J. Phys. Chem. 1981, 85,1713-1718
2H(ads) + 0 = H 2 0 + 0
a gaseous mixture containing 14N0and I5NH3. At the early stage of the reaction the only product besides water was mixed nitrogen 14N15N,which directly indicates that 1mol of NO reacts with 1 mol of NH3. In their experiments O2 was not added to the reaction mixture. It was found that the CuO catalyst was reduced to CuzO or Cu during the course of the reaction and that the formation of N20 and 14N14N occurred at the later stage of the reaction. Therefore, if the reaction were carried out with excess 02, the nitrogen product would be always 14N15N. Otto et al.9 proposed a mechanism for the production of N2 and N20 in the absence of 02. The mechanism included primary and secondary reaction steps for the formation of each product as in eq 4-9. For the overall NH3(ads) = NH2(ads) + H(ads) (4) NO(ads) + ",(ads) = N2 + H20(ads) NO(ads) + NH2(ads) = NzO + 2H(ads) NO(ads) + H(ads) = HNO(ads) 2HNO(ads) = N20(ads) + H20(ads) 2H(ads)
+ 2HNO(ads) = N2 + 2H20(ads)
(6)
(7) (8) (9)
.
(11)
+ 20 = 2 0
(12) 0 = adsorbed oxygen or lattice oxygen; 0 = oxygen adsorption site or lattice site. First, the reaction between adsorbed NH, and adsorbed NO takes place and adsorbed hydrogen is produced. Then, adsorbed hydrogen is consumed by adsorbed oxygen or lattice oxygen. The oxygen adsorption site or lattice site is reproduced by adsorption of gaseous oxygen. Reaction 10 plus one-half reaction 11 plus one-quarter reaction 12 gives reaction 3. In the absence of oxygen, reaction 12 cannot proceed. The catalyst is reduced by adsorbed hydrogen, or adsorbed oxygen is consumed by adsorbed hydrogen. As a result the active site of the catalyst decreases, and reaction 10 does not proceed. Although we did not observe a reduction state of the catalyst in the absence of 02, Otto et al. observed that CuO catalyst was reduced to Cu20or Cu. Therefore it is probable that the iron oxide-titanium oxide is reduced in the absence of 02. Reaction 10 is the summation of reactions 4 and 5. NH3 reacts with O2 at a considerable rate, for example, at 350 "C. However, NH3 reacts preferentially with NO in the presence of 02. Therefore it seems that reaction 10 or 5 must be faster than a reaction between ",(ads) and adsorbed oxygen species. Reaction 10 seems to be more probable than reactions 4 and 5, because the decomposition of NH, by O2 was completely inhibited by the presence of NO. If the dissociation of NH3 were the first step in the NO-NH, reaction, the decomposition of NH3 should proceed competitively with the NO-NH, reaction. As mentioned before in the present paper, the reaction rate of NO with NH3 is retarded by H20. It is considered that H 2 0 adsorbs competitively with NH3 on the active site of the catalyst. The reaction mechanism proposed above gives a good explanation of the results obtained in this study. The reaction of NO2 and a mixture of NO-NO2 with NH, was also investigated. Details of the reaction mechanism of NO, with NH3 will be reported later. 0 2
(5)
reaction, the surface dissociation of NH3 (eq 3) is considered to be the rate-controlling step. In the present study the formation of NzO was negligible on the iron oxidetitanium oxide catalyst. Therefore reactions 5-8 are considered to be minor reactions. Tamaru et a1.16 postulated NO2-likespecies for the adsorbed state of NO on V205catalyst. We have also studied the reaction of NO2 with NH,. Contrary to the case of NO-NH, reaction, the reaction ratio of NO2 with NH, is 3:4. Although we did not try to observe the adsorbed state of NO, it seems to us that NO2-likespecies are of minor importance in the iron oxide-titanium oxide catalyst. From the information obtained in the present study and the previous studies, the following reaction mechanism for NO with NH3 in the presence of excess O2 is proposed: ",(ads) + NO(ads) = N2 + H 2 0 + H(ads) (10)
