Electrode Potentials in Acetonitrile. Estimation of the Liquid Junction

ELECTRODE POTENTIALS IN ACETONITRILE

3049

Electrode Potentials in Acetonitrile. Estimation of the Liquid Junction Potential between Acetonitrile Solutions and the Aqueous Saturated Calomel Electrode'

by I. M. Kolthoff and F. G. Thomas SchooE of Chemktru, University of Minnesota, Minneapolis, Minnesota, 66466 (Received March 26, 1966)

Standard potentials in acetonitrile (AN) have been determined of the systems ferroceneferricinium picrate and tris(o-phenanthroline)iron(II)-(111) perchlorates, using a platinum indicator electrode and silver-0.01 M silver nitrate in AN as reference electrode. Also, the standard hydrogen potential has been estimated from hydrogen electrode potentials in sulfuric acid-tetraethylammonium bisulfate mixtures in AN vs. the above reference electrode, Conductance measurements of various salts are reported. Assuming that the tris(ophenanthroline)iron(II)-(111) system has the same potential in water as in AN, we have derived the following values of standard potentials in AN os. the standard hydrogen electrode in water (Eo&q: tris(o-phenanthroline)iron(II)-(111) perchlorate, 1.120 v. ; ferrocene-ferrocinium, 0.348 v.; '/zH%/H+, 0.30 v.; Ag/Ag+, 0.40 v. The liquid junction potential between a dilute solution in AN and the s.c.e. in water is of the order of 0.25 v. The solubility of ferrocene in water is 1.7 X 10-5 M .

Introduction In polarographic studies in acetonitrile (AN) as solvent, the aqueous saturated calomel electrode (s.c.e.) has been used extensively as a reference electrode.2-5 Although the use of the s.c.e. as a reference electrode in voltammetric studies in AN gives reproducible results, it nevertheless has the disadvantage of introducing an unknown liquid junction potential (Elj) into the measurements. An exact comparison of electrode potentials in various solvents forever will be impossible because of the unknown liquid junction potential. By application of extra-thermodynamic considerations, efforts have been made in the literature to find a system the electrode potential of which is the same in various solvents, a t the same activities of the constituents of the system, relative to the normal hydrogen electrode in water. The e.m.f. of such a system in two different solvents would be equal to Eli. PleskovGv7 proposed the standard potential of the Rb-Rb+ ) 8 ( E ' H ) ~as~an , absolute constant electrode, ( E o R ~us. in all solvents since the rubidium ion is large with a charge of one and is only slightly polarizable. Thus the electrostatic interaction between the rubidium ion and the solvent would be expected to be very similar in a variety of solvents and so the differences in the solva-

tion energies (and the differences in eo^&) are expected to be negligible. StrehlowBt9improved on the assumption of Pleskov6J by calculating the solvation energies of the rubidium ion in various solvents from the concentrations of the saturated solutions of the alkali halides in the various solvents, making use of the method of Latimer, et aLIO Thus he was able t o calculate the standard potential of the Rb-Rb+ electrode in other solvents and relate the electrode

(1) Acknowledgment is made to the donors of the Petroleum R e search Fund, administered by the American Chemical Society, for support of this research. (2) I. M. Kolthoff and J. F. Coetzee, J. Am. Chem. Soc., 79, 870, 1852,6110 (1957). (3) J. F. Coetzee and G. R. Padmanabhan, J. Phys. Chem., 66,1708 (1962). (4) J. F. Coetzee, D. K. McGuire, and J. L. Hedrick, ibid., 67, 1814 (1963). (5) I. M. Kolthoff and F. G. Thomas, J. Electrochem. Soc., 111, 1064 (1964). (6) V. A. Pleskov, Usp. Khim., 16, 254 (1947). (7) V. A. Pleskov, Zh. Fiz. Khim., 22, 351 (1948). (8) H.Strehlow, 2.Elektrochem., 56, 827 (1952). (9) H.M. Koepp, H. Wendt, and H. Strehlow, ibid., 64,483 (1960). (10) W. M. Latimer, K. S. Pitser, and C. M. Slanski, J. Chem. Phys., 7, 108 (1939).

Volume 69, Number 9 September 1966

3050

I. M. KOLTHOFF AND F. G. THOMAS

potential scales in these solvents to the standard hydrogen electrode in water, Strehlowg further suggested that an oxidationreduction system involving a metal complex, in which the multivalent metal ion is symmetrically surrounded by one or more large organic ligands, would be more suitable for interrelating the standard potentials in different solvents since the electric field a t the periphery of such ions is much weaker than that of simple ions. Thus the differences in electrostatic interaction with the various solvents are minimized and the potentials at given activities of the constituents become less dependent on the solvent. Strehlow emphasized that the charges on the complex ions should be small and one of the species of the oxidation-reduction couple should preferably have zero charge. The couples suggested (ferrocene-ferricinium and cobaltocene-cobalticinium) , however, were found to be influenced by the solvent and the difference in the standard electrode potentials for these couples in water and AN was calculated to be 0.06 the potential being more negative in AN than in water. Wardl1 measured the potential of several cells of the type

AN. The potentials of all the electrodes studied in AN were also measured against the s.c.e. in order to estimate Elj.

