University
Zealand
Code Number .....
PHYSICAl:
SCIENCE!
LII!AARY
THESIS
THE THERMODYNAMIC DISSOCIATION CONSTANT
OF
ACETIC
.:..I.:..::.N_ _
MI ><ED
!;._
!\C I D
IN TROD UC TION
The classical theory of acid and bare dissociation,
characterised a.cids by their ability to split off hydrogen
ions, and bases by their ability to split off hydroxyl ions
when dissolved in water.
These views were based on the
Arrhenius theory of dissociation of electrolytes in waterlland
did not explain the complementary yet opposite properties of
acids and bases, nor did it extend the treatment beyond e;queous
solutions ..
For example, pure hydrochloric or acetic acids
would not be considered as acids in themselves as hydrogen ions
are not detectable in them in the pure state ..
The classical
theory is, therefore, incon sistent,in so far as the description
ecld or base, is only allowed after the adcli tion of a second
The role the water played in the
substance, nen1ely water ..
mechanism was for a long time unrecognised.
The generalization which brought clarity and carrel
lation into the whole field was advanced in 1923 by Lowry e-nd
2
Bronsted
independently.
They represent all such dissociations
in the scheme
A
B
acid
base
+ ~ •..•...•........ (1)
in which an acid is defined as a substance capable of donating
protons, thus becoming a base.
Conversely a base can accept
protons and become an acid, the acld and base in each case being
referred to as conjugate acid-base pair.S.
It follows from (1)
thB.t an acld always carries one more posi tlve charge than its
conjugate base, typical conjugate pairs being
NH 3 + H'"
CH • coo- + H"'
co 3.......
3
NH4
CH3. COOH
HC03-
1-
base
acid
The close relationship between these two groups of substances
depends on their relationship to the proton, a possible parallel
being found in
oxid~'ttion
reduction systems where the electron
plays a similar role.
The above scheme must be modified some·what, as it is
the solvated proton which occurs in acid solutions, as shown for
example, by :t
high heat of hydration.
+ H2o
Base2
~
CH3. coo- -+ H3o+
Base 1
where subscripts indicate conjugate pairs.
Acid2
In this case there-
fore, water is acting as a base .. ··.It can however act equally
>
well as an acid
The wide applicabillty of thls generalization is shown
in its application to other solvents such as liquid ammonia. The
ionisation of this substance gives rise to H+ and
counterparts of H+
and oH- as in water.
NH2
ions as
Thus when an ammonium
-3salt is dissolved in liquid ammonia, dissociation occurs with
the production of solvated hydrogen ions.
The solution there-
fore functions as an acid, even to its ability to dissolve
metals.
NH Cl
4
NH+
1~
NH
4
3
+
Cl-
+ H...,.
Although the general equation (1) for acid•base dissociation may fail to give a true kinetic picture of the process,
this does not affect the application of
the~odynamically
derived relationships, such as the law of mass action, as such
relationships are independent of the actual kinetic mechanism
involved.
It is reasonable to assume the proton is hydrated by
one molecule of water, just as it unites with one molecule of
ammonia..
This is in agreement with the work of Lowry3 , Bron-
sted4 and others..
Its importance lies in the fact that its
conjugate base is water..
This protolysis is thus· seen to be a
general reaction embracing such topics as dissociation of acids
and bases, hydrolysis of salts, neutralisation etc. as treated
in classical theory.
ACID STRENGTH AND ACIDITY.
In classical theory, acidity has been defined as the concentration of hydrogen ions in a solution.
Such a measure cannot
be treated thermodynamically with exactitude, owing to deviations
of solutions from the perfect behaviour ..
An exact measure would
be given by the activity of the hydrogen ions AH+
as introduced
-4This function has the dimensions of concen-
by G. N. Lewis ..
tration, and may be regarded as an effective concentration 1
the actual free energy of the hydrogen ions in the solution
being given by
-
Go
referring to a standard state.
Such a term is useful only
as a mathematical concept, for, as pointed out by Guggenheim 8 ,
the concept of individual ion activities is incapable of precise
definition ..
The activity of an acid is a quite separate idea
depending also on the activity of the anion.
Basicity is defined as the reciprocal of acidity.
Acid and basic strength are defined as the quantitative tendency
to lose or gain protons respectively.
It has been assumed that
these terms are determinable by measurements of the dissociation
constant in dilute aqueous solution, as
K
Classically, the
=
U!J!i 1 ii
bra.cltet terms have been measured in con-
centrations, but activities give a real thermodynamic constant.
In seeking a general measure of strength for va.,riations of both
acid and medium, it can be seen from the general equation
A
B
+ H+
that, although strength may be measured in solutions under comparable conditions i.e .. when the ratio between the concentration
of acid and base is constant, which can arbitrarily be made unity,
so that
K
acidity
Kbasicity
:::
=
constants are obtained which are again useful only mathematically,
as they invoke a single ion activity.
These constants are
a
measure of the tendency of a molecule to lose or gain a proton.
If absolute activities are used in place
concentrations,
a real thermodynamic dissociation constant, as measured in the
present work, is obtained, which is capable of experimental
measurement ..
"
· Kactivi ty
But this constant can only be used as a comparison of
acid strengths for the same acid in different media, but this is
by no means so for different actds in different media..
water,
1.6
o·... nitrobenzoic acid give K ... 6.2
lo-3 compared with
lo-3 for 3:5 d.initrobenzoic acid, while in ethyl alcohol
the respective constants are 2.42
such a consts.nt
in di
Thus in
lo-9 and 8.16JI.l0-9.
Thus
ls to give a general scale of acid strength
erent solvents.
This fact emerging from Golds·chmidt 1 s5
work in methyl and ethyl alcohols and confirmed by Larrson6 and
Halford?, means it is impossible to transfer a scale of acidity
from one solvent to another.
Before extending this analysls to actual dissociation
phenomena, the influence of acld base properties of the solvent
-6must be discussed.
Obv.busly dissociation of an acid will be
helped by the ease with which the proton is accepted by the
solvent;
the mechanism can be regarded as a competitive effect
If the acidity of
for the proton by the acid and solvent.
water is defined by the method given above, a
11
rational constant"
K'tcidi ty
is obtained, but as an explicit value cannot be given to
a
n conventional"
0a2 0
1
constant is d_efined,
Ko
acidity
and similarly
1
K.0
-lJasi
oi ty --
~·
by analogy with the omission of molecular concentration in the
ssociation of pure liquids.
In stqueous solutions 1 a general dissociation equation
of the type
+
B
will lead to a rational equilibrium const&tnt of the form
=
Kr
or a conventional dissociation constant
::
From ( 3)
ICC
~
=
~
CA ..
Crt o+ •
3
~
acid
Kacidlty
1
AH-t-
••••••••• ( 4)
H 0
X
Kb~sici ty
Thus the dissociation constant of an acid is equal to
its acidity
const~:mt
multiplied by the basicity constant of the
medium, a relationship such as would be expectedo
and K0
Both Kacidity
are sui table for measures of strength as long as the
mediwn is kept constant..
Also both these constants are changed
to the same extent by changing from one medium to another, since
Kc
is, according to equation (4) independent of
the ratio Kacidity
the nature of the acld ..
As pointed out above, these rational and conventional
constants are not thermodynamic quantities but are rele,ted to the
true thermodynamic values by the relation
A
where
=
fc
a
·=
the activity or
f
=
the activity coefficient, and may be regarded as
a devisttion factor, from the perfect beha:vbur.
11
effective massn
The Solvent influences acid-base equilibria in two
major ways.
(1)
Through its dielectric constant.
(2)
:I'hrough its acid base properties.
-8The second f.Ewtor ha.s already been discussed.,
It is generally recognised that the ionisation of acids and
bases increases
th increasing dielectric constant of the
solvent, due to diminished interionic attraction.
In the
series of acid-:base pairs
Et+
A
A+
A"•·+
H+
H"'"
B-B+ B
+
+
+
the ions attract each other in the first two cases, have no
important electrostatic influence in the third, and repel each
other in the fourth case.
Thus dissociation will be decreased
rst t\VO cases, unaffected in the third case, and in-
in the
creased in the fourth by low
the di
ectric constant, as
by transfer from water to an acetone-water mixture ..
A more quantitative tre:atment can be derived as
By a consio.era.tion of the work necessary to charge
follows.
a small spherical particle in a given dielectric, the formula
for the change in energy of an ion on transfer from a medium
of one d1 electric constant to Em other is
9· 10
where
t
=
charge on the ion
r
-
ionic radius
dielectric constants of the two media.
-9Consider now one
gram-molecule of weak acid HB in
equilibrium Viri th the ions in estch of the two media.
HB
~
1
In the medium,solvent 1 of dielectric constant D
+
=
where ~
GT_
represent partial molal free energies.
The partial molal free energies of H+ and B- can be further
analysed into
( 1)
(11)
The, chemical contribution of the species in the system ..
The electrostatic contribution of the charge in the
dielectrtc medium.
Guggenheim11 points out such a decomposition into two terms is,
in general, arbitrary and of no thermodynamic significance.
No
thermodynamic measurements could give any information concerning
the separate terms, but only concerning their sum.
Thus
GI'
./?
::;:;
G_.o1
.... RT ln
1
A-t
where
A
+
N
r
=
=
activity of H+Avagadro's number
1 oni c radius
Similarly in solvent 11 of dielectric constant n11
=
+
RT
ln
L:
NE2
2rl D~
+
-10-
In these formulae, ~
are integration constants, while the minus
sign before the electrostatic term indicates the energy is possessIf we assume the undissociated molecules
ed by ·the medium.
fre~
possess the same
energy in both solvents, a justifiable
assumption in dilute solutions, and as
G.;0
etc. are integration
constants,
RT
ln
But
-
K
and
RT
Axm
&A-
...
AHB
All
HB
so the equation reduces to
ln
RT
ln
Putting "'AII • 2r+
or A.
or A
ln
PK
K
I
n.. (l)
(1))
NE2
2. 30ft{'RT
A.
From measurements of PK values, a value for
(1 )
( i5')
11 A11
may be calculated,
or if it varies in the two solvents, a msan value may be obtained.
B tonsted4 consi<lers this dielectric. ef'fect to predominate.
12
Hartley
and co-workers consider that in mixed aqueous solvents
ions tend to associate with water ra.ther than the other solvent
present ..
They have sho'Am lith iu.m
ions behave almost iden-
tically in water and in 30% alcohol-water mixture.
Also the
addition of a small amount of water into a non-hydrox.ylic solvent
causes a marked change in di ssociati.on.
-111
Pring 3 (1923) showed electrometrioally that monovalent
bases (aniline and derivatives) underwent no large change of PK
on transfer from water to a 90% acetone-water mixture.