1713
Standard Reduction Potential of the Indium-Indium(II1) Electrode J. Vanhees, J.-P. Francois, and L. C. Van Poucke" Limburgs Universitair Centrum, Departement SBM, Universitaire Campus, B-36 10 Diepenbeek, Belgium (Received: August 12, 1980; In Final Form: February 23, 198 1)
The standard reduction potential of the indium-indium(II1) electrode has been determined at 25.0 "C in the absence of hydrolysis and complex formation. A value of -322.6 mV has been found, differing considerably from the values published before. Introduction Several investigators'" have attempted to determine the standard reduction potential of the In;In3+electrode using electrochemical cells. The reported values range between -335 and -341 mV. In most of these investigations the (1) Hakomori, S. J. Am. Chem. SOC.1930,52, 2372. (2) Hattox, E. M.; De Vries, T. J. Am. Chem. SOC.1936, 58, 2126. (3) Sunden, N. Z. Elektrochem. 1953,57, 100. (4) Kangro, W.; Weingartner, F. Z. Elektrochem. 1954, 58, 505. (5) Covington, A. K.; Hakeem, M. A.; Wynne-Jones, W. F. K. J. Chem. SOC.1963, 4394.
calculations are based on the assumption that the indium salt dissociates completely in aqueous solution. For indium chloride, however, this assumption can seriously be questioned. It has been found by Ferri6 and De Poorter' that chloride forms with In3+relatively stable complexes. As hydrolysis of In3+becomes more and more important in dilute solutions, the extrapolation of experimental data to ionic strength zero can also be a possible source of error. (6) Ferri, D. Acta Chem. Scand. 1972, 26, 21. (7) De Poorter, J. Ph.D. Thesis, Ghent, 1977.
0022-3654/81/2085-1713$01.25/00 1981 American Chemical Society
1714
The Journal of Physlcal Chemlstty, Vol. 85,No. 12, 1981
CampbellEhas pointed out that for indium chloride hydrolysis increases sharply when the concentration falls below 0.015 N. Ferrig has found that in indium chloride solutions mixed chloro-hydroxo complexes can also be formed. This means that indium chloride cannot be used because of incomplete dissociation in concentrated and hydrolysis in dilute solutions. Addition of hydrochloric acid, as was done by Hakomori,l suppresses hydrolysis but increases complex formation. Furthermore the calculation of the activity coefficients becomes problematic in that case. The substitution of indium sulfate for indium chloride is also not desirable; sulfate complexes can be formed, and, in addition, the sulfate ion increases hydrolysis, as was mentioned by Biedermann.lo Complex formation is also expected in the case of indium nitrates6 Since the noncomplexing of indium(II1) in aqueous perchlorate solution has been shown by Raman spectroscopy,ll indium perchlorate seems to be one of the few salts which fulfill the condition of complete dissociation. Hydrolysis of the In3+ion still occurs, and this can only be prevented by adding a sufficient amount of perchloric acid by analogy with the work of Hak0mori.l This requires the determination of the activity coefficient of indium perchlorate in the presence of perchloric acid, which can be done by a method described by Stokes and Stokes.12 This method can be applied here since use can be made of perchlorate specific ion electrodes which have been shown to function well in acid medium. As hitherto no determinations of the standard reduction potential of the indium-indium(II1) electrode has been performed in indium perchlorate and perchloric acid solutions with electrochemical cells without liquid junction potentials, the present investigation was undertaken.