Exuerimental

Materials. Acetonitrile was purified by the method of Coetzee, et a1.,12 the final distillation being from phosphorus pentoxide under a nitrogen atmosphere (b.p. 80.9-81.0" a t 746 mm.; specific conductivity ohm-' cm.-l a t 25"). 1.64 to 2.18 X Tetraethylammonium perchlorate was prepared as described2; tetraethylammonium bisulfate and anhydrous sulfuric acid were obtained from Dr. M. K. Chantooni, Jr.13 Silver Nitrate. Analytical reagent grade material was dried at 120" under vacuum and stored over anhydrous magnesium perchlorate. Biscyclopentadienyliron(I1)-ferrocene was Matheson Coleman and Bell commercial grade recrystallized from petroleum ether B, m.p. 174". Biscyclopentadienyliron(II1) picrate-ferricinium picrate was prepared by dissolving ferrocene (1 g.) and picric acid (1. 3 g.) in benzene (100 ml.) and adding benzoquinone (0.29 g.) dissolved in 75 :25 benzeneethyl alcohol mixture (50 ml.).14 The resulting mixture was cooled in ice, the olive green solid PtlMAa2+,Ma2 +j 10.01 M AgNOa/Ag filtered, and recrystallized from aqueous alcohol. in AN, with M being iron or osmium and A being An aqueous solution of the resulting orange-olive solid bipyridine, terpyridine, or o-phenanthroline. Aswas analyzed spectrophotometrically and it was found suming these oxidation-reduction couples have the that [Fe(C&Jz+] = [CaH~N307-]within 2% with a same standard potentials in water and AN (relative total purity of 98 2%. The product was used as to (EoH)aq), Ward calculated the potential of the such and stored over anhydrous calcium chloride. silver401 M silver nitrate reference electrode in AN Tris(o-phenanthroline)iron(II) perchlorate was preto be 0.291 v. reIative to (EoH)aq.Ward also measured pared as described,l5 recrystallized from acetone, and the potentials of the cells dried under vacuum at 150" to give the anhydrous salt11 which was stored over anhydrous calcium chloPt IOs(Bipy)~~+, Os(Bipy)2+//Os(Bipy)2+, O~(Bipy),~+lPt ride. Tris(o-phenanthroline)iron(III) perchlorate was prepared as described,16 dried under vacuum a t 150" and to give the dihydrate,ll and stored over anhydrous AgjAgNOa(O.Ol M ) ( A N ) IAgNOs(O.Ol M )(water) IAg calcium chloride. Hydrogen (Airco High Purity) was passed through and was able to estimate the liquid junction potentials a commercial Deoxo Catalytic Purifier, dried by passing between these aqueous and AN solutions. These were through concentrated sulfuric acid and then through found to be 0.225 and 0.269 v., respectively. potassium hydroxide pellets, and finally saturated with I n the present work, the effect of ionic strength on the potentials of two of the oxidation-reduction couples (11) W. Ward, Ph.D. Thesis, University of Iowa, 1958; W. E. Benstudied by Ward," ferrocene-ferricinium and tris(onett and W. Ward, Abstracts of the 133rd National Meeting of the phenanthroline)iron(II)-tris(o-phena n t h r o line) ironAmerican Chemical Society, San Francisco, Calif., April 1958,p. 40L. (111), has been determined and the conductivity of (12) J. F. Coetzee, G. P. Cunningham, D. K. McGuire, and G. R. Padmanabhan, AmZ. Chem., 34, 1139 (1962). solutions of the salts of the metal complexes has been (13) I. hl. Kolthoff, S. Bruckenstein, and M. K. Chantooni, Jr., measured in AN. The standard potential of the hyJ . Am. Chem. SOC.,83, 3927 (1961). drogen electrode in AN, (EOH)AN,has also been es(14) P. L. Pauson, Quart. Rev. (London), 9,391 (1955). timated relative to (EoH)as using a platinum-hydrogen (16) F. P. Dwyer and H. A. McKenzie, J . Proc. Roy. Soc. N . S . W., 81, electrode in bisulfate-sulfuric acid buffer solutions in 93 (1947). ~

.

,

*

1

~

*

I

The Journal of P h y E a Chemistry


7

6

A

B

Figure 1. Half-cells used for potentiometric studies: A, reference half-cell; B, oxidation-reduction half-cell. Notes: 1. silver-plated platinum wire; 2. electrode compartment; 3. reservoir; 4. side arm; 5. thre4way stopcock; 6. mercury contact; 7. ground-glass stopper; 8. polyethylene plugs; 9. intermediate compartment; 10. electrode compartment; 11. sinter disk; 12. platinum spiral electrode; 13. liquid level (slightly lower in the intermediate compartment); 14. connected to potentiometer.

AN vapor before bubbling over the platinized platinum electrode in the buffer solutions. Cells. The reference cell (Figure 1) contained a platinum wire, electroplated with silver, sealed into the reference electrode compartment (2 in Figure 1) which was connected to a reservoir and side arm via a three-way stopcock. The three sections (2, 3, and 4) were filled with 0.1 M silver nitrate in AN. The reference electrode was protected from the atmosphere by ground-glass stoppers. Electrical connection to the silver electrode was made by means of a mercury contact. The oxidation-reduction half-cell consisted of an electrode and an intermediate compartment separated by a gkss sinter. The solution under study was placed in both compartments. A bright platinum spiral electrode was placed in the electrode compartment through a polyethylene plug used to seal the compartment from the atmosphere. Electrical connection between the two half-cells was made by inserting the side arm of the reference half-cell into the solution in the intermediate compartment through a polyethylene plug.

