Colin A. Vincent St. Salvatorts College I Thermodynamic parameters from

University of St. Andrews st. Andrews, Fife, Scotland 1 an Electrochemical Cell

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 a t 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 transi- tions, and AC, is the change in total heat capacity ac- companying the reaction. Now provided that the temperature range for the investigation of the cell reaction, TI t o T%, is such that

ST: A c - ~ T

and

are negligible and that no phase changes occur within it, we can say that

AG = AH - TAS

where

and

Further

For standard states we therefore have three basic equa-

tions for deriving thermodynamic parameters from cell measurements

AGO = -zFEo

bEO AS* = LF - - bT

and

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

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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 di- vider 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 proh-

lem 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 (Beck- man 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 approxi- mately 0.1 M HC1, was prepared by diluting "AnalaR" hydro- chloric acid with disbilled water. Oxygen was removed from the solution by passing oxygen-free nitrogen through it. The deoxy- genated solution was then carefully added to the cell with mini- mum 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

easily prepared second type (Fig. lA), formed by the chloridiaa- tion of silver wire.

The thermd-electrolytic electrodes which have been described in detail hv Bates (7) and elsewhere. were constructed bv sealine a small p l~ t inum 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 a t 90°C before being reduced to silver a t 4SO°C. A further ooat of paste was ap- plied and the procedure repeated. Each electrode finally can- tained about 60 mg of silver oxide. The electrodes were ehlari- dized 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 w a 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

I t was straightforward to show that the emf was independent of the concentration of chloride ion; nor was i t 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, i t 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. I t 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.

366 / Journal of Chemical Education

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

2Ag(s) + Hg~Ch(8) + 2AgCl(s) + 2Hg(l)

we have AGO = -zFE'

= -2 X 96,491 X 0.0456 = -8 .80kJ

and bE0 ASQ = +zF - bT

= 2 X 96,491 X 3 . 3 4 X lo-' = 64.5 J°K-1

Thus TASo = 19.22 kJ for T = 298'K

and

Discussion

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 a t 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

Sommcl, = 195.8 J0K-' (16)

Therefore

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).

I t may be noted that the standard entropy of two moles of silver chloride a t 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<-' for two moles). There remains a difference of approximately 23.6 JQK-I mole-I between the entropies of the two metals.

To investigate this further, it is instrnctive to examine the C, against T and C,/T against T curves as shown in Figures 3 and 4, respectively. C , data from 15'K to 300°K for mercury were taken from the work of Busey and Giauque (15) and for silver from Meads, Forsythe, and Giauque (16). For both metals points on the curves below 10°K were determined from the limiting Debye approximation

assuming that C , = Cp over this temperature range. OD, the Debye temperature was taken as 90°1< for

Volume 47, Number 5, May 1970 / 367

300 200 1 0 0

r c:n) Figure 4. Plot of Cp versus T for Hg ond Ag. Shaded orea represent%

mercury and 215'Ii for silver. I n Figure 4 the shaded area corresponds to the 23.6

J 0 I i - 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

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 a t low temperatures.

Literature Cited

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(1955). (5 ) Lmmue , M. H.. AND STOUQHTON, R. W.. 3. CHEM. EDUC.. 39. 230

(1962). (6) HILL^. G. J.. Ann IVEB, D. J . G.. "Referenoe Electrodes." (Editors:

Ivas, D. J. G., hno Jnaz.G. J.), Academic Press. London, 1961, p. ."- MU.

(7) BITES. R. G.. "Eleotrometric pH Determination," John Wiley & Sona. Ine..New York, 1954,p.200.

(8) VINCENT. C. A,. AND \\'ARD, J. G.. J. C H E M . E Y Y C . , ~ ~ . ~ ~ ~ (1969). (Y) U ~ r c n , H.. ~~oS~leabz,G. Z.. Z.physih. Chem.. 177,103 (1936).

(10) Knuez. K.. Gosmz . E. P., AND PETERU~LLER, EL. 2. Richtiochem. 1981, 55, 405.

(11) MncINNEa. D. A,. "The Principles of Eleotro~hemistry." Dover Publi- estiona, N e w York, 1 9 6 1 , ~ . 114.

(12) L E ~ I S , G. N.. AND RANDAL= M.. (Revi~ed by: PITZER. K. S., AND Ilnrwzn, L.) (2nd ed.) "Thermodynamies." MeGrsu,-liill. New York. 1 9 6 1 , ~ . 674.

(13) B u s ~ r , R. H.. AND Guuaa., W. F., J . Amer. Chern. Soc.,75,806 (1953). (14) EnaTUAN, E. D., r m Wmaen, R. T., J . Chem. P h ~ s . . 1,444 (1933). (15) MEAL?^, P. F., F o n s r ~ x ~ . \!'. R., *No Gr~uQum. W. F.. J. Amer. Chem. *"" 6 , ,on" < > . , A > , -"*., -", .""" (161 Lmtar~n. W. M.. "Oxidatim Potenti&!' (2nd ed,. Prentice-Hall. N e w . . . .

york, i 0 5 2 , ~ . w z . (17) POGLITZER, F., Z. EleLlroehcm., 19,513 (1913). (18) Dz Rossl, M., PECCI. G., A N D SCROIATI, I>., Rie. Sci., 37, 342 (1967).

368 / Journol of Chemicol Education