I
Peter A. Rock University of Callfornla Davis, 95616
Electrochemical Double Cells
Electrochemical double cells without liquid junction offer unique advantages for the study of a variety of chemical reactions, including solute-transfer reactions, protontransfer reactions, isotope-exchange reactions, and phase changes, among others. The basic idea involved in the use of electrochemical douhle cells is to set up the two appropriate electrochemical cells, connected without liquid junction through a common central electrode, in series-opposition t o one another. The series-opposition, double-cell arrangement enables one to measure directly the thermodynamic properties of the reaction of interest, rather than obtaining the desired quantity as a small difference between two large, separately measured numbers. Transfer Reactions Helmholtz was apparently the first to use a double cell. Helmholtz double cells are usually referred to as concentration cells without transference ( 1 ) .The net cell reaction of a concentration cell involves the transfer of solute from a solution of one concentration to a solution of another concentration. For example, the electrode reactions of the double (concentration) cell
(where Xz and Xz'are the mole fractions of NaCl in the respective cell solutions) is NaCKX,H,O)
=
NaCIiX,',D20)
(5)
and
For cell (4) a0 + 0,because AGO Z 0 for reaction (5); AGO for reaction (5)is the standard Gibbs energy change (on the mole fraction composition scale) for the transfer of NaCl from light to heavy water. Electrochemical douhle cells can be used to measure directly ApK, values for Bronsted acids. For example, the following double cell has been used t o determine directly Hammett suhstituent constants (2)
Ag(s)lAgCl(s)lNaCl(aam,)lNaiHg)lNaCliaqm,)lAgCl(s)lAg(s) NaCl(%)lH,(g,Pt)
(1
are
+
+
(7)
Ads) CI-(m,) = AgClis) e~ a + ( m ,+ ) e- = Na(Hg) ) Na(Hg) = ~ a + ( m+~ eAgCKs) e = Ag(s) C1-(m,)
(where X represents a meta or para suhstituent, and the mi values are the molalities in water). The Hammett substituent constant, 0 , is defined by the relation
and the net cell reaction is given by the sum of the above four electrode reactions, namely
where K' is the thermodynamic acid dissociation constant for benzoic acid in water a t 2 5 T , and K is the thermodynamic dissociation constant of a meta- or para- substituted benzoic acid in water a t 25% The net cell reaction for cell (7) is (2) (where R = right side and L = left side of the cell)
+
+
a
The dilute sodium amalgam, Na(Hg), functions as the cathode of the left half of the double cell and the anode of the right half of the double cell, and consequently the Na(Hg) does not appear in the net cell reaction. Because the Na(Hg) does not appear in the net cell reaction, we do not need to know the concentration of sodium in the amalgam. Similarly, the Ag(s) and AgCl(s) phases do not appear in the net cell reaction because they are common to both halves of the cell. Of course, in such a case the pair of silver-silver chloride electrodes should he checked for bias potentials by a measurement of the cell voltage when m l mz. Application of the Nernst equation to reaction (2) yields
-
A knowledge of ary,cl(,q,m,,, together with a measured value of 8 gives ~ N ~ c I ( ~ ~ . ~ ~ ~ In cell (1) the solvent is the same in both halves of the double ceil; if a different solvent is chosen for the two cell solutions, then the double cell can be used to measure Gibhs energies of transfer of the solute from one solvent to the other. For example, the overall cell reaction of the double cell
= log(K1K')
(8)
Application of the Nernst equation to reaction (9) under conditions where the hydrogen pressures are equal, and using the thermodynamic expressions for K' and K, together with eqn. (E), yields (w = RTIF)
