LITERATURE CITED (1) M. K. Schwartz, Anal. Chem., 45, 739A (1973). (2) J. M. Fitzgerald, Ed., "Analytical Photochemistry and Photochemical Analysis: Solids, Solutions, and Polymers", Marcel Dekker Inc., New York, NY, 1971, Chapters 4 and 5. (3) J. G. Calvert and J. N. Pitts, Jr., "Photochemistry", John Wiley and Sons, New York, NY, 1967, Chapters 3-6. (4) R. S. Becker, "Theory and interpretation of Fluorescence and Phosphorescence", W. A. Benjamin & Co., New York, NY, 1969, Chapters 3, 7, 9. 15, 17. (5) N. J. Turro, "Molecular Photochemistry". W. A. Benjamin & Co., New York, NY, 1965, Chapters 5 and 6. (6) J. D. Margerum, A. M. Lackner, M. J. Little, and C. T. Petrusis, J. Phys. Chem., 75, 3066 (1971). (7) W. G. Herkstroeter, A. A. Lamola, and G. S.Hammond, J. Am. Chem. Soc., 88, 4537 (1964). (8) R. P. Wayne, "Photochemistry", American Elsevier. New York. NY, 1970, Chapters 4-6. (9) V. R. White and J. M. Fitzgeraid, Anal. Chem., 44, 1267 (1972). (10) L. Weil, Science, 107, 426 (1948): (11) T. Gomyo, Y. Yang, and M. Fujimaki, Agric. Biol. Chem., 32 1061 (1968). (12) L. Weil, T. S. Seibies, and T. T. Herskovits, Arch. Biochem. Biophys., 111, 308 (1965). (13) L. Weil, Arch. Biochem. Biophys., 110, 57 (1965). (14) J. S.Bellin and C. A. Yankus, Arch. Biochem. Biophys., 123, 18 (1968). (15) J. S. Bond, S. H. Francis, and J. H. Park, J. Bid. Chem., 245, 1041 (1970). (16) M. I. Simon and H. VanVonakis, Arch. Biochem. Biophys., 105, 197 (1964).
(17) F. W. Morthland, P. P. H. DeBruyn, and N. H. Smith, Exp. CellRes., 7, 201 (1954). (18) G. Oster and N. Wotherspoon, J. Am. Chem. Soc., 79, 4836 (1957). (19) L. Weil and J. Maher, Arch. Biochem., 29, 241 (1950). (20) R. F. Bartholomew and R. S.Davidson. Chem. Commun., 1970, 1174. (21) R. F. Bartholomew and R. S.Davidson. J. Chem. Soc., C, 1971, 2347. (22) C.S.Foote and R. W. Denny, J. Am. Chem. SOC.,93,5168 (1971). (23) L. P. Simpson. J. S.Kirby, and M. L. Randoipy, Nature. 199, 243 (1963). (24) R. M. Danziger, K. H. Bar-Eli, and K. Weiss, J. Phys. Chem., 71, 2633 (1967). (25) C. A. Parker, J. Am. Chem. Soc., 83, 26 (1959). (26) W. M. Clark, "Oxidation-Reduction Potentials of Organic Systems", Williams and Wilkins Co., Baltimore, MD. 1960, Chapter 5. (27) C. Bodea and I. Silberg, Adv. Heterocycl. Chem., 9, 322-449 (1968). (26) 0. Tomicek, "Chemical Indicators", Butterworths, London 195 1. (29) H. A. Strobei, "Chemical Instrumentation: A Systematic Approach", 2nd edition, Addison-Wesley, Reading, MA, 1973, pp 285-66. (30) H. L. J. Backstom and K. Sandros, Acta Chem. Scand., 14, 48 (1960). (31) G. N. Lewis, 0. Goldschmid, T. T. Magel, and J. Bigeleisen, J. Am. Chem. Soc., 85, 1150 (1943). (32) G. N. Lewis and J. Bigeieisen, J. Am. Chem. SOC.,85, 1144 (1943). (33) G. W. Ewing, "instrumental Methods of Chemical Analysis", McGrawHili, New York, NY, 1969, pp 62-63.
RECEIVEDfor review June 10, 1974. Accepted October 23, 1974. Financial support for this work was provided by Grant E-384 from the Robert A. Welch Foundation.
