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e Ionization Constants of the Second
Hydrogen Ion of Dibasic Acids.
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A DISSERTATION
SUBMITTED TO THE FACULTIES OF THE GRADUATE :
SCRIOOJ.S OF ARTS, LITERATURE, AND SCIENCE,
IN CANDIDACY FOR THE DEGREE OF DOCTOR
OF PHILOSOPHY.
BY E. E. CHANDLER.
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The University of Chicago.
Founded by JoHN D. RocKEFELLER.
---
The Ionization Constants of the Second
Hydrogen Ion of Dibasic Acids.
A DISSERTATION
SUBMITTED TO THE FACULTIES OF THE GRADUATE
SCHOOLS OF ARTS, LITERATURE, AND SCIENCE,
IN CANDIDACY FOR THE DEGREE OF DOCTOR
OF PHILOSOPHY.
DEPARTMENT OF CHEMISTRY.
By E. E. CHANDLER.
EASTON, PA.:
PRESS OF THE ESCHENBACH PRINTING CO.
1908
The Ionization Constants of the Second Hydro-
gen Ion of Díbasic Acids.
It is generally believed that dibasic acids ionize in two stages,
thus:
H, X → H + HX and HX → H + X.
From a study of the conductivities of dibasic acids, Ostwald'
concluded that, excepting strong acids like Oxalic, the second
stage of the ionization did not take place to an appreciable extent
at concentrations greater than milli-normal, since the primary
ionization constant, k, as calculated from the relation,
H - HX = k1 - H. X, (I)
where the formulae H, HX, etc., represent molecular or ionic con-
centrations, 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 in-
creased appreciably. This increase is the result of the ionization
of the second hydrogen ion.
If the secondary ionization constant, i. e., the ionization constant
of the second hydrogen ion of a dibasic acid, is called k, then
H - HX = k,H - X. (2)
The magnitude of this constant has been determined previously
for a considerable number of acids by four entirely different
methods.
Trevor” determined the rate at which dilute solutions of acid
salts of dibasic acids invert cane sugar, and from the results calcu-
lated the concentrations of the hydrogen ions in the solutions
used. It was assumed that the dissociation of a salt like NaHX
into Na and HX ions is practically complete in dilute solutions
and that further ionization of the HX then yields H ions, the
concentration of which governs the speed of inversion. A little
* Z. physik. Chem., 3, 281 (1889),
* Ibid., Io, 321 (1892).
4.
later A. A. Noyes' developed a formula by means of which he
calculated from Trevor's data the secondary ionization constants
of the dibasic acids corresponding to the salts used by Trevor.
Tower” found values approximating those of Trevor and Noyes
by the use of oxidation cells. Smith" carefully repeated and ex-
tended Trevor's work, experiments being made to test the re-
liability of the method. Wegscheiderº obtained secondary ioniza-
tion constants from the conductivity of the free acids. A fourth,
entirely distinct method was used by McCoy to find the secondary
ionization constant of carbonic acid.” This method was later
extended and applied to the study of succinic acid." The method
of McCoy, as used for the latter acid, is based on the following
considerations. It was shown that when an acid salt as NaHX,
of a dibasic acid is dissolved in water it reacts thus:
2NaHX → H. X + Na, X.
The state of equilibrium in such a solution, as well as in one con-
taining any arbitrary ratio of total acid and base, is governed by
the relations expressed by equations (1) and (2), which by com-
bination give
HX* k,
H, X. X k, (3)
In order to determine the state of equilibrium one must know the
concentrations of the components. To find the concentration
H., X the solution may be shaken, until equilibrium is reached,
with an immiscible or partially miscible solvent, such as ether, in
which the free acid is soluble, but the salt insoluble. The con-
centration of the acid in the ethereal layer, multiplied by a factor,
which is a constant for a given acid at a fixed temperature, gives
the concentration of the free acid, in molecular form, in the aqueous
solution. This factor is the partition coefficient of the free acid
for water and ether, which in this case is the ratio of the concen-
* Z. physik. Chem., II, 495 (1893).
* Ibid., 18, 17 (1895).
* Ibid., 25, 144, 193 (1898).
* Monalsh., 23, 599 (1902); 26, 1235 (1905).
* Am. Chem. J., 29, 437 (1903).
" Preceding paper,
5
tration of the molecular H, X in an aqueous solution of the acid
alone, to that of the total acid in an ethereal solution which is in
equilibrium with the former. If the total concentration of the
base, m, is known for the aqueous solution containing H., X, NaHX
and Na X, a determination of the total acidity, as shown by a
titration, gives the remaining factor for the calculation of the
concentrations of HX and X. The formulae by which these
calculations are made are deduced in the preceding paper. It
is there shown that in general 3.
o,C O., C \?
Hx-* W(*)—baſis, (4).
and
C HX
X = (*# —º).
0.1 2 0.1 (5)
C is the equivalent acid concentration of the water solution minus
P times the equivalent acid concentration of the ether solution;
P is the partition coefficient; a , and a, are the degrees of ioniza-
tion of the acid and neutral salts respectively, and k, is the primary
ionization constant of the free dibasic acid; m is the total con-
centration of the base (say sodium) in the solution. In most
cases these formulas may be greatly simplified; where kia, H., X
sº .., , (a,C\”
is very small compared with (**) y
HX = a,C nearly. (6)
In such cases
x - c.(*). (7)
The method just outlined was applied to the sodium salts of
succinic acid by Professor McCoy, at whose suggestion I have
studied the conditions of equilibrium in solutions of the salts of a
number of other dibasic acids and from the results have calculated
their secondary ionization constants. In the preceding paper it
is shown how the secondary constants may also be calculated from
the conductivities of the solutions of the acid and normal salts.
I have also determined the conductivities of solutions of the salts
of those acids studied by the partition method and from the results
6
have obtained a set of independent values of the secondary ioniza-
tion constants.
The experimental work described in the paper consists of three
principal parts: the determination of
(I) The Partition Coefficients;
(2) The Equilibrium Constants;
(3) The Conductivities of the Salt Solutions.
I. The Partition Coefficients.
It is well-known that a quantity of a substance shaken with a
mixture of two immiscible or slightly miscible solvents at a fixed
temperature is divided between the two in a constant ratio,' if
the solute has the same molecular composition in the two solvents.
If there is in either solvent partial dissociation or association of
the solute, then it is found that a constant ratio of concentrations
obtains only for those portions of the solute having the same
molecular composition in the two solvents.”