3051

The half-cell for the hydrogen electrode was similar to the oxidation-reduction half-cell with the following modifications: hydrogen, saturated with AN, was admitted to the electrode compartment via a glass sinter in the base; three heavily coated platinized platinum electrodes, prepared by the usual electrodeposition technique from hexachloroplatinic acid solution,l* were used instead of the bright platinum spiral. The s.c.e. was prepared in the usual manner.ls The conductivity cell had a cell constant of 0.0370 cm.-I. The polarographic cell has been described previously. Instruments. A Leeds and Northrup Student potentiometer was used to measure all potentials to h0.2 mv. and conductivity measurements were made with an a.c. resistance bridge to within *l%. All current-potential curves were recorded on a Leeds and Northrup Electrochemograph Type E. The dropping mercury electrode (d.m.e.) employed had = 1.621 mg.”* the following characteristics: mz/at1/6 set.-"', t = 3.95 sec., a t zero applied voltage in 0.1 M tetraethylammonium perchlorate in AN with a mercury height of 53.7 cm. (cor.). The rotated platinum electrode (r.p.e.) consisted of a l-cm. length of platinum wire sealed through glass and was rotated a t 600 r.p.m. Technique. All measurements were carried out a t 25.00 f 0.02’. When measuring potentials relative to the silver-O.01 M silver nitrate in AN electrode, electrical contact between the two half-cells via the side arm of the reference electrode was maintained only long enough for each individual potential to be measured; between measurements on a given solution, the side arm was raised above the level of the solution in the intermediate compartment. The potentials of the two oxidation-reduction couples studied were determined using approximately equimolar mixtures of the reduced and oxidized forms. The effect of ionic strength on the potentials was determined by varying the concentrations of the components of the oxidationreduction couples and by adding an indifferent electrolyte (tetraethylammonium perchlorate). Potentials were measured at regular intervals up to 70 min. after mixing. In the case of the tris(o-phenanthroline)iron (11)-tris (o-phenanthroline)iron (111) couple, the potential a t zero time (time of mixing) was found by extrapolation.’l In the case of the ferroceneferricinium couple the steady potential, attained 5 min. after standing in the cell, was recorded. (16) D.J. G.Ives and G. J. Jrtnz, “Reference Electrodes,” Academic Press, New York, N. Y., 1961. (17) L.A. Knecht and I. M. Kolthoff, Inorg. Chem., 1, 195 (1962).

Volume 69,Number 9 September 1966

3052

The potential of the hydrogen electrode in bisulfatesulfuric acid mixtures in AN, with hydrogen passing through the solution, was found to reach a steady value within 3 min. a t each of the three electrodes used and to remain constant for a t least 25 min. before some drifting occurred. Potential measurements with the s.c.e. as reference electrode were carried out in a similar manner to those with the silver-O.O1M silver nitrate in AN reference electrode. The current-potential curves of aqueous solutions of ferricinium picrate and of AN solutions of ferrocene were determined at the d.m.e. and the currentrpotential curves of aqueous solutions of these compounds were measured a t the r.p.e.


190k.

200

Results Conductivity Measurements. Tr&(o-phenanthro1ine)iron (11)Perchlorate. The conductivities of solutions of the anhydrous salt in AN in the concentration range to 1.14 X M were measured and 4.67 X plotted against the square root of the concentration, C1", in Figure 2, curve A. The results are expressed by the relation Ac = A. - 1410C'/' and give a value of 191.9 ohm-1 cm.2 for Ao. Thus Xo for the tris(ophenanthroline)iron(II) cation is 87.4 ohm-' cm.2 ((Xo)cl0,- = 104.5 ohm-' cm.2Is). Tris(o-phenanthroline)iron(III)Perchlorate. Conductivities of solutions of the dihydrate in AN in the concentration range 8.09 X lo-$ to 1.26 X low3M are plotted against C1'* in Figure 2, curve B. Two series of results were obtained. I n series 1, transference of solutions from volumetric flasks to the conductance cell was done in the atmosphere, and with the more dilute solutions a color change from blue to reddish purple was observed, indicating that moisture from the atmosphere was causing decomposition of the tris(o-phenanthroline)iron(III) cation. When the measurements were repeated, series 2, using fresh solutions and doing all operations in a glove box filled with dry nitrogen, no color change was noticed with the dilute solutions for several hours and the plot of A, os. C"' was found to remain linear down to the lowest concentrations studied. These results show that a t M the small amount concentrations greater than of moisture from the atmosphere has no appreciable effect on the conductivities of these solutions. However, on standing for several days, 1.0 mlM solutions of tris(o-phenanthroline)iron(III) perchlorate became purplish in color, even when sealed from the atmosphere, indicating that the tris(o-phenanthr0line)iron(111) cation is slowly decomposed in AN solutions. Because of this, all solutions of this ion were freshly prepared prior to any measurements (potentiometric The Journal of Physical Chemistry

9 4

d.4

oie

IIP

I16

2:o

214

ke

3j2

3!6

100 cl'2

Figure 2. Conductivities in acetonitrile: A, tris(o-phenanthroline)iron(11) perchlorate, 0 ; B, tris(o-phenanthroline)iron(111) perchlorate dihydrate, 0 , series 1; m, series 2; C, ferricinium picrate, A; a, b, and c, Onsager plots for A, B, and C, respectively.

or conductometric) being made. The results obey the relation Ac = ho - 1920 C'Iz and give a value of 194.2 ohm-l cm.2for Ao; i.e., ho for the tris(o-phenanthro1ine)iron(II1) cation is 89.7 ohm-' cm.2. Ferriciniuln Picrate. The conductivities of A N solutions of this salt are plotted against C1lain Figure 2, curve C. The results are described by the relation A, = A. - 1820C"' and give a value of 152.1 ohm-' cm.2for Ao; i e . , Xo for the ferricinium ion is 74.4 ohm-l cm.2 ( ( X O ) C ~ F ~ ~ N= ~ O77.7 ~ohm-1 cme218). Potential Measurements. (a) Using the S&!ver-O.Ol M Silver Nitrate (in A N ) Reference Electrode. Tris(0phenanthroline)iron(II)-Tris(o-p h e n a n t h r o Zin e) iron(111)Couple. The potentials developed by this couple a t a bright platinum electrode, relative to that of the a t various ionic reference electrode (E'-OIA~)AN, strengths were measured and used to calculate values of E' from the equation

E' = Eell

- 0.0591 log [ F e ( ~ h e n ) ~ ~ + + I / tFe(phenh2+1 (1)

(18) P.Wdden and E. J. Birr, 2.physik. Chem., 144A,269 (1929).


