( 764 ) 
4. In the spontaneous transformation of the hydroxy-acids the C,, 
has not been determined and this is necessary in order to calculate 
B and «. The question therefore arises how these may be determined. 
es wed dy : 
In the condition of equilibrium — — — 0 therefore: 
dt 
ky y= k, (C, ni, C) 
y= 3IWARC + — Kl, so 
EO EO 
PRT, OEE) 
nD 
bo 
x 
we 
| 
| 
=~ 
C',, the initial concentration is known, also & the dissociation-con- 
stant. If now we know = the reciprocal value of the equilibrium- 
a 
constant of the transformation : 
positive ions + negative ions = lactone, 
C,, may be calculated. 
This equilibrium-constant may be found from a series of deter- 
minations where the end-condition has been determined of a definite 
quantity of hydroxybutyrie-acid when HCI was added, therefore having 
H-ions as active constituents. On pg. 112 of his treatise the author 
states that to 20 ce. of the hydroxy-acid was added 5 ce. of the acid 
to be investigated (HCI or H,5O,); according to table 64 on pg. 116 
5 ec. of N HCl are added, the solution therefore becomes N/, HCI 
and in case of complete splitting of the HCI in that concentration also 
quadri-normal in H-ions. 
In the condition of equilibrium the positive H-ions of the y-hydroxy- 
acid and those of the HCl and the negative ions of the hydroxy- 
acid are therefore in equilibrium with the lactone. 
From the data of the above mentioned table 64 we may calculate that 
hy . 
HOP alll Ome 
1 
The transformation of hydroxyvaleric-acid also leads to an equi- 
librium, but, whereas in the condition of equilibrium the hydroxy- 
butyric-acid was converted to the extent of about 65°/,, the hydroxy- 
valeric-acid had been converted to the extent of 95 °/ 
In this transformation was found for : 
fie 
k, A 
== 15 x 107, 
ky, 
Paur Henry disregards in this transformation the occurring equili- 
brium as it is shifted so much towards the side of the decomposition- 
products. This should not happen if this transformation is regarded 