where the activity coefficient term is essentially zero when the ionic strengths of the two cell solutions are equal. Equation (10) shows that the double cell (9) gives a directly, rather than as a small difference between two relatively large numbers. Isotope-Exchange Reactions Electrochemical douhle cells have been used to study a variety of isotope-exchange reactions (3, 4). The cell diagram of a douhle cell used for the study of lithium-isotope-exchange reactions is Volume 52. Number 12, December 1975 / 787
+
The following electrode reactions orcur consecutively (leftto-riaht) at the four electrodes of the double rell 'Li(s1 = '~i+(soln) eTlBr(s) e- = TI(Hg) Br-(sold TKHg) Br-(soh) = TIBr(sj + e'~i+(soln) e- = 'Li(s) The net cell reaction is given by the sum of these four electrode reactions, namely
+
'Li(s)
+
+
+
+
+ 'LiBdsoln) = 'Li(sj + ' ~ i ~ d s o l n )
(12)
For the case in which propylene carbonate is the solvent the measured value of 6O for reaction (12) is 6O = 0.76 f 0.13 mV, whicb corresponds to an equilibrium constant of K = 1.030 0.005 (297'K, strong electrolyte standard states). The investigation of lithium-isotope-exchange reactions involving the isotopic metals and the isotopic ions in aqueous solution presents a special problem in cell design because of the spontaneous reaction of lithium metal with water. This problem can he overcome by means of a quadruple cell (51, which is designed so as to isolate the lithium metal from the aqueous phase. The cell diagram of the quadruple cell used is
*
where pc denotes the solvent propylene carbonate. The electrode reactions of the quadruple cell are
D,(g)
+ 2HCl(soln')
-
D,(g,Pt)lDCl(soln)T1Cl(s)~TI(Hg)lTICI(s)lHCl(soln')lH2(g.Pt) (15) where the prime allows for the possibility that the solvents may be different in the two halves of the double cell. The electrode reactions for the douhle cell (15) are as follows 788 / Journal of Chemical Education
+ +
= Hl(g)
+ 2DCl(soln)
(16) A case in which the solvent is the same on both halves of the double cell involves the solvent N,N-dimethylfurmamide (DMF) (6): the net cell reaction is
for which go = 7.64 f 0.38 mV and K = 1.82 f 0.05 (297'K, strong electrolyte standard states). A case in which the solvent is different in the two halves of the double cell is (7) DdgPt) I DCKROD)I T1CKs)jTl(Hg)/TICl(s)lHCI(ROH)IH,(gpt) (18) (where ROH = CH3(CHz)4CHz0H and ROD = CH3(CH2)&H20D). The net cell reaction for cell (18) is
The results of measurements on cell (18) yield an 6l value for reaction (19) of 6l = 4.03 0.95 mV, whicb corresponds to an equilibrium constant of 1.37 f 0.10 (296OK, strong electrolytes, mole fraction composition scale). Isotope-exchange reactions involving exchange between ions in solution and solid salts of the ions can be studied in electrochemical double cells involving electrodes of the third kind (8,9). For example, the reaction
*
can be studied in the douhle cell (10) Pb(Hg) "c~co,(s) = PbCO,(s) "Caaf(aq) 2eHg,Cl,(s) 2e- = 2Hg(l) 2'2-(aq) 2Hg(l) XI-(aq) = Hg,Cl,(s) + 2ePbCO,(s) + "CaZ+(aq) 2e- = Pb(Hg) qo&C!O&) The electrode reactions of cell (21) are Pb(Hg)IPbCOJ(s),"CaCO,(s~l'BCaCl,(aq)/Hg,Cl,(s)l Hg(1)2-phase (21) PMHg) -Hg(l)1 Hg,Cl,(s)l 'o~a~l,(aq)l'oCa~~,(s)pb~~,(s)l 2-phase The sum of the four electrode reactions yields reaction (20). Phase Transformations Electrochemical douhle cells can be used, a t least in principle, to determine directly the Gibbs energy change associated with phase transformations. For example, the net cell reaction of the double cell Hg(l)l HgO(s,redJNaOH(aq,m,)lNa(Hg)l NaOH(aq,mdHgO(s,yellow)lHdl) (22) is HgO(s,yellow) = HgO(s,rrd) (23) and AG for the phase transformation can he ohtained directly from the measured voltage. The calcite-to-aragonite phase transition is of considerable interest to geologists because of its use as a geobarometer. The electrochemical douhle cell Pb(Hg)lPbCO,(s),CaCO,(calcite) ICaCl,(aq,mJ Hg,Cl,(s)lHgKI> 2-phase Hg(l)I Hg,Ch(s) 1 CaClz4aq,m3ICaC03((aragonite)PbC03(s)lPb(Hg) 2-phase
+
