605 



<[ — 0,354. As now according to (4) (f = (1 -j- /?) A6 : {v — h), we 

 have also : 



Lb b 



b v-b 



For Tjc, with v = 26, tlie value cp : (1 -|- ()') follows from this for 

 h b : b. For ^ resp. = 0, Vs- ^^id 1 we. find therefore resp. the 

 values < — 0,16, < — 0,167 and < — 0,177 from this. When 

 accordingly A6 : b becomes smaller than about — Ye- ^h® value of 

 the factor (3;?^^^ — 2n) -. m^ can become <Ci. For a value 0,88 (see 

 above) it will therefore be necessary that — Ab : b be about 0,2 — 

 a value which in view of the value for H^O (which has been found 

 of the same order of magnitude) is not at all impossible for methyl- 

 alcohol either. 



At any rate it is seen from the above, tiiat for associating sub- 

 stances {b) cannot be put simply proportional to {Tk : pk) ■■ {s : Sa),hut 

 that the factor (3??i^ — 2n) : m^ must be taken into account. Nor may 

 for the calculation of /? from s : s^ simply 2 : CI -f- /^) = i + -^' be 

 written for the latter ratio ; another factor 7f : m" (4??. — 3m) must 

 be added to it, which factor amounts to about 0,8 (see the above 

 table) in the case Ab = between j5 = 0,3 and (5 = 0,5 or 0,6, which 

 differs too much from 1 to be neglected. 



The error made by van der Waals is according to ^ 2 owing to 

 this, that he believed he could assume values for RT^ : (1 -\-ai) and 

 2)k, which do not differ (at least differ little) from the corresponding 

 values for non-associating substances. 



The calculation (given by me already in the cited TEYLER-article 

 in 1908) teaches something entirely different : for p;^ (with Ab =z 0) 

 e.g. the deviation can amount to more than 547o- 



The finding of a too large value for {Tk • pk) : {s : Sg), viz. 5,43 

 instead of about 4,8 points out, that necessarily for CH3OH the 

 quantity Ab : b will have a pretty large negative value, namely 

 about — 0,2, If ,i were about ^/j, then b would be = (1 — ,^) ^/^ b^^ -{- 

 + i^b, = 7, b, + V3 b„ and from 



A6^-V,_^._+ii^_02 



b Vb K + Vb k 



would follow 16: 13 r= 1,23 for the ratio ^/^b^:b^, i.e. the double 

 molecules would be about 1,23 times as large as two single mole- 

 cules — which is by no means impossible. 



5. On this occasion I will draw attention at the same time that 

 in § 7, p. 40 — 42 of the cited TEYLER-article also the quantity 



