Vincent_JCE1970p0365..

I Colin A. Vincent
St. Salvatorts College
1 University of St. Andrews
st. Andrews, Fife, Scotland
In the teaching of thermodynamics it is
common to explain how the free energy and entropy
changes of a reaction may he determined by measuring
the electromotive force of a suitable electrochemical
cell over a range of temperatures. The free energy
change is related to the emf by
where z is the number of electrons tranferred in the
cell equation and F is Faraday's constant. Also
where AHo and ASo refer to changes at absolute zero.
ZL is the sum of molar latent heats corresponding to
phase transitions occurring at T,K (where TL < T),
Z(L/T,) defines the entropy due to such phase transitions,
and AC, is the change in total heat capacity accompanying
the reaction. Now provided that the
temperature range for the investigation of the cell
reaction, TI to T%, is such that
ST: Ac-~T
and
are negligible and that no phase changes occur within
it, we can say that
where
and
Further
AG = AH - TAS
For standard states we therefore have three basic equa-
Thermodynamic parameters from
an Electrochemical Cell
tions for deriving thermodynamic parameters from cell
measurements
and
AGO = -zFEo
bEO
AS* = LF --
bT
In practice however, it is not easy to illustrate these
relationships in a simple manner: the main reason is
that most reactions for which reversible cells may be
set up have very low entropy changes. They have
therefore small temperature coefficients of emf, and
measuring instruments of great precision are required
for their investigation. A notable exception to this is
a system involving a reactant in the gas phase, as in the
cell
Pt,HnlHClIAgClIAg
The use of a hydrogen electrode requires a supply of the
gas of adequate purity and involves many difficulties
at the teaching level.
The reaction now to be discussed has a number of
interesting features from the theoretical point of view
and many practical advantages
2Ag(s) + HgsCIds) - 2Hg(l) + 2AgCKs)
The electrochemistry of this reaction has been treated
a number of times in the literature (1-5); here a cell
of simple construction is described which permits a
reasonably accurate assessment of the thermodynamic
parameters with unsophisticated equipment. The cell
is
and the half-cell reactions are
The electrode potentials are given respectively, by
RT
El = EOA~IA~CIICI- - - In act-
F
and
Volume 47, Number 5, May 1970 / 365

Ed, = & - E,
= EOH~IHC.CI~ICI- - E0i\~~hgc~~ci-
= EOdl
Thc cell emjis independent of the activity of the chloride
ion in solution and is thus unaffected by the chloride
salt used, its concentration, the solvent, and the presence
of other electrolytes, provided that the electrodes remain
reversible solely to the chloride ion.
There are three particular practical advantages of
using this cell for teaching purposes
1) A relat.ively high value of bE/aT coupled withavery small
emf permits sufficiently accurate meawrements to he made with
"stodent!' Poggendorf potent,iomelers by using the potential divider
key in the 0.1 position-i.e., reading 0-170 mV.
2) The electrodes, which are fairly simple to - prepare, - are not,
readily polarized.
3) There is no liquid junction and hence theverydifficult prohlem
of variation of liquid junction potential with temperature is
eliminated.
Experimental
The cell and electrodes are shown in Figure 1. The cell, (C),
consist,^ of a glass U-tube with one wide and one narrow limb.
The wide limb contains the electrodes and cell solution while the
narrow tuhe permits electrical connection to he made to the mer-
cury of the calomel electrode by means of the plstinum wire
contact (Dl.
Figure 1. Cell and electroder.
Calmnrl Elrctrodc. This was prepared aft,er the mrtnner of Hills
and Ives (6). Mercury was chemically purified in the standard
manner and distilled. Mercurous chloride was precipitated from
0.1 M HCl by acidified Hg2(NO&; the precipitate was stirred for
24 hr during which time the HCI was decanted and replaced three
bimes. The cxlomel was filtered, washed, and finally dried under
vacuum. A few milligrams were then taken and shaken with 1
ml of clean mernny ta produce a. calomel "skin!' The cell was
rendered hydrophobic by treatment with "Desicote" liquid (Beckman
Instruments Ltd.) to prevent the so-called "wedge effect"
where cell solution seeping between the mercury and cell walls
produces erratic behavior in the electrode. The electrode was
iiet up by introducing mercury to the cell and then transferring a
nmall amount of the calomel skin to bhe mercury surface, over
which it rapidly spread. The cell solut,ion, normally approximately
0.1 M HC1, was prepared by diluting "AnalaR" hydrochloric
acid with disbilled water. Oxygen was removed from the
solution by passing oxygen-free nitrogen through it. The deoxygenated
solution was then carefully added to the cell with minimum
disturbance of the mercury surface.
SilverISilver Chloride Electrode. Two tvoes of AelAeClIC1-
-, -
were uskd. The first (Fig. 1B) of the thermal-electrolytic type,
proved more reliable over the long term compared wit,h the more
366 / Journal of Chemical Education
easily prepared second type (Fig. lA), formed by the chloridiaation
of silver wire.
The thermd-electrolytic electrodes which have been described
in detail hv Bates (7) and elsewhere. were constructed bv sealine
a small pl~tinum wire spiral into a soda-glass tube in suih a way
that the wire protruded inside the tuhe to form a, mercury contact.
After cleaning the spirals in hailing concentrated HNOs, apaste of
spectroscopicdy pure silver oxide in distilled water was applied to
them. This paste was then dried out in an oven at 90°C before
being reduced to silver at 4SO°C. A further ooat of paste was applied
and the procedure repeated. Each electrode finally cantained
about 60 mg of silver oxide. The electrodes were ehlaridized
by making them the anodes of electrolytic cells containing
preelectralyzed 1.0 M HC1 as electrolyte solution and an isolated
platinum cathode. Using the amperostat described previously
(S), the electrolyses were carried out at a constant current of 10
mA for 800 sec to produce a -15% convemion to silver chloride.
The simpler type of AgjAgCl/Cl-electrodes were prepared from
10 cm of 0.02 in. best grade silver wire. The latter wa wound in
a wide spiral (Fig. 1.4) and then etched by treating it with 5 M
HNO. for 60 sec. The wire was then thoroughly washed with
distilled water before beine soaked in oonoentrated ammonia.
use.
Emjmeasurementk were made with a "portable potentiometer''
(W. G. Pye and Co. Ltd.) which with its range switch at X0.1 had
an absolute accuracv of 3~0.1 mV. A number of results were also
read on a digital voltmeter (Solmtron Electronic Group Ltd.,
type LM1420.2).
The cell wss immersed in a thermostatted bath, the tempers,
ture of which could he regulated to *O.OSDC.
Results
It was straightforward to show that the emf was
independent of the concentration of chloride ion;
nor was it influeuced by the medium. A range of HC1
and KC1 concentrations were studied. Further solu-
tions were made up in dioxan-water mixtures and others
had quantities of NaCIOa added to them. The emf
was unaffected.
While cells with both types of AglAgCIIC1- electrode
maintained constant emf values within better than 0.1
mV for several days, it was found that a number of cells
with type A electrodes (based on silver wire) showed
variations of *1 mV after numerous heating and
cooling cycles. It was essential to ensure that none
of the materials used was contaminated with bromide
or iodide ion. Erratic results were sometimes oh-
tained if the precautions described in the Experimental
section were not carried out.
The mean value for the cell emfat 298'IC was 45.6 mV,
which agrees well with previous measurements (1, 3).
The emf as a function of temperature over the range
15-50°C is shown in Figure 2. Within the accuracy
Figure 2. Typical experimental variation of cell voltage with temperature.