Method Sunden3 has found that for pH values below 1.5 the electrode potential of the indium electrode exhibits a strong dependence on the hydrogen ion concentration, as can be expected from the electropositive behavior of indium. Furthermore, the indium electrode reaches a steady potential only after several hours, and in addition small quantities of In+ can be formed when metallic indium comes in contact with a solution of a trivalent indium salt, as mentioned by Biedermann and Wallin.13 These difficulties can largely be avoided by the use of amalgam electrodes with a low and constant indium content. EoIn,the standard redox potential of the indium electrode, can be determined by means of cells I and 11. The In(Hg);HC104(aq,ml),In(C104)3(aq,m2) 11 C104- electrode (1)
EI = EoClor- EoIn-Hg - (k/3) log m2(ml + 3m2)3(4/3)k log ~ 2 ( m ,ml) , (1) emf of cell I is given by eq 1, with k = 2.303RT/F and Y ~ ( = ~activity ~ ~ coefficient ) of component 2 with molality m2 in the presence of component 1with molality ml; in this case component 2 is In(C104)3and component 1is HCIOI. The emf of cell I1 is given by eq 2. EoIn-Hg and EoInare In;InCl,(aq,m);In in Hg (11) (2) E11 = E’In-Hg - E o I n shorthand notations for Eoha+;h-Hg and Eoha+;h.The term (8)Campbell, A. N. Can. J. Chem. 1975, 51, 3006. (9) Ferri, D.Acta Chem. Scand. 1972, 26, 741. (10)Biedermann, G.Ark. Kemi 1956, 9, 277. (11)Heater, R. E.;Plane, R. A. Inorg. Chem. 1964, 3, 769. (12)Stokes, J. M.;Stokes, R. H. J. Phys. Chem. 1963, 67, 2442. (13)Biedermann, G.;Wallin, T. Acta Chem. Scand. 1960, 14, 594.
Vanhees et al.
can be eliminated by summing eq 1 and 2 (eq 3). EI + EII = Eoclo4-- EoIn- (k/3) log m2 (ml + 3 mJ34 /3k log ~ 2 ( m z , m l )(3) EoIncan be calculated by means of eq 3 from measured E1 and EII values provided that E0clo4-and Y ~ ( ~ are ~ , known. Eoclo,-is determined in two different ways. In the first method the emf EIIIof cell 111, given by eq 4, is measured. Ag,AgCl;NaCl(aq,m ?,NaC104(aq,m’?11 C104- electrode (111) EoIn-Hg
~ ~ )
E111 =
Equation 4 permits the calculation of E°C104-Bs YNaC104(rn‘,Jn’) and YNaCl(m‘,m”) can be calculated with the aid of Harned’s rule. The second method consists in measuring the emf s of cells IV and V. If ENand Ev are the values of the emfs C104- electrode 11 HC104(aq,mHC10,)11 glass electrode (IV) Ag,AgC1;HCl(aq,mHcl)11 glass electrode
(V)
can of cells IV and V, respectively, then eq 5 holds. EoClO,EIv - Ev = E’A~,A~cI - E’CIO~-212 1% aHCIOl - 2% log ~ H C I(5) be calculated from eq 5 and tabulated values of the activity coefficients of HC104 and HCl. The remaining unknown, ~ 2 ( ~ , , ~ can , ) , be determined when m2 = 0 following the method described by Stokes and Stokes.12 This method allows the calculation of the activity coefficient of an electrolyte 2, with vanishing concentration, in a solution of electrolyte 1. In order to determine y2(0F1), the emf EvI of cell VI is measured as a function of m2 at C104- electrode 11 HC104(aq,ml),In(C104)3(aq,m2) 11 glass electrode (VI) EVI
=
EOglass
- E’C~O~. +k
log ml(mi + 3m2) + 212 log Yi(rn1,rnd (6)
constant values of mi; the experiment is repeated for different ml values. The emf E ~isIgiven by eq 6. From eq 6, one can derive eq 7a and 7b. From eq 7b and from E$, = EvI - k log ml(ml + 3mz) (74 [dE$~/dmdm, = 212
[a log ~l(ml,m~)/dm2lrn~(7b)
the well-known relationship in eq 8, eq 9 holds. Stokes [a log ~1(ml,mz)/~m21ml = 2[d log ~~(m~,m~)/dmilrn~ (8) [dE$1/dm21,, = 4k[d log ~ 2 ( m ~ , m l ) / ~ m l l r n z (9) and Stoked2 have shown that it is possible to calculate -y2(0,ml) by means of eq loa. Y is defined by eq lob. log