This ratio is known as the partition coefficient. I have found
ether to be the best solvent in general for use in the determination t
of the state of equilibrium in solutions of dibasic acids and their
salts. The experiments of McCoy showed that the salts of succinic
acid are not taken up by the ether. In most cases ether dissolves
the acids satisfactorily and gives for aqueous solutions of the free
acid a constant partition coefficient when allowance is made for
ionization, thereby indicating that in the ethereal solution the
acid exists in the simple molecular form. In other solvents, i. e.,
chloroform, many acids are partially associated.” Moreover, an
ethereal solution will readily separate from an aqueous solution,
with which it has been shaken, while solutions of some of the
other solvents tried do not readily do so. To purify the ether it
was shaken with dilute sodium hydroxide solution, washed re-
peatedly with water, and finally distilled. The middle portion
only was used. All of the partition coefficients were determined
at 25° -- o.or, except one series at oº. The substances were
* Berthelot and Jungfleisch, Ann. chim. phys. [4], 26, 396 (1874).
* Nernst, Z. physik. Chem., 8, I IO (1891). Hendrixson, Z. anorg. Chem., 13
73 (1897).
8 Hendrixson, Loc. cit
7
shaken together in a plain cork-stoppered bottle in a thermostat,
first by a mechanical shaker, until they had come to the tempera-
ture of the bath, and then violently for a few minutes by hand and,
finally, allowed to settle for about half an hour. This procedure
was found sufficient to insure the attainment of equilibrium and
to effect a complete separation of the ethereal and aqueous layers.
In order to remove a sample of the aqueous solution unmixed with
ether, the top stem of the pipette was closed by the moistened
forefinger of one hand as the pipette was passed through the ether
layer; the body of the pipette was then grasped in the other hand.
Sufficient heat was thus communicated to expand the enclosed air
and expel the drop or two of ether that had entered the stem of the
pipette. The solutions were titrated with standard barium hy-
droxide, phenolphthalein being used as indicator. Before the titra-
tion of the ethereal solution, water was added and the ether distilled
off. Most of the acids used were products of the firm of C. A. F.
Kahlbaum. -
The results of the partition experiments with the free acids are
given in the tables of Series I. The first column gives the molar
concentration, A, of the aqueous solutions after treatment with
ether. The degree of ionization, a., of an acid was calculated
from its primary ionization constant, k, by means of the equation
02
Giºv-ºr
For oxalic and dibromsuccinic acids and for dilute solutions of
maleic acid k, is not constant; for Oxalic and maleic acids, a was
obtained by interpolation from the results of Ostwald' and for
dibromsuccinic acid from those of Walden.” The third column
contains the values of the ratio, p, of the concentration of an
aqueous solution of the acid to that of the corresponding ethereal
solution. This ratio may be called the uncorrected partition
coefficient. The true partition coefficient, P, is the ratio of the
concentration of the unionized or molecular acid in the two sol-
vents. It is easily seen that P = p(I — a). The values con-
tained in the last column are calculated from this relationship
* Z. physik. Chem., 3, 281 (1889).
* Ibid., 8, 479 (1891).
8
All of the tables except one refer to partition between water and
ether at 25° -- o.o.1. Table IV refers to succinic acid and these
Solvents at O’.
Series I. Partition Coefficients.
TABLE I.—OXALIC ACID.
Io"k, = 38ooo.
A. I O OOZ. p. P.,
O. 3815 36 I3.86 8.87
O. 2767 42 I5. 44 8.84
O. 225 I 44 I5. 74 8.8 I
O. I9 II 46 I6.35 8.83
O. I339 5 I 17.77 8, 6 I
o.O887 6O 2 I. 66 8.64
O. O.I.98 79 42.54 8.85
O. OIO3 86 61.38 8.35
O. OO54 9I. 5 IOO . OO 8.5o
8.64
TABLE II.-MALONIC ACID.
Io"k1 = 1580.
A. IOO O". p. P.
O. I478 9.8 IO. 94 9.86
O. II 2 I II. 5 II. O7 9. 79
O. O862 I 2.8 II. 28 3. 9.86
O. O.33 I I9.6 I 2 . 22 9.82
9.83
TABLE III.-SUCCINIC ACID.
Io"ki = 66.5.
A. IOO O". p. P.
O. I708 I. 9 7. 73 - 7.59
O. O582 3.2 7. 79 7. 54.
O. O287 4. 7 7. 73 7.36
O. O2 I? 5.4 7.81 7. 39
O . OI2O 7.2 7. 95 7. 37
O. OO59 IO ... O 8.39 7. 55
O. OO39 I2 .. 2 8.42 7. 39
O. OO23 I5.6 8. 79 7.42
9
. O705
. O7O2
. O374
. O2OO
. OI26
. OII6
. OO63
. OO39
. OO998
. OO7O2
. OO480
. OO284
. OOI79
. O28O
. OO85
. OO72
. OO63
. OO56
Oog86
. OC544
. OOI75
. OOO84
OOO49
TABLE IV.-SUCCINIC ACID AT o?.
IOO O". p.
4
45
43
. 59
. 64
. 68
.67
.85
TABLE V.—PIMELIC ACID.
IO"k, = 32.3.
IOO O". p.
5. 54. O. 7095
6. 56 O. 7 I 70
7.87 O. 7 IQ5
II. 3O O. 748O
I2.6O O. 7075
TABLE VI.-GLUTARIC ACID.
IO"k1 = 47.4.
IOO O". p.
4. O 3. 72
7.2 3.84
7.8 3.9 I
8. 3 3. 92
8. 9 3.93
TABLE VII.-SUBERIC ACID.
IO"ki = 29.9.
IOO OZ. p.
5.3 O. 2 I5
7.2 O. 228
I2. 2 O. 246
I7.2 O. 258
2I. 9 O. 274
3
3
4
3
O
6
6
3
3.59
O. 204
O . 2 II
O. 2 I6
O. 2 I4.
O. 2 I4.
IO
:
OO3 IO
. OOI78
. OOI23
. OOO96
OOO77
. OOO64
OOO58
. OOO5 I
. OOO46
OOO33
. OOO62
. OOO58
. OOO47
. OOO36
. O26I
. OIQ7
. OI3 I
. OII9
OO85
. OO57
OO56
A
OOO398
OOO272
OOO263
. OOO250
IO"k, = 25.3.
IOO O". p.
