A new method for measuring the electrolytic dissociation of water

A^ric. Dcpt,

Issued September 1, 1909.

United States Department of Agriculture,

BUREAU OF CHEMISTRY— Circular No. 45.
H. W. WILEY, Chief of Bureau.

A NEW METHOD FOR MEASURING THE ELECTROLYTIC DISSOCIATION
I OF WATER.

By C. S. HUDSON, Assistant Chemist.

In a recent article a it was shown that the measurements of the veloc-
ity-coefficient of the mutarotation of glucose in acid, alkaline, or neutral
solutions are accurately expressed over the whole range by the formula
•k= AH-B(H') + C(OH'), where k is the velocity-coefficient, A, B, and C
ape constants, and H' and OH7 are the concentrations of hydrogen- and
hydroxyl-ions, respectively, in the solutions. For neutral solutions or
pure water let the velocity-coefficient be written kw, and the hydrogen-
ion concentration which is equal for this case to that of the hydroxyl-ion
be written HW'; the above formula then takes the form, for pure water
or neutral solutions, kw = A + ( B + C ) Hw* . Solving this expression gives

(k —A)

Hw' = -j^ . This relation gives a new method for measuring the
(B-f 0;

hydrogen-ion concentration or, in other words, the electrolytic disso-
ciation of water, for the four quantities on the right-hand side of the
equation can be determined experimentally by measuring the rate of
mutarotation of glucose in ordinary distilled water and in acid and
alkaline solutions. The first formula above is based on measurements
of the rate of mutarotation of glucose in alkaline solutions by Osaka,b
and similar ones in acid solutions by the writer,a and has the form, as
was shown in the previous article, k = 0.0096 + 0.258 (H') -f-9750(OH'),
k being expressed in minutes and decimal logarithms, H' and OH'
in gram-molecules per liter, and the temperature being 25° C. The
constants for glucose at 25° are therefore A = 0.0096, B = 0.258, and
0 = 9750. The velocity-coefficient for pure water was found at the same
,time to be k<#= 0.0106, which agrees closely with the value which Osaka
found, 0.0104. The substitution of these constants in the formula pre-
ceding gives Hw' = 1.0(10)~7, a value which is in close agreement with
those that have been found in the past from measurements that are
based on entirely different facts and principles. In the following table
is recorded a list of the values for the hydrogen-ion concentration of
pure water, which have been found by various investigators, together
with a statement of the method by which the value was found. Those
values which were later shown to be erroneous are inclosed in brackets.

• J. Amer. Chera. Soc., 1907, 23:1571^
bZts. physik. Chem., 1900, 55:702. "

The hydrogen-ion concentration of pure water near 25° C.

H'=OH'

(gram-mole-
cules per
HterXlO?).

Temper-
ature
(°C).

Investigator.

Date.

Method of determination.

6.0]
9.0J
1.1
[0.11

25

?

25
11

Ostwald*---
Ostwald*---
Arrheniusb.
Wijsc

1893
1893
1893
1*93

Electrical conductance of pure water.
Acid-alkali hydrogen cell.
Hydrolysis of sodium acetate by ester saponification.
Aqueous saponification of methyl acetate.

[6.0J
1 2

25
25

Bredigd

Wijse .

1893
1893

Hydrolysis of aniline acetate from conductivity meas-
urements.
Aqueous saponification of methyl acetate.

0.8
1.05

1.2
0.91

1.0

18
25

25
25

25

Nernst*
Kohlrausch
and Heyd-
weiller.s
L6vvenherzh
A.A.Noyes
and Ka-
nolt*
Hudson

1894
1894

1896
1907

1909

Acid-alkali hydrogen cell.
Electrical conductance of pure water.

Acid-alkali hydrogen cell.
Hydrolysis of ammonium diketotetrahydrathiazole
from conductivity measurements.

Catalysis of the mutarotation of glucose by acids and
alkalis.

»Zts. physik. Chem., 1893, 72:521.

Hbid., 1893. 21:823; see also Shields, ibid., 1893,

If:184.

cibid., 1893, 12:492.
dlbid., 1893, 11:829; see Arrhenius, ibid., 1890,

5:19, and Walker, 1889, 4:334.
elbid., 1893, 12:514.

flbid., 1894, 14:155. A new theory of this method
is there given by Nernst.

eibid , 1894, 14:330.

hlbid., 1896,20:293

1 Carnegie Institution of Washington, 1907, Pub-
lication 63, p 297.

The accuracy of the method which is here described for measuring
the electrolytic dissociation of water depends primarily on the accuracy
with which the difference &w — A can be measured. For glucose this
difference is only 10 per cent of the separate quantities, and conse-
quently the accuracy of the method is not great, probably about 20 per
cent, but from recent measurements which the writer a has made on the
rate of mutarotation of the related sugar fructose in pure water and
acid solutions, it appears that the above difference for this sugar is far
greater than for glucose, being over 40 per cent of the separate quanti-
ties. Measurements on fructose will, therefore, in all probability give
with closer accuracy the electrolytic dissociation of water.

°J. Amer. Chem. Soc., 1908, 30:1578.

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