vanishes for ml = m2 = 0, and, following Stokes and Stokes,12 Ym,1/2 is then equal to -6kA with A = 0.5115 mol-lI2 kg1Iz at 25.0 “C. For the determination of EOI,,,eq 3 is transformed into eq l l a , where E’is given by eq l l b . The limit of eq l l a E‘= - E O In - 4/3k log ~ 2 ( m , , m l ) Wa) ~ ~ ( 0 , ~ ~ )
The Journal of Physical Chemistry, Vol. 85, No. 12, 1981 1715
Indium-Indium(II1) Electrode
E’ = EI + EII+ (k/3) log m2(ml + 3m2)3- E0c1o4is taken for m2
-
(1lb) 0 (eq 12). As 72(o,m,) can be obtained
lim E’r E”’ = -EoIn - 4/3k log Yz(o,ml)
m2-0
(12)
for any value of ml with the method of Stokes and Stokes,12 EoIncan be calculated by means of eq 1 2 provided Eo’is known. The extrapolation procedure for m2 0 is discussed in the following sections. It follows from eq 12 that the value of the limit Eo’ is always finite. The value of Eohcan also be determined with a double extrapolation procedure. First eq l l a is extrapolated for m2 0 at constant m1 values. The extrapolated values Eo’(ml) are plotted against m11/2and an extrapolation for ml 0 is carried out. The final extrapolated value is -E”h since log y2(o,o) equals zero. The standard reduction potential of the indium-indium(II1) electrode can also be determined in the following way. The emf EI of cell I is measured as a function of increasing ml values at constant m2 values. This experiment was repeated for different values of m2. For each m2 value, the E’values were calculated according to eq l l b and extrapolated for ml1I2 0.
-
-
-
-
lim E’ E(o)’ = -EoIn- Y3k log 7z(mz,0)(13)
rnl‘lW
In order to determine EoInfrom the set of E(o)‘ values, no hypothesis concerning the activity coefficient of indium is made except the validity of the limperchlorate y2(?l,,0). iting law. For indium perchlorate being a 3-1 electrolyte the limiting law can be written as eq 14. It follows from log ~ z ( ~ , , o )= (-0.5115)(3)P/2
(14)
eq 13 and 14 that, by plotting (E“)’+ Eoh)/(4kPl2)vs. PI2, one obtains an intercept of 0.5115 if and only if the right value for Eohhas been chosen. It is found that the curves are rather sensitive to the choice of the Eohvalues so that by trial and error a value for the standard reduction potential can be obtained. The concentrations of perchloric acid in the solutions, which are used in these methods, are always large enough, so that complete suppression of hydrolysis can be assumed. Experimental Section Perchloric acid (Merck p.a.) solutions were standardized (by weight) against a sodium hydroxide solution (Merck TitrisolO.l M) by using methyl red as an indicator. Sodium chloride (Merck p.a.) was heated at 500 “C before use. Sodium perchlorate (Merck p.a.) was dried at 180 “C. A stock solution of indium perchlorate was prepared by dissolving 99.99% pure metal in concentrated nitric acid (Merck p.a.) followed by addition of a large excess of concentrated perchloric acid. The nitric acid and, to a large extent, the perchloric acid were expelled by heating under an infrared lamp. Chloride, nitrate, and iron(II1) could not be detected in the final product. The indium content of the stock solution was determined gravimetrically as In20314and by an EDTA titration with xylenol orange as an i n d i ~ a t o r .The ~ amount of perchloric acid in the stock solution was determined by substituting In3+for H+ with the ion exchanger Dowex 50 WX-8 (100-200 mesh) (in the acid form) and titrating the eluate with 0.1 M sodium hydroxide solution. The result of this determination was checked by a potentiometric titration of the (14) Duval, C. “Trait6 de Micro-Analyse Min6rale”; Presses Scientifiques Internationales: Paris, 1954; tome I.
