Physics. — “Derivation of a formula for the temperature depend- 
ence of the velocity constants in gas reactions from a special 
image of the process.” By Dr. J. Trestine. (Communicated 
by Prof. H. A. Lorentz). 
(Communicated in the meeting of March 27, 1920). 
Using a definite image of the dissociation Bo.tzMann derived a 
formula for the equilibrium constant in gas reactions. By means of 
a similar image we only need a short calculation to find the tem- 
perature dependence of the velocity constants in gas reactions. 
As to the dissociation let us e.g. consider that of /, into / + /. 
We have then the following image of the dissociation : 
A iodine atom be a centre of force. It will act on a neighbouring 
atom only then when their distance lies between a and a + da. 
We call a sphere with radius a the attraction sphere of the atom. 
The action will be thus that at the passage of the layer da the 
potential energy will decrease from O to w (p being a negative 
quantity). Pairs of atoms, the mutual distance of which is less than 
a, will be regarded as /,-molecules. 
From the kinetic theory of gases we know the number 7, of 
simple atoms and the number 7», of pairs, we may expect in the 
gas viz: 
n, — Ae—hme’ du dv dw de dy dz 
Ny == Ate-hmldhet) hb du dv dwda dy dz du do dw'da' dy’ dz' 
where 
1 
IT 
A is defined by the total quantity of iodine. 
Each pair the atoms of which lie in their mutual spheres of 
attraction forms a molecule. Let us now arbitrarily choose in each 
molecule one atom as the “first one” and the other as the “second 
one’. We then see that the number of molecules n,, the first atom 
of which lies in an element de dy dz du dv dw, while the second one 
is situated in the element da’ dy’ dz’ du’ dv’ dw’, is given by the 
half of n,*) viz: 
DRE 
Co Ue ys: eae Cea ut: 9? SE we, 
1) E.g. Jeans. The Dynamical Theory of Gases. 2nd Kd. pg. 92 s.q.q., pg. 211 s.q.q. 
4) Prof. Lorentz called my attention to this factor '/g. 
