Temperature on Homogeneous Gas Reactions. 221 



Since 1 + - 3 < 1 + 1 and 1 + s < 1 + 1, 



X' 



n n <} 2 e-^. Xl - 1 2 ' 2 "]' u } 



\n 



2 ' ll |n * (n + l).xf+ 2 ' 



If we take x=2 (a low value) and neglect all terms after 

 the first, U n < 0*002. Thus we are justified in taking 



i 



e-*.dx = ie- x i*a?-\ 



Substituting in equations (i.) and (ii.) we obtain 



n =-h? e ~ x *b + ^\- ■ ■ ■ &•) 



Reaction Velocity and Temperature. 



Let us apply our result to the homogeneous gas reaction 

 represented by f 



A + B->. 



Let n a be the number of A molecules per c.c. which may 

 react with B molecules on collision, i. e., the number of 

 A molecules which have velocities greater than a certain 

 critical value characteristic of the gas A. Let n b have the 

 same significance for the B gas. The molecules with less 

 than the critical kinetic energy will be merely diluents so 

 that the velocity of the reaction will be 



V cc n a n b 



from equation (iv.). 



The velocity of reaction is not only proportional to the 

 product of the molecules having the requisite energy for 

 combination but also to the frequency of collision. Maxwell 

 showed that the frequency of collision is given bv 



12 



KX* 



"■*> 



where (l + ^j is a term correcting for molecular attraction, 