Cray
and Westrip1 4 (1925) in the same laboratory investigated numerous
indicator and buffer properties in 90% Acetone-water mixture, as
well as hydrochloric,, phthali
concluded that monovalent
acetic ancl chloracetio acids.
carb~ylic
PK units in this solvent (D = 26).
They
acids are weakened by 4 - 5
They used a quinhydrone
electrode, and it is not olea>r that this woula. function satisfactorily in such a high proportion of acetone, owing to its greatly increased solubility.
1
AFFECT OF TENWERATURE ON ACID STBENGTH 5
The curve obtained by plotting l;og K against tempera>ture
shows a maximum value, which may occur at different temperatures
with different acids.
Thus butyric acid shows a maximum value
about 10° while lactic acid shows a maximum about 20°.
The curves
out at approximately 15° , so it follows that above this temperature lactic acid is the stronger, while below it, n.butyric
acid is the stronger. Everett and Wynne-Jones16 give these so
. ca"lled "inversion temperatures 11 for a number of acids which lie
within the range of temperature examined experimentally.
Until recently it has been assumed that the thermodynt:tmic dissocia.tion constl'mt gave a measure of relative strength 1
but these constants were usually recorded at room temperature. The
fact that these constants vary differently with temperature, maLe
-12-
it difficult to ascribe a precise meaning to relative acid
strengths, unless such comparison is made at a given temperature.
This discussion shows that the concept of absolute acid
strength is by no means simple,
A precise
definition involves
such inaccessible terms as individual ionic activities and
electrostatic energy factors.
In practice, we can only deal
with relative strengths of acids and bases in the same medium
and at the same temperature.
DI SSO OIATION CONSTANT MEASUREMENTS.
Four main methods have been used up to the present for
determining these constants.
(1)
(11)
(111)
They can be grouped as follows.
Conductivity method.
Catalytic effects of hydrogen ions.
E.M.F. measurements, includi
electometric
ti tre,tions.
The conductivity method has probably been applied most
intensively.
Ori ne.lly used by Ostwald17' Walden l8 and
others, this gives a conventional constant, Kc, which varies with
dilution.
It
was assumed that the Arrhenius coefficient
gives the degree of dissocic;tion, an assumption which is not
strictly accurate, as it requires that
coefficient, is equal to 1.
J1:. ,
the mean activity
By applying the Debye-Hucket-Onsager
theory, however, a corrected conductimetric method has been
20
1
vised by Davies 9, Saxton , Macinnes and Shedlovsk~ 1 , Sherrill
and Noyes 22 · and others. Thermodynamic constants ce.n thus be
-13determined
which agree well with those found from E.M.F. measure-
ments.
Thus for acetic acid in water 1 Macinnes and Shledoosky
found K •753 x lo-5, whereas Hamed and Ehlers 2 3 obtained
K = 1 .. 748 x lo-5 from E.~vl.F .. data~ after correcting thelr value
from molal to volume concentrations.
The second method is by measuring the number of
hydrogen ions by their catalytic effect on the velocity of any
suitable reaction, such as ester hydrolysis.
In this method, it
is necessary to know which ion catalyses the reaction, and also the
relationship between the activity of the hydrogen ion and the rate
of reaction.
These facts must be determined for every case, and
.the method therefore is not a general or fundamental one.
Glasstone 2 4 considers the evidence is inconclusive
as to whether catalytic power is proportional to concentrations or
to activities.
The method of electrometric Titration, has been
extensively used.
The calomel electrode is used in conjunction
th various types of salt bridge to eliminate the liquid junction
potential.
This gives a constant which is better than Kc but still
varies somewhat with
lution.
The main source of error arises
from uncertainty as to the 11 annulled 11 liquid junction potential.
Hamer and Acree 2 5 in 1936 investigated the errors in measurements
of pH, dissociation constants, hydrogen ion activity,co-efflcients
etc..
They uged a saturated calomel electrode 3 and sodltun malonate
buffer solutions.
They found partial corrections lead to larger
errors than no corrections at all.
in
may be only
Also although maximum errors
4-2%, the maximum errors in derived quantities
-14such as dissociation constants may become as great as 46%.
In 1930 Harned and Owen26
evolved a method sub-
sequently modified by Harned and Eh1.ers23 , which uses cells
without liquid junction, and gives a thermodynamic dissociation
constant,
K
::::::
a
__&_A.~-
~
which is independent of dilution.
Various acids have been
measured by this method, some values obtained being formic
27
23
28
1.77 x 1o-4
acetic 1.754 x lo-4
propionic 1.34 x l0-5
29
30
chloracetic 1.38 x lo-3 glycollic
butyric 1. 51 x lo-5
31
32
2nd carbonic 5.86 x lo-ll
•
The method is
1. 48 X 10-4
probably limited in application to ionisation constants of order
lo-3 or less, the theory being discussed later. Harned and Owen 2 6
expect agreement between the corrected conductimetric method and
the electromotive force method, of the order of 1%.
Very little accurate work has been done on solvents
other than water.
In order to get a broader view of such
phenomena as solubility, dissociation constants etc., a wider
range of solvents is required.
Harned and Embree33 have
measured Ka
for acetic acid in 10% and 20% methanol-water mixtures, and Harned and Kazanjian 34 in 20%, 45% and 70% di~ane­
water mixtures.
The dissociation constants for oxalic acid
in 10% and 20% methanol3 5 , and the value of Ka for benzoic acid
6
in 10% and 20% 3 methanol have been dete~1ined in this laboratory.
In the present work, this method of Harned and co-workers is used
to measure the dissociation constant of acetic acid in an acetonewater mlxture, consisting of 1 part of acetone to 10 parts of
water by weight.
-15The basis of the method lies in having a known con. centration of hydrogen ions in a solution of halogen acid, and
computing that of the unknown solution by using a sui table cell.
It follows that the exactness of the method is dependent on the
accuracy with which the hydrogen ion concentration in the real
.,-
.<
halogen acid solution is known.
The cell used in measuring"~the dissociation constant
was
0H3- COON a
(A)
No.,Cl
m3
m2
in which one electrode is reversible to the hydrogen ion and one
to the chloride ion.
The electro-motive force is therefore
given by
where E0 is the normal electrode potential of the cell
~ l
HOI
,
Ag 01
1
.Ag
etc. represent molal concentrations and activity
coefficients of the species indicated by subscripts.
The product mH+ fH+ can be eliminated with ~he
expression for the thermodynamic dissociation constant of
the acid
=
eombining these
equations~
the formula
=is obtained.
log Ka- log
coOJ
3
f'cH coo3
f'cr-fcH
-16This equation is easy to use if values of E0 are
known over the desired temperature range.
The left hand
side can be evaluated experimentally, as
The
value of mH+
is found by the method of successive
approximations.
the first place mH+ is assumed
zero~
which will be almost correct for a weak acid in the presence
of its sodium salt, and a value of - log Ka , or pka
analogy w1 th pH, is calculated.
by
From this value of pK, a
new value of mH"i" is calculated which is used in evaluating a
second value of pK.
change in pK occurs.
This process is carried on until no
Weak acids such as acetic or benzoic
require only one or two approximations, while for a stronger
acid such as oxalic acids first dissociation35
1
as many as 14
approximations are· required.
This is probably the upper limit
of accuracy of the method.
T.he term on the right hand side
involves the logarithm of the activity coefficient ratio of two
univalent ions and the logarithm of the activity coefficient
of a neutral molecule, both of whtch.have be~n shown 26, 37
to vary linearly with the ionic strength in dilute solutions.
A plot of the left hand side of the equation against the ionic
strength therefore, can be extrapolated to)l
7ct-
fcH3COOH
= o,
where log
equals 0 by definition, and a value of pK
fc:w.3coo&termlned.
Such cells are suited to the measurement of
dissociation coneants, as buffer action controls the hydrogen
ion concentration in the solution and renders the hydrogen
THE EVALUATION OF
The formula for the electromotive force of the cell
HC\
(m)
I
Ag
I
C\
Ag
in which one electrode is reversible to the chloride ion and
one to the hydrogen ion is given by
E
e
= E0
where
Eo
-
RT
T ln
· -
fL.FTln
.A,J, and m,Ere activities,
Dl:H+
AH-t
J
A
01
H+
_
mc' -
J
Ci -
activity coefficients and
molalities of the ions denoted by subscripts.
All the evidence of modern theory37 and investigation23
shows hydrochloric acid to be a very strong electrolyte, i.e.
the equilibrium
lies almost entirely., if not wholly to the right.
The law of
mass action applied in this case would give
K.a
. AH+Ac,-
~Cl
co.
Lewis39 prefers ,to equate the dissociation constant to unity 1
than to use the extremely large value of K obtained above.
The activity of the undissociated molecules, is therefore
defined as
-18a mean ionic activity
=
for a unive.lent electrolyte.
Similarly, a mean e.ctivity co-
efficient is defined
or assuming complete dissocie,tion, a stoichiometric aotivi ty
coefficient
!=
This function{
includes deviation from perfect behavlour and
also from compl
e dissociation.
The formula therefore reduces
to
E
Thus
...
Eo
ln
-
Eo
2RT
'lr ln
m
ln
J ....
(1)
Eo can be eve.luated by mee.suring E at any values of m
for which activity coefficients are known.
are available for obtaining activity data.
Several methods
These will be
briefly summarised.
This gives an accurate method of obtaining activities
as methods have been dev
oped, note.bly by Harkins4° 1 of
measuring depressions to the fourth place of decimals.
The
rigorous analytical method of calculating the activity is somewhat involved.
-19been developed by
The elevation of boiling point
Smi th41 at Yale to the same degree of c:wcuracy, and by reclucing the pressure over water_, he has obte.ined activity data
from 70°- 100°.
(11) Vapour Pressure
Method~.
Accurate methods of deriving activity coefficients (from
ve.pour pressure measurements) e.re now available, notably the
isotonic method, first
ested by Ostwald and improved by
6
Berkeley and Hartley 3 and others, and more recently the iso-
ao
piestic method developed by Robinson and Sinclair.
(a)
a quantity
EO
usually
m*.
E6
m
T
m ....
ln/
lnf
are plotted a.gainst some function of m,
Since when m • o,
. follows a value of
desired E0 •
ln
T
may be defined as
ln
Then values of
2RT
E = Eo
From equation (1)
E6
jC =1
by definition 1 it
extrapolated to m
=o
should give the
This method has been used by Lewis and Randall43
for aqueous HCl, but they find the extrapolation is linear only
extreme dilution, where measurements of E.M.F. are difficult.
Also the solubility of the AgC'l.
can no longer be regarded as
having no effect on the ionic concentration.
This method has
been used by Harned and Ehlers28, Linhart44, Nonhebel45 1
Scatchard46 and others, to obtain Eo·
Their results have
been analysed by Prentiss and Scatchard47 , who give a value
-20-
This method is not used in modern work.
of .. 2225 volts.