NOTES
Theory for Adsorption Re-Equilibration in Reverse Step of Double Potential Step Chronocoulometry of Adsorbed Reactants C. Michael Elliott and Royce W. Murray Kenan Laboratories of Chemistry, University of North Carolina, Chapel Hi//, N C 275 74
Double potential step chronocoulometry is today the method of choice for the study of adsorbed electroactive species ( I ) . For a reducible species, the method consists of allowing the working electrode to come to equilibrium with a solution of the adsorbing species 0 a t a potential E i n i t where no faradaic reaction occurs, then stepping the electrode potential to E f i n a l on the diffusion limiting plateau of the reduction wave of 0, for some time T , while measuring the charge flow, Qf. At time T , the electrode reaction is reversed by returning the potential to E i n i t , and the reverse charge flow, Qr, is measured until t = 27. Double potential step chronocoulometry was introduced by Anson ( 2 ) ,theoretically described by Christie et al. (3),and applied to adsorption by Anson et al. ( 4 ) . The relations for charge during the forward and reverse potential steps are: Qf = Q(t Qb = Q ( t =
908
7)
7)
= KO
+
Qd,
(1)
+
ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
+
where K = ~ ~ F A C O ~ ( D O /BT=) ' (/t~-, T ) ' / ~ - t1/2, I'o is the surface excess of 0 a t E i n i t , and Qdl is the difference in double layer charge between E i n i t and Efinal. Data analysis is accomplished by least squares plots of Qf vs. t1l2 and Qr vs. B (using a linearized form of Equation 2) (3), taking the difference between their intercepts to cancel Qdl and extract n F A r o . Double potential step chronocoulometry owes its superiority over the single potential step method (5, 6) to its effective correction for the double layer charge term Qdl, using data from a single experiment, and in a more nearly rigorous form. The term Q d l appearing in Equations 1 and 2 is the change in double layer charge between Einit and E f i n a l with adsorbed reactant being present a t Einit. Any changes in the double layer charge a t E i n i t due to the absorption of 0 are thus automatically taken into account. The double potential step method does include one major assumption, which is that the adsorbed layer, and the appropriate Qdl, becomes instantaneously (or a t least very rapidly compared to T ) re-established upon reverse potential stepping. If such re-equilibrium did not occur,
t
/
t
i
/
12
I6
20
n FAr I K T ‘I2
Figure 1. Graphical representation of Equation 6 and the minimum re-equilibration time, tea
and if Q d l were a function of nFAro, then an error in nFAro would result in that the Qdl of Equations 1 and 2 would differ and thus would not exactly cancel. That the reverse step re-equilibration assumption is valid seemed to be settled in early applications of the double potential step method to adsorbed metal complexes ( 4 , 7 ) . Typically, the first 5-10% of the backstep data would be discarded to ensure that the data analyzed for rodid not include erroneous Q d l values. We have recently (8, 9) conducted double potential step chronocoulometric measurements of metal complex adsorptions where the values of nFAr0 were quite large. Considering that longer times would be required during reverse potential stepping to re-establish an adsorbed layer with large nFAro, we re-investigated the reverse step re-equilibration and report here a rigorous theoretical description for it. The minimum time required for re-establishing the adsorbed layer during the reverse step is that time required to generate an accumulated flux for 0 equal to nFAro. This minimum time period, which occurs after T in the initial period of the reverse step, and which we shall call teq, corresponds to a large adsorption coefficient for 0, Le., all 0 contacting the electrode surface for t > T will adsorb until an adsorbed layer equivalent to nFAro has been regenerated. Species 0 is regenerated a t the surface by two processes after T: continued diffusion of 0 from the bulk solution, and the re-oxidation of the reduced form accumulated during the forward step. The charge due to diffusion and readsorption of 0 from the solution after T is given by
Qi’= Q ( t
>
7)
- Q(t =
7)
= Kt‘/2
- K r 1 l 2 (3)
The charge due to reoxidation of reduced form, Qb’, is given by Equation 2 with the Q d l term omitted. The minimum time for re-equilibration, or when t = t e , T , is then
+
nFAro = Qf’ +
(4 )
Qb’
or
gAro= K(teq+
7)”’
- K7‘”
+ KG + eq
A rearrangement yields
This expression is presented in graphical form in Figure 1.