of the present measurements the results may be repre-
sented by a straight line of slope +3.34 X V°K-1,
which is again in agreement with the findings of other
workers. For the reaction
we have
and
Thus
and
Discussion
2Ag(s) + Hg~Ch(8) + 2AgCl(s) + 2Hg(l)
AGO = -zFE'
= -2 X 96,491 X 0.0456
= -8.80kJ
bE0
ASQ = +zF -
bT
= 2 X 96,491 X 3.34 X lo-'
= 64.5 J°K-1
TASo = 19.22 kJ for T = 298'K
Perhaps the main interest in this reaction lies in the
fact that the thermodynamic parameters derived from
the cell measurements refer to pure single components,
and do not involve solution species. Provided that
both electrodes remain reversible and have their po-
tentials determined solely by the chloride ion, what
comprises the solution phase is of no consequence.
Attempts have been made in the past to measure the
emf of the cell in nonaqueous solvents, mainly with a
view to checking the reversibility of the electrodes for
their subsequent use as reference electrodes. Un-
fortunately, irreproducible results were obtained
with acetone (9), acetonitrile (9, lo), and cyclohexanol
(lo), pfobably due to disproportionation of the mer-
curous ion. A constant value of 46.5 mV at 25'C after
an equilibration period has been found with formamide
as solvent (18).
A somewhat unusual feature of the reaction, as is
pointed out by MacInnes (11), is that the enthalpy
change is opposite in sign to the free energy change-
that is to say, the reaction as written is a spontaneous
endothermic process.
The reaction enthalpy may be calculated from stan-
dard heats of formation determined from calorimetric
data (18). Thus
This compares well with the result from the cell, con-
sidering the uncertainty of the thermal data.
The reaction entropy may be derived from standard
entropy values determined from heat capacity measure-
ments together with data on the heat and temperature
of melting of mercury.
At 29X°K we have
Figure 3. Variation of speciflc heat with temperature for silver and
merFUry.
and
Therefore
Sommcl, = 195.8 J0K-' (16)
Again the agreement is very reasonable, since there is
considerable uncertainty in the standard entropy of
calomel, which may be lower than the value here
selected (17).
It may be noted that the standard entropy of two
moles of silver chloride at 29XoI< is almost the same as
that of one mole of mercurous chloride at the same
temperature. Hence the reaction entropy is effectively
that of
Now assuming the absence of phase changes in the solid
state the standard entropy of silver is
and for mercury is
where C, is the molar heat capacity at constant pressure
and L is the molar heat of fusion at T,, the melting
point. For mercury the heat of fusion is 2.295 kJ
mole-' at 234.3'1C (IS) so that the entropy of fusion
is 9.8 J°K-1 mole-I (or 19.6 JOI

300 200 100
r c:n)
Figure 4. Plot of Cp versus T for Hg ond Ag. Shaded orea represent%
mercury and 215'Ii for silver.
In Figure 4 the shaded area corresponds to the 23.6
J0Ii-I mole-' difference in the standard entropy of
the two metals. Using the Einstein or Debye sta-
tistical thermodynamic models of monatomic crystals,
one can explain this difference in terms of the mercury
atoms exerting weaker interatomic forces than the
368 / Journol of Chemicol Education
silver atoms. The mercury thus has a lower character-
istic (or cut-off) frequency of vibration in the lattice,
and more heat may therefore be absorbed by it at low
temperatures.
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