8.6 O. O679
II .. 2 O. O702
I3 - 4 o.O7I8
I5. O O. O747
I6.6 O. O753
I8. O O. O.782
I8.8 O. O8OO
I9. 9 O. O8 IO
2O. 9 O.O823
24. I O. O868
TABLE VIII.-AZELAIC ACID.
TABLE IX. —SEBACIC ACID.
Io"k, = 23.8.
IOO OZ. p.
I7.8 O. O2.I.3
I8. 3 O. O2 I3
2O. I O . O22 I
22.6 O. O232
TABLE X.—ORTHOPHTHALIC ACID.
IO"k, = I2 IO.
IOO O.
I9. 4
2 I. 9
26. I
27.2
28.4
36.7
36.9
IOO CY.
56. 2
62.7
62. 9
64. I
p.
.809
. 822
.873
.894
. 932
. 996
. OO6
TABLE XI.-METAPHTHALIC ACID.
Io"k, = 287.
p.
O. O.82I
O. O943
O. O944
O. O949
O
6
2
7
II
TABLE XII.-CAMPHORIC ACID.
IO"k, = 229.
A. IOO O". p. P.
O. OO229 9.5 O. O387 O. O350
O. OOI63 II .. 2 O. O398 O. O.353
O. OOI48 II. 7 O. O403 O. O.357
O. O.353
TABLE XIII-ITACONIC ACID.
IO"k, = I51.
A. IOO Cº. p. P.
O. O615 4.8 2.9 2.83
O. O.306 6.8 3. O6 2.87
O. OI6I 9. 2 3. I8 2.88
O. OIO3 II.4. 3.2O 2.8 I
O. OO9I I3.8 3. 22 2.83
O. OO39 2 I. 5 3.48 2.85
2.86
TABLE XIV.-MALEIC ACID.
IO"k, = II 700.
A. IOO O". p. P.
O. O993 29. O 9.6O 6.82
O. O486 38.5 II. I9 6.88
O. O337 44 . I I2 . 20 6.82
O. O253 48.7 I3. 27 6.82
O. OIQ6 53. O I4. 4O 6.78
O. O.I.43 58.4 I6. O6 6.69
O. O IOO 63. 7 17.78 6.45
O. OO54 73. I 23. 7O 6.38
t - 6.7I
TABLE XV.-FUMARIC ACID.
& IO"k, = 930.
A. IOO OV. p. P.
O. O.27I I6.9 O. 782 O. 650
O. OII.4. 24.8 O.87I O. 655
O. OO96 26.6 O.889 O. 652
O. OO92 27. I O. 893 o. 648
O. OO4. I 37.6 I. O53 o. 658
O. OO4. I 37.6 I. O4O O. 650
I 2
TABLE XVI.-MONOBROMSUCCINIC ACID.
- Io"k, = 2780.
A. IOO CE. p. P.
O. O879 I6.3 O. 4 I 3 O. 344.
O. O283 26.8 O. 479 O. 352
O. O.253 28, 2 O. 482 O. 348
O. O.I.3.I 36.7 'O. 599 O. 380
O. OO56 49.9 O. 678 O. 34O
O. 345
TABLE XVII.-DIBROMSUCCINIC ACID.
IO"k, = 34OOO.
A. IOO O". p. P.
O. O327 67.6 O. O578 O. OI87
O. O3O7 68. 6 O. O595 O. OI87
O. O3O2 69. I O. O603 O. OI86
o.ors?
The results found for Oxalic acid are remarkable; while the
value of p increases more than sevenfold within the range of con-
centrations used the value of P is so nearly constant that the
variations may reasonably be considered as due to experimental
errors. Now the value of a used in calculating P by means of the
equation P = p(I — a) is that determined from the conductivity
of the acid. In its change of ionization with change of concentra-
tion, Oxalic acid does not follow exactly the Ostwald dilution law,
in which respect it resembles salts and the stronger acids and
bases. One of the most important problems connected with the
ionic theory has been to decide whether the degree of ionization
as determined in the ordinary way from the results of conductivity
measurements of a good electrolyte is correct. Assuming the
validity of the partition law, the constancy of the value of P seems
clearly to indicate the accuracy of the values of a used. The view
that the correct value of a is given by conductivity measurements
is in accord with the conclusion of A. A. Noyes, who has subjected
all the other evidence on this point to a critical review." The
constancy of the partition coefficient, P, is equally good for the
balance of the acids, for most of which the dilution law holds true.
* International Congress, St. Louis, 1904, Vol. IV, p. 311.
I3
II. Equilibrium in Solutions of Dibasic Acids; Determination
of Equilibrium Constants.
It has been shown that the state of equilibrium in a solution
containing neutral salt, acid salt and free dibasic acid is represented
by the equation -
2-2
#. x=} (3)
2 2
The methods of determining the concentration of each of the
constituents of such a solution was outlined in the introduction.
In order to calculate the total concentration of the basic ion it is
necessary to know the final volume of the aqueous solution. When
water is shaken with ether, previously saturated with water, the
volume of the aqueous layer increases; this increase in volume was
in some cases measured directly in the manner indicated by Mc-
Coy for succinic solutions. In most experiments, however, it was
found more convenient to determine the increase in volume in
another way. It was found by experiment that when water or a
dilute solution, such as was used in these experiments, was shaken
with ether previously saturated with water, that the increase in
volume of the aqueous solution always amounted, at 25°, to
7.8 per cent., and at O’, to 15 per cent. The details of the ex-
perimental procedure for the determination of the equilibrium
constant may be illustrated by an example taken from the work of
glutaric acid. A quantity of pure glutaric acid sufficient to give
a mixture of the acid and neutral salts was added to 25.OO co. of
exactly normal sodium hydroxide and the solution diluted to 250 cc.;
exactly 20 cc. of the resulting solution were shaken in a plain
250 cc. bottle with about 75 cc. of ether at a temperature of 25°
+ O.OI until equilibrium was reached. This occurred, within ten
minutes. After the solution had stood in the thermostat for
about thirty minutes longer and the ether and the aqueous layers
had completely separated, a portion of each was removed, in the
manner described for the determination of the partition coeffi-
cients, and titrated with standard barium hydroxide, the ether
solution being first evaporated after the addition of water. In
all cases phenolphthalein was used as indicator. 20 cc. of the
I4.
aqueous solution required Io.70 cc. of o.o.972 normal barium
hydroxide; 50 cc. of the ether solution required 18.60 cc. of O.Oogg2
normal barium hydroxide. Therefore the (equivalent) acid con-
e e IO. 7 O X, O.O.Q.72
centration of the aqueous solution = 7o X 972 O.O52O,
, 2C)
and the (equivalent) acid concentration of the ethereal solution
18.60 × O.OO992
50
= O.OO369.
