Jijid 
dC 1 
dy je Pp 
From this and the previous equation follows : 
dC ak Y k ry. id al " Y ¥ 
— —=— C— — (¢, — C) =k," € — k," (€C, — C) 
die P p 
and this is the differential-equation for a unimolecular reaction in 
which an equilibrium is formed. 
6. If we add instead of HCI or H,SO, an acid like acetic-acid 
which is partly split into ions, then, although H-ions are being added, 
the concentration of the H-ions during the whole progress of the 
reaction must no longer be considered as constant. 
Suppose the initial-concentration of the hydroxy-acid = (,, that 
of the acetic-acid C’ and that of the hydroxy-acid after a time ¢ ( 
and let us suppose that a portion a of the hydroxy-acid is split up 
into ions and a portion 5 of the acetic-acid then : 
Chydroxy-acid = (d WEE CHions— al ZIT bc" 
Cacetic-acid il b) C; Cheg. ions hydroxy-acid — ac’ 
lil 
At each period the hydroxy-acid is in equilibrium with the 
( neg. ions acetic acid 
H-ions and its negative ions and the same applies to the acetic 
acid, therefore the two following equilibrium-equations apply : 
a (aC +bC’) b(aC+bC’) 
TE —— k, and — PE == hee 
The dissociation-constants 4, and /, of the hydroxy-acid and the 
acetic acid are nearly alike, consequently @ — 6 and 
Gaza) 
Stes — ON 0020 
En 
_ VAR th(CC) +P — 
a — a 
2 (cs (") 
C tons hyd aa CVE (WIE SUE 
neg. tons hydroxy-acid — EW ial Se fs 
NEEN 
= = ee GG 
CH-ions = a (C HC) — 4 (V4k(C 7+’) =F El TRE js 
From this follows: 
C= or f(y +h A V(y + hb)? + 4k C}. 
We again have: 
negative ions + positive ions = lactone, therefore : 