(b)
It had been suggested at intervals, that strong
electrolytes are completely dissociated, and. their anomalous
behaviour, compared with weak electrolytes, might be due to
electrostatic attraction between the ions..
In 1912 Milner48
undertook a mathematical investigation, but owing to the complexity of his tree.tment, his work did not attract much
attention although his equations represented the form of the
deviations.
In 1923, Debye and Huckel49 treated the question
in a more straightforward way by introducing Poisson 1 s equation ..
The fundrunental Debye-Huckel assumption is that dissociation is
complete in strong electrolytes, a fact supported by modern
theory and investigotion.
for the activity coefficient
ln
/=
They derive a theoretical equation
A,
where A is the Debye Ruckel constant varying as (DT)-
~
andp 9
is the ionic strength in traduced by Lewis and Rsmdall and
defined by
JU' == l: ir ( czz)
where Z is the valency of the ion present in concentration C.
This function can be regarded as a measure of field intensity
existing in the solution.
Thus the Debye·Huckel theory gives
a theoretical basis for the empirical discovery of Lewis and
Randa115° that the activity coefficient of an ion depends on
its ionic strength.
The Debye Ruckel rels.tionship is a
limiting law, giving better agreement as dilution increases.
Other assumptions made in the theory were. that the ions were
point charges and that the solvent is a continuous dielectric.
Extensions have been made to the theory, notably by Gronwall,
La Mer and Sandvea_5l and others, to allow for these additional
fe.ctors.
A more eocact equation is
A./;i!
lnJ =
where
llall
I
+
'~
is the average effective diameter of the ions, B a
Then equation {11)
function of (DTjt.
E
=
2~T ln
Eo ....
1
2;T
m
lnf
becomes, by substituting k for
E
t
where.)U =
= Eo
~.mzZ
-
1
2k
2kAJAi.cf~·
log m
1 -taB
~}icr~
m being the molal concentration.
In mixed solvents, this is extended further to
2k log m -+
2kA ~let
1-aB .(iJlf..
_
2k log ( 1+• oo.zG0 m)
where G0 is the mean molecular weight of the solvent;
in the
present work
where Me
.:::
molecular wt. of the acetone
M1
=
molecular wt. of the water.
The Debye Ruckel function was first applied to the
evaluation of E by Hi tchcock5 2 • 'l his worker reca.lcula·ted
1
0
values for E0 as a function of M and calculatedJU•
only the original Debye-Huokel expres s.i on
He used
E0
=
E
+
2k log m
2A ./ji
He got a good value for E0 which was more constant in stronger
solutions than
nharti) using method lll(a)
Harned and Ehlers 28
value using the Debye ··Ruckel
equation for the Ag/AgCt electrode in hydrochloric acid
solution at 25° is given as .2224 volt.
Harned and co-workers at Yale to-day publish
values to five places and claim an accuracy
.05 m.v.
EO
MATERIALS
Hydrochloric Acid.
Constant boiling point acid was
prepared from Hopkin and Williams'
"Analarll Hyclrochloric Acid by the methocl of Foulk and Hollingsworth53..
This actd was made approximately .1M by dilution
and was standardised by volume and weight by gravimetric
analysis as silver chloride, using a sintered glass crucible.
Most of the water on the precipitate was removed by washing
with e.lcohol followed by ether, 54
and then drying at 18o 0 ..
This was checked by analysis against Sodium Carbonate, the
results checking to .. 05%·
Sodium Hydroxide.
Carbonate free Sodium Hydroxide was
prepared by the method recommended by
Vogel 55.
A saturated solution of
11
.Analarn Sodium Chloride was
electrolysed using a mercury cathode.
A separating funnel
was used as a cell, to enable the Sodium Amalgam to be run off
rapidly ..
Contact w1 th the mercury was made by a platinum wire
sealed in a glass tube, while the anode consisted of a platinum
iridium plate, sealed to a glass tube..
Vogel recommends a current
of .. 5 - 1 amperes at a potential of 6 - 8 volts, but a current
-24of 2 amperes was found more satisfactory in the cell used ..
The cell was cooled by immersion in circulating cold water.
Current efficiency was found to be about 60%.
After 36 hours,
the amalgam was run off into freshly boiled and cooled distilled water, and washed rapidly until the washings gave no
test for chloride.
The amalgam was then run into a Pyraw
flask of boiled distilled water, the· air above the solution
displaced by hydrogen and the flask closed with access to air
through a soda lime tube.
12 - 18 hours.
The amalgam is 75% decomposed in
This solution was standardised against the
HCl standard, the value being checl{ed by titration against
11
Analar 11 Potassium Hifdrogen Phthalate recrystallis
above 30° and dried at 125°.
Acetic Acid ..
from water
These two values checked to
IIAnalarn Acetic Acid was purified in a
PyreX apparatus, by distillation through
a spiral condenser.
Difficulty was experienced by the vapours
attacking the rubber stoppers in the apparatus giving a clear
distillate, but an opalescence on dilution due to the rubber
separating in a colloidal form.
trouble to a less
extent.
Cork stoppers gave the same
This was finally overcome by using
cork stoppers, and separating them from the vapours by at least
two inches of closely packed glass wool.
The glacial Acetic
Acid was distilled three times through an efficient still head
-2530 ems. high, the first two times, from a 2% solution of
chromic anhydride as recommended by Harned and Ehlers 2 3 1 to
remove oxidisable impurity.
The middle fraction of the
third distillate was diluted to form an approximately 2M.
solution, which was standardised by titration against the
standard NaOH using an N.P. L. standardised
burette.
from the mean of several titrations was not more than
Deviation
.05%·
IIAnalarll Sodium Chloride was
Sodium Chloride.
purified by precipitating a saturated
solution with pure HCl gas.
'rhese. crystals were washed rapidly
with cUstllled water to remove excess HCl and were then recrystallised from distilled water.
This was followed by dry-
ing and heating in a muffle furnace to 500° to constant weight
as recommended by Kalthoff and Sandell56.
The purified salt
was stored in a dessicator.
Acetone,.
May and Baker's B.P. Acetone was purified by
methods given by Weissberger and Proskauer57;
The Acetone was stood over freshly dried potassium carbonate
for two days, with frequent shaking and was then filtered off
and distilled, the first and last fractions being rejected.
The middle fraction was stood over calciwn chloride for a week,
and was then filtered off through a sintered glass filter.
Instead of using reduced pressure under the filter, a column
of acetone two metres high was used above the filter.
This
-26cut down losses caused by using reduced pressure.
The acetone
cient still head rejecting
was then distilled off through an
Any polymerides formed during the
first and final fractions.
drying over Calcium Chloride would be high boiling point products, so a larger end fraction than usual was rejected.
The
middle fraction was kept in a storage vessel fitted with a
The following constants
siphon and calcium chloride tube.
were determined and agreed well with values list
in the
literature ..
Densi t~,.
A
series of determinations of density
using a quartz pycnometer~ gave a value of • 7914 at 20°,
Other valt:tes cited_ are • 7910 58
1
The most recent value (1940) of ·7960
61
•
7912 59 , •7916 60 .
seems higher than
the average ..
Using a calibrated Abbe
refractometer, a value of
the literature are not in
N~
00
= 1,.3595.
Values
ement emong themselves.
61
62
Some values given are N020°~ 1.3 602 , 1.3590 • Drude
63
gives a value of lo 3606 , increasing with water content
to a maximum at 66%.
Boiling Point ..
super~heat,
The tendency of Acetone to
caused difficulty in the determination of
boiling point.
The method of Cumming,Hopper & Wheeler 64
was used in which the Acetone is heated in a small tube,
into which dips the open end of a sealed melting point tube.
-27As heating progresses a point is reached when a regular
stream of bubbles is emitted from the tube, and on cooling,
the liquid is seen to suddenly re-enter the capillary.
The mee;n is taken as the boiling point.
seyeral determinations gave a value of
listed are
56.24
061
and
56.3
062
A mean of
55.8°.
Values
•
The stock solution was made up from
Stock Solution.
the Sodium hydroxide within a day,
to prevent eny attacking of the glass by the caustic solution.
It was made by mixing the solutions in the rat:to 2 moles Acetic
Acid : 1 mol Sodium Hydroxide.
A 1 : 1 buffer solution is
ideal experimentally, and as 2 kilograms of solution were made
up on a balance sensitive to .01 gr. this was readily accomplishedo
The molal strength of the Acetic Acid solution and
of the Sodium Hydroxide solution being known, the
molar
quantities of Acetic Acid and Sodium Acetate could be calculated, after
An
a~lowing
equ~olecular
for the water formed during neutralisation.
emount of Sodium Chloride was added, and this
stock solution kept in a storage vessel fitted with a siphon
and calcium chloride tube.
The molalities of the acetate
components were considered known to .05% while the error in
salt concentration was much less.
From this stock solution,
cell solutions for the determination of PK values were made up
by weight dilution.
In all cell solutions, the requisite
-28amount of pure Acetone was weighed into the solution after
As the weight of Acetone added each time was of
d.ilution.
the order of 30 grs., the Acetone concentration was considered
known to • 04%·
Pure electrolytic
Hydrogen.
from a cylinder.
h~drogen
was obtained
The only impurity present
was therefore oxygen, which was readily removed.
It was
forced through the cells by means of an aspirator, after
passing over platinised asbestos in a combustion tube maintained at 250° C. in an electric furnace.
Macinnes and
Cowperthwaite 66 observed differences up to 50 m.v. when
c omm erci al hydrogen is used.
Lorch 67 also points out the
necessity of purification.
Platiniseci asbestos had been shown
by previous workers in this labore.tory to be more efficient
than a copper catalyst e.t 400
0
C.
Macinnes and Cowperthwaite
also detected oxygen diffusing through the rubber connections
and in the present work., gla.ss-to•glass rubber connections
were made as far a.s possible.
In addition, the full pressure
of the aspira.tor was maJ.ntained in the a.ppa.ra.tus right up to
the hydrogen bubbling tube, where it waR stepped down by a
screw clip.
ELECTROD~.
The li tere.ture does not record any previous instance
when hydrogen electrodes have been used in e.cetone water mixtures.
Prevbus workers in this laboratory have used the
-29quinhydrone electrode in acetone water mixtures.
The hydrogen
electrode has been made to function satisfactorily in dioxanwater, methanol-water, ethanol-water and isopropanol-water
.mixtures.
In the present work, the hydrogen electrode
functioned satisfactorily in the cell,
NaCl
Solvent (x) Ha..O (Y)
Pt, H2.. INaAc.
lAg C1- Ag
HAc
despite the very low
concentration of hydrogen ions.
In the cell
Pt, H~
I
HCl
Solvent (x)
H\0 (Y:)
the cell required longer to come to equilibrium.
I AgCl
-
In general 1
it a<Jpea.rs the hydrogen electrode functions best in buffered
solutions ..