The portion of the reverse potential stepping period, t e q / T , which is required for re-equilibration is seen to depend on T , ro, and Cob. At large values of ro, small T , or low concentrations of electroactive species 0, the re-equilibration time can require a large fraction of the reverse step. We emphasize that our assumption of very strong adsorption, e.g., that all 0 species reaching the electrode adsorb until equilibrium is reached, makes t,, a minimum time. For weakly adsorbing systems, our treatment will substantially underestimate the actual equilibration time required, perhaps by several-fold. Whether a large value *of teq/iresults in error of course depends on the relative magnitudes of n F r o a n d Qdl, and whether the value of Qdl actually is sensitive to the presence of adsorption. These results were used to peruse a sampling of earlier double potential step chronocoulometric data on metal complex adsorptions. For most of the data examined conditions of Cob and ro were such that t,, was small relative to T. There were, however, a few cases found where significant portions of the back step data used corresponded to times before the re-equilibration was established. Anson and Barclay ( 7 ) , in a study of Cd(I1) adsorption from iodide, cited 0.2mM Cd(I1) and 0.05M iodide as the “worst” reequilibration case and used an approximate relation to predict teq/T = 0.09 for this case. The relation used actually gave a poor indication of the time required for re-equilibration since the more rigorous approach above indicates teq/T = 0.43. That is, the adsorbed Cd(I1) layer could not have been re-established until 43% of the reverse step period had elapsed. The value of t e q / r of course decreases at higher Cd(I1) concentrations; for 0.05M iodide and 0.4, 0.8, and 1.2mM Cd2+, the worst case in each data set was teq/T = 0.18, 0.06, and 0.03, respectively. In each case, 0.1 T was allowed for re-equilibration. In another study, Herman et al. (9) investigated adsorption isotherm discontinuities leading to very large r for the adsorption of Pb(I1) from bromide and iodide solutions. In bromide solutions a t -0.3 volt with l.OmM Pb(II), teq/T was only 0.06 before the isotherm discontinuity, but 0.40 after. At a lower O.lmM Pb(I1) concentration, in iodide solutions at -0.3 volt, a “worst case,” adsorption re-equilibration is much less complete since teqlr was 0.40 for iodide concentrations before the isotherm discontinuity but >4 after. Clearly in the latter case, the adsorbed PbI2 layer was far from being re-established even a t the termination of the experiment. While the assumption of re-equilibration of the adsorbed layer for t > T has clearly been violated in the above examples, we do not believe that the adsorption surface excess results in these particular studies are in difficulties on this account. In the Cd(I1) adsorption study, the overall data show that Qdl is not significantly altered by the adsorption of Cd(I1) halide complexes. Thus, re-equilibration is not essential. In the Pb(I1) adsorption study, the values of r p b are so large that any error in Qdl as deduced from the back step intercept would have an insignificant effect on r p b . For example, in the severe case cited above for O.lmM Pb(I1) in iodide, a (highly improbable) 50% error in Qdl results in only 10% error in r p b . Also, the metal complex adsorption again seemed to produce no significant change in Qdl. In fact, that large effects on Qdl are absent seems to be common among metal complex adsorptions, although there are exceptions (IO). As noted above, when Q d l is not a function of adsorption, or when ro is so large that errors in Q d l lose significance, complete re-equilibration of the adsorbed layer on the reverse step is not essential to accurate functioning of the double potential step method. On the other hand, Figure 1 shows that the method can encounter real difficulties if Qdl is significantly altered by adsorption and C o b and To are in ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
909
ranges making ro error-prone, as might be encountered in strong adsorption of bulky electroactive organics. Virtually the only experimental adjustment available is the back step time T , and this has only limited effect because of its square root function (Equation 6). In a situation where Qdl is adsorption-dependent, and an adjustment of T to the extent indicated by Figure 1 is impractical, it may be necessary to resort to the older single potential step method. In this method, one must include a correction experiment for the adsorption-induced change in Qdl a t Einit as well as the normal double layer charge blank correction, and such multiple corrections lessen the sensitivity and precision of the I'o measurement.
LITERATURE CITED (1)R. W. Murray, "Chronoamperometry, Chronocouiometry, and Chronopotentiometry," in "Techniques of Chemistry," Volume I, Part IIA, A.
Weissberger and E. Rossiter, Ed., Wiley-lnterscience, New York, NY, 1971.
(2) F. C. Anson, Anal. Chem., 38,55 (1966). (3)J. H. Christie, R . A. Osteryoung. and F. C. Anson. J. Nectroanal. Chem., 13, 236 (1967). (4)F. C. Anson, J. H. Christie, and R . A. Osteryoung, J. Nectroanal. Chem., 13, 343 (1967). (5) J. H. Christie, G. Lauer, R . A. Osteryoung, and F. C. Anson, Anal. Chem., 35, 1979 (1963). (6) F. C. Anson. Anal. Chem., 36, 932 (1964). (7)F. C. Anson and D. J. Barclay, Anal. Chem., 40, 1791 (1968). (8)C. M. Elliott and R. W. Murray, J. Am. Chem. SOC.,96,3321 (1974). (9)H. B. Herman, R. L. McNeely. P. Surana, C. M. Elliott, and R . W. Murray, Anal. Chem., 46, 1258 (1974). (10)S.N. Frank and F. C. Anson, J. Nectroanal. Chem., 54,55 (1974).