3053

i.e., E' is the standard potential of this couple a t the given ionic strength, I = 1/2ZCiZi2 relative to (EO.O~A~)AN. E' is plotted as a function of the square in Figure 3, curves A1 root of the ionic strength, 11/', and A2, in the absence and presence, respectively, of tetraethylammonium perchlorate. Extrapolation of these plots to zero ionic strength gives a value of 0.8459 v. for the standard potential of this couple in AN (relative to (E'.O'AB)AN. The Ferrocene-Ferricinium Couple. The potentials developed by this couple (at a bright platinum electrode) with respect to the silver-silver nitrate reference electrode were measured and used to calculate values of E" a t various ionic strengths from the relation

E''

=

Em11

+ 0.0591 log

aferrooene/aierricinium+

(2)

0.85

-

--- --4 0.75 0.80

ul

c

A2

W

B3 0.06

0.04

82

Lc

E'' is plotted against the square root of the ionic strength in Figure 3, curves B1 and B2 (absence and presence of tetraethylammonium perchlorate, respec0'02 00 0 . 1 0.2 0.3 tively). The extrapolation of curves B1 and B2 to zero ionic strength gives values of 0.0740 and 0.0738 *lfZ v. for the standard potential of this couple vs. Figure 3. Effect of ionic strength on electrode potentials (Eo.O:AB) A N , respectively. in acetonitrile: Al, Fe(phen)aa+-Fe(phen),8+; A2, The potentials of the hydrogen electrode in various Fe(phen)aB+-Fe(phen)*8+ EtrNC104; B1, nonaged bisulfate-sulfuric acid buffers vs. (EO.O~A~)ANf e r r o c e n e - f e r r i c i ; B2, ferroceneferricinium + Et;NCIOI are listed in Table I together with the calculated values using [ferricinium]; B3, as B2 wing aferriainium. of the hydrogen ion concentration and mean ionic activities for the various solutions. The values of E"' measured a t three different electrodes. Two of the for the five buffer solutions studied were calculated electrodes, a and b, gave identical steady values for from the equation EWn (recorded in Table I) while the third gave values E"' = Em11 - 0.0591 log U H + / { P H ~(instm.)j1'' (3) between 0.5 and 1.0 mv. higher. It was noted that EWn for the second buffer solution listed in Table I where pH,is the pressure of hydrogen at the platinized increased by 12 mv. on standing for 18 hr. This platinum electrode. The measured pressure was corindicates that the proton activity slowly decreases on rected for the vapor pressure of the solvent and the aging in agreement with previous observations on AN solutions which contain appreciable concentrations of Table I: E.m.f. of the Hydrogen Electrode in solvated protomla Because of this, all buffer soluBisulfate-SulfuricAcid Buffers in AN us. Silver-O.01 M tions were prepared immediately before the potential Silver Nitrate Reference Electrode in AN measurementswere made. (b) Using the S.c.e. as Reference Electrode. The [(CaHdrIonic NHSO41 [HZSOII [H'l, strength, four half-cells used above were connected to an aqueous added, added, M I Eoe.11, E"', s.c.e. via a potassium n i t r a m g a r salt bridge and the mM mM X 106 f& X 10: mm. V. V. potentials of the resulting cells are recorded in Table 11. 0.848 0.948 0.208 662.8 -0.2600 0.0316 5.1 0.204 Polarographic Studies. (a) AN Solutions. Fer2.662 0.897 1.018 662.8 -0.2270 0.0385 20.0 1.02 1.323 0.866 1.964 646.0 -0.2366 0.0418 20.0 2.04 rocene in AN gives well d e h e d anodic waves at the 8.33 0.860 2.084 662.8 -0.1917 0.0437 50.0 2.04 d.m.e. in the concentration range 0.200 mM to 1.00 -.0.1646 0.0468 662.8 0.866 2.238 84.2 22.65 2.04 mM using 0.1 M tetraethylammonium perchlorate as supporting electrolyte. The plots of log i / ( i d - 23 height of the solution above the electrode. Extrapous. Ed.m.e. (corrected for iR drop) for the five curves studied in this concentration range have a mean slope lation to zero ionic strength gives a value of 0.030 v. 0.0006 v. which compares favorably with of 0.0585 for the standard potential of the hydrogen electrode in the theoretical slope of 0.0591 for a reversible, oneAN (Eo*OIAg)~N.All the hydrogen potentials were

1 +

*

Volume 60, Nu*

9 #-

1066

3054


5-

Table 11: Potential Measurements Using the S.o.e. as Reference Electrode 4-

E Half-cell (AN solutions)

PtlFe(phen)sz+(1.881 X loW4 M), Fe(phen)aa+ (1.882 X lod4M) PtlFe(phen)aZ+(1.881 X M), Fe(phen)8*+ (1.882 X M ) , (C&)aClOa (0.1 M ) Pt/Fe(C5H& (1.871 X IO-' M ) , Fe(CsHsI2+ (1.734 X lo-' M) Pt]Fe(CsH& (1.871 X IO-' M ) , Fe(c~&)z+ (1.734 X M ) , (CpH6),NC1O4(0.1 M ) H2 (646mm.) , Pt](C&)SJHS04, HaSO4, H + (1.323 X 10-6 M) Hz (646 D.), Pt CzH6)4NHS04, HzSOd, H +

