THEORETICAL REMARKS 1247 



6. Theoretical Remarks 



We have used above the values Qio (temperature coefficient) and Ea 

 (activation energy) to characterize the temperature dependence of photo- 

 synthesis. A few words are needed here on the theoretical meaning of these 

 constants. The temperature coefficient, Qio, is defined as the ratio of the 

 reaction rates at two temperatures differing by 10° C; the assumption 

 that Qio is a constant is equivalent to the postulate that the reaction rate, 

 V, is an exponential function of temperature (van't Hoff's rule) : 



(31.2) V = const. X e^ 



Qio is determined by the constant a in (31.2); it can be calculated from 

 two rate measurements at temperatures differing by less (or more) than 

 10°, by means of the equation: 



,„. „. , ^ 10 Id {V1/V2) 10 A In ;; 



\oi.6) in yio = m _ rp — Tm " 



Equation (31.2) is empirical. Arrhenius found that a better approxima- 

 tion to experimental results can be attained by representing In y as a linear 

 function of 1/T (rather than of T) : 



(31.4a) V = A X e-Ea/RT 



(31.4b) In z; = log A - Ea/RT 



Equations (31.4), originally also empirical formulae, later received 

 theoretical justification, and it was shown that Ea is the "activation energy" 

 required to bring the reaction about, whereas A is a frequency, or prob- 

 ability factor. From the point of view of theory, equations (31.4) are only 

 approximate; the ''constant" A must also be dependent on T. For ex- 

 ample, in the simplest form of the collision theory of chemical reactions, in 

 which activation is provided exclusively by the relative kinetic energy of 

 the two colliding particles, the collision frequency (and consequently also 

 the factor A) is proportional to -\/T, and the correct form of the rate equa- 

 tion must therefore be : 



31.5) V = A' VT 



■Ea/RT 



instead of (31.4a). If polyatomic molecules react by binary colhsions, 

 and the activation energy can be supplied not only by the translational 

 degrees of freedom, but also by the degrees of freedom of rotation and 

 vibration, the more complicated formula (31.6) must be substituted for 

 (31.5): 



(31.6) ^ = ^'^^ XT-lV.'' '-'^''' 