C = O.O.520 – 3.58 X O.OO369 = 0.0388.
H2X = 0.5 × 3.58 × 0.00369 = O.OO66.
Since the aqueous volume is increased 7.8 per cent, by the
absorption of ether, the total concentration of the sodium = m =
O.I./I.078 = 0.0928. HX and X may be calculated by the simpli-
—C
fied formulas: HX = a,C, and X = o,(*). o, - O.79 and
a, a o 70. Therefore, HX = 0.0306 and X = 0.0189.
v. * HX*
... = Hix. x = 750.
Io"k, = 47. Therefore, Io"k, = 6.3.
Since the sodium salts of monobasic acids are, in general, very
nearly equally ionized at equal concentrations, it seems probable
that the tendency of an acid salt, NaHX, to ionize into Na and
HX must be about the same as that of the simpler salts, Nax.
Consequently it has been assumed that a, the degree of ionization
of NaHX, is equal to that of Sodium acetate at the same concen-
tration. The degree or ionization, a, of a normal salt Na, X has
been taken the same as that of normal Sodium succinate at the
same concentration. The equilibrium concentrations have been
determined for solutions of the sodium salts of all the acids in
Series I with the exception of Oxalic, in which case the potassium
salts were used on account of their greater solubility in water.
Some difficulties were encountered in certain cases. The aqueous
solution of potassium acid oxalate contains but a very small
proportion of free acid and neutral salt. This condition is un-
favorable for an accurate determination of the equilibrium con-
centrations and therefore of the ratio ki/k, The same kind of
difficulty in still greater degree appeared in the study of maleic
I5
acid solutions. It was necessary in each case to use a propor-
tionately large quantity of ether solution to obtain an accurate
titration. Mono- and dibromsuccinic acids also present difficulties
in that each is acted upon slowly by water, the first to give hy-
drobromic and malic acids," and the second to give hydrobromic
and brom maleic acids.” However, the action of water at 25°
is too slow to cause very appreciable errors.
TABLE XVIII.-GLUTARIC ACID.
aq. a. m. C. H.2×. HX. X. ki/k, ki/k,.
o. 75 O. 64 O. I855 O. O.808 O. OI67 O. O606 O. O.335 6.6
O. 75 O.64 O. I855 O. O.807 O.OI7O O. O605 O. O.335 6.4 6.5
O. 78 O. 695 O. IO22 O. O4O5 O. OO68 O. O316 O. O2 I4 6.8
O. 78 O. 695 O. IO22 O. O437 O.OO89 O. O34I O.O2O3 6.4
O. 78 O.695 O. IO22 O. O448 O. OO90 O. O349 O. O2OO 6.8 6.7
O. 79 O. 7O O. O936 O. O464 O. OII4 O. O.366 O. OI65 7. I
O. 79 O. 7O O. O936 O. O528 O. OI65 O. O4I7 O. OI43 7.4
O. 79 O. 7O O. O936 O. O529 O. OI65 O. O418 O. OI42 7.4
O. 79 O. 7O O. O936 O. O480 O. OII9 O. O379 O. OI60 7.6 7.4
O. 79 O. 7O O. O928 O. O388 O. OO66 O. O3O6 O. OI89 7.5
O. 79 O. 7O O. O928 O. O464 O. OII3 O. O.366 O. OI62 7.3 7.4
O.8I O. 73 O. O618 O. OO84 O. OO25 O. OO68 O. OI95 9.5
O.8I O. 73 O. O618 O. OI64 O. OI5I; O. OI33 O. OI66 7. I
O.8I O. 73 O. O618 O. O.269 O. O489; O. O.218 O. OI27 7.6
O.8I O. 73 O. O618 O. O316 O. O763 in O. O.256 O. OI IO 7.6
O.8I O. 73 O. O618 O. O344 O. O445. O. O.279 O. OIOO 8.2
O.8I O. 73 O. O618 O. O406 O. OI5O. O. O.329 O.OO77 9.4 8. I
O.83 O. 76 O. O464 O. O.254 O. OO64; O. O2 II O.OO8O 8.7
o. 83 O. 76 O. O464 O. O.26I O. OO68 O. O2 I'7 O. OO77 8.9
o. 83 O. 76 O. O464 O. O.248 O. OO7O O. O2O6 O. OO82 7.4
o. 83 O. 76 O. O464 O. O.248 O. OO67 O. O2O6 O. OO82 7.7
o. 83 O. 76 O. O464 O. O.252 O. OO68 O. O.209 O. OO8I 8. O 8.2
O.84 O. 77 O. O.366 O. O.199 O.OO526 O. OI67 O. OO643 8.3
O. 84 O. 77 O. O.362 O. OIQ7 O. OO514 O. OI65 O. OO635 8.4
O.85 O.87 O. O316 O. OI72 O. OO490 O. O.I.46 O. O562 7.8
O. 85 O. 87 O. O3O9 O. OI72 O. OO490 O. OI46 O. OO534 8. 2 8.2
O. 90 O.83 O. O155 O. OO83 O.OO2O4. O. OO75 O. OO299 9. I
O. 90 O.83 O. OI55 O.OO86 O. OO236 O. OO77 O. OO286 8.9 9. O
Table XVIII gives the details of all experiments with glutaric
acid. The symbols m, C, HX, and X represent the respective
* Tantor, J. Russ. Chem. Soc., 23, 339 (1892). Beilstein, Org. Chem., I, 658.
* Van't Hoff, Etudes de Dyn. Chem. Amsterdam, page 14.
I6
concentrations in terms of gram equivalents per liter, while H, X
refers to gram molecules per liter. The simpler formulae, (6)
and (7), have been used for calculating HX and X in all cases,
except for Oxalic and dibromsuccinic acids. Table XIX gives,
in condensed form, the results for other acids; in each case several
determinations were made at each concentration, as in the case
of glutaric acid. The details are omitted in order to save space.
S
Oxalic. . . . . . . .
Malonic. . . . . . .
Succinic. . . . . . .
Glutaric. . . . . .
Suberic. . . . . . .
Pimelic. . . . . .
4%,
k1/k,
777,
k1/k,
4%, .
ki/k,
4%,
k1/k,
%,
k1/k,
777,
k1/k,
Azelaic. . . . . . .