original solution with a standard bicarbonate solution.6 The equivalence point of the titration was determined by means of a Gran plot.15 Electrodes. Silver-Silver chloride electrodes were of the thermoelectrical type and prepared as described by Bates.16 A value of 222.34 mV for EoAg,AgClis accepted according to Robinson and Stokes.17 Glass electrodes (LOT 201-NS) were purchased from Ingold. The perchlorate electrodes were constructed by using Orion series 92 membrane electrode bodies equipped with Orion nitrate porous membrane supports. The inner reference system comprised a silver-silver chloride electrode immersed in an aqueous solution containing chloride and perchlorate ions. The perchlorate salt of N-ethylbenzothiazol-2,2’-azoviolene(NEBA-ClOJ was synthesized according to Sharp.ls In order to make the electrode suitable for measurements in acid medium for which the H+concentration can be up to 0.1 M, we used an acid inner reference solution (0.1 M HC1,O.l M NaC10J as proposed by De P ~ o r t e r .A~ saturated solution of NEBA-ClO., in a solvent composed of 50% 1,2-dichlorobenzene (Merck p.a.) and 50 % P,P-dichlorodiethyl ether (Fluka purissimum) was used as the liquid ion exchanger. Preliminary investigations were done in order to check the Nernstian behavior of the perchlorate electrode in pure perchloric acid solutions and in mixtures of perchloric acid and lithium perchlorate. Indium amalgam (0.18% indium) was prepared by dissolving freshly cut pieces of indium metal in distilled mercury. The apparatus described by Ohtakilgwas quite efficient as the amalgam can be transferred to the cell avoiding any contact with stopcocks and air. The composition of the indium amalgam was kept constant throughout all experiments. In order to assure good functioning of the indium amalgam electrode, we replaced the original amalgam pool by a new one during each run; the cell potentials always agreed within 0.02 mV. The solution was freed from oxygen by passing nitrogen through it for 30 min before the introduction of the indium amalgam. All solutions were prepared with bidistilled water. The indium electrode was prepared according to Covi n g t ~ ntaking ,~ into account the difficulties mentioned by Biedermann and Wallin.13 Apparatus. The emf measurements were carried out with a Keithley digital voltmeter 190 equipped with an Analog Devices Model 52 J operational amplifier. The cells were thermostated by means of a water jacket. Cells and jackets were placed in a themostated case. All measurements were performed at 25.0 i 0.1 “C. Results and Discussion Response Behavior of Electrodes. Perchlorate Electrode. The pH dependence of the perchlorate electrode (15) Gran, G. Analyst (London) 1952, 77, 661. (16) Bates, R. G. “The Determination of pH in Theory and Practice”; Wiley: New York, 1964. (17) Robinson, R. A.; Stokes, R. H. “Electrolyte Solutions”; Butterworths: London, 1953. (18) Sharp, M. Anal. Chim. Acta 1971, 65, 405. (19) Ohtaki, H.; Tsurumi, M.; Takayoshi, K. Anal. Chem. 1977, 49, 190. (20) De Levie, R. J. Electrochem. Soc. 1971,118, 185C. (21) Losev, V.; Moldov, A. I. Electrochim. Acta 1962, 6, 81. (22) Ives, D. J. G.; Janz, G. J. “Reference Electrodes Theory and Practice”; Academic Press: London, 1961. (23) Cousens, R. H.; Ives, D. J. G.; Pittman, R. W. J. Chem. SOC.1953, 3972. (24) Peeters, L. Ph.D. Thesis, Ghent, 1976.
