694
E. E. CHANDLER.
b=
k,m(Al--o.6d,-2o) 2 4
+ 605
In equation ( 2 6 ) the value of H is expressed in terms of quantities which are either known or easily determined experimentally, and, therefore, k , may now be obtained by substitution of the value of H , so found, in equation (16). The following application to the case of tartaric acid will serve as an illustration of the method, while numerous additional acids are similarlq- treated in MI-. Chandler's article. For tartaric acid,
X IO-^,
n = -2.167
k2
=
34.3
c =
-t 6.480 X IO-^, H
X IO^. The ratio k , / k ,
[CONTRIBUTION FROM THE
=
--
1 1 7 . 6 Y IO-^
,Ind
28.3.
KENTCHEMICAL LABORATORY, UNIVERSITY
01;
CHICAGO.]
THE IONIZATION CONSTANTS OF THE SECOND HYDROGEN ION OF DIBASIC ACIDS, l3s
E. E.
CHANDLER.
Received March 3, 1908.
It is generally believed that dibasic acids ionize in two stages, thus: H,X H -1 HS and H); 14 .1-S. From a study of the conductiyities of dibasic acids, Ostwald* concluded that, excepting strong acids likc oxalic, the second stage of the ionization did not take place to an appreciablr extent at concentrations greater than milli-normal, since the primary ionization constant, k , , as calculated from the relation, H * H X == k , H,X, (1) where the formulae H , H X , etc., represent molecular or ionic concentrations, was really a constant for all concentrations greater than 1/1024 normal. For smaller concentrations the apparent value of k , as calculated on the basis of equation ( I ) usually increased appreciably. 'l'his increase is the result of the ionization of the second hydrogen ion. If the secondary ionization constant, i. P . , the ionization constant of the second hydrogen ion of a dihasic acid. is called k,, then H - H X = k,*HX. (2) The magnitude of this constant has been determined previously for LL considerable number of acids by four entirely different methods. 'frevor3 determined the rate a t which dilute solutions of acid salts of dibasic acids invert cane sugar, and from the results calculated the concentrations of the hydrogen ions in the solutions used. It was assumed
3
' Walden, a
2.physik. Chew&.,8, 445 (1891) Ibid., 3, 281 (1889). Ibid., IO, 3 2 1 (180~).
-I:COSD
I I \ 1)IIOt;EY
ION OF DIBASIC ACIDS.
695
t l i ~ tlic t clissociation of d salt like NaHX into Na and H X ions is practically complete in dilute solutions and that further ionization of the H S tlicn yields 13 ioni, the concentration of which governs the speed of inversion. A little later -1.A. Noyes’ developed a formula by ineans of 13 hich he calculated from Trevor’s data the secondary ionization cons t m t s of the dibasic acids corresponding to the salts used by ‘1 i i1 0 1 ’rower* found values approximating those of Trevor and Noyes bi thc I I of ~ osidation cells. Smith3 carefully repeated and extended I \ o r ’ i n o i k . c q x r i m e n t s being made to test the reliability of the i i tliotl ~ Xl’cgscheider4 obtained secondary ionization constants from 1 I iontluctis-ity of thc f r c t acids. fourth, entirely distinct methocl >t i i ~ l)? d AIcCoy to find thv secondary ionization constant of carbonic lhi\ nietliod \\A\ later extended and applied to the study of !ti(! iiiic ,tcitl 8 I lic iwthotl of XcCo? a5 used for the latter .icid. is based -11 f o l l o n m ~cori~ider,ition~ It was shown that when a i ne11 as in one contaiiiing ,~ibitrar?ratio of total acid and base, is governed b? t h e iclations cd b\. rquations i I and (z), which by combination give
I iit -,title iiix
oitlci t o cleterniinc. t l i c s t a t c of equilibrium one must know the conI‘o find the concentration H,X the solutiitratioris of the componrnt.. i i o ~ im,iy 1)r shaken. until equilibrium iq reached with an immiscible plrtialls. misciblc sol.\-cnt. such as ether, in which the free acid is solufile concentration of the acid in the ethereal 1n11 the salt inroluhli i,!x c milltiplieti I n - :I factor nhich is n con5tniit for given acid a t a i i u d temperature, gixcq tlic concentration of the fice acid, in molecular I‘his factor is the partition coefficient ~ ~ i n 111 i ttic q u e o i i s solution I , [ tlie frev x i d ior \\.Iter ‘iiid etliei, nhich in this case is the ratio of the c oncc litration ot t hc niolrciilar H 2 S in an aqueous solution of the acid .ilont . t o that of I Iic total ,tcitl in an ethereal solution which is in equilibrium 13 ith the iorrncr If thc total concentration of the base, vz, is know11 fnt t’iv aqueous sol~itioncontaining H,X, NaHX and XaX, a determinati011 of t!ie total acidit! as shown by a titration, give5 the remaining ’[‘he forf . l c ’ t ( , i fox the calculation of the concentrations of H S m d X . 111