Sebacic. . . .
o-Phthalic. . .
ſm-Phthalic. . . .
Camphoric. . .
Itaconic. . . . . .
Maleic. . . . . . . .
k1/k,
... ???,
k/k,
I
O. 269 I
87 I
O. 3 I34.
357
. I87O
. 5
. I855
. 5
. I855
... 2
. I 859
. 9
. I855
... 2
. I855
... O
1858
I
3
O. I346
981
O. I88O
39C)
. O834
. 9
. I O2 2
. 7
. O824
. 7
. O833
4
. O824
.8
. O824
... 2
. O825
O
O
. O463
6
oA61
3
. O468
. 9
I
4
O
TABLE XIX.
RATIO OF IONIZATION CONSTANTs, ki/k, AT VARIOUS CONCENTRATIONS, m.
O. O769
9 IQ
O. II 8o
444
. O3 I2
. 2
..O936
4
. O3 II
4
. O3O9
... 2
. O3 II
... 2
. O337
8
2
I
O. O598
84O
O. O94O
459
O. OI7O
... O
. O6 I8
... I
. OI69
... I
. OI69
. 6
. OI69
... 8
. OI69
. 7
. OI7O
65
O. OO84
I3. 2
O. OO84
57. O
O. O448
IO87
O. O784
474
O. OO46
26.6
O. O464
8 . 2
O. OO46
O. OO89
29O
O. O245
88O
O. O587
47O
O. O362
8.4
O. OOI8
9. I
O. O47O
488
O. O.I.55
9. O
O. OOO92.
9. 2
O. O393
4.93
O. OOO46
IO .. 4
&
TABLE XIX—(Continued).
Fumaric. . . . . . 777, O. O926 O. O468 O. OI56 O. OO84
k1/k, I8.3 2O. 3 25.8 3O. O
Monobromsuc-
cinic. . . . . . . . 777, O. O926 O. O463 O. O.I.56 O. OO84
k/k, 46. O 54 - O 69. O 9I. O
Dibromsuccinic m o ooz7 o on 62 o or sº
k1/k
19
In discussing the results we may consider the influence of three
factors upon the value of the equilibrium constant: (1) The
effect of the ratio of the total base to the total acid in solutions
of the salts where the concentration of the base is constant; (2)
The effect of the total concentration of the base; (3) The effect
of temperature. The experiments of McCoy on carbonates and
succinates showed that, for constant concentrations of the total
base, the value of ki/k, is independent of the ratio of base to acid.
My experiments lead to the same conclusion. If an aqueous solu-
tion of the pure acid salt (that is, one having equal molecular
concentrations of base and acid) is shaken with ether the ratio
of base to acid becomes greater than unity. In the experiments
here described no attempt was made to maintain equal concen-
trations of base and acid in the aqueous solution; indeed in the
case of glutaric acid the ratio was varied greatly in order to test
the independence of ki/k,. The ratio of total base, m, to total
m
*H* + H.x
periment with glutaric acid this ratio is I.O44; in the tenth it
is 1.282; and in the twelfth it is 1.644. Such a high value of
the ratio as the last is unfavorable to accuracy because of the
exceedingly small titer of the ether solution; this doubtless ac-
counts for the abnormal value found for ki/k,.
On the other hand, in the seventeenth experiment the ratio
is o. 735 and it is interesting to note that in spite of the large excess
of acid above that required to form the dry acid salt the solution
contains an appreciable amount of the ion of the neutral salt.
Here the great excess of acid is also unfavorable for an accurate
determinaton of the constant; nevertheless, the value found
is not far from the mean. In the first experiment with a sebacic
acid the ratio of base to acid is 1.84. Owing to the limited solu-
bility of the acid in water, it is impossible to decrease this ratio
very much at large concentrations of the base. Sebacic acid,
however, is so much more soluble in ether than in water that
there is always sufficient acid in the ether solution to make an
accurate titration possible and no difficulty was found in getting
concordant values of ki/k,.
In the seventh ex-
acid in any experiment, is
2O
I have found that ki/k, increases with decreasing concentra-
tion of the total base. A similar result was found by McCoy
for carbonates. Smith also observed a diminishing value of
k, with dilution. This is equivalent to an increase of ki/k, if
k, is constant.
The values of ki/k, have been found by inter- and extrapolation
for the concentrations O.I., O.OI and O.OOI of the total base, with
results shown in the following table. The last two columns contain
the ionization constants of the first and second hydrogen ions.
The values of k, were calculated from those of ki/k, for o.oO1
normal concentration:
TABLE XX.
k/k,
- Conc. o. I. Conc. o.o.1. Conc. o.oOI. Ioºk 1. Io9k2.
Oxalic. . . . . . . . . . . . 930. O 93O 93O 380OO 40.9
Malonic. . . . . . . . . . . 460 6IO 78O I58O 2. O3
Succinic. . . . . . . . ... 16.5 23.5 3O. 5 66.5 2 . I 8
Glutaric. . . . . . . . . . 7. O 9.8 I4 - O 47.4 3.38
Suberic. . . . . . . . . . . 4.6 4 8. I 29.9 3.67
Pimelic. . . . . . . . . . . 4 - 4 5.9 7.4 32.3 4. 37
Azelaic. . . . . . . . . . . 4.6 6. I 7.6 25.3 3. 33
Sebadic. . . . . . . . . . . 4. . I 6.5 9. 2 23.8 2.59
o-Phthalic. . . . . . . . . IQO 29O 390 I 2 IO 3. IO
m-Phthalic. . . . . . . . 5. 2 8. I IO.8 287 26.6
Camphoric. . . . . . . . 8. O I 2.4 I6.4 229 I4. O
Itaconic. . . . . . . . . . 32. O I 7O I5 I 2. I6
Maleic. . . . . . . . . . . . 3OOOO (45000) (6OOOO) II.7OO O . 2C)
Fumaric. . . . . . . . . . I7. O 3O 43 93O 2I. 6
Monobromsuccinic. 44. O 78 II 2 2780 24.8
Dibromsuccinic. . . . Io (16) (22) 34OOO 1540
The values in parentheses, for maleic and dibromsuccinic acids,
are uncertain.
The effect of temperature was determined by means of a series
of experiments at o? with succinates. The following results
were obtained.
