1079 



For the quantity — we liiid (see my preceding communication 



p. 889, These Proc. Feb. 1914) the value of 10,415 much too large 



for — ^. Also by comparison of these values (l+.x');) might be deter- 



mined, but with less certainty. 



The critical temperature of an associating substance is therefore 



greater than might be inferred from the molecular size of the single 



molecule — but the critical pressure has not changed. 



•pv 

 Let us now return to the determmation of — for the critical 



T 



pv 

 circumstances of the associating substance, and compare this with — for 



the critical circumstances for permanent single molecules. For the 



associating substance this value is equal to ( — ^ ) . If we replace 



V Tk Jx 

 the value of (v^•) by {l-\-x)v^ for {pk)x and {2\)x, we have to 



determine the value of — — v^ (1 -j- Xj, and if we now substitute 



ipki) for {pk).i; and (^-^-i) (1 + -O for (T/,)^., the required value 

 becomes equal to : 



And now we have still to show that Vi = ivk)i. 



If b is variable, the critical volume is, indeed, not 3/a/, but i b,,, 

 in which / is somewhat smaller than 2, or /' bk, when /' is somewhat 

 greater than 2, so that {vk)x ^ I b,, {l-\-Xk). On the supposition that 

 / has the same value for all substances, at least for substances with 

 not too small a number of atoms in the molecule, we have shown 

 by this that 



(pkvk\ _ rpjfvk 



\Tk Jx V '^k 



and that therefore the quantity ,v may be put equal to 3,77 also 

 for the associating substance. 



The foregoing considerations are not confined to cases in which 

 real association exists, but may also be applied to cases in which 

 what I have called quasi association is found. This probably occurs 

 already to an appreciable degree in the critical circumstances for 

 alcohols. In case of real association there are double and triple 