RECEIVEDfor review October 21, 1974. Accepted December 17, 1974. This research was assisted by the National Science Foundation under grant GP-38633X and by the Materials Research Center, U.N.C., under National Science Foundation grant GH-33632.
Titration of Acids in Benzene-Nitrobenzene, BenzeneNitromethane, and Benzene-Acetone Binary Solvent Systems A.
K. Amirjahed
College of Pharmacy, The University of Toledo, Toledo, OH 43606
Martin 1. Blake Department of Pharmacy, University of Illinois at the Medical Center, Chicago lL 606 12
Fritz ( I ) performed a series of potentiometric titrations on certain amines in acetonitrile. He observed that the millivolt reading a t the half neutralization point of a potentiometric titration designated as H N P or the half neutralization potential could be correlated with the base strength of the amine. Thus, the potentiometric measurement of H N P offered a method for relating the base strengths of amines in non-protolytic solvents. Hall (2) used this method to determine the base strength of a number of mono- and diamines in several nonaqueous solvents. He found that the observed order of the base strength of the alkylamines was similar to that found in water, and when the data obtained for the nonaqueous solvents were plotted vs. that for water, linear relationship resulted. Chatten and Harris ( 3 ) studied certain basic amines and phenothiazines in five organic solvents and reported a linear relationship between the pKb and the H N P of the amines. Miron and Hercules ( 4 ) also observed a linear relationship between the acidity strength expressed in millivolts and the pK, of the acid for a series of substituted benzoic acids and phenols which were titrated in a variety of nonaqueous solvents. Davis and Paabo (5) studied the comparative strengths of certain acids in benzene and obtained linear relationships. In a study of the relative acidity strengths of meta- and para-substituted benzoic acids and aliphatic monocarboxylic acids in pyridine and water, Streuli and Miron (6) obtained linear relationships. Other studies on acids and bases have been reported (7-16) in which relative strengths in nonaqueous and aqueous media have been compared. In general, there is considerable evidence that a linear relationship exists between the relative strengths of a series of acids or bases in nonaqueous media and their pK, or pKb values, respectively. In determining the HNP's to establish this relationship, the fluctuating variables inherent to potentiometric measurements in nonaqueous media in910
ANALYTICAL CHEMISTRY, VOL. 47, NO. 6, MAY 1975
troduce large variabilities in the results. Some of these variables are: the nature of the medium, the interactions between molecules of the medium and the acid, the standard potential of the reference electrode and the cell, the liquid junction potential, and the loss of protons by the glass membrane. Dielectric constant of the medium, (Dm),is one of the major factors influencing the linear relationship and is often difficult to control. I t can be closely controlled, however, by using one of the nonaqueous binary solvent systems previously described ( 1 7 ) . In that paper, experimental procedural details were given for determining the dielectric constant of a series of nonaqueous binary solvent systems and for preparing nonaqueous solvent mixtures having specific dielectric constants within a range of values provided by the system. Formulas relating the dielectric constant and the composition of the solvent mixture were developed. In a second paper (181, procedural details were presented for determining the H N P of a series of acids of varying pK, in the benzene-acetonitrile solvent system.
EXPERIMENTAL The details of the experimental procedures reported earlier (17, 18) are applied to the study of three additional nonaqueous binary
solvent systems. Each system consists of a polar and a nonpolar component. The nonpolar component in the three solvent systems is benzene. The polar components are nitrobenzene, nitromethane, and acetone in the three systems, respectively. In the benzene-nitrobenzene and benzene-nitromethane solvent systems, the solvent mixtures have dielectric constants of 5 , 10, 15, 20, 25, and 30. The mixtures of the benzene-acetone solvent system have dielectric constants of 5 , 10, 15, and 20. The same acids reported earlier (18)were used in this investigation. They were selected such that the effect of the structure of the acids was randomly distributed. The same principle of randomness was built into the weighing of the acids, their titration, construction of the titration curves, and in the determination of the millivolt readings corresponding to the HNP's. The HNP values of the acids determined in a specific solvent mixture (of the particular bi-
