towards a Dynamical Theory of Solutions. 29 



exists as dihydrol and (A + pA 2 /2) /p 1 p 2 p = 0'1821, and to write 

 (A+pA'/'2)/p l p 2 p 



= 0-1821-0-414(0-25-/7 1 p 2 ) forp 1 <0'5 . (13) 

 = 0-1821 + 0-375(0"25-p 1 p 2 ) forp 2 >0'5 . (14) 



These equations probably tell us that in all cases the chief 

 action between alcohol and water consists of two parts, one 

 proportional to p x p 2 and the other to pip%, which indicates 

 that an important part is played by molecular conjunctions 

 of two elements of alcohol and two elements of water. The 

 net result is approximately that all the water is changed 

 to dihydrol when pi reaches 05 and to hydrol when p x 

 nearly reaches 1. Theoretically we must contemplate the 

 coexistence of (H 2 0) 8 , (H,0)„ H 2 0, (C 2 H 5 OH) 2 , and C 2 H 5 OH. 

 To keep the complications manageable for present purposes, 

 I have neglected the amount of C 2 H 5 OH in all cases, the 

 amount of H 2 when ^ x < 0*4:6 or 0*5, and the amount 

 of (H 2 0) 3 when p 1 >0'£6 or 0*5. If we calculate from 

 A when p l is 0'4G the density of the trihydrol changed by 

 alcohol into dihydrol of density 1*09, taking water at 15° 0. 

 to contain 1/3 of trihydrol, it comes out 0*873 at 15° in 

 place of 0*88 at C deduced from the density of ice. So 

 too, if we use (12) to find A/p. 2 when p 2 is small and find the 

 density of hydrol with that of dihydrol 1*09, the result is 

 1*31 at 15° in place of 1*26 deduced from the densities of 

 salts containing water of crystallization. 



The case of acetic acid and water can now be presented 

 briefly. 



Table II. 



Contraction on making 1 gramme of mixture of Acetic Acid 

 and Water at 15° C. Acetic acid as liquid 1, water 2. 

 Pl =l-0553, /o 2 =0-9992. 



lOOp! 12 3 4 5 6 8 



10> 10007 10022 10037 10052 10067 10083 10113 



10 5 A 100 190 290 390 480 580 770 



lO\A+p^/2)/p } p-2p 1009 967 993 1010 1003 1020 1034 



calc. 1003 1008 1012 1017 1021 1026 1035 



100/?! 10 20 30 40 £0 60 70 



lO 4 ^ 10142 10284 10412 10523 10615 105S5 10733 



10 5 A 948 1778 2441 2922 3214 3299 3185 



10\A+pA 2 /2)/p,p. zP 1044 1090 1128 1175 1231 1309 1437 



calc. 1044 1089 1134 1179 1224 1275 1428 



lOOpx 80 90 92 94 96 98 



10V 10748 10713 10696 10674 10644 10601 



10 5 A 2784 1947 1700 1390 1020 570 



lO\A+pA 2 /2)/PiPnP 1( ^8 2040 2173 2326 2496 2743 



calc. 1682 2038 2122 2209 2300 2390 