(I

u8.

s.c.e., V.

i ( corr) 3

-

( PO)

1.1155 2-

1.0350 0.3442

I -

0.3260 0 -

0.0248 I

I

I

I

to.20

I

I

+0.10

1 0

_.

electron oxidation. The mean value of the diffusion current constant, ID,for these curves a t 0.55 v. us. s.c.e. is 3.99 f 0.05 pa. m o l e - * set.'/' mg.*/* and El,,is0.379 =kO.OOlv.us.s.c.e. (b) Aqueous Solutions. The currentrpotential curve of an aqueous ferricinium solution (2 X M) using the d.m.e. and 0.1 M tetraethylammonium perchlorate supporting electrolyte is well developed with El/*= 0.147 v. vs. s.c.e. However, the top portion of the wave is drawn out and a plot of Ed.m.e. us. log (id - i)/iis only linear (slope 0.053) between = 0.20 to 0.12 v. At more negative voltages the slope continuously increases to a value of 0.88 a t 0.02 v. This indicates that a t the foot of the wave a reversible one-electron reduction max occur but a t potentials more negative than El/, the reduction becomes irreversible. At higher concentrations of Fe(C6&)2+ only the foot of the wave is observed, the currentpotential curve passes through a maximum, and the current drops to a value smaller than the expected limiting current. This indicates that a film of the very slightly soluble ferrocene is formed on the drop which interferes with the reduction urocess. This is further indicated by the unusual shape of the instantaneous current-time curves for the individual drops a t voltages more negative than that a t which the maximum is observed on the current-potential curve. Current-potential curves determined a t the r.p.e. are shown in Figure 4 for: (41.114 X lo-' M Fe(CsHtJz+ in aqueous 0.1 M tetraethylammonium perchlorate solution (curve A); (b) saturated aqueous solutions of ferrocene with 0.083 M (curve B) and 0.0204 M (curve perchlorate as electrolyte. The characteristics of these waves are

Figure 4. Current-potential curves of ferrocene and ferricinium ion in water using the r.p.e.: A, 1.114 x 10-4 M ferricinium ion, 0.1 M tetraethylammonium perchlorate supporting electrolyte; B, saturated ferrocene solution, 0.083 M tetraethylammonium perchlorate supporting electrolyte; C, saturated ferrocene solution, 0.0204 M tetraethylammonium perchlorate supporting electrolyte.

given in Table 111. The slopes of the plots of log (id - i)/ius. Er.p.e. indicate that both the oxidation and reduction are reversible and involve a one-electron process with Et, of 0.146 v. This is further supported by the observation that mixtures of these two species (ferrocene and ferricinium) yield composite currenbpotential curves a t the r.p.e. which have El/zvalues for the total wave of 0.145 to 0.146 v. in 0.1 M tetraethylammonium perchlorate supporting electrolyte. If it is assumed that in aqueous media the limiting currents a t the r.p.e. of equimolar solutions of ferrocene and ferricinium are the same in the same supporting electrolyte, then it is possible to estimate the concentration of ferrocene in its saturated solution in aqueous 0.1 M tetraethylammonium perchlorate. From the data of Table I11 this is found to be (0.715/ 4.60) x 1.114 x 10-4 M = 1.7 x 10-5 M . The plots of C"* us. &, for AN solutions of tris(ophenanthroline)iron(II) perchlorate and tris(o-phenanthroline)iron(III) perchlorate (Figure 2, curves A and B) show these salts to be strong electrolytes which are highly dissociated at the concentrations used in the potentiometric studies. The Onsager relationshipsla for these salts were calculated to be: (19) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," 2nd Ed., Butterworth and CO.Ltd., London, 1959.


3055

Table III : Characteristics of Current-Potential Curves of Ferrocene and Ferricinium Ion in Water a t the R.p.e. (Supporting Electrolyte Tetraethylammonium Perchlorate)

System

Supporting electrolyte concn., M

Limiting current,

Electrode process

Ferricinium, 1.114 X lo-* M Ferrocene (saturated) Ferrocene (saturated)

0.1 0.083 0.0204

Fe(CsHs)z+ e + Fe(CzH& Fe(C6Hs)z-, Fe(CsH&+ e Fe(CsHs)r+ Fe(CsHs)z+ -k e

+

Ira.

+

4.60 0.715 0.705

Slope of Er.p,e, log (il - i ) / i plot

(v. us, 8.c.e.)

us.

0.0615

0.145

-0.0575

0.144

-0.058

0.148

A, = A0 - 1020C'/2 for Fe(phen)3(C104)2and A, = A, - 1912C'/' for F e ( ~ h e n ) ~ ( C l O and ~ )are ~ plotted in