Note that both the lithium amalgam and LiBr(pc) phases, as well as the central Hg(l) and HgzClz phases do not appear in the net cell reaction. Consequently, we do not need to know the concentrations of 7Li and 6Li in the amalgams, or of 7LiBr and 6LiBr in the propylene carbonate solutions. The key to the success of the above quadruple cell is the combination of a high overvoltage for hydrogen evolution on a mercury surface (-lV), together with a very low conThe recentration of lithium in the amalgam (XLI sults of measurements on the quadruple cell show that reaction (14) is indeed the cell reaction of the quadruple cell. The measured value is 1.16 f 0.30 mV, which corresponds to an equilibrium constant of 1.046 f 0.013 (297OK). The general cell diagram of a double cell that has been used to study hydrogen-isotope-exchange reactions is (6)
+
2D+(soln) 2e2Cl-(soh) 2TI(Hg) 2TICl(s) 2eH,(g)
The net cell reaction is given by the sum of the four electrode reactions
+
and the sum of the above eight electrode reactions yields
-
D & (l)! 2TICKs) 2e- = 2TKHg) + XI-(soln') = 2~+(soln')2e- =
+
+
+
+
+
+
(24)
has the net cell reaction
case the second and third electrode reactions given ahove for cell (26) become 6 ~ + ( 4 % ) 6X(memb) = 6 ~ ~ + ( m e m b ) 6 ~ ~ ' ( m e m b )= 6 ~ + ( m ) 6X(memb) where X is the ion-carrier in the liquid ion-exchanger phase (e.g., valinomycin or a suitable crown ether in n-hexanol). The use of electrochemical double cells in the study of redox couples has already heen described (13). T o the best of the author's knowledge the principles involved in the desien of electrochemical double cells have yet to he exploited hy electn~chemisrsin thu design of rerharreable batteries. All commerciallv a~lccessful.recharpeahle%attery systems are cells witho& liquid junction that involve only a single electrolyte phase. A cell with liquid junction he., two dissimilar, interdiffusing, electrolyte solutions in contact) is not useful in a rechargeable battery because the two electrolyte solutions would eventually intermix. However, liquid junctions can often he eliminated by the ceutral-electrode technique used in douhle cells, as can be seen in the following modification of the Daniel1 cell
+
The basic assumption underlying cells (22) and (24) is that the presence of crystals of a particular phase of a suhstance will determine the soluhility of that phase in the cell electrolyte. Presumably, in the absence of crystals of the more stable phase, the solubility will he determined by the crystals of the less stable phase. Electrochemical douhle cells appear to have considerable (as yet largely unexploited) potential for the study of phase transformations. Gibbs Energies of Formation
Electrochemical cells have been, and continue to he, a major source of thermodynamic data on chemical compounds. The use of douhle cells allows the extension of these electrochemical methods to chemical compounds involving more than one type of cation or anion. For example, the douhle cell (11) Zn(Hg)l K,ZnJFe(CNX~~SH,O(s)lK,Fe(CN),(aqmJIK(Hg> satd -0.01% -KCl(a%%)lHg,Cl,(s)/ @(I) (26) has the following electrode reactions
The net cell reaction is given by the sum of the ahove four electrode reactions
Thus the douhle cell (26) enables us to determine, in a cell without liquid junction, the thermodynamic properties of the mixed-cationic salt K2Zns[Fe(CN)]2.8H20(s). In all of the douhle cells discussed in this section and in the preceding sections the common central electrode was either an alkali metal amalgam electrode or a conventional anionic-responsive electrode of the second kind. However, the common central electrode can he replaced by an ionselective, liquid-ion-exchanger phase, or an ion-selective, electrolytically conducting crystalline phase, as is done in the wide variety of commercial ion-selective electrodes (12). For example, the potassium amalgam in cell (26) could he replaced by a Kt-selective .liquid-ion-exchanger phase, which is separated from the two cell electrolytes by means of millipore acetate filter discs that have been specially treated to render them hydrophobic (12). In such a
+
Zn(s)lZnSO,(ad I Hg,S04(s)/Hg(l)lHg80
