370 



2k 



V 



hlh 



RT \^k '■ aip{a) 



a {v — biim) V 



This would therefore be the equation of state of an associated 

 substance of unchanging mean degree of association «. But we may 

 also look upon this equation as referring to a substance undergoing 

 a molecular transformation, if .we consider a as a function off and 

 J" expressing how the mean degree of association depends on volume 

 and temperature. Tliis is the function which we propose to determine. 



5. But before proceeding to do this we shall first consider (6") 

 once more as the equation of state of a substance with constant u. 

 The critical constants are found to be by the usual method 



{v,),^K,h^ {pk).. = K,^q{a) R{l\).= K,~a<f{a) (7) 



where the numerical coefficients K^, K, and /v,, the so-called critical 

 coefticients ^), have values which change with k ^). Hence : 



{vky. = {vk), ip,^-U = {pi,)^ff{a) iTi.U = {Tk),a<f(a) ') . (7') 



According to the above assumptions, therefore, the critical volume 

 of all polymers would be the same; i.e. the same as that of the 

 pure substance with the simplest molecules; the critical pressure 

 would also remain constant, if e were zero (equation 4'), and T.y.jc 

 would then be proportional to a, whereas with e := 1 (equation 4") 

 pak would be inversely proportional to <(^. and T^t inversely to a. 

 With the more general form (5) it becomes somewhat less simple: 

 Pat is then found to diminish continually with increasing a, and T^k 

 first increases and afterwards also diminishes '). 



^) Vide H.Kamerlingh Onnes and W. H. Keesom, Die Zustandsgleichung, p. 703 (89). 



2) The following results are obtained: 



kz=l b= b^ K,z=3 K,=^^ = 0,m70 A", = ^ = 0,296 



/;z=7, 1 6^ 2,80 0,0408 0,308 



^ = 16^ 2,32 0,0540 0.342 



k^ — 'l, \b^ 1,59 0,0952 0,422 



^' = — 1 oc 1 



3) Although these relations are derived from a special form of the equation, it 

 is quite possible that independently of it they may be at least approximately valid, 

 in the same way as the law of corresponding states, although it was found by 

 means of the original equation of state of van dee Waals, is not bound to this 

 particular one. But the necessary experimental data to test the equations (7') by 

 experiment are nol available. 



*) In the well known case of polymerisation: acetaldehyde (G^H^O: ^jt = 188°C.)- 

 paraldehyde (G0H12O3 ; tb = 290°' G ) the relation (7') gives a correct result for 

 the critical temperatures with f = i about; unfortunately the critical pressures 

 and volumes of these substances are not known, so that a further test is impos- 

 sible. However, it is doubtful, whether the above theory would be applicable to 

 a chemical transformation of that kind. 



