INFLUENCE OF TEMPERATURE ON CHEMICAL REACTION 219 
of molecular movement, which in gases, and probably also in liquids, 
varies with the square root of the absolute temperature. At ordinary 
temperatures this acceleration would be about one sixth of one per 
cent, per degree : the corresponding acceleration of the reaction velocity 
is, however, seldom observed to be less than five per cent, per degree. 
This remarkable discrepancy, moreover, is not to be accounted for by 
the influence of superimposed effects such as change in viscosity, as 
has been demonstrated conclusively in certain simple cases by careful 
calculation. It results, therefore, that we must consider the reaction 
velocity to be yet further influenced, and to a very great degree, by 
causes not yet considered. In fact, its great acceleration with rise of 
temperature can be accounted for kinetically only upon the assumption 
that those molecules alone react which attain a certain high velocity 
beyond the mean. This indicates, of course, that the phenomena are 
of a character not to be explained by any such generalizations as the 
Guldberg-Waage and the van t'Hoff equations; for these, like the 
thermodynamic laws from which they may be derived, are statistical 
in their nature, in this sense, that they are based on considerations 
such as apply to average molecular velocities alone. 
Enough has been said to show that for the practical estimation of 
the influi^nce of temperature on reaction velocities we must at the 
present time fall back upon rough empirical generalizations based 
upon the unanalyzed data at our command. It is a singular fact that 
despite the complexity of the phenomena that condition reaction 
velocities, their acceleration by change of temperature is not as widely 
variable as might be expected. "The ratio of velocities for a given 
temperature interval," says van t'Hoff (11), "usually differs but 
little from reaction to reaction; and for ten degrees ... it often lies 
between two and three. , . . By far the greater number of reactions 
double or treble their velocity with a ten degree rise of temperature." 
Illustrating this statement, van t'Hoff tabulates the accelerations of 
twenty reactions of varied character, the actual velocity constants 
of which vary between exceedingly wide limits, and finds that the 
acceleration for a rise of ten degrees shows an extreme variation of i .2 
to 7.14 for all, while for all but three the variation lies between 1.89 
and 3.68. This list is supplemented in an interesting way by Euler 
(12), who tabulates the acceleration coefficients of seventeen enzyme 
reactions, and finds among these an extreme variation for ten degrees 
of 1.3 to 5.3. Even this degree of uniformity is remarkable; for a 
^2 By definition of temperature {vide supra). 
