L’XIX.
--?’he
Elect?-icul
Cmductivity
of
Acids
a~d
Bases
is1
A
q
u
eous
So
lut
iosw
By
JNANENDRA CIIANDRA
GHOSH.
IN
previous
papws (this vol.,
pp.
449, 627,
707),
itl
has
beeii
shown
that
the
variation
of
elyuivalent conductivity with dilution,
in
the
case1
of
all binary univalent
salts,
is
represented by
the
equatioii
where1
.V
is
Avogadro’s
11uxnber*,
E
the
absolute
charge
or1
an
ion,
D
the1
dielectric constant
of
the
solvent, and
V
the dilution.
Ab.no.rnzally
Ziyh
Values
of
Activity-coefficients
vf
A
cids
and
Bases.-Aqueolus solu tioiis
of
strong acids
like
hydrochloric
or
nitric
acids,
and
of
strong bases
like
sodium
or
potassium hydroxides,
holwever, prove excephions
to
the1 above1 rule. This irregular
belriaviotir will
be
at
once
evident
from table
1,
where
the
values
olf
the activit\y-coef€icients calculated from equatioii
(1)
are
coIrri-
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ACIDS
AND
BASES
IX
AQTJEOTTS
SOTATTTIONS.
791
pared with
the
observed values
(Noyes
and
FiLlk,
J.
.4rrzer.
(!lien2.
,Y/W.>
1912,
34,
474).
v=
10.
20.
50.
100.
200.
500.
-"-
calc.
...............
0.544
0-875
0.906
0.924
0.940
0.955
Px
obs.
for
HCI.
......
0.925
0-944 0.962 0.972 0.981
0.988
EL0
PX
'!
obs.
for
KO€€
...
0.887
0.910
0.933
0.945
-
0.970
Poc
This irregularity disappears as we
pass
from the aqueous
to
non-
aqueous sollutions
of
strong acids. In alcoholic solutions, for
ex-
ample, equation
(1)
is exactly followed. In table
11,
the observed
values
of
the
molecular conductivity
of
hydrochloric acid in methyl
alcohol are taken from thel work
of
Goldschmidtl and Thuesen
(Zeitsch.
physikal.
Chenz.,
1912,
81,
32).
For dilute solutions, the
agreement between observed and calculated values is always within
1
per cent.,
and
the valirlitYy
of
equation
(1)
is therelfore proved
beyond
rloiiht.
TATH,F:
11.
7'-
25O.
px
calc.
from
pa,,=
192.2
,uX
obtained by
extrapolntiori
=
192.1
V
:?
40.
80.
160.
320.
640.
pLu
talc.
142.5
151.8 169.6
166.7 170.9
7
p,,
o~)s. 141.0
161.8
160.5
167.2 171.9
A
Onorndlg
Ifiyh
Valiies
oj'
the
Electrical Cotiductivity
of
ScitTs
(117~1
Rnses.-It has always appeared remarkable that the values
of
the equivalent conductivity
of
acids
and bases in aqueons solutions
are not
of
the same order
of
mnagnitlude as those
of
other
salts.
Thus
the
conductivities
o€
hydrogen and hydroxyl ions in aqueous
solutions are
318
and
175
respectively at
18O,
whilst those
of
the
other ions never exceed
70.
an non-aqueous solutions, again, this
abnormality is
notl
observed. Thus in ethyl alcohoI,
the
con-
ductivities of hydrogen and hydroxyl ions are
32.1
and
16.5,
whilst
those
of
potassium and ammoniuni
ions
are
21.5
and
20
respectively
(Go'dlewski,
Zeitsch.
yh?ysikaZ.
CIiem.,
1905,
51,
751
;
Hagglund,
Arkiv.
]<em.
&fin.
Geol.,
1911,
4,
No.
11).
Eere
the values are
od
the
same
order. This
is
also
true
for solutions in other solvents,
for
example, methyl alcohol
or
acetone.
