( 763 ) 
Suppose the initial concentration of the y-hydroxy-acid 
Suppose the concentration after a time ¢ 
C, 
& 
Suppose that the portion p of the hydroxy-acid is then split into 
ions, the concentration of the hydroxy-acid will then be (1 — p) C 
and the concentration of the ions pC. 
According to equation (1) 
oC 
P =S 
lI ll 
1—p 
Jk is the dissociation-constant of the hydroxy-acid. 
Suppose the concentration of the ions after a time ¢= y, then is: 
y PCE ARC HEK 
The scheme: 
positive ions + negative ions = lactone + water, 
gives as reaction-equation, when the concentration-change of the 
water is neglected 
dy ; : : 
aor rg Ot ee lt): 
In this 
kC,—y?—ky 
—— 
k 
is the concentration of the formed lactone. 
The above differential-equation gives, after introduction of this value 
for C,— C and after integration 
yt =1(y — a) —l(y — B) + const. 
For t=0 is y=y,, that is the initial concentration of the ions 
and the equation becomes: 
we WEE) oa) 
Tt ye) 
This equation is the same as the one deduced in my dissertation 
for all bimolecular reactions where an equilibrium is formed. 
In this equilibrium : 
Yo = 3 {V4LC, + 2? — A} the initial concentration of the ions, 
PIVO ER the concentration of the ions after 
a time f, 
B= y,= 3 V4kC, +2 — the end-concentration of the ions, 
n= DE (see p. 14 of my dissertation). 
The C, and C were determined by titration with barium hydroxide. 
k is the dissociation-constant of the hydroxy-acid and could be 
obtained by conductivity-determinations. 
yt 
Nm 
Proceedings Royal Acad. Amsterdam. Vol. VIL. 