curve Bl), it is considered that the simple conductance ratio gives a reasonable value for the activity coefficient of the ferricinium ion and that the average of Figure 2, curves a and b, respectively. The latter is these three values of E" (0.0740 v.) is a reliable value almost identical with the experimental plot (Figure 2, curve B). This agreement is rather fortuitous, esfor E" for this couple vs. (E'*'~A~)AN. Ward1' gives a pecially a t the higher concentrations, because of the value of 0.0716 v. for this couple a t 30". This is the limitations of the Onsager equation, particularly average of several experiments in which the concenwhen applied to 3: 1 electrolytes in solvents of only tration of ferricinium picrate was 2.17 to 8.65 X M moderate dielectric strength (dielectric constant of and that of ferrocene was 5.0 to 6.71 X lo-* M. No AN = 36.7).19 The conductivity results indicate corrections were made for the activity coefficients of the ferricinium ion in his work. that very little error will be introduced into the value of E" for the tris(o-phenanthroline)iron(II)-tris(oThe concentrations of the solvated proton [H+] phenanthroline)iron(III) couple calculated on the and the activity coefficients of the ions in the bufbasis of complete dissociation of the salts. Thus the fer solutions used to determine the standard potential of the hydrogen electrode in AN were calculated from values of E' (Figure 3, curve A l ) give a reliable value of E" (0.8459 v.) for this couple os. ( E o * O 1 ~ when g ) ~ ~ ,the stoichiometry of the system and the relationships extrapolated to zero ionic strength. Ward" gives a value of 0.831 v. for this cell a t 30" and an ionic strength of 5.4 X in good agreement with our results. Regarding the effect of added tetraethylammonium perchlorate on the potential of this couple, the neutral salt added suppresses the dissociation of the iron(II1) salt more than that of the iron(I1) salt. Therefore, the potential of the system should become less positive (as is found). Also, there is the ionic strength effect and the Debye-Huckel expression which manifests itself in the same way as the salt effect on the dissociation. 1.594I'/' logf= (7) On the other hand, ferricinium picrate appears to 1 4- O.48aI1/' be only a moderately strong electrolyte in AN since where I is the ionic strength and a is "the distance of the experimental results deviate appreciably from the closest approach" of the ions which has been taken as Onsager plot (Figure 2, curve c for which A, = & - 338 C'/'), indicating that significant ion pair forma- 5 8. for all ions in this system. The activity coefficients of uncharged species and ion pairs were taken tion occurs. I n order to allow for this in the calculato be unity. tion of the standard oxidation-reduction potential of The standard potential E"' in Table I should be a the ferrocene-ferricinium couple, the activity of the constant. The deviation from constancy may be due ferricinium was calculated by multiplying the conin part to incorrectly approximated values of activity centration of the salt by Ac/Aa. Values of & were coefficients, in part to liquid junction potentials, and interpolated from Figure 2, curve C for the concenof the hydrogen electrode in finally to abnormalities trations of ferricinium picrate used in the potential solutions containing relatively high concentrations of measurements. Since the values of E" calculated for sulfuric acid. With decreasing ionic strength the this couple using these assumptions were practically constant for the three experiments in which no tetra(20) I. M. Kolthoff and M. K. Chantooni, Jr., J. Phys. Chem., 66, ethylammonium perchlorate was added (Figure 3, 1075 (1962). Volurne 60, Number Q September 1966

3056

I. 34. KOLTHOFF AND F. G. THOMAS

liquid junction potential should become negligible because a t a smaller ionic strength the ions present have about the same mobility. A value of E"' = 0.030 v. vs. (EO.O'A,)AN is extrapolated. The standard potentials of the three electrodes ~ listed in Table IV, studied relative to ( E 0 * O 1 A g ) ~ are column 2 and relative to ( E ' A ~ ) AinN column 3. The potentials of these electrode systems relative to the standard potential of the silver electrode in AN, Table IV: Standard Electrode Potentials in AN a t 25" E a , v. (EO*O~A~)AN----U8. This work Ward's dataD U8. (E'A~)AN ( E o ~ l a q

---US.

Electrode

PtIFe(Dhen)2 +, Fe(phen);;f' Pt@e(CsH&, Fe(C6H5h+ PtlH2, H +

A!&+

0.5459

0.831

0.0740

0.0716

-0.0561

0.1203'

-0.100 0

0.030 0. 13Olb

...

0.7158

1.120

0.348 0.304 0.404

From ref. 11, at 30'; not corrected for ionic strength effects, activity coefficients all taken to be unity. Calculated from the Nemst equation (see text). c Calculated from the Nermt tion, assuming CZA=+ = 0.01 M .

'

expected to be quite small (in the case of the hydrogen electrode this is true only in very dilute solutions), probably no more than 2 or 3 mv. Assuming that the standard potential of the tris(ophenanthroline)iron(II)-tris(o-phenanthroline)iron(III) couple is the same in AN as it is in water (1.120 v. vs. (EoH)aq),l5 the values of the standard potentials of the four electrode systems studied, relative to (EoH)sq, were calculated and are ,listed in the final column of Table IV. The potential of the silver-O.O1 M silver nitrate in AN reference electrode is 0.274 v. on this scale. The value for ( E a A g ) A N vs. ( E o H ) a q of 0.404 v. is in good agreement with that quoted by Ward" (0.41 v.) but is 0.034 v. more positive than S t r e h l o w ' ~ ~ ~ ~ value of 0.37 v., based on the rubidium scale, corrected for solvent effects. In view of the assumDtions made regarding activity coefficients and liquid junction potentials, these values are considered to be in error by no morethan5 mv. Strehlow8pggives a value of 0.14 v. for (E'B)ANvs. ( E ' H ) ~ This ~ . is considerably in error. It is based on the measurement of Hammett's acidity functionz1 Of dilute solutions of sulfuric acid in AN with o-nitroaniline as indicator and Pleskov's data on the measured pH of hydrochloric acid solutions in AN. Strehlow erroneously assumed that sulfuric acid is completely dissociated in AN. In solutions which are not too dilute, sulfuric acid dissociates mainly according to the equation

