T for the temperatures 270°, 280°, 290°, 300° and 310° K. 

 are 0.370, 0.357, 0.345, 0.333 and 0.322— z. e., they fall almost exactly on a 

 straight line. Thus, if equation (31.8) appHes, the values of Qw, calcu- 

 lated from measurements at 0-10°, 10-20° and 20-30° C, although not 

 exactly equal, will differ by not more than a few per cent, a variation in- 

 significant in most kinetic measurements, particularly those in biochemis- 

 try. Thus, the Qio formula (31.3) can be used as a practical substitute 

 for the theoretically more significant Arrhenius equation (31.8). A simple 

 relation exists between Qio and Ea, namely: 



(31.9) Ea = 0.457^1^2 log Qio 



For Ti = 15° C. and Ta = 25° C, the relation becomes: 



(31.10) Ea = 3.92 X 10^ log Qio (cal/mole) 

 leading to the accompanying reduction table (Table 31. VI). 



Table 31.VI 

 Temperature Coefficient and Activation Energy 



Qio (15-25° C.) Ea (kc.al/mole) 



1 



1.5 6.9 



2 11.8 



2.5 15.6 



3 18.7 



As discussed on page 1239, the temperature dependence of photosynthesis 

 does not always follow equation (31.8) with a constant Ea', an apparent 

 increase in activation energy usually is observed below 5° or 10° C, and a 

 decrease above 20-25° ; (formally, Ea becomes zero at the optimum tem- 

 perature and negative above it). In some experiments {cf. figs. 31.13 and 

 31.14) the log P = / (1/7") curve appeared to be nonlinear over its whole 

 length. 



Similar deviations from Arrhenius' law have been found in the study 

 of most biological processes, and some authors, e. g., Belehradek, in his 

 monograph Temperature and Living Matter (1935), became altogether scep- 

 tical as to the usefulness of Arrhenius' formula in V)iochemistry. Belehra- 

 dek found that the equation 



(31.11) log V = const. X log (r - 5) 



reproduces the rate of most biological processes more closely and over a 

 wider range of temperatures than the formula (31.8). By an appropriate 



