towards a Dynamical Theory of Solutions. 31 



given is 0-23 (1- 1/1*09 + l-l/l-26')/2 = 0*0332, which, in 

 the circumstances, I take to be near enough to O0294 to 

 justify provisionally the opinion that the maximum density 

 and viscosity arise from the packing of the molecules of 

 acetic acid and water as (CH 3 COOH) 2 + H 2 + i(H 2 0) s . 

 If this is so, then the chief difference of the action of acetic 

 acid on water from that of alcohol on water is that from the 

 very beginning acetic acid both destroys trihydrol and pro- 

 duces hydrol, whereas alcohol changes trihydrol to dihydrol 

 first. So we should expect in both case?, when there is a 

 large excess of alcohol or acetic acid, that the contraction will 

 be that due to the conversion of all the water into hydrol. 

 So the limiting value of A//> 2 for small values of p 2 should 

 be the same with alcohol and acetic acid and equal to 

 1-1/1-26 = 0-2064. For alcohol from (12) this limiting 

 value is 0*2364, and for acetic acid from (19) it is 0*3072. 

 The discrepancy in the case of alcohol is not necessarily 

 serious, as we are dealing with a limit, but in the case of 

 acetic acid the difference between 0*3072 and 0*2064 is so 

 large as to require scrutiny. The value 0*3072 would mean 

 that in a large excess of acetic acid hydrol has a density 

 1*443 instead of 1*26, which is the equivalent in the liquid 

 state of 1*31, the mean density of solid hydrol in crystals 

 having water of crystallization. The largest density found 

 for solid hydrol is that in ChiCl 2 -f 2H 2 0, namely 1*440, and 

 the smallest is that in Na 2 C0 3 -f- 10H 2 O, namely 1*200. 

 Thus we see that the discrepancy found in the case of acetic 

 acid is only a little larger than that already observed with 

 CuCl 2 in relation to its water of crystallization. So it 

 cannot be said that the discrepancy makes untenable the 

 hypothesis that in excess of acetic acid water is changed 

 into hydrol, but we must seek for further proof elsewhere, in 

 connexion with other physical properties. 



For mixtures of propionic and butyric acid with water 

 densities at 25° C. are given by Liideking (AVied. Ann. 

 xxvii. p. 72, 1886). These give for propionic acid and wafer 

 with water as liquid 2 and ^ = 0*9873 : — 



(A + pA 2 /2) l Pl p 2 p = 0*100 -f 0-026>j 



from Pl = to 0*5 . . (20) 

 or =0*107 from^rrO to 0*5 . . (21) 



and =0*113 -{- 0*38 (0*25-p lj? ; 2 ) 



frompi = 0-5 to 1. . . (22) 



These give p with a maximum error of the order 13 in 