( E o A g ) were ~ ~ , calculated from the potentials relative to (E""A~)ANand the Nernst equation assuming that the activity coefficient of the silver ion in 0.01 M silver nitrate in AN is given by the conductivity ratio 2H2S04 H+AN H2S04HS04(8) (AO.O~/AO)A~~-JO~ in AN. This assumption was made with a dissociation constant given by eq. 5.13 Conbecause the experimental plot of A, vs. C1la(from the sidering the change of the acidity function as an apdata of Walden and Birrla) has a slope approximately proximate indicator of the change of the standard twice that of the theoretical Onsager plot, indicating hydrogen potential, a shift of 0.258 v. instead of 0.113 v. that silver nitrate is only a moderately strong electrois calculated from Strehlow's data. From our own lyte in AN (similar to ferricinium picrate). The measurements of the acidity functionl3 and the data value of &,.ol/Ao for 0.01 M silver nitrate in AN is of CoetzeeZ2for the constant est,imated to be 0.63 from the results of Walden and Birr.18 The use of the conductivity ratio to obtain K f ~ =~ [BH+]/[BI[(H+)ANI + the silver ion activity, a A g + , is considered to result in a B representing a variety of bases, it can be concluded better value for (E'A,)AN than that obtained using the that (E'H)ANmust be close to 0.30 v., which agrees concentration of silver, uncorrected for ionic strength and ion-pair effects, and the value 0.130 v. vs. (E""A~)ANwith our experimentally determined value. Pleskov' measured the potential of the hydrogen electrode in AN (Table IV) obtained using UA,+ should not be in error solutions of hydrochloric acid, and assuming (E'R~)AN by more than 1or 2 mv. = ( E ' R I , ) ~obtained ~, a value of 0.25 v. for (E'=)AN The potentials listed in Table IV ignore the liquid vs. (EoH)aq. Pleskov also assumed that hydrochloric junction potentials between the silver-silver nitrate acid is completely dissociated in AN, whereas it is in reference electrode and the half-cell under study. fact a weak electr01yte.l~ Although Pleskov allowed Ward" has shown that in 0.01 M silver nitrate solutions in AN, the transference number of the silver ion (21) L. P. Hammett and A. J. Deyrup, J. Am. Chem. SOC.,54, 272 is 0.499, and since the mobilities of the main current(1932); L. P. Hammett and M. A. Paul, ibid., 56, 827 (1934). carrying ions in each of the three electrode systems (22) J. F. Coetzee and D. K. McGuire, J. Phys. Chem., 67, 1810 (1963). are similar, the liquid junction potentials involved are

+

The Journal of Physical Chemistry


for the volatility of hydrochloric acid from its solutions in AN, he was unaware of the decrease in both the hydrogen ion activity and the volatility of hydrochloric acid on aging the solution^.'^ S t r e h l o ~ , ~using ,~ Pleskov's' value of 0.25 v. for (E'H)AN (based on (EoRb)AN = (EoRb)aq = -2.92 v.) arrived a t his value of 0.14 v. for (EoH)A~on the basis of his corrected value of -3.03 v. for (EoRb)AN. Similarly, Strehlow's value of 0.37 v. for (EoAg)ANis also based on Pleskov's value measured relative to (E'R~)AN.Since our value for (EoAg)A~is 0.034 v. more positive than Strehlow's, it would appear that his calculated value for (EoRb)ANof -0.11 v. relative to (EoRb)aqis in error by about 0.03 v. and that (E'R~)ANis close to -3.00 v., relative to (E'R),~. The uncertainty in his calculations is apparently due to his use of concentrations instead of activities of the saturated alkali halide solutions in AN and water to determine their solvation energies in AN. Using a similar procedure to that used for the rubidium case, StrehlowaV9calculated the difference between (EOferrocene)AN and (Eoferroaene)aq and so obtained a value Of 0.34 V. for (Eoferroaene)AN us. This compares favorably with our value of 0.348 v. and indicates that the assumption used in this work that (E°Fe(phen)8z+)AN us. (EoH)aq equals (EOFe(phen)sZ+)aqis a good one. The effect of added electrolyte (tetraethylammonium perchlorate) on the potentials of the iron phenanthroline and ferrocene half-cells is shown in Figure 3, curves A2, B2, and B3. I n calculating the ionic strength of these solutions, allowance was made for the ion-pair formation of tetraethylammonium perchlorate using the relationship

I n curves A2 and B2, concentrations were used to calculate the potentials from the Nernst equation and, as expected, increasing ionic strength has the greatest effect on the potential of the iron-phenanthroline system (curve A2) because of the charges on the ions involved (2+ and 3+). I n curve B3, the activity of the ferricinium ion was used to calculate values of E" (eq. 2). The deviation of E" from a constant value is quite small, indicating that the Debye-Huckel relationship (eq. 7) gives reasonable values for the activity coefficients in this system provided the liquid junction potential between the two half-cells does not vary in the range of ionic strengths studied. Assuming that a plot of Ell, for the oxidation of ferrocene in water a t the r.p.e. us. Ill' is linear, then a value of 0.152 v. (vs. s.c.e.) is estimated for El/, for