TABLE XXI.
m. . . . . . . . . . . . O. I739 O. O869 O. O497 O. O29O O. OI58
k/k,. . . . . . . . . I5. 5 I6.7 I8. O I9.7 23. I -
It will be seen that although the partition coefficient of suc-
cinic acid at o° (fourth table, Series I) is 4.30, instead of 7.45
2 I
at 25°, yet the value of ki/k, is practically the same at the two
temperatures. This fact is in accord with many well-known
results, which show that degrees of ionization and ionization
constants are, for most substances, nearly the same at O’ and
at 25°. *
It is interesting to note that ki/k, for the dibromSuccinic acid
is not greatly different from ki/k, for succinic acid, although both
k, and k, are enormously greater. Halogen substitution has
therefore affected the dissociation of the two hydrogens about
equally.
A series of experiments was carried out with sebacic acid, using
chloroform instead of ether. The results of the partition experi-
ments, conducted at 25° -- o.o.1 are given in the following table.
A, and A. represent the molecular concentrations of the acid
in water and chloroform solutions respectively. It is well known
that there is association of the molecules of many substances
when dissolved in chloroform. Allowance for a only, there-
fore, fails to make the values of P constant. The smaller values
of P for the more concentrated solutions indicate, of course,
a greater degree of association in the chloroform.
TABLE XXII.-PARTITION COEFFICIENTS OF SEBACIC ACID.
Aw. Ac. Oğ. p. P.
O . OO IOO O. OOO963 I4. 3 I. O4. O. 89
O.OOO59 O. OOO438 I8. 2 I. 36 I. O9
O. OOO3O O. OOOI76 24. 5 I. 7O I. 29
O. OOOI8 O. OOOO87 3O .. 3 2. O8 I .45
The following table contains the results obtained in the de-
termination of ki/k, for sebacic acid by the chloroform method.
The column headings have the same significance as in the tables
where ether was used, but in the column headed A, gives in addi-
tion the concentration of the acid in the chloroform. The ex-
perimental treatment it the same as that described for ether
extraction except in two particulars. (1) The solubility of
chloroform in water is so slight that the volume of the water
solution is not changed when it is mixed with chloroform, so that
the concentration of the total base is not altered thereby. (2)
Inasmuch as there is no constant partition coefficient, its value
22
for each experiment with a salt solution usually must be deter-
mined by interpolation. No partition experiment was made with
the free sebacic acid in which the chloroform concentration was
so great as that of the first experiment of the following table.
The corresponding value of P, o.84, was obtained by graphical
extrapolation:
&
Cºz.
O. 7O
O. 82
.
%2,.
. 2008O
. O924.5
. O924.5
. O3346
. O3346
. OI826
. OI826
.
TABLE XXIII.-SEBACIC ACID.
C.
. O2 IO4.
OI I82
. OII 95
. OC454
OO484
. OO269
. OO253
.
Ac.
. OOI 48
. OOO85
. OCO94
. OOO26
. OCO33
. OOOI6
. OCO I4.
P.
.84
.9 I
. 89
. I 7
. I4
. 3O
. 33
i
H., X.
. OOI 25
. OOO77
. OOO83
. OOO3 I
. OOO38
. OOO2 I
OOOI9
.
HX.
. O I 54.
. OO93
. OO94.
. OO39
. OC4I
. OO24.
. OO22
A.
. O566
O282
. O282
. O II 3
... O II 2
. OO64
. OO65
k/ka.
.
... O I
. 79
. 34
. 29
. 92
24
The first value of ki/k, is uncertain on account of the uncer-
tainty of the factor P = O.84. The remaining values of ki/k,
are almost constant. However, too much stress should not be
laid on the constancy, as the method is evolved by the phenom-
enon of association.
For an acid which is difficultly soluble in water, ki/k, may
be determined in a manner still different from that described
above. The solubility of the acid in pure water is first determined
and allowance made for dissociation in the usual way. When
the solid acid is present in excess the concentration of the un-
dissociated portion of the dissolved acid in aqueous solution of
the free acid is equal to its concentration when the salts also are
present. It is, well known that it is not easy to determine with
accuracy the solubility of a difficultly soluble substance. About
two months were spent in an endeavor to find the solubility of
sebacic acid in water. Equilibrium between the dissolved and
undissolved acid was sought by approaching 25° from both a
higher and a lower temperature. Rapid shaking was found
to increase the solubility considerably. The result is probably
to be explained by the comminution of the crystals by the greater
agitation, it being apparently well established that smaller par-
ticles are more soluble than larger ones." Forty-four experiments
gave an average molar concentration of O.OOI 18; individual
values ranged from O.OOI 25 to O.OOIO5. At a molar concentra-
tion of O.Oor 18, the degree of dissociation is 13.3 per cent. There-
fore the concentration of the undissociated portion is o.oOI 18 X
O.867 = O.OOIo. To filter the solution, it was drawn into a pipette
by means of a filter pump through a closely packed cotton plug.
It was then titrated. That error did not arise from imperfect
filtration was shown by the fact that separately filtered portions
of the same solution had the same concentrations.
To determine ki/k, sodium hydroxide of known concentration
was shaken with excess of acid, filtered as described, and titrated.
The factors of equation (3) are determined in the same manner
as for the partition method, except that the concentration, H, X,
remains O.OOIO for all experiments. This method of determining
k,/k, for Sebacic acid was not satisfactory. It was even more
* Ostwald, Z. phys. Chem., 34, 495 (1900); Hulett, Ibid., 37, 385 (1901).
25
difficult to get a constant equilibrium between the acid salt,
the neutral salt, the dissolved and undissolved acid than between
the last two alone.
The values found for k/k, averaged about 5, but some values
more than double this amount were found without my being able
to assign any reason therefore.
The same method was also tried with suberic acid, but only
one experiment was made. The molar concentration of its sat-
urated solution was found to be O.OI44, at which concentration
the degree of dissociation is 4.4 per cent. and the molar concen-
tration of the undissociated acid is o.or 38. In a single experiment
in which the total concentration of sodium was O.2OI the value
5.5 was found for k/k, for suberic acid. It is possible that an
acid of about this solubility would give constant results and
regret is expressed that more experiments were not made with
suberic acid by this method.
III. The Determination of the Secondary Ionization Constant of a
Dibasic Acid by the Conductivity Method.