Hydrogen Electrodeq.
The bases of the platinum
·electrodes were constructed of
platinum foil {1.5 ems. by 1 em.) welded to a platinum wire
sealed in the end of a glass tube.
Electrod-es were cleaned
by electrolysing as the anode for 15 minutes in concentrated
hydrochloric acid (Analar), a current density being used such
that no evolution of chlorine was visible.
pair of electrodes was found most efficient.
.15 amp. per
A thin bright
coating of gold was then deposited from a solution of potassium
aurocyanide, 2. 5 milliamperes per pair of electrodes being
passed for 30 minutes.
These were then washed in tap water
followecl by distilled water, and the platinum black deposited
from a 2% solution of chloroplatinio acid containing .. 02 grs.
lead per 100 co.
..5 amps. per pair of electrodes being
-30sed for 5 minutes.
The electrodes were again washed and
hydrogenated as cathodes in a 7% sulphuric acid solution to
remove occluded chlorine.
Electrodes were stood in distill
er prior to use •
. Beans and Hammett 68 do not consider gold plating
an advantage, but Lewis Brighton and Sebastian69 find a gold
Its function seems to be due
plated electrode superioro
to the fact that gold, unlike platinum, does not absorb large
e.mounts
gases end equilibrium is therefore attained more
rapidly ..
A much more adherent film of platinum is formed
on gold, but the mein advantage is that it makes electrolytic
cleaning possible7°.
In the platini sing
lead is objectionable.
no delet
electrodes 1 Ellis7 2 suggests
Denham and Allmand73 maintain lead has
ous effect, and Britton74 considers its presence
increases the efficiency.
Ellis also prescribes platinising
until the coat of platinum is thick enough to fall o , but
Clari0 recommends only sufficient platinum black should be
depo
ted to cover the glint of the polished metal. Popoff
and Kunz 75 show not only does a thick coating require a longer
time to equilibre.te, but is also more liable to poisoning.
In
the present work, all electrodes were used once only, to
vent any pol soning.
The silver chloride electrode
has been extensively studied
by Jalm7 6 and
o by Halla77.
In modern practlce, three
-31forms are commonly used.
They are the thermal, thermal elec-
trolytic» and electrolytic types, the latter two being the
more popule"r.
Smith and Taylor7 8 investigated the three types
and showed their potentials all agreed to .02 m v.
Freshly
prepared electrodes must be allowed to age, as fresh electrodes
behave as cathodes to aged electrodes, due to a smaller concentration of electrolyte in the interstices of the
Chloride.
lver
The graph of E.M.F. against hours, shows an
initial excess
liii. F. of up to • 8 m. v. falling sharply in the
first 20 hours end assuming their true value after about f:JJ
hours, depending on the porosity of the deposit; and the concentration of the ageing solution.
In this work, the electrolytic tspe of electrode was
They consisted of .75 em. squares of platinum gauze
used.
welded to a square of platinum wire which was sealed in the
glass tube containing the mercury for making contact.
Elec-
trodes were cleaned by removing Silver chloride with .880
ammonia, and after washing, the silver was removed in warm
c.) dilute (1:1) nitric acid.
(50°
They were then rinsed in
tap water and stood in distilled water until required for
plating.
AgNo
3
Silver was depos1 ted from a cyanide solution (7 grs.
+ 10 gra. KCN 1n.200 co. distilled water,) using a
lver rod as anode;
for 16 hours ..
2 milliamps
per electrode being passed
The excess potassium cyanide dissolves the
silver cyanide as it is formed at the anode.
ectrodes were
-32then washed in running tap water for 8 hours and stood overnight in distilled water.
Thorough washing is essential to
Plated electrodes were
remove the poisonous cyanide ion.
chloridised by electrolysing in .lN 11Analar11 hydrochloric
acid, as anodes with a current of 6 milliamps. per electrode,
as recommended by Allmand and Hunter.79
Electrodes were
allowed to age by standing in the acid solution for at least
100 hours; followed by washing in
stilled water, and stand-
ing overnight in distilled water prior to use.
so prepared were tested
found to .,1 m.v. or less.
ectrodes
intervals before use 1 and agreement
In some cases, divergences occurred
due to either cracks in the seal or a
fferent modification of
Silver chloride being thrown down for some unexplained reason.
This was of a lighter colour than the usual de
of the Silver Chloride.
Macinnes and Parkerso:
Cells.
plum colour
Its formation was also noticed by
Such electrodes were rejected.
The U -tube type of cell as used by Harned and
co-workers was used.
( F'i
I)
The 1
t hand
s.rm, A, contained the silver chloride electrode mounted in a
rubber stopper, while the right hand arm B cant
ned the
hydrogen electrode and bubbling tube,
o mounted
a rubber
stopper ..
Harned and Morrison 81 state that contact of liquid
or vapour with rubber, renders measurements erratic.
In the
filling process described below, the liquid does not come in
contact with rubber, while the stoppers in the cells were given
a thin coating of acetone
collodion.
The capillary tube
C
-J >..
DIAGRAI11.
D
A
c
-3430 ems. long provided an outlet for the hydrogen without
allowing back diffusion of oxygen.
This deviee is considered
satisfactory by C1a.rk71 ..
The side arm D and tap were used
for filling the cell.
Hydrogen was admitted to the compartment B by
capillary tubing drawn out into a small curved jet as shown
so that the small bubble played on the platinum surface of
the electrode as they rose through the solutlon.
Hamer and
Acree8 2 point out that the hyirogen electrode functions best
when only partially immersed in the solution.
The cells were
therefore only filled to the level shown.
Before ent
ng the electrode side arm, the hydrogen
passed through two double bulb saturators immersed in a thermostat and containing pure solvent.
In addition it passed
through an ordinary straight tube saturator half filled with
solvent.
The empty space in the latter was provided as a
safety measure to prevent any solvent being forced over into
the cells if a sudden increase in hydrogen pressure occurred
as discussed later.
The dilution of solutions was such that
the difference in vapour pressure of solvent and solution could_
be neglected ..
Complete saturation of the hydrogen is important
in preventing concentration changes, e.g. the vapour pressure
of the solvent at 45° is 167.4 m.. m..
Confirmation of adequate
saturation was found in the constancy of E.M.F. over a test
period of 36 hours.
-1 ~-
-39Although the resistance of the cells was considerable
especially in the more dilute solutions 1 changes of .1 m.v ..
could be .detected on the galvanometer used.
Between runs, the
cells, hydrogen tubes and taps were cleaned in a hot chromic
actd bath, washed thoroughly in tap water followed by distilled
water, and finally dried in an atr oven.
Cell Mantnulation.
Prevtous investigators have shown
elimtna tion of air from cells and
solution to be essential.
This was found to be particularly
so in measuring E0 values, slight traces of air causing not
only extension of the equilibrium time 7 but in some cases,
upsetting readings altogether.
A modified vacuum technique
based on that used by Harned and Morrison8 1 , and Hamer and
Acree82
diagram.
was used for filling the cells, and is shown in the
The purified hydrogen enters at 1, while a vacuum
pump ·capable of 15 m.m. is connected at 6..
The advantage
of the otherwise compltcated apparatus is that everything is
maintained in an atmosphere of hydrogen once a run is begun.
(a)
Removal of Air from the Apparatus.•
The hydrogen supply was cut off at 1, and the
saturators cut off at 10.
The apparatus was then evacuated
by opening the vacuum lead at 6.
open, except
All other clips were left
1S, 16 and 7, which opened to the atmosphere.
In
-37this
w~
the saturators were evacuated through the hydrogen
bubbling tubes, thus preventing liquid being drawn into the
hydrogen line, marked in blue.
The saturators were then isolated by closing cllps
11 and 12, the vacuum stopped by closing clip 6, and hydrogen
cautiously allowed to enter by opening the hydrogen supply at
1.
When the apparatus was full of hydrogen, the gas was
allowed to enter the saturators slowly by opening clip 10.
This prevented the liquid in the saturators from being forced
from one to the other.
The hydrogen supply was then cut off at 1 and the
evacuation r
eated as above.
This process was repeated three
times.
After the apparatus had been filled with hydrogen,
any last traces of air were swept out of the cells as follows.
All clips were shut except those leading hydrogen to clip 9·
This was left open as were 13, 14 :
15, 16.
In this way a
rapid stream of hydrogen was passed through the cells end out
to the atmosphere at 15 and 16.
{b)
Removal of Air
from the Solution,.
All clips were closed except the following.
Hydrogen was admitted to the cells through the saturators by
opening 1
5 10 11 and 12.
In this way the gas was
se_turated with acetone and water vapour in the correct proportions and allowed to escape by passing through 13 and 14,
then bubbling through the s olu.ti on and escaping to the
atmosphere through a. capillary tube of medium bore at 7•
Complete elimination of air is stressed by Harned
and Morrison 81 .
(c)
Fi!ling the Cells.
All clips were closed except the following.
Clips
1, 2 end 8 allowed the hydrogen pressure to reach the solution
in the filling flask A.
Clips 15 and 16 were then slightly
opened to allow the hydrogen in the cells to come to atmospheric pressure.
On opening taps
13 and 14, solution was
forced over into the cells by the hydrogen pressure, at A.
{d)
As'l-J.g,.§j;h_ng_ :the Level o.f Liquid.
The filling procedure outlined above causes liquid to
be higher in the hydrogen electrode compartment than in the
other, so these levels must be adjusted.
Taps
13 end 14 were closed and most of the solution
in the filling tube B was forced back into the flask by
momente.rily opening 9·
To prevent any back diffusion of air
at 15 and 16 during level adjustment, hydrogen was allowed to
pass through the hydrogen line by opening 5
10
11
and 12
slightly.
Pressure in the filling cell A
WI:;<
s then reduced by
opening the vacuum clip 6 for a short time, thus reducing the
pressure above the taps
13 and 14.
By cautiously opening
-39these, the solution was slowly dre.vm back to an equal level
in each compartment.
The hydrogen bubbling through the
electrode bubbling tubes and leaving the cell at the clips·
15
and 16, prevented air entering the c
•
The amount of liquid used in filling the cells,
so that the final level covered only h'alf the hydrogen
electrode, could only be estimated after some experience
in manipula.tion of the apparatus.
A further advantage of
this method, is the possibility of flushing a cell out with
fresh solution should any discrepancy
se.
In some cases where cells differed by a millivolt
or so, changing the solution would bring the values back to
the usual agreement..
~iusted
The rate of hydrogen flow was ad-
to about two to three bubbles a second, although withtn
fairly \rlde limits the potential was independent of the rate
of bubbling, unless cells were unsatisfactory, as
scussed on p. 6.
In measuring E0 values, potentials were sometimes
sensitive to hyclrogen pressure, the results obtained being
erroneous.
As would be expected on theoretical grounds 1 too
rapid a flow in all cases, increased the electro,motive force.