The
Conductivity
of
Aqueous
Solutioizs
of
Acids
and
Bnses-not
entirely
a
Convection
P.rocess.---lt
is thus evident that the abnormal
conductivities
of
hydrogen and hydroxyl ions,
iu
aqueous
solutions,
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792
GHOSH
:
THE
ELECTRICAL
CONDUCTIVITY
OF
are
solmehow related
to
the high values of the activity-coefficients of
acids and bases, both these abnolrmalities disappearing when the
solvent, meldium
is
other than water. Equation
(I)
has a good
theloretical baais,
and
it appears more, reasonable
to
assume that
the observed ratio -ELfor acids and bases in aqueous solutions is
P
UC
not
a
real expression for the activity-coefficient, than
to
impugn its
validity.
It
appears
to
the author that the observed conductivity
of
hydrogen and hydroxyl ions
in
wat’er is the additive effect
of
two separate and independent processes, namely,
(1)
the transfer-
ence
of
electricity by the convection
of
charged bodies, and
(2)
the
transference of electric charge through molecules
of
water by the
alternate processes
of
dissociation and recombination during impact
with hydrogen
or
hydroxyl ion.
The first process
is,
of
course, thel ordinary method
of
ielectro-
lytic conduction met with in salt solutions. Here, only the free
ions take part in the transference
of
electricity, and t)heir nunibei
is given
by
the1 equation
4
N=SN.
e-zl:T
.
.
. ~
, ,
.
(2)
The mechanism
of
transport
of
electricity through molecules
of
waher may be conceiveld
as
follows.
A
molecule
of
water
is
capable1
of
dissociating into hydrogen and
hydroxyl ions, the
only
ions that possess abnormal conductivity.
Now,
in
a
dilute solution
of
hydrochloric acid the hydrogen ion is
surrounded by water molelcules on all sides.
It
appears probable
that when a hydrogen ion strikes against a motleculei of water, the
latter in some cases undergoes dissociation. The hydrogen ion thus
produced carries away tBhe electric charge
by
convect-ion, whilst
the
hydroxyl ion
of
the water molecule combines with the impinging
hydrogen ion to generate a molecule
of
water. The conception
of
the process is similar to that imagined by Grotthuss
to
explain the
phenomenon
of
electrolytic conduction.
It
may well
be
that the
hydrogen atom
of
the water molecnle, which is farthest from the
point
of
impact, shoots
off
as a charged particle(, and
if
the process
of
dissociation and recombination is instantaneous, the electric
charge
(+E)
appears
to
be carried instantaneously through a
distance proportional
to
the diameter
S
of
the water molecule.
Thus at each impact attended with dissociation a distance
li,S
is
saved, where
X,
is always a fractional quantity.
The
result
is
that
the
hydrogen ion appears
to
move with a velocity much greater
than its true characteristic velocity.
Now
let
UF1.
be
the
real
velocity
of
the hydrogen ion. The total number
of
impacts with
water molecules
per
second is
K2N.
a
.
Sl2UU,.
.
w,
where
m
is
the
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ACIDS
AND
BASES
IN
AQUEOUS
SOLUTIONS.
793
number of water molecules in
a
C.C.
and
Sl
the diameter
of
the
hydrogen ion. The number of impacts attended with dissociation
is
K3.
K,
.
N
.
T
.
,Yl2UIX.
.?/,
and the distance saveid pelr second=
K,
.
S
.
K,
. Kt2 .
iV
.
7
.
S,2
.
U,.
.
n
=C
at a constant temperature,
since
R,,
K2,
R3,
U,,.,
have always the1 same value at constant
tlemperature.
C
also does not vary with dilution
if
n
and
N
do
not vary.
Now
in the case
of
dilute solutions, the number
of
solvent molecules in
a
C.C.
may always be regarded as constant,
independent
of
concentration, without introducing much error.
Since, according to the theory developeid before!, strong electrolytes
are completely dissociated in dilute solutions,
the
number
of
hydrogen ions in a solution containing a gram-molehcule
is
always
constant. Whilst in the first process-the transf erencel of electric
charge by convection-only the8 free hydrogen ions take part, this
is not the case in the second process. Here
it
stands more to reasoln
to assume that all the hydrogen ions are equally efficient,
for,
con-
sidering that some
of
the hydrogen ions are stationary, there
is
nothiTg to prevent their collision with water molecules,
for
the
latter are1 always free
to
move.
