173 
Let 
iN i= vd or Sn=ridq. - . ee ees 
represent any possible) chemical reaction in the system, i.e. a 
reaction which is compatible with the given numbers of atoms 
NX, Y, Z;¥,,¥,,..., 0; are certain positive or negative whole numbers, 
which give the numbers of the molecules which are formed or 
disappear in the elementary reaction ’). 
The kinetic and thermodynamic deductions of the dissociation- 
equilibrium may now be given side by side: 
(kinetic) | (thermodynamic) 
dog iy }== 0. (84) OS Sa Oa Vee oo ee) 
BEI M= id 0 (85) | 0 inten bn 
JE=d(K+ >My) =O (36)| DE=S Tn (CT +b)=0 (36) 
Substitution of the expressions (26), (31) § 5 for log (y) and S 
and further development of the maximum-problems lead to 
1 
> rilog N; = (logV) ZE vit = vilog aj! | Evilogn;=(log VY = vit Erie OR) 
AS Di ae! (ft) Se ee 
— — > jy TS | ——— 3 0b; + (log 7). — 2 vi Ci 
Be ae Jo |e EON ) 
In (37’) we shall express V in the pressure p of the gas-mixture 
by means of the equation 
pV Fe Sara oe cs ig Se LO) 
Further in (87) we shall put 
7 
Kar, prEN .. . . (899) 
1) In general more than one reaction is possible between the molecules of the 
mixture each characterized by a special set of values of the numbers 
RAV ee, vj. 
In order to establish the dissociation-equilibrium completely, and to obtain the 
necessary number of equations between the equilibrium concentrations, all the 
different reactions [variations] have to be taken in succession [Comp. M. PLANCK, 
Thermodynamik § 247]. 
2) M. Puanck, Thermodynamik § 244 
3) Properly speaking these two equations must be taken as giving definitions of 
the quantities p and 7: the phase-region in the ‘‘y-space’’ which corresponds to 
the prescribed values of V, E and Nj, Nz, .. . Nj contains beside MAxWELL- 
BoLTZMANN states, others which deviate strongly from those and for which 
therefore in themselves the conceptions of “pressure and temperature of the gas” 
have no meaning at all. However, the very great majority of the phase-points of 
this region are of the MAXWEeLL-BOLTZMANN-type of distribution or closely 
resembling ones, and for those the relations (39) hold with the ordinary meaning 
of the quantities p and 7. 