Cell Measurements.
The cells and saturators were immersed
the
thermostat at such a level that all vapour and liquid spaces
were below the surface.
Cells were measured in duplicate,
values more than £.1 m. v. from the mean value being considered
-40erroneous.
In measuring Pk values, the cells were allowed
to equilibre,te overnight at
15°, preliminary experiments
showing the time varied from 4 - 6 hours at this temperature.
In measuring E0 values 1 a much more elaborate equilibration
48 hours at 15°. It was finally
found that equilibration at 45° for 12 hours was, in most
was required, as much as
cases, satisfactory, but occasionally even this procedure
needed longer.
Constancy of E.M.F. over a
45 minute inter-
val· was regarded as an indication of equilibrium.
Each set
of cells was measured over the complete temperature range of
15°- 45° C., while typical cells were in some cases returned
to
15° through the whole range again, and showed no temper-
ature hysteresis.
Measurements were reduced to a normal pressure of
760 m.m. by the thermodynamic formula
log
760
~b - Pv
where Pb is the barometric pressure and Pv the vapour pressure
of the solvent in millimetres of mercury.
The values for Pv were obtained from data given by
This correction is important, amounting to
approximately ·3 m.v. at
45°, corresponding to .. 052 PK units ..
Any back pressure due to the 1 - 2 em. head of solution under
which the hydrogen bubbled out, was considered sufficiently
small to be safely neglected.
A correction was
so applied
for variation of E.M..F. in the standarCl. Cadmium cell from data
-41given by Wolff 84 (1908)
.000041
(t - 20)
The temperature of the water thermostat was maintained constant
± .02°,
fluctuations being recorded on a Beckmann thermometer.
Constant stirring wEw maintained by an aluminium propeller c:md
an
i
h.p. electric motor.
During the changing of temperatures,
stirring speed was incree.sed by means of a variable resistance.
The thermoste.t was heB·ted by gas, controlled by a mercury
toluene regulator.
Temperatures were recorded by a thermometer graduated in 1/lO's of a degree and calibrated against
the laboratory standard.
Control
15° was maintained by a
cooling coil consisting of three turns of 1/2 inch lead piping
pla.ced at the inside wall at the bottom of the thermostat,
through which water of known. temperature
passing through a pre-cooling coil.
''laS
circule.ted, after
The electromotive forces
v.rere mea.sured on a Cambridge Instrument Co. potentiometer of
range 0 - 1.8 vol
ment Co.
11
accurate to .1 m.v.
A Cambridge Instru-
pot 11 galvanometer with a sensitivity of 170 m.m,.
scale divisions per micro-ampere was used, being supported on
a vibrationless stand.
Contact
bet\~een
the insult3ted potentiometer leads
and electrodes in the cells was by mercury contained in the
glass tube formi
the electrode support.
effects could be detected.
No thermoelectric
The solvent consisted of 10 parts of water
1 acetone
by weight ..
I
Dielectric Constants.
0
These were obtained by data due to Akerlof
85
, by assuming
linear interpolation over the short range of acetone concentration from his values in 10% acetone water mixtures.
D
75·34
log D
1.8770
250
300
40°
73·52
71.86
68 .. 53
1.8664
1 .. 8565
This
1. 8359
These can be expressed as a function of temperature
log
D =
1.8770
from which values at 15°
T.O C
D
35°
.. 00 20 6 ( t
and 450
-
20)
were calculated.
30°
35°
71.86 70.16
40°
68.53
-43II
Vapour Pres sur~.
Acetone water mixtures show a large positive
deviation from Raoults Law.
Vapour pressure corrections
of E.M.F. measurements are very important.
Modern values
for the vapour pressure of the solvent were not listed in the
literature, the values used in the present work being interpolated linearly over a short range from vapour pressure
measurements on water and 10% acetone water mixtures due to
Taylor83 (1900)
%Acetone
25°
23 .. 5
0
55
107
82
65
10
139
71·5
177
92
221
These values could_ be expressed by
P =
4
2.69
(t
r
25) + .142
which expresses the data with fair agreement.
was used to calculate values at
(t- 25}
This formula
15P 20° 1 the values then
being linearly interpolated to 10 parts water : 1 part acetone.
T..
V.P.,
The desirability of more accurate data of partial vapour pressure
over mixed solvents is stressed by Robinson and Harned86 •
-44Density ..
The value of the density was found by direct
measurement using a quartz pycnometer.
In filling
this~
care had to be talr.en to prevent the relative quanti ties
being
a~tered
by excessive heating.
A vacuum technique
was used to fill most of the pycnometer.
With its exit
tube dipping under the surface of the solution in a small
container~
it was placed in an empty desiccator, which was
rapidly evacuated and filled with air alternately.
The
change in solution composition due to the rapid evacuations
was considered small enough to be neglected.
The final
filling was done by careful warming e.nd cooling in the usual
way.
T? C
d ..
15°
20°
·9881 .9864
25°
·9846
30°
35°
40°
45°
·9827
·9806
·9784 ·9759
-45~CULATION
A.
OF RESULTS.
A.
Eo Values
The method used for the calculation of E0 values,
was a modified form of Hitchcock 1 s5 2 method, in which the
Debye Ruckel expression for the activity coefficient was
used as
In this work the expression
lll/ ;
1
A Jjjj'(L
+ aB j'iiid:' +
bm
b being some funetion, or the full expression
E~
=
E
+
2k
2kA~
log m -
1 + aB
( §
where
The factors A
m
2k log
(1 + .OO:l.lnG)
Introduction)
and B are given by
1 e 8J 2
1Q6
X
(DT) 3/2
B
-
"a"
=
5·034
(DT)
109
X
i
4 • 3
l
(assumed)
Other terms in the equation are
m =molality (grs. HCl per 1000 grs. mixed solvent)
d
=density of the solution at the appropriate temperature.
-46As the solutions were dilute, d was calculated from
d
= d0 +
.0178 m
at all tempere"tures..
The value
.0178 was that used by Harned and Calmon87 in 10% Ethanol
use is justi
water mixtures, and i
ed for measurements of
the order of accuracy obtainable in this work.
The value used for
tt an,
of the ions, is also important.
the me en effective diameter
Harned and
ers28 calculated
values of llan in water from 0°- 6o 0 and found it is constant
over this range of
temperature~
and Thomas8 8 found the same
the value being
4·3
@
A.
Harned
ect in methanol water mixtures.
the present work, the value of
4·3
was taken as the most
probably value.
From the equation, values of ~ are calculated, and
plotted again mi end extrapolated to m ~ o, thus giving the
required standarcl molal
ectrode potenti
of the Ag -
01
These results are drawn up in the following tables,
electrode.
while Graph I was used for the extrapolation.
In Te_ble IX are listed for purposes of comparison,
the values for the standard potential of the silver -silver
chloride electrode in various orgctnic solvent-water mixtures
·Constants used in
2.303 -~
s\ ( D·ll Con st.)
B ( 0-H Con st.. )
P (Vap. press., in
d0 (Solvent)
m.~}
°
t5°
20°
.. 057t7
.5469
• 058l6
• 059l5
5522
.5585
.. 338
48.7
• 9881
• 339
51..7
.340
.,9864
.9846
0
25
61.2
30°
35°
40°
45°
.,060 l5
,.5636
.34l
77.4
• 9827
.. 06Ll4
.. 5702
.342
101
.9806
• 06213
,.5765
,.344
l3l.4
• 9784
.. 063l2
.5835
.345
167.4
.9759
-47~E
I
150
1 Acetone ••
E'0
lVI
.08002
• 3581
.2200
.06o02
·3719
.2208
.04736
' . 3823
·2205
.03001
• 4031
.2204
.00998
·4549
• 2208
.00909
·4589
• 2203
Extrapolated
TABLE
Eo
.2206
.;::;
II
20°
M
Ecorr.
E~
.08002
• 3575
.2170
.. 06o02
• 3715
.2178
.04736
·3821
.2173
.. 03001
• 4033
.2174
.. 00998
·4559
.. 2176
.00909
·4603
.2175
Extrapolated Eo =
• 2175
10 water
-48III
TABLE
250
M
E
Corr.
E~ (D-H factor
Ea
0
.08002
• 3569
.2138
.21)7
.06002
• 3707
.. 2142
.2134
.04736
·3816
:.'2140
.2118
.03001
• 4033
.2141
.2106
.. 00998
-4566
.2143
.2101
.. 00909
.4615
.2145
.. 2086
Extrapolated E0
TABLE
= .2143
IV
300
M
Ecorr.,
E'0
.08002
. 3567
.2110
.. 06002
• 3701
.2109
.04736
• 3812
.2107
.03001
• 4032
.2107
.00998
·4575
• 4620
.2110
.00909
.2108
Extrapole.t ed E0 =
.2110
Eo =
.2143
-49-
35°
E
Ea
0
Corr.
.08002
• 3559
.2078
.06002
• 3690
,.2070
.04736
• 3810
.2076
.03001
• 4031
.2073
.00908
·4581
.2076
.00909
•4Q26
.2072
Extrapolated E0 =
40°
M
.2074
El
E
Corr.
0
.08002
·3550
.2044
.06002
·3687
.2040
.. 04736
·3808
.2044
.03001
• 4031
.. 2041
.00908
·4591
.. 2044
.00909
.. 4636
.2040
Extrapolated E0
.... 2042
-50TABLE
VII
45°
M
Ecorr.
E'0
.08002
• 3538
.2006
.06002
• 3675
• 380'4
.. 2000
. 4031
.2007
·4595
. 4642
.2007
.04736
.03001
.00998
.00909
Extrapolated
TABLE
.. 2012
.2004
E6 •
.. 2005
VIII
Standard molal potentials of the Silver chloride
electrode •
150
.. 2206
20°
.2175
25°
.2143
.. 2110
30°
.2074
35°
40°
. 2042
45°
.2005
0
L LJ
-
- 51-
r
4.
~
<'.i
l
I
...i
I.
:1:-+
t
-
0
.
..
""';._
. a
....
I.
1 r-~
+
.....e
c:o
q
N
- c;>
Si
-52-
The Values Of -o
~·
a t each t empera t ure are
plotted as a function of mi , and extrapolated to zero concentration.
The extended Debye Ruckel
expression for the activity coefficient was used 1 and a
practically horizontal plot obtained, showing the value of
11
an
= 4.. 3 A is
the same in this solvent.
This is in agree-
ment with the ,}:fork of Harned and Thomas88 who found the same
value for nan in methanol water mixtures over an extended
temperature range.
The values of
obtained by using the
original Debye Huckel aqua tion
-
ZA ..1}1,'" at
purposes.
25°
are plott
lnJ =
as a function of m for comparison
The plot is again practically linear with consid-
erable slope, extrapolating to the same value of E0 •
As can be seen from the extrapolations (Ref.l) the points at
each temperature lie on a straight line...