1716
The Journal of Physical Chemistry, Vol. 85,No. 12, 1981
was tested by means of cell VI1 with c1 = 0.001 M and c2 Ag,AgC1;NaCl(aq,cl),NaC104(aq,cz) /I C104- electrode (VIU = 0.3 M. The cell solution was titrated with a solution containing 0.001 M NaCl and 0.3 M HC104. The emf EvII is given by eq 15. A rather random change was found for Cc1-
Yc1-
= E°C104- - EoAg,AgCl + k log -+ k log YCIO~cc104(15) E m from pH 7 (81.88 mV) to pH 1 (81.97 mV). Since the last term in eq 15 cannot be expected to change considerably with the pH, and in this manner obscuring a possible pH dependence of the perchlorate electrode, it can safely be assumed that Eoclo4does not change appreciably in the pH range studied. The Nernstian behavior of the perchlorate electrode was checked by measuring the emf of cell IV; the molality of the perchloric acid was varied by titration. The emf EIv is given by eq 16. Equation 16 can be transformed into E I V = E’glass - E°C104- + 2k 1% mHC104YHC104 (16) &I1
eq 17. Curve fitting of E’, as a function of log mHClo4 gave
E’IV EN - 2k log YHClO, = EOglass
- E O C I O ~+
2k log mHC104 (17)
a straight line with a slope of 118.36 mV/decade. The YHC104 values needed to calculate Eiv were evaluated according to C ~ v i n g t o n .In ~ ~addition it has been claimed7J8 that the perchlorate electrode used in this work exhibits an almost perfect Nernstian response to changes in perchlorate ion activity over the range 1-10-5 M. Taking into account the response and selectivity characteristics cited above, one can conclude that the perchlorate electrode is suitable for accurate measurements.
Indium Amalgam Electrode A distinctive feature of the electrochemical behavior of indium and indium amalgam is the low value of the exchange current in acid solutions, in the absence of complexing anions.20p21In view of the slowness of the reaction In3+ + 3e F! In(Hg) in perchlorate media, the chances are high that electroactive impurities capable of sustaining a higher exchange current would cause the measurement of mixed potentials. However, by the method described by IvesZ2and C o u s e n ~we , ~ have ~ found that, under suitable circumstances, In(Hg) electrodes give reversible potentials in mixtures of indium perchlorate and perchloric acid. In solutions of 0.1 I mIn(C1033 I 0.01 the amalgam electrode attained a steady potential within 15 min and remained constant for several hours within 0.02 mV. For mIn(C104)3 = 0.001, -0.5 h was necessary to attain equilibrium potentials. The emf values were reproducible to within 0.03 mV. Measurements at constant ionic strength ( I = 1,0.5, and 0.2 M C10,) with NaC104as the supporting electrolyte showed that In(Hg) electrodes give a linear response to changes in concentration of the In3+ion as predicted by the Nernst equation. A similar result has been reported by Ferri6for I = 3 M ClO;, who found also that only below an In3+ concentration of 0.0005 M are mixed potentials measured with the indium amalgam electrode. Determination of the emf EII For each determination of the emf EII of cell 11, one amalgam and three indium electrodes were used. A mean (25) Covington, A. K.; Prue, Jj. E.J. Chem. SOC.1957, 1567.
Vanhees et al.
TABLE I: Determination of Yrn,l/zfrom Experimental Data Obtained with Cell I DE’,,/ Yml1/’/ m, 1O3mZ E,,, mV am,],, (2k) 0.005 0 420.89 0.8754 419.54 - 1654.0 1.63 418.78 - 1294.5 2.2879 418.25 - 1193.5 -1.1035 2.8659 417.97 -1050.3 0.01 0 420.31 1.764 418.35 - 1107.1 3.286 -899.6 417.35 4.612 416.52 -821.3 5.778 415.99 -757.0 6.810 -687.7 -1.021 415.62 0.02 0 419.12 1.832 -706.9 417.83 3.510 416.92 - 626.2 5.077 416.19 - 576.7 6.537 415.71 - 521.3 7.899 415.17 - 500.3 - 0.904 0.03934 0 416.50 3.579 414.94 -436.2 5.267 414.35 - 409.3 6.893 - 379.1 413.89 9.97 1 413.25 - 326.9 12.84 412.76 -291.9 15.51 412.22 -276.3 411.34 22.56 -228.9 -0.766 0.0608 0 414.05 4.562 -236.73 412.97 8.79 - 194.08 412.35 - 185.22 12.72 411.70 16.38 -175.15 411.18 19.80 410.97 -159.60 28.82 -138.72 -0.497 410.06 0.09981 0 413.18 4.205 -151.71 412.55 8.101 412.15 - 127.02 -117.15 11.72 411.81 15.10 -107.45 411.56 - 100.93 18.24 411.34 26.55 410.94 - 84.48 -0.412
value of 66.39 mV was found for EIIfor a 0.05% amalgam electrode and 74.79 mV for a 0.18% amalgam electrode. The difference between both values is in good agreement with the value predicted by the Nernst equation, namely, 8.61 mV.
