Standard Potentials of Solid-state Metal Ion-Selective Electrodes Manfred Koebell Orion Research Inc., Cambridge, Mass. 02139
The thermodynamic relationships for mixed metal sulfide electrodes of the type Ag2S-MeS are given. The standard potentials of these electrodes are determined by the activities of metal (or sulfur) In the sensing material. These activities depend strongly on the exact composition of the metal sulfldes. When silver metal is used as a direct electrical contact material, the activity of silver in the pellet Is fixed at 1.00. This in turn fixes the activity of metal of the second metal sulfide and, thus, the standard potential. In the case of an inert contact material like carbon, no activity is fixed, thus allowing for a wide range of standard potentials. An interesting situation arlses in the case of copperselective electrodes: whereas a carbon-contacted Ag2SCuS electrode may contain CuS, the system in equilibrium with a silver metal contact is Ag2S-Cu2S.
Ion selective electrodes based on mixed metal sulfides, one of which is silver sulfide, have been developed for copper2+, lead2+, and cadmium2+ ( I , 2). In the early versions of these electrodes, liquid internal reference systems were used, and they could therefore still be considered membrane electrodes. In these versions, the potential of the electrode at unit metal ion activity is determined by the properties of the internal reference system and the metal ion activity in the internal solution. No conclusion can be drawn about the standard potential of the sensing pellet material. A more recent design uses a solid state connection (silver metal) to the mixed sulfide pellet ( 3 ) , in which case it is meaningful to talk about the standard potential of the electrode. One possible way to treat this problem is to consider the electrode to be of the third kind, using the standard potential of silver and the solubility products of the two metal sulfides. There are, however, experimental data for single metal sulfide electrodes which do not agree with the theoretical values thus expected ( 4 ) . Although such Me/Me,S electrodes ( y = 1 or 2) give a Nernstian response when changing the metal ion activity in solution, the standard potentials are often more positive than theoretical. Furthermore, the contact material usually has little or no influence on the experimental values. Many of the experimentally observed facts can be better understood when the exact stoichiometry and the related activities of metal or sulfur of the sensing material are considered. The present paper discusses the basic thermodynamic quantities involved. [All values given in this paper refer to 25 "C. Energies are in cal/mole, potentials in mV, Present address, Brown, Boveri & Cie, CH-5401 Baden, Switzerland. (1) J. W. Ross in: "Ion Selective Electrodes," NBS Spec. Publ., 314, 79 (1969). (2) M. S. Frant. and J. W. Ross, U S . Patent, No. 3,591,464. (3) Orion Research Inc.. Cambridge, Mass., "Analytical Methods Guide." 1972-73. (4) G. Truempler, Z.Phys. dhem., 99, 9 (1921).
and standard potentials are referred to the standard hydrogen electrode (SHE).] The Standard Potentials of Silver Sulfide Electrodes. An especially simple situation exists for a sensing crystal consisting only of one single sulfide-e.g., silver sulfide. This case has already been discussed by Sato ( 5 ) ,and we shall take a slightly different approach. We consider the cell:
c
I
Ag
a
Iv' I
I
1
&a,'
b
Ag2+,S
111
I1
I
d
C
c
(1)
rv
Contacting silver sulfide with graphite is thermodynamically meaningful, because the chemical potential of electrons in silver sulfide is not infinitely small. This follows from the fact that silver sulfide has electronic conductivity in addition to ionic conductivity (6, 7 ) . The value of 6 defines the exact stoichiometry of the silver sulfide. If the transference number of silver ions in the aqueous phase I1 is 1.00 (unless redox systems are present, this is usually the case), the EMF of the cell is given by the difference of the chemical potentials of elementary silver in phases I and 111:
where 1 1 1 is~ the ~ ~chemical potential of elementary silver in the silver sulfide of a particular composition and ~ O the A ~ chemical potential of silver in pure silver metal (phase I). We have assumed that the chemical potential of Ag is constant over the entire thickness of the silver sulfide layer. This means, that the diffusion coefficient of the neutral species Ag must be reasonably high, which has been shown to be a characteristic property of the silver sulfide (6, 7 ) . This is due basically to its high ionic and electronic conductivities. Other metal sdfides usually have much smaller diffusion coefficients for neutral species, and we will refer to the consequences later. A more precise deduction of Equation 1 has been given by Wagner (8) in conjunction with corrosion theory and is based on the Nernst-Planck equation. Considering again cell I, the electronic current density at any point x between phase boundaries b and d is given by: N
where K , is the local electronic conductivity, p e the chemical potential of the electrons, and p the electric potential. z,, F , and x have their usual meaning. Assuming further mobility of silver ions only in the cell, we denote with subscript i the corresponding current density for silver ions: (5) M. Sato, Electrochim. Acta, 11, 361 (1966). (6) M. Koebel, N. Ibl, and A. M. Frei, Nectrochlm. Acta, 19, 287 (1974). (7) M. Koebel, Thesis, Swiss Federal Institute of Technology, No. 4853 (1972). ( 8 ) C. Wagner, Z.Phys. Chem. B, 21, 25 (1933).