Harned and
eysher 89
and Butler and Robertson9° have found in stronger solutions
the points lie on a slight curve.
It was found measurements
below .01 M were difficult to me.ke and also the cells became
less stable
ove approximately
35°.
The circles are drawn
with a radius of • 2 m.. v. as an estimated possible error ..
GRAPILll.
o--o
Ref. 1.
G---0-
-Ref. 2.
~ef. 3.
ef. 4.
,f.
5.
•z-2eo
Jef. 6.
-{ef.l-7.
Eo
I
\Jl
VJ
I
==
0
....J
L.'">
.-
0>
.~2IDQO
1.0
=•
oc
LL.I
fJJ
-54-
Reference
D
Solvent
Born equation
1 ..
2 ..
Methc:mol water
..
II
3·
~0
§o.
Ethanol water
II
II
74.0
.2154
69e2
..2088
72.8
.2144
67.0
.. 2074
10
Harned & Thomas88
tl
II
Harned
&
Calmon87
II
II
Harned and Morrison9 1
4·
Dioxan water
6o.8
• 2030
5·
Isopropanolwater
71·4
.2136 .Harned
6 ..
Glycerol-water
77·0
.2196
7·
Acetone-water
73·5
.2143 Present work.
8
& ,.Cll:ilmon7
Lucasse9 2
It can readily be seen that no simple relationship
sts
between the dielectric constant of the solvent D and the value
of the standard potenti
It would seem possible and even
likely that some such relationship would exist for a s
es of
alcohols in their mixed aqueous solution ..
1
In Graph II, the data list
are plotted against
the reciprocal of the dielectric constant.
plots at the left is the E0 value in
er.
The origin of the
The straight black
line (Ref.l) sho·wn is obtained from the simpli
as used by Harned and Calmon87
rr
ed Born equation
5iNhere Eo(w) is the stano.ard electrode potential in water E0
the standard in the mixed solvent which differs in dielectric
constant by
b.(~),
2:(~ J
and
the sum of the reciprocals of
the ionic radii in !ngstrom units.
this is 0.9
The
vs~ue
4·3A as us
corresponding to
employed for
in the Debye Huckel
All the lines obte,ined are slightly curved and
expression.
all deviate from the Born equation&
rrhe three monohydric
alcohols show the best agreement.t and also a certain regularity
The value for Acetone-water is rather iso-
among themselves.
lated as only one point is available.
A comprehensive review of the work done in the thermoo.ynamics of strong electrolytes is contained in a recent paper
by Robinson and Harned~ 6
An interesting relationship between
the standard electrode potential of the AgCl mixed aqueous solvents is also developed.
electrode in
They consider the
sts.ndard potential of the cell,
H2/ HCl (m) Solvent (N 2 ) Water (N\ ) / Ag Cl The various standard potential expressions on the molality, (
concentrationt
E~
0
EN
Eg
1:;
=
ru1d mol fraction scales
0
E41l
-t
.. 1183
(
log
.. 1183 log
do
1000
Mxy
where for mixed solvents lVlxy is defi nect as
IVIxy
=
100
X
m\
+
il..
E~ are related by
6where x and y are ·wetght percente,ges of the two solvents of
molecular weight m, and mll,.
The trensfer from water to water-
solvent of the acid is treated as follows.
these cells at
E
E
11:1
-
25°
Eg
~~
The E.M.F. of
c may be represented as
-
&05915
log
m,,,f,
~
.. 05915
log
m H {~ m
~t~~
• • • • • • • (a)
f~l
•.•••.• (b)
Where ~is the standard potential in a purely aqueous solution,
JH
j'ct is the activity coefficient in any of these solutions
I
~'·"~
relative to unl ty at infinl te dilution in water, and
is the
standard potential in any mixture relativeto unit activity coefficient
f~
f,,'
at infinite dilution in that solvent.
These
equa. tions combine to give
Eg'
=
.05915
• •••••. • (c)
log
"
By using the thermodynamic rele.tionships of the reaction
••••••••••• (d)·
equations (e.) (b) t:md (d) may be combined to give
(
-
( If.:g' ..... 05915
'
log Aw)
..05915
....
log
Gi
f~l~t
where the superscipt is used when a transfer of an electr.olyte
from one medium to another is un<ler consideration, and
the activity of we.ter in the mixture.
Eg -
(Eg
9
-
.05915
log Aw)
•
By convention Aw for pure water = 1.
Eg'-
.05915
is
Simile,rly
.. 05915
log
Cl
fH-P' f<=•'
Vapour pressure data
indicate we ce.n replace Aw by N, the mol fraction..
suggests a plot of
Aw
log N, against
This
' , and is
lf
-57and is shown on the lower part of Graph II.
observed the poi
It will be
for all solvents including the present
work fe"ll very. nearly on the same line..
This observetion,
as pointed out by the authors may prove of considerable
value in correlating data.
-58-
The formula used for the dissociation constant is:
+
log
fc1 /cH~cooH
=
=
3
jcH Coo~'
[Cl jCH 3cooH
jcH3coo-
log
~,
The first term on the left contains E
ch is measured ln Section B.
second term, the true molalities
acid MCH COOH
+
PK'
ch was found in
0
Section A, and E
_log K1
In the
the undissociated acetic
tmd of the acetate ion must be evaluated by
3
arithmetical approxlma ti on ..
its disso
zero.
As acetic
ation, for the fi
The first term on the
~;wid
is very weak in
approximation MH was assumed
ght he.nd side involving the
logarithm of the activity coefficient ratio of two univalent
ions and the logarithm of the activity coefficient of a
neutral molecule, has been shown to vary linearly with the
ionic strength in dilute solutions.26,37,
left hand sicle of the equation
the ionic strength
n
therefore can be exflrapolated to.,
r
A p 1 o t o_r th. e
=o
where log
equals zero by defin:l ti on a.nd a value of
..fiJ .£cHJCOQ!I
3co
CH
found ..
From the equation
PK
+ log
M
CH cooH
3
\!ihich is v
icl for a weak acid in a not too
lute solution
-59the
of the solution can be found by assuming MCH
.
and MCH COOH
3
-= M1
-
3
coo-
£tnd hence a new value
which is used in a second e"ppr6ximation.
approximations e"re repeated until PK does not vary..
The
In
the present work it was found; as by Harned smd Embree33 that
(M1 - MH) ~nd
(~+ MH) could be replaced by M1 and M2 with-
out causing error grectter than the experimental ..
The ionic
rength was calculated as follows from
the Lewts and Randall 49formula
where
This summation
m =
molality of each ion
'2. =
valence of each ion
is
for all ions present.
are present acetic acid !IJI1
hydrogen ions
~
In this case there
which has dissociated to give
, also sodium acetate M2 and sodium chloride
M •
As both the latter are salts 1 complete dissociation was
3
assumed.
Then
CH3·COO-(M )
N+
2 + a (M2)
-60That is, the ions are:
H+
::;;
=
=
cH coo3
Na+
Cl-
"'
•.
u
=
t
=
M2
1
.::::
MH (1)2
+
M3
lVIH
M2
+ MH
M2
+
M3
M3
+
*
(M2+~) (1)2
+•
("
(lli12+M3) (1)2
+ MH
The importance of using molal concentrations in investigations
over an extended range of temperature is that there is no
change in value
th varying temperature as occurs with con-
centration expressions ..
(1)'
-61TABLE
X
Electromotive Force of the Cells.
H2 (1 atmos .. )
H Ac(M-)
~l
Na Ac(M )
2
10 Water
:
Ag Cl- Ag
Na Cl(,,
l1Jl3)
1 Acetone
(in Volts)
~=M2M3
150
20°
25°
300
35°
40°
45°
.09039
·5659
• 5685
• 5706
·5732
·5750
. 5769
·5788
.06244
·5750
. 5775
·5797
.5B22
.5851
.5878
·5917
.04366
.. 5830
.. 5859
.. 5885
·5915
·5941
• 5969
·5995
.00908
. 6216
"6245
• 6273
• 6304
.. 6333
• 6364
• 6394
.00543
• 6340
.. 6378
.. 6416
• 6455
.. 6493
• 6537
.. 6549
.00262
-.6519
.6562
.. 6601
.. 6644
.. 6696
• 6719
0
676o
-62-
j
I
~
4. 94
F -S.
I
0
•
4, 93
-
""',~4. S9
0..
0'1
0
....J
I
~
~
f
1::
~
4.:93
t
t
•9
4. 93
,.
; t i
I
~
.........
4. 99
.. • ~9
Ionic -s trength =)J.
''
TABLE
.)1
15°
20°
4·999
4-990
25°
XI
30°
4-978
35°
4·978
4·956
4·959
40°
45°
4·950
. 18078
.12488
.. 08732
. 01816
.. 01086
4·973
4· 968
,.00524
4·964
4·979
4·952
4·987 4·972 4·975 4·973 4·970 4·965
4·974 4-966 4-964 4-964 4-962 4· 963
4·957 ( 4· 942) (4. 930) ( 4· 924) ( 4· 914) (4.911)
4·961 4·958 . 4o 958 4·963 4·939 4·936
4·961 4·954 4·955 4·954 4·946 4·954
Extra.p.O
4·966
4·960
4·995
4·982
4·956
DISCUSSION
Great difficulty was experienced in making the
electrodes behave reversibly in the acetone-water mixture.
In measuring E0 values with the HCl solution it was found
many times that the hydrogen electrode potential was
~
sensitive to rate of bubbling, thermal hysteresis 1 and
similar effects ..
were prepared
The reason for this is obscure, as cells
ch functioned normally and well..
Absolute
exclusion of air was of the utmost importance and a long
period of equilibration was
so required, especially in
the HCl solution ·when a period of 36 hours equilibratlon
Altogether more than 50% of completed
was found neces
runs had to be disca_rded or repeated as unsatisfactory..
The
same tr·ouble was experienced in the measurement of the dissociation conste.nt, when for no reason the PK values obtained
would suddenly show a drop (Table XI }l = .01816).
This cell
on the whole Wcls much easier to use the.n that for measuring
E0 values ana_ only 30% of the runs had to be discarded.
PK value is very sensitive to both E and E0
~md
The
hence there is
a cumulative error due to both these being measured in the
present work.
Values
40°
ru1d
45°
could not be obtained,
for the following probable reasons:-
(1)
(
Uncertainty in the extrapolation of E0 at these
temperatures ..
)
m.
culty in the measurement of E values ..
-65High vaBour pressure corrections; especially
at 45 where the correctlon amounts to
.051 PK units.
(111)
For these reasons, only the values of PK from 15°- 35° are
consldered.
The dissociation constant of acetic acid has been
measured by the same method in water anc1 in dioxane-water
mixtures.
'rhese results are compared later.