3057

ferrocene in water at zero ionic strength from the values of El/2for this oxidation in 0.083 and 0.0204 M aqueous tetraethylammonium perchlorate solutions (Table 111). Since the oxidation a t the r.p.e. is reversible, E,,, may be identified with Eo for this system and hence (E'ferrooenJaq is estimated to be 0.394 v. (Eos.c.e.0.242 v.") in good agreement with Strehlow's value of +0.40 v.899 Thus, in this case, Ellrcan be identified with E o for the system; however, in AN solution, in the presence of 0.1 M tetraethylammonium perchlorate E" is 0.332 v. us. s.c.e. (from Table I1 and eq. 2), whereas Ellzfor the oxidation of ferrocene at the d.m.e. is 0.379 v. us. s.c.e. Thus, the oxidation of ferrocene appears to be retarded a t a mercury electrode, cf. a platinum electrode, indicating that, although the oxidation is reversible, some interaction between the mercury and the ferrocene or ferricinium occurs which inhibits the oxidation process. Liquid Junction Potential between AN Solutions and the S.c.e. The potentials of the cells of Table I1 without added tetraethylammonium perchlorate were corrected for the effects of ionic strength using the plots of Figure 3 (curves A1 and Bl). Using these potentials us. s.c.e., corrected for ionic strength (Table V, column 2), the liquid junction potentials between the s.c.e. and AN solutions at zero ionic strength, (E&,, were calculated using the data of .Table IV and are given in Table V, column 3. I n addition, the liquid junction potentials of these cells when 0.1 M tetraethylammonium perchlorate is present in the AN solutions were also estimated from the data in Tables I1 and IV and are given in column 4 of Table V. Quite good agreement for the values of (E& is obtained with the four electrode systems studied in this work. The variation in the values of for these four electrodes is undoubtedly due to the different effects of ionic strength on the potentials of the four electrodes, this effect being most pronounced on the tris(o-phenanthroline)iron (11)-tris (0 - phenanthroline)iron(111) electrode as expected. The results of other workers are also listed in Table V for comparison. By directly comparing a given electrode system in water with the same electrode system in AN, Ward1' obtains values of Elj which are in good agreement with our measurements using the s.c.e. From the difference between Ell2of the alkali ions in water and AN in 0.1 M tetraethylammonium perchlorate and the difference in the standard potentials of the alkali metals in both solvents, Elj can be found from the measurements of Coetzee, et aL4 Also from Coetzee's meas(23) "Handbook of Chemistry and Physics," 42nd Ed., Chemical Rubber Publishing Co., Cleveland, Ohio, 1960-1961.

Volums 69,Number 9 September 1966

3058


Table V : Liquid Junction Potentiale between Aqueous and AN System

Pt Fe(phen)2+, Fe(phen)aa+fj(s.c.e. Pt Fe( C6H& Fe(CsH&+lls.c.e. Pt H2, H+l/s.c.e.

1.127 0.351 0.306 0.409 0 .225c -0.11QC

0.249 0.245 0.248 0.247 0.26

0.157 0.220

...

0.227

Q.232d 0.286“

This work This work This work This work 3 11 11

0.23 to 0.26’

5

E-11 (Table IV) corrected for ionic strength effects and activity coefficients in AN solutions. Based on ( E 0 & ) A N = 0.404 v,; (EOJ’&,)AN = 0.274 v. (vs. Uncorrected for ionic strength effects. Corrected for activity coefficients ( f & + ) * ~= E-11. 0.632 (see text), (fh+)8q = 0.900 (ref. 19). Assuming ( E o R b ) A N vs. (EoH)aq = 3.00 v. (see text). a

’

urements, it appears that Elj is of the same order of value of 0.88 v. (vs. (Eo&J for the oxidation potential magnitude in propionitrile, isobutyronitrile, benzoof this compound in 0.1 M aqueous sulfuric acid, ie., nitrile, phenylacetonitrile, and acetone as it is in AN. 0.64 v. us. s.c.e. This indicates that Nelson and From the data of Table V it can be concluded that Iwamoto’s “extrapolation” technique for determining after correcting for ionic strength effects in the AN the oxidation-reduction potentials in water is questionsolutions, Eli of solutions in AN us. the s.c.e. is of the able. Using Brandt and Smith’s value of the oxidaorder of 0.25 v.; Le., 0.25 v. must be subtracted from tion potential in water and assuming that the corthe measured potential vs. s.c.e. rections for ionic strength effects are the same for this in the two solvents as they are for the tris(osystem This value is completely a t variance with the values phenanthroline)iron(II) system, we calculate that the of Eli (us. s.c.e.) estimated by Nelson and I w a m o t ~ . ~ ~ liquid junction potential is 0.28 v., in fair agreement They determined the half-wave potentials at the r.p.e. with our results. The data obtained by Nelson and us. s.c.e. of the reversible anodic waves of tris(4,7-diIwamotoZ4 with ferrocene do not differ much from our methyl(o-phenanthroline)iron(II), bis(2,9-dimethyl-oresults (the small difference probably being due to the phenanthroline)copper(I), ferrocene, and benzyl ferdifferent types of junctions used between the solutions rocene in solutions in a variety of organic solvents which and the s.c.e.; they used a flowing type whereas we contained 0.1 M lithium perchlorate as supporting used an agar-saturated potassium nitrate bridge) electrolyte. Correction was made for the iR drop. and after allowing for ionic strength effects we derive a We will only consider their results in water and AN value of 0.26 v. for Eli from their results. Thus, the for the two systems (ferrocene and 4,7-dimethyl(oconclusion drawn by Nelson and Iwamoto regarding phenanthroline)iron(II)) which they studied in both the small value of Eli in a host of organic solvents is solvents. With the 4,7-dimethyl(o-phenanthroline)not acceptable. iron system they report a value of Ell2in AN of 0.860 in water of v. and an “extrapolated value” of El/, (24) I. V. Nelson and R. T.Iwamoto, Anal. Chem., 33, 1795 (1961); 0.830 v. vs. s.c.e. This would indicate that Elj is 35, 867 (1963). only 0.030 v. However, Brandt and Smithz6report a (25) W. W. Brandt and G. F.Smith, {bid., 21, 1313 (1949).

Ths Journal of Physiccrl Chembtry

Electrode Potentials in Acetonitrile. Estimation of the Liquid Junction

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