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(3 ) As we are measuring the equilibrium potential of cell I, the external current density is zero. We therefore have:
ii
or
+
ie = 0
(4)
where
Making use of the general thermodynamic relation dpi
we obtain
+
dpe
=
the silver sulfide layer, as the diffusion coefficient of silver in its sulfide is sufficiently high. We therefore have:
(6)
dpAg
This is identical with Equation 1, as I ~ =A ~ Further, I I I ~ Ais~ the chemical potential of silver in silver sulfide, which depends on the exact stoichiometry of the compound. The composition range of Agz+&Shas been measured by Valverde (9) and found to be -3.5 X d /< +1.8 X IOw5a t 150 "C. According to Yushina, Karpachev, and Fedyaev (IO),the composition range is wider a t room temperature. Two points of composition of silver sulfide are readily established, corresponding to pellets in equilibrium with silver and sulfur, respectively. We first consider a silver sulfide in equilibrium with silver. In this case we have IIIpAg
Integrating Equation 7 over the phases I1 and 111, we obtain:
The integration has to be carried out over the entire thickness of phases I1 and 111; (PII thus denotes the potential a t the interface b in phase 11, and MII the potential a t the interface d in phase 111. The total EMF of cell I is then given by:
E = -
CPIV (@IV
-
(9)
cpIV# @ I I I ) + (@I11
((PI1
911) -k
-
PI)
+
(VI - C P I V , )
The potential differences (rplv - ( ~ I I I ) , - q),and ( p ~p~v') are given by the general equilibrium condition for electrons between these phases: IVPe
- FVIV =
I I Cle I
111P-e
FVII=
iie - F ~ = I
(10)
- FPI
(11)
Pe - F V I V ~
(12)
IPe
IV'
- FWIII
IvPe
=
IV* P
e
(13)
we obtain:
PAg
0
(16)
and, therefore, the EMF of cell I equals zero. Such a silver sulfide electrode, therefore, has the same standard potential as the parent metal electrode: Eo = f 7 9 9 mV us. NHE. It is usually realized in practice by contacting silver sulfide with silver metal or by treating silver sulfide with a strong reducing agent. When using a solid silver contact IIIAg2+&3IIvAg, the resulting interface is usually easily polarized, because the exchange of silver ions is slow a t this interface, unless special precautions are taken to increase this exchange current. The result is usually a more positive standard potential than expected (6, 7 ) . Let us now consider a silver sulfide pellet in equilibrium with sulfur. Silver sulfide prepared by precipitation under oxidizing conditions usually has this composition. It may also be obtained by heating a silver-rich silver sulfide in a sulfur atmosphere or by electrolyzing a silver-rich pellet in cell I with the positive pole on the right hand side. Clearly, in this case, an inert contact material such as graphite must be used. The chemical potential of silver in such a crystal is easily obtained from the equation describing the formation of silver sulfide:
2 Ag
+
S = Ag,S PAg
Combining Equations 8 to 12 and remembering
=
A G f 2 9 8 = -9360 c a l ( l Z ) (17) + PS =
pAg2S
(18)
As the deviations from stoichiometry are very small, the chemical potential of Ag2S corresponds to its standard (at 25 "C). We thus obtain: value PAg
= A G f Z g 8= -9360 c a l = pAg2s0
(19)
Using this value in Equation 1 we obtain E = $203 mV and the corresponding standard potential EO ( p s = 0 ) = +799 203 = +lo02 mV (NHE). A silver sulfide electrode thus may take any standard potential between the standard potential of the silver electrode and a value 203 mV more positive than the latter. By choosing silver as a contact material, the composition of silver sulfide is fixed. Speaking in terms of the phase rule, we lose one degree of freedom when we add another phase (Ag or S) to the silver sulfide ( F = N - R + 2 - P, where the number of chemical species, N = 3 [Ag, S,Ag2S], the number of chemical reactions, R = 1 (Equation 17), the number
+
The E M F therefore depends only on the integral given by Equation 14. When using silver sulfide as an ion selective electrode material, the following conditions are usually fulfilled: a) The transference number ti of the silver ions in phase I1 is usually 1.00. This condition no longer holds when redox systems are present in the solution which can react a t the electrodes by an electron transfer. As the silver ion conductivity of the solution decreases with decreasing sample silver ion concentration, small concentrations of redox systems will interfere much more a t lower silver concentrations. b) There is usually no gradient in the silver activity over 1560
(9) N. Valverde, Z. Phys. Chern. (frankfurtarn Main), 7 0 , 113 (1970). (10) L. D. Yushina, S. V. Karpachev, and Yu. S. Fedyaev, Soviet Electfochern., 8, 1513 (1972) (11) F. D. Rossini et a/., 'Selected Values of Chemical Thermodynamic Properties," NBS Circular 500 (1952).