A regularity in change of slope of the plots with
temperature was observed similar to that obtained by Harned
~md Ehlers93 with propionic acid ancl also with acetic acid 2 3
in aqueous solution •
The circles are dra' 1m with radius
• 005 PK units which Harned considers the limit of experimental error.
Previous workers in this laboratory35' 3 6 have
measured eli ssociati on constants of acids in methanol-water
mixtures and have not apparently had the same dif{iculties
in that solvent.
It would thus seem likely that one of
the electrodes used does not function as v:rell as might be
expected in mixed aqueous solvents contt::dning acetone.
It
would seem probEJb1e that the trouble arises in the hydrogen
electrode, as this
v~ould
affected to any degree.
certainly be the one which would be
Whether it is due to imperfect
saturation of the Platinum black with hydrogen or some similar
reason, cannot be decided until more work has been done with
the hyc1rogen electroc:te in Acetone-vw,ter mixtures.
-66-
~e
C'l
0
.....J
OBOn
:q_
I
·+-..
CTI:"
i
~
-E#J:..
t-
-. 6M
Ref. 1.
0
ltef. 2.
Ref.- 3.
R-ef• 4.
-67-
~,cetic
Acid in Acetone-Hater
8 .. 29,.2°
Q ..
Log Km= 5.045
22.,60
Log Km ..
5.. 244
s) 0
(t-e)2
Lng K
!1'14.. 2
5. 24l7
... 0
002
6
-- • 005
-9.,2
5.. 2437
- .,000
-46
5,.044
·-..oot
.. 4.2
5.,2440
- .ooo
t2o4
30
5.044
-. 001
+0.8
-.,DOl
ljo7.4
35
5. 041
M.004
-t5.. 8
5.. 2430
5. 2375
5. 23ll
·.... oo7
+l2.,4
- • Ol3
+L7. 4
- • 021
+22.4
t 0c
Log K
L5
5,.034
-.... Oll
20
5,040
25
Log K <!l- Log Km
40
Log K - Log Km
"'
45
5.. 2227
REFE~ENGE ( 3)
REFERENCE .(4l
Formic Acid in Hata1•
B "'
24.7° Log K01
t 0c
Log K
l5
5.,2417
20
5o 2437
25
So2440
30
5.,2430
35
So 2375
5. 23tl
5. 2227
..
~~l-Hater
4. 248
~-
45
.
21.2°
Log K10
6135
(t- 9) 0
Log K
Log K - Log Km
... 002
• 7o6
5.602
- • 0115
-l2.2
- .ooo
- .ooo
- •oot
.. 46
'"'
.... 0035
- 7.. 2
+ 2.4
5. 6l3
.,0005
- 2.2°
t 7.4
5.,613
·v .0005
+
- • 007
+l2.4
5.,610
.... 0035
+ 7. 8°
Ol3
tH.4
- .,0085
+L2. 8°
- • 021
+22.4
... 0155
+17. 8°
Log K ... Log Km
~
40
(t-
M
•
s. 610
(t-rU 0
0
0
.,
5.605
5. 598
Q
z. ao
- -~o s GRAPH V.
~_
-:oGO
~ 1~
~
~ +
I
i
+
;-
+t
...,..._
I
I
I
t
t-
• OQ339
I
+
+
l
• 003441
·~
.' ~0!49
.
I
~
Q--0-
~ ef. 1.
ef. 2.
~·I t~~~~-----+---<-- ~-:--
~
l
!l ¥·1
I
-
~
.._
44. 8
(1og K -
~0
Log T)
45J 0
~
t-
-69-
t 0c
Log K
pt2
(Log K +
15
20
5.034
5.040
.011
.020
; .. 045
5.o6o
5·035
;.041
25
30
5·044
5.044
5. 041
.031
.045
.061
5.075
5.089
5.102
5.044
5.045
5.043
35
G
t0c
20
= 29.2°c
Log T
.1
T0 Abs.
15
20
49-20
49·41
.003467
.003388
25
49·484
30
49· 63
49·774
.003356
.003300
.003245
35
Log ~
pt2)
Log K (calculated)
= 5·045
Log K
(Log K +
20
5.034
5·040
;.044
44·234
44·450
44·528
5-044
'5.0 LjJ.
44·674
44.815
Log T)
-70-
In
1934,
Harned and Embree2 7 at Yale were able to
show that the varla_tion of dissociation conste.nt with
temperature of the we:::1k electrolytes measureCl. at Yale, could
be expressed as a uniform function.
It was observed that
the dissociation constants passed through a maximum, and on
plotting log K against t 0 c, the curves were superposable as
shown on Graph IV.
Thfs Graph also shows data for the plot
of (Log K - Log Km) e,gainst ( t -
e),
where Km is the maximum
observed value of the dissociation constant, e.nd
e
the
temperature at which this maximum occurs for each electrolyte.
In the neighbourhood of the maximum (:I: 7. 5°) the
curve was shown to be parabolic ..
Thus the equation
Log K - Log Km • - p ( t - e) 2 ................. (1)
or
(Log K + pt 2 )
=
{Log
Km-
pe 2 )
+
2pt
was obtained, p being a parameter.
F,or acetic acid, the best value of p was found to
be 5 x lo-5 degree - 2 while for boric acid and oxaLic acid
(second dissociation) the values were 8 x lo-5 and 6 x lo-5
respectively.
The second form of the equation is very simple to
use.
A plot of (log K
+ pt 2 )
against t gives a straight
line of slope 2p whose intercept
as shmm in Graph V.
calculated ..
t t
= 0°c
nee p is knovm,
e
is (log KID - pe2)
and Log
~
were
-71On substituting the successive values of t in the
equation
Km
Log K - log
(t - e)2
=
values of K were obtained
ch agreed well with the observed
values, the largest divergency at 35° of .002 pK units, being
within experimental error.
Harned and Embree consider there is no general
quantitative rel
on between
e
as a very rough generalization,
Ace
electrolyte.
and Km•
e
They state that
is greater for a weaker
c Acio in dioxan water
fall in line, e decreasing with K.
-
xtures does not
In the present work, 6
he,s a ve.lue 29.20 Log Km ... '5.045 while Harned and Embree find
for ac
c acid in water
e = 22.6°
Log Km=
-5.244 ..
The
theoretical interest of e has already be en discussed in the
ght of work by Everett and Wynne Jone
temperBtures 11
6 on lltnversion
Any discussion of dissociation conste.nts
•
e constitution of the ionising electrolyte
in the light of
should evidently be made a.t the maximum or corresponding
temperatures.
By cUfiferentiation of equation ( 1) illli th respect
to
solute temperature
=
anc1 combining
th the
d ln K
dT
=
-2p
(t-
0)
........... (2)
Van 1 t Hoff Isochore
OHo
:RirE'
-72where R equals the
t, an equation for the h
cons
content change on dissociation into ions from the neutral
molecule at unit activity, is obtained
x
... 4· 575
ther eli
x
lo-4
-2p ( t - e)
e) •..••••••• ( 3)
T2 ( t -
eren tia tion with respect to 'I' 1 gives the corres-
poncUng heat ca"paci ty change
4• 575 x 10-4
))..... (4:
T (T + 2 ( t
The standard free energy change is obtai
from
the Vant Hoff Isotherm
RT
1 og K •••••.. • • • •• ( 5)
and the standard entropy change from the fundamental therm.odynamic relationship
•
T
•
•
lit
••
0
0
••••
e. •
(
6)
These quanti ties have been calculated at the various temperatures ancl are shovvn in Table XIV.
The exact form of the equation connecting the
ionisation
const~:mt
of a weak acid wi
temperature cannot
be predicted as yet from purely theoretical grounds..
this reason purely empi
For
cal relationships have been advanced
from time to time since it was observed that a characteristic
-73of such a dissoci
on was the occurrence of a critical
temperature, 6 1
which log K was a maximum.
s led
form of Harned and Embree 1 s equation,
to the generalis
log K = log
Kn1ax.-
p(t - e)
2
••••••e•<t••ll!••••••(7)
From this equation the values of the various thermodynamic
~0
quanti ties .bH 0
listed above are calculated.
p
Lewis and RB. ndall42 arssume heat content changes can
be expressed as a power series in T, the
T2.
required bei
t exponent
Molft equations are based on this
Thus if the equation for
as sump ti on.
~o •
it follows by
A - BT - D
ff eren
is given by
8880ftjo01fll>•R•ettll'a•aa<;a8808(8)
on, and Vatit Hoff Isochore etc.
4e<•••••••oC~olle•••••••••••o(9)
a.,G0
= A + BT ln T - CT + DT2 .............. ( 10)
AS 0
~
(C- B)- B 1n T- 2DT •............ (11)
ed these equations, and a critical
Other workers have
survey of these equatlons has been made by
Robinson94.,
They show
ed and
ve equations have been advanced as
senting the temperature variati.on of the ionisation
constants
weak
ectrolytes.
of these represent
the observed data within the limits of e
erimental error.
They are
e.a.o =
A+ BT ln T
t:rJJO =
A+ BT ln T
Jl(JO
A -. CT
=
+
DT 2
CT
................... ( 12)
:.-&··············~···(13)
-74Computations involving equations (10) and (
) are extremely
ect equation (13) as the most useful
laboriou.s, and they s
as it is particularly well adapted to the evaluation of the
parameters by the method of least squares.
From equation
(13)
1 t follows
A-D~
2DT
c -
6
o •
e
•
o
•
o o
e
* •
0
•
•
.-
•
•
0
6
•
•
•
* •
0
•
•
•
0
(
14)
···········Cl··················(l5)
2D~e
............................... ( 16)
The values of these quenti ties obtained from these equations
are also
sted in Table XIV 1 the equa·ti on for
evaluateo_ by least squares from
being
values obtained team
equat:lon (5).
An interesting point concerning the value of'
is that equation
(15)
while the value for
shows it to depend on the temperature 1
- - B derived from equation ( 12) shows
it to be ind.ependent of the temperature.
Harned and Robinson
point out as each is equally applicable, over the limited
temperature range available, each equation is equally applicable
end therefore it cennot as yet be stated whether
on temperature or not.
If o.Cp is a function
depends
temperature
it does not change by more than about .1 cal. deg.
The importence of the thermochemice.l quanti ties
derived from Harned end Embree 1 s equation, rneri ts some brief
discus
on as to their accuracy.
-75The value of
~0
is accurate
the error in its
estlmation is less than 0.1%, with the order of
accuracy claimed by Harned and co-workers.
Gla.Sstone95
points out the measurement of M by this means has long been
recognised as more convenient and exact than thermochemical
measurements ..
Owing to the di
by di
culty of determining a quantity
erentiation the values of
are subject to
a, large error estimated of the order of 100 calories.