The conductivity of the negative ion HX, of an acid salt, NaHX,
cannot be found in the usual way on account of the ionic inter-
actions of the solution of the acid salt. The values used by Ost-
wald' and Bredigº as the conductivities of HX ions, for the cal-
culations of the degree of ionization, from the conductivities
of the free dibasic acids, were merely estimated from the com-
position of the ion. -
I have found the approximate values of such ion conductivities
in the following manner: The concentrations of acid and neutral
salts and of free H ions were calculated for a dilute solution, say
N/Looo, of the pure acid salt, by means of the value ki/k, found
by partition experiments. The observed equivalent conduc-
tivity of the solution of the acid salt diminished by the conduc-
tivity due to the neutral salt and H ions represents the conductivity
of the ions of the acid salt. This difference, by division of a
number representing the fraction of the sodium actually in the
form of acid salt, gave the true (hypothetical) equivalent conduc-
* Z. phys. Chem., 2,840 (1888); 3, 281 (1889).
* Ibid., 13, 191 (1894).
26
tivity of the acid salt. By subtracting from the latter value the
known ionic conductivity of sodium the ionic conductivity of
HX remained.
The results so obtained clearly revealed a very simple relation-
ship. The conductivities of the HX ions were all approximately
proportional to those of the corresponding X ions. The detailed
results of these calculations are omitted, but the relationship
discovered has been utilized to calculate the secondary ionization
constants by a method entirely independent of the data of the
partition experiments. The good agreement between the values
of k, as found by the partition and conductivity methods serves,
of course, as an equally satisfactory test of the accuracy of the
law just announced.
The same relationship between the conductivities of HX and
X was observed when the conductivities of the HX ions were
estimated in another way. The work of Ostwald' and Bredigº
has served to show that the conductivity of an organic ion is
dependent upon its composition. Univalent, isomeric ions are
equally mobile, and univalent ions, composed of the same number
of atoms, have practically the same conductivity. One may
therefore safely assume that the conductivity of any ion, HX,
of a dibasic acid, H., X, is equal to that of an ion of the most nearly
related monobasic acid. Thus the conductivity of the acid suc-
cinic ion, HCO,.C.H.C.H.CO, may be considered equal to that
of the ion of butyric acid, CHA.C.H.C.H.CO,.
In Table XXIV, #x-A is the equivalent conductivity of the
X ion of the corresponding dibasic acid; A is the equivalent con-
ductivity of the negative ion of that monobasic acid most closely
resembling the dibasic acid of the same line. The ratio, A/4\x,
is nearly a constant, the mean value of which is O. 595; or prac-
tically o.6. We may therefore consider that
AHx = 0.6 X #Ax = O.3\x. (8)
It is readily seen that the value of Aux, last column, Table XXIV,
calculated by this equation, does not differ greatly, in any case,
from that of A.
* Loc. cit.
27
TABLE XXIV.
}\x. - A. M% Ax. O.3\x=\hy.
Oxalic. . . . . . . . . . . . 72.4 Acetic. . . . . . . 41.6 O. 575 43.4
Malonic. . . . . . . . . . . 64. I Propionic. . . . 36.8 O. 574 38.5
Succinic. . . . . . . . . . 56. O Butyric. . . . . . 33. O O. 589 33.6
Glutaric. . . . . . . . . . 51. O Valerianic. . . . 31. O O. 608 3O. 6
Suberic. . . . . . . . . . . 44.3 Phthaluric. . . 26.5 O. 598 26.5
Azelaic. . . . . . . . . . . 43.3 Phthalanilic. . 26.2 o. 605 26. O
Sebacic. . . . . . . . . . . 4O. I 24. I
Camphoric. . . . . . . . 40.8 24.5
o-Phthalic... . . . . . . 49.8 Toluic. . . . . . . 32. I O. 65I 29.9
m-Phthalic. . . . . . . . 50. O “ . . . . . . . . . 32. I O. 642 3O. O
Itaconic. . . . . . . . . . 55. 7 Angelic. . . . . . 3I. 5 O. 566 33.4
Maleic. . . . . . . . . . . . 60. O Crotonic. . . . . 34.5 O. 575 36. O
Fumaric. . . . . . . . . . 6O. 6 " . . . . . . . 34.5 O. 569 36.4
Monobromsuccinic. 56.4. Butyric. . . . . . 33. O O. 585 33.8
Dibromsuccinic. . . . 55.2 " . . . . . . . 33. O O. 598 33. I
Mean, O. 595
By means of the relationship just discussed, McCoy has shown
in the preceding paper, how the concentration of hydrogen
ions in the solution of an acid salt of a dibasic acid may be cal-
culated from conductivity data. For the acid sodium salt of
N/IO24 concentration,
H = a + Wa” + b (9),
where
(Al-A,) — k,(o.7 A, + 141)
O = % (IO)
2A, H– 605
and
b kam (Al-O.6A, -20)
24, -ī- 605
and A, and A, represent the observed equivalent conductivities
of the acid and normal salts respectively, at 25° and N/Io24
concentration. The value of H calculated by means of the pre-
ceding equations may be used to calculate k, by substitution
in Noyes's equation:
(II) º
* Z. physik. Chem., II, 495 (1893).
28
(k, -i- m + H).H.”
k, = k (I2)
1(m—H)
I have measured the conductivities of those acid and normal
salts studied by the partition method. The results are given in
Tables XXV and XXVI. The conductivities of the acid salts
of oxalic and malonic acids, as well as of many of the neutral
salts, have been measured previously by Walden' and Bredig.”
My results agree well in general with those of Walden and Bredig,
in so far as comparison is possible.
* Z. physik. Chem., 8, 433 (1891).
* Ibid., 13, 191 (1894).
&
TABLE XXV.-CONDUCTIVITIES AT 25° IN RECIPROCAL OHMS OF ACID SALTs—NaHX.
Dilution. 32. 64. I28. 256. . 5I2. IO24. 2O48. 4096.
Oxalic. . . . . . . . . . . . . . . . . 97 IO9 I23 I39 I58 182 2 II 25O
Malonic. . . . . . . . . . . . . . . . 8o. 5 84 87 90.6 97.3 IO4.8 II.3 I 26
Succinic. . . . . . . . . . . . . . . . 76 8O 83.3 86.5 89.5 94. IOI - III
Glutaric. . . . . . . . . . . . . . . . 73.4 78.7 82.4 85 88 9I. 6 98 IO6.