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of phases: P = 1 [no free Ag or S present], and P = 2 [free Ag or S present]). Thus, there are three degrees of freedom F when only one phase exists (pressure, temperature, chemical potential of one species) but only two (e.g., pressure and temperature) when two phases coexist. This is the reason why graphite was chosen as a contact material of the Ag2S in cell I, which is not involved in Equilibrium 17. The Standard Potentials of Mixed AgzS-MeS Electrodes. Let us consider the cell: C
1
Me
1
1
Mew2+ Mel,,S Ag2*6S
1
C
(m
I I1 I11 IV This cell measures directly the difference in chemical po~ and tential of the metal Me between phase I ( p = ~pOMej phase I11 ( p 2 p~o M e~) . If all phases involved in this cell are in equilibrium with each otherrer, its E M F E is given by an equation similar to Equation 1: I 1 1 P M e - !M '/ eo = - 2FE (20) The standard potential of the mixed sulfide electrode then follows directly from the standard potential EOM~of the parent metal electrode:
IV'
As in the case of the silver sulfide electrode, the standard potential will therefore depend on the chemical potential of metal in the pellet. I t has been assumed that all phases are in equilibrium with each other. This means, that the following conditions must, be met: a) The exchange rate of charge-carriers (Me2+ or electrons) a t every interface of cell I1 must be high. b) This also implies a finite, nonzero value of the chemical potential of electrons in phase 111; Le., the sensing phase will show some electronic conductivity. c) For thermodynamical considerations, the sensing phase 111 consists now of two phases supposed to be in equilibrium with each other. The two equilibrium conditions relating them are the following:
2PAg PMe
+
PS
+ PS =
PAqS
(18)
PMeS
(22)
In practice situations with a third phase in equilibrium with Ag2S and MeS are of special interest, as the chemical potential of one species (and thus of all the others) is thus easily fixed. There are three possible situations: Ps = pso = 0 IAg
= pago
PMe
=
PMeo
0 =
(as = 1) ( a A g = 1) ( a M e = 1)
( 2 31 (24) (25)
We further make the following assumptions: a) The deviations from stoichiometry of Ag2S and MeS are small. We therefore have: ~ A = ~ ~ (AgZS) s and p h l e s = AGf (MeS). b) There is no effect of mixing AgPS and MeS, i.e.,thermodynamically they behave like separate phases. Using Equations 18 and 20 to 25, as well as tabulated values of the free energies of formation of the metal sulfides ( 2 1 ) and the standard potentials of the parent metal electrodes (1.21, we can calculate the standard potentials of the three types of mixed metal sulfide electrodes (Conditions 23 to 25). The results are tabulated in Tables I and I1 for Pb2+ and Cd2+ electrodes, respectively. The special case of the Cu'+ electrodes will be dealt with in the next paragraph. I t is interesting to realize that the chemical potential of (12) N. A. Lange, "Handbook of Chemistry," 10th ed., p 1223.
Table I. Calculated Standard Potentials of Different Pb2f Electrodes PA^
AGizes
-22150
-4860 0 +7120
PPh
PS
0 -9360 -23600
-22150 -12790 0
E
Eo,,
+480 $277 0
-126
Eofiipi,)
+354
+151 - 126
Table 11. Calculated Standard Potentials of Different Cd2+Electrodes ACi298
-33600
PA^
PS
-4860 0 $12120
0 -9360 -33600
PCd
-33600 -24240 0
E
+72S +525 0
EQc 1.8. Its role in the mixed metal sulfide electrodes is to provide them with a means of free metal diffusion, the diffusing metal still being silver.
RECEIVEDfor review December 28, 1973. Accepted May 24, 1974. (21) N. Ibl and M. Koebel, Nectrochim. Acta, to be published.
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