This
error is due to empirical curve fitting, and so is minimj.sed
by the study of a large· temperature range.
deriv
work therefom>e,
cannot be consi
In the present
from Harned and. Elnbree 1 s equa t:t on
red as accurate.
tzer96, however, estimates
the error in direct calorimetric determinations at 3 - 15% and
that the values of
obtained by the two methods generally
lie within these limits.
The absolu:be value of this quantity is probably
1
known within± 3 calories deg:
error is less than this, as in
IJ.he error in
but the relative
H0 •
is determined by the error in
ana_ therefore amounts to approximately 0. 3
calories per degree.
-7
The e,bove method of computation' gives best results in the
neighbourhood of the maximum of log K
i.e. 10° - 40°· Also
the above mentioned errors are of the same order
temperatures within this range.
all
Unfortunately no
the1~0-
chemical data is avellab1e for comparison in the present work.
Pi tzer96 has pointed out ,that
for most of
weak electrolytes so far measured is of the order - 40 cals.
~~
If this value is assum
de g.
ionisation constant
to apply to the first
electrolytes, then by the follow-
of
ing thermodynamic formulae
£).H =
£~G
~So
T
+
ln T
RT ln K =
=
bOp
+
~Cp
T,
T..
t:Cp ( T - T 1n T)
-
/
some temperature say T then
K is known, and hence
G
-
=
(T -
T+
1
T
T - T ln T)
end
T"
::::::
= -40
298.1°
then
=
246
5425
8.1
T
+
40 T
T
or an equation
1n K •
ln K
which
terms of
=
Const.
+
T
A+
i
cons t •
- 20 log T
20 log T
the srune form as arbitrary expressions for log Kin
T~
as simplified by the
C!ICP assumption..
This
-77TABLE
XIV
Derived 'I!!J?rmochemica1 Quantities
-P :::: 5
10 Water
X
10-5
1 Acetone¥
tOe
e:.G0 Cals.
l:s.H0 Cal s.
Equation ( 3) R.& R. Is
Eguati~m
Eguatio!!iSl. H.& R. 1 s Eguatio
150
539·1
614
6546
6547
20
361..4
419
6651
6652
25
169.2
222
6757
6760
30
-33·6
21
6871
6871
35
-251.7
-185
6990
6986
(~0~ ca1s. deg. -a
Equation ( 4) H.&.R.}s Equation
~0
-1
Ca1s. deg.
Equation ~ 6) H. &IL I 8 Equation
150
- 34· 21
-38·59
-20.85
-20.60
20°
-36· 81
-39.26
-21.47
-21.27
250
-39. L16
-39.93
-22.11
-21.94
300
-42.23
-40.60
-22.79
-22. 61
35°
-44.89
-41.27
-23 .. 51
-23.28
-78data, including the present work as shown
equation expresses
in Graph V, and extends over a wider temperature range, even
water for vrhi
includi
e
n in
This
is off-set by a consi.derable loss in
simplicity, es the two parameters A and B must be obtained to a
reproduc
and
11
ficant figures if log K is to be
e number of si
atively
within experimental error.
For ease of calculation
ence, therefore, the relationship of Harned
ide rule" conv
and Embree is to be preferred.
Pi tzer 1 s equation contains two arbitrary constants A
and B as does that of H.9.rned and Embree, and he points out that
for T
= 298.1°
and
e
25°
(t- e)
2
=
-40 .. 6 - o.273 (25
e)
the two equations yield essentially the same results.
where
e
is not of
water, Pitzer's equation
0
is the closer approximation.
dissoci
cases
He also estimated
80
the first
calories, an
ion constt7.nts to be of the
observation confirmed in the present work ..
The above
s has been confined to purely a
thermodynamical treatment of the ioni
a consid.eration of interparticle forces.
on eqtlilibrium, without
Moelwyn-Hughes95 has
derived from 1cinetic considerations a n sem:l.-empi
for the dissociation constant of
cal 11 equation
ectrolytes,
From
-79equilibrium constant measurements little or no informe.tion
concerning the absolute rB.te of the
for~Jvard
and back reactions
can be obtained,·but the converse is not true.
Moelwyn-Hughes
obtains expresstons for the ra. te of dissociation of unionised
molecules a.nd the re.te of recombin.s.tion of tb.e ions, whence K
&
=
He clerives vo.1ues of K, the eq1J.i1tbrium constant, of the
kli!,.
orcler 10-5 which on differentiation give ACS
- 38 calories.
He points out thet it is noteworthy that in only one type does
ocg
fall below -30.0) nernely for amino acids functioning as
bases.
In all other cases 1
c~
is
- 30 calories.
Anotb.er
observation in this same paper, is that ~C~ values increase
slightly v.ri th tempere.ture as is predicted by the theoretical
equation he derives
NoZa Zg,
£'17"' T. + (112.)
Dr
v;rhere
ZA
(lf)p
= charge on positive ion (+1 in this case
Za -
=
charge on negative ion (-0}
~J
where
HT 2 (( llln
::::: viscosity coeff.
)T
)P
D
= eli electric cons te.nt of the rnedi um
N0
r
=
=
mean <'listB.nce of anoroach of the ions
L
-
latent heat per mol. of solvent, for which most
AV<").gadro 's Number
of the aveilable data refers to aqueou.s solutions
e.t 25°.
This is a.n improvement on Pi tze!'' 1 s assumption that
pencl.ent of temperature.
6C:B
is inde-
-80Gurney 98 has carri ect the analy
e electrostatic forces and non electro-
proposed to s
ste.tic forces, and has interpreted
hes been
la
erent types of ionic
s basis.
equilibria on
r
s further
ties99;
to show some interesting
in general, reections mey be
ed in three
groups
HA +
H o+
H2o
H
3
<-
+NH 3RCOOH
NH2R COO
H0 0
o+
+
3
coo- + Oir
H20
+
+NH 3Rcoo-
ts vri th a common
comparing all the
erence reaction,
such as the ionisation of water, the relati
becomes more
signifl01mt.
Then from the above
HA + H2o
+ H20
+NH R
3
coo-
+H 2o
+H2o
This classi
(1)
H o+
A-
3
+
!::!
orr
01
+NH R COOH - og-
3
NH2 R
coo-
cation J
is more clos
to
+H
o+
3
sever~tl
y associ
-41
•
• • • • 41 • • (
a)
0 ......... (b)
5 •••••.••• (c)
- 20 ....•... ' • (d)
important conclttsl ons.
ed VJi 1;h the type of
ree.ction than the other thermodynamic quan
and
o
ties
-81-
The i soelectri c reaction prod.uces prEwti cally
( 11)
no cha.nge in hea. t capacity, while equation
(a) forming ions from neutral molecules produces the e:reatest chaJ1ge in heat capacity.
m.eactions (c) and (d) are of the same electrical
( 111)
type but give rise to C0°
p of quite different
magnitudes.
By subtracting equation (c) from equation (d) a second isoelectric reaction is obtained
with a characteristic value of Cl,Cp.
This clearly shows chemical as well as electrical
type of reaction is important in determining the magnitude of t~Cc
I
The Medium and Dissociation Constant.
The change in dissociation constant with solvent can
be discussed on1y in an approximate1y quantitative manner.
As
the d.lelectric constant is lowered, inter-ionic attraction
increases, and the dissociation const8nt falls as shown in-values at
1
against f)
25°.
It was shown on page 10 that a plot of PK
should give a straight line.
Harned and IDnbree33
considered this relatl on ship holds for acetl c acid in methanol
water mixtures, .s.nd the graph shows this is also the case for
the second dissociation constant of Oxalic Acid in meth<mol-
-82GRAPH VI ,
Ref. 3,
Ref. 4.
o--o
• 0150
±.......L L
1
I
~
Refo-5•
L
L h_CL t
.e ~6o
L
L
i.L...l~
!+!:
Acid in m
(Vvater)
D
=
D =
D ""
PK
PK
= 4· 415
-
•
4.904
5.079
34
D •
.(vV'ater)
D
D
=
:::
PK
78.04
73·52
PK
PK
=
-
:::
4· 415
4·956
36
(Water)
(Water)
D
D
::::::
D
:::
D
=
D
:::
=
D . =
78.04
74.05
69 .. 20
78.04
74.05
69.2
PK
:::
PK
:::::
PK
:::
PK
•
PK
=
4-201
4·387
4-721
4· 300
= 4-455
4.825
le for benzoic acid, the three points
water mixtures,
available are insufficient to decide.
J:lhe graph does show, however, that the dielectric
1
constant is the predomi
factor.
'"
¥1ynne J ones 100 has suggested
e extrapolation of
this mixed solvent data to a hypothetical D
electrostatic effects are eliminated.
extrapolated K as the
11
whereby
desi
es the
intrinsic strength 11 , and suggests
and Embree state the.t extrapolation of
40% methanol 1 s not valid,
This change
has
1
ng K to acid constitution.
its usefulness in
cons
=
Harned
r data beyond_
:nly not to D =JI>.
cert
ssociation constant with
en the study of
electric
101
zutani
,
chaell s
102
1
nderstrom - Long
, Pring 3, Cray and Westrip 1 4
practi
and turned
use
analy
acids such as HCl are not affect
others
cal chemistry.
by
of
Strong
ectric
consta.nt, b ei:ng completely di ssocla ted, v.rhereas weak acids
such as <we
ectr c constant
lowering of
acetone.
r:n tra
on of a mixture
ti on of' say 90%
the
a s
in water 1ni 11 therefore give the to
tit
to the strong
acid
dity
e the
This has proved of
for exe.mple, in the
10
tents for llfl"ee HCln. 3
and
acidity wh1le
on in 90(7~ acetone solution will
bi ochemi.
by a
c acid are practically suppress
v
e in
sis of gastric con-
-85-
1 ..
From measurements of cells vvi thout liquid junction,
the standard molal potential of the Ag 01 - Ag electrode
5° intervals from 15° - 45° in-
has been evaluated e.t
acetone 1 part.
elusive, in a solvent of water 10 parts
11.
Using the method of He>rned and Ehlers of cells without l:Lquid junction, the dissociation constant of acetic
acid has been evaluated from
15° - 35° at 5° intervals in
the same solvent.
111 ..
The empirict:tl relationship of HE1rned and Embree
Log K- Log
Km = 5
x lo-5 ( t - 6) 2 •..•.... (a)
is shown to reproduce the experimental dissociation
constants within experimental error.
lV.
From equation (a) the heats of ionisation O.H 0 ,
the
difference of specific heats of the ions and undissociated
v.
0
0
molecule
Cp' the free energy change b»G
change
of the ionisation reaction have been calcule.tect.
The values of
[)H
0
and the entropy
S0 from Harned and
Robinson 1 s equ.a ti on
have been computed and compared with the values obtained
above.
Vl..
empi
relations of Pitzer and Mo
Hughes have been discussed.
rrhe appll cation
Vll ..
acid
tration
been
these results to differential
cated,.
...87.-.
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31
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( 1937)
).4,
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ERRATUM
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