Suberic. . . . . . . . . . . . . . . . 68.9 72. 5 75. 7 78.3 8I. 5 85 9I 99
Azelaic. . . . . . . . . . . . . . . . 68.9 72. 5 75. 7 79.3 8I. 5 85 89.8 97
Sebacic. . . . . . . . . . . . . . . . 75 78 8O 82.9 88.3 95
o-Phthalic. . . . . . . . . . . . . . 7o. 6 75 8O 85 92 IOO II 2 I25
m-Phthalic. . . . . . . . . . . . . 9I. 3 IOO. 6 II.5 I36, I71
Itaconic. . . . . . . . . . . . . . . . 74. 77.8 81.4 85.2 89 94.8 IO2.6 II6
Maleic. . . . . . . . . . . . . . . . . 79 84 88 9I. 5 95 99.5 IO4 I IO
Fumaric. . . . . . . . . . . . . . . 8O. 5 86. 2 93 IO4. , I 18.7 I4O I 7O 2O5
Monobromsuccinic. . . . . . . 78.6 86 96.5 IO9 I27 . I 5 I I8O. 6 217
Dibromsuccinic. . . . . . . . . I5O 187 23 I 28O 33 I 381 422 456
3
Sebacic. . . . . . . . . . . . . . . . .
o-Phthalic. . . . . . . . . . . . . . .
ſm-Phthalic. . . . . . . . . . . . . .
Itaconic. . . . . . . .
TABLE XXVI.-NORMAL SALTs—Na,X.
Dilution.
Malonic. . . . . . . .
Succinic. . . . . . . . tº e e
Glutaric. . . . . . . . . . . . . . . . .
Suberic. . . . . . . . . . . . . . . . .
8
7
;
64.
90.
95
94 .
9 I
I28.
I IO
I O2 .
96.
92.
85.
84
8 I
9I
95
99
98.
95
94.
256.
II.5
IO5.
99.
95
88.
87
84
94.
92
98.
I O2 .
I O2
99
98
:
512.
II.8
IO9
I O2
97
90.
89
86
96
95
I O2
IO5.
IO5
IO2
IOI
6
4
2O48.
I 2 I
II.4.
IO5.5
IOI
94 .
92
90
99
IOI
IO5
IO9
I IO
IO8
IO7
4096.
I 2.2
II.5.
IO6
I O2
96
9I
IOO
IO5
IO6
IO9.
II 2
II 2
I IO
3I
Table XXVII gives the results calculated from these conduc-
tivities by equations (9) and (I2):
TABLE XXVII.
A1. A2 Ioºk 1. IOGH. Io9k2.
Oxalic. . . . . . . . . . . . . . . . . I82 I 20 38OOO I93 49
Malonic. . . . . . . . . . . . . . . . IO4.8 II2 I58O 35 2 . I
Succinic. . . . . . . . . . . . . . . 94. IO4. 66.5 I2. 9 2.7
Glutaric. . . . . . . . . . . . . . . 9I.6 99 47. 4 II. 4 2.9
Suberic. . . . . . . . . . . . . . . . 85 92.3 29.9 7.4 I. 9
Azelaic. . . . . . . . . . . . . . . . 85 9I 25.3 7.7 24 .
Sebacic. . . . . . . . . . . . . . . . 82.9 88 23.8 7.6 2.5
o-Phthalic.. . . . . . . . . . . . . IOO 98 I 2 IO 44 - 4 3.9
m-Phthalic. . . . . . . . . . . . . I I5 98 287 67. 9 24.
Itaconic. . . . . . . . . . . . . . . 94.8 IO4 I5I. 18.7 2.8
Maleic. . . . . . . . . . . . . . . . . 99.5 IO8 II 7OO I5. I O. 26
Fumaric. . . . . . . . . . . . . . . I4O IO8 93O II.3 32
MonobromSuccinic. . . . . . I5I IO5 278O I5I 39
Dibromsuccinic. . . . . . . . . 381 IO4. 34OOO 675 I6OO
Table XXVIII contains all of the values which I have found
for the ionization constants of the second hydrogen ion of the
dibasic acids studied, together with those found by Smith, Weg-
scheider and Trevor.
TABLE XXVIII.-SECONDARY IONIZATION CONSTANTs, Io"k,.
Partition. Conductivity. Smith. Wegscheider. Trevor.
Oxalic. . . . . . . . . . . . 4I 49 - e. * * I6. O
Malonic. . . . . . . . . . . 2 . O 2 . I I . O IO
Succinic. . . . . . . . . . 2 . 2 2. 7 2. 3
Glutaric. . . . . . . . . . 3.4 2.9 2. 7 * -
Suberic. . . . . . . . . 3. 7 I. 9 2. 5. 3. 3
Pimelic. . . . . . . . . . . 4 - 4 e - tº e - -
Azelaic. . . . . . . . . . . 3. 3 2.4 2. 7
Sebacic. . . . . . . . . . . . 2 . 6 2.5 2.6
o-Phthalic... . . . . . . 3. I 3.9 I. 7 e * *
ſm-Phthalic. . . . . . . 27 24 - - tº - IO ... O
Camphoric. . . . . . . . I4 O. 7
Itaconic. . . . . . . . . . 2 . 2 2.8 2. 3 • -
Maleic. . . . . . . . . . . . O . 2C) O. 26 O. 4. 8. O
Fumaric. . . . . . . . . . 22 - 32 I8 29
MonobromSuccinic. 25 39 - - 39
Dibromsuccinic. . . . I54O I6OO - -
The methods of Trevor and Smith are similar, except that a
different constant is used for the inversion effect of a completely
32
dissociated acid. Their solutions were 1/128 normal with respect
to the acid salts and the experiments were carried out at Ioo?,
as the speed of inversion was too slow at 25°. This should not
materially affect the value of k, unless there was some decompo-
sition of the acid at high temperature. Smith found that malonic
acid suffered decided decomposition at Ioo? and the value given
is an interpolation. He also found that a neutral salt or even
water caused quite as rapid an inversion as an acid salt, although
in the former cases the rate was irregular. From these consider-
ations, it is remarkable that values obtained by Smith's method
agree so well with others.
The method of Wegscheider, using the free acid, is probably
less accurate than the method using the acid salt. Even though
the latter is complicated by the presence of the neutral salt. The
former method is evidently more accurate for acids having a
large value of k, than for those for which k, is small. The values
found by Wegscheider for suberic, fumaric and monobromsuc-
cinic acids agree very well with those I have found. But his
values of k, for maleic and malonic acids, which other experi-
menters find to be small, are certainly too large.
In conclusion, I wish to express my obligation to Dr. McCoy,
under whose supervision the foregoing work has been carried out.
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