Determination of the Standard Potential of the Perchlorate Electrode For the determination of the standard potential of the perchlorate electrode, the following numerical data were used for the activity coefficients. First method: YNaCl(m),ml)) = 0.780 and YNaClO,(m”,m’) 0.775 for a solution with the composition m’ = 0.005 m NaCl and m ” = 0.095 m NaC104. The value for Y N ~ c ~ (,) ~ , was calculated with Harned’s rule, given by eq 18. Kc(18) log YNaCl(m’,m”) = log YNaCl(m’,m”) - CU7l’’ cording to PeetersZ401 = -0.0114 when m’ + m‘‘ = 0.1 m. For YNaC104(m”,m‘) the value for YNaC104(m”,0) was used. Second method: YHClO, = 0.911 for a 0.01 m HCIOl solution according to C~vington,’~ and YHCl = 0.796 for a 0.1 m HC1 solution following Robinson and Stokes.17 For each run the EoClO4value was determined by using both methods; the agreement was 0.03 mV or better. The experimental data for 6EfvI/6mz,used for the determination of log Y ~ ( ~ ,are ~ ~summarized ) , in Table I. It should be noted that, because of a slight drift of the perchlorate electrode, the values for E’w,which are also given in Table I, are apparatus dependent. However, that is not the case for the values of the derivative. Plotting aEtW/am2
The Journal of Physical Chemistry, Vol. 85,No. 12, 1981
Indium-Indium(II1) Electrode
1717
TABLE 11: Y ~ ~ ( c ~ ~ , Values ) , ( ~ ,Compared ~,) with Values for 7 ~ a c 1 ,and 7 H C 1 0 ,
0.05 0.06 0.08 0.10 0.14 0.18 0.20 0.22 0.26 0.30
0.860 0.837 0.796 0.759 0.694 0.641 0.618 0.598 0.567 0.544
0.942 0.927 0.911 0.890 0.864 0.853 0.844 0.827 0.810
0.827 0.783 0.744 0.677 0.623 0.600 0.579 0.541 0.510
2.96 3.00 2.96 3.14 3.03 3.03 3.02 2.97 2.88
TABLE 111: E" Values Obtained from Experimental Data of Cells I and I1 0.816 0.759 0.694 0.646 0.618 0.595
-321.85 -322.13 -322.75 - 322.75 - 323.48 -325.41 mean value: -323.1 f 1.3
- 328.82 -331.60 -335.27 - 337.71 -339.95 - 343.15
0.005 0.01 0.02 0.03 0.04 0.05
TABLE IV: E(')' and 7 2 ( m , , o ) Values Calculated with E",,=-322.6 mV m2
E(')', mV
0.001 0.002 0.005 0.01
330.26 332.91 336.73 340.30
E'%,)
+ 325
0.1
0.2
72(m2,0)
0.800 0.740 0.662 0.596
m2
E('', mV Yz(m,,o)
0.02 0.05 0.10
344.88 351.12 354.22
.2
.3
0.522 0.435 0.397
T
rn2/rn,+3m;
Figure 1. Determination of EoIn(mV) according to the first method.
against ml gives a good linear relationship. In Table I the values for Yrnl1l2/2k are reported for each value of ml. From these data, log Y ~ ( ~ , ~was ! ) obtained by using eq loa. The values for y2(0,m1) are given in Table I1 under the entry YIn(