In fact, thel inactive hydrogen ions
are always capable
of
vibratory motion.
The
distance
C
saved per
second is thus independent
ol
dilution.
Hence,
for
solutions of hydrochloric acid, on the1 basis that the
activity-coefficientl
a
at any dilution is the same as that
of
uni-
valent binary salts, we1 get
pv=a(UH.+
Ucl,)+C1
.
.
. .
.
.
(3)
where
01
is tho activity-coefficient" at dilutioa
v,
and
C,
a constant
independent
of
dilutliun.
a
can always
be
calculatled from
equation
(1).
Again,
From
quai-ions
(3)
and
(4>,
,uE
=
Urr.+
Ucl+CI
.
a
-
.
. .
(4)
and
q=pK
-up--
uc,,
.
0
.
.
. .
(6)
UH.,
the real ionic mobility
of
the hydrogen ion, and
C,,
the con-
ductivity
due
to the second process, can thus at once be calculated
from available data.
Bxperinzental Confirmation
of
the
above
HypotJ~esis.--The
ex-
perimental data on the conductivity
of
acids must, always yield the
same value
of
C,
and
Uli.
provided the acid
is
a
strong electrolyte.
This expectation
has
been fully realised.
Thiis,
for
a
sdutlioln
of
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794
CIHOSH
:
THE
RLXCTRIGATA
CCPNDTTCTIVITY
OF
hydrochloric acid at dilution
10
andl
temperature
25O,
pu
-
390.4,
pa:
=426,
UC1,
2-75.8,
and
a-0.844,
whence!
UIx.
=152.4
and
C,
=
197.8.
Again, for solutions
of
nitric acid,
ab
dilution 10, the available
data give’
for
U,.
151.3
and
198.8
for
C,
(Noyes and
Falk,
Zoc.
cit.).
‘The values
olf
(IH.
and
C,
obtaineid from the data on the
conductivity
of
hydrochloric and nitric acids thelref orel agrx within
1
per cent. We may take
152
as
the mean value
of
U,.
and
198-5
as that’ of
C,.
The real molbility
of
hydrogen ion
is
therefore
of
the same1 order
of
magnitude as those
of
the other ions. The second
process is thus responsible for the transference
od
about half the
electric current in acid solutions.
The vaIuels
olf
UK.
and
c‘,
having once been determined,
it
is
possible to calculate
the1
molecular conductivity
of
any strong acid
at any dilution from equation
(3).
Tables
111
and
IV
show how
the calculated values agree with the observed ones.
In
table
111,
the observed values
are
taken
from
the
work
of
Noyes and Falk
(Zoc.
cit.),
whilst the data in table1
IV
are obtained
from
a paper
by
Wegscheider
and
T,UX
(Mo:int.ch.,
1909,
30,
436).
HC1
...............
HNO,
............
Naphthalene
-
,8
-
TABLE
111.
V-
20.
100.
500.
1000.
“000.
f,~y
talc..
593.1
404.5
411.0
-
4
15.0
(~u
C~C.
397.6
408.9
416.6
418.4
-
-\pv
obs.
398.4
410.5
418.5 420.4
1
p”
obs.
393.3
406.0
41
3.0
4
17.0
TABJ,E:
Ji7.
V:--
100.
400.
111.
1600.
f
P7,
calc.
637.3
372-4
375.3
376.3
&lphonic
acid
..
..-\;L~
obs.
367.4
374.9
376.9
377-4
sulphonic
acid..
.
,..I
p,,
obs.
368.4
375.3
378.2
3
7
9.0
Toluene-p
-
{pv
WAC.
369.9
375.0
377.6
378.5
Thel agreement, between
the
observed
niid
calcrdated
valnes
i::
always within
0.5
pelr
cent.
The real values
of
bTOEt
and
C,
for
bases can also
ba
obtained in
the
same way.
Thus, at dilution
10,
pv
for potassium hydroxide
is
213;
pOc
is
240.2.
From
these data, the value
of
UOH,
is
109
and
of
C,
for
bases
66.
Table
V
shows
how exactly the observed
values
of
the modecular conductivity
of
potassium hydroxide agree
with those calculated
from
equation
(3).
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