(20) J. E. Falk, "Porphyrins and Metalloporphyrins", Vol. II, Elsevier, New York, 1964. (21) A. Wolberg and J. Manassen, J. Am. Chem. SOC., 92, 2982 (1970). (22) M. Momenteau, M. Fournier, and M. Rougie, J. Chim. Phys., 67, 926 (1970). (23) S. B. Brown and I. R. Lantzke, Biochem. J., 115, 279 (1969). (24) R. T. Sanderson. "Inorganic Chemistry", Reinhold Publishing Corp., New York. 1967, p 136. (25) D. Dolphin, A. Forman, D. C. Borg, J. Fajer, and R. H. Felton, froc. Nat. Acad. Sci. USA, 68, 614 (1971). (26) L. J. Boucher, "Manganese Porphyrin Complexes Il-Electronic Spectroscopy and Structure" in "Coordination Chemistry", Plenum Press, New York, 1969.
(27) D. V . Stynes. H. C.Stynes, B. R. James, and J. A. Ibers.. J. Am. Chem. Soc.. 95. 1796 11973). (28) K. Yamamoto and T. Kwan, J. Cats/., 18, 354 (1970). (29) L. Meites, "Polarographic Techniques", 2nd ed.. Interscience Publlshers, New York, 1966. (30) W. R. Scheldt and J. L. Hoard, J. Am. Chem. Soc., 95, 8281 (1973). (31) W. R. Scheidt, J. Am. Chem. SOC., 96, 84 (1974).
RECEIVEDfor review March 28, 1975. Accepted August 4, 1975. The National Science Foundation (GP-42479X) provided financial assistance.
Application of the Semiintegral Method to the CE Mechanism J. H. Carney Department of Chemistry, York College, Jamaica, N. Y.
1145 1
A successive approximation method of applying the semiintegrai to chemical reactions preceding a reversible electron transfer is described and tested on the cadmlum and lead nitrilotriacetic acid systems. Both the equilibrium and rate constants may be obtained by this method. This particular approach is applicable over a wide range of rate parameters and in the presence of significantly large values of uncompensated resistance.
We wish to report an extension of the semiintegral method to analysis of electrochemical systems represented by Equation 1 which are complicated by a homogeneous reaction that precedes a reversible electron transfer. kf
%+Ox
+ ne-
s Red
(1)
The transform variable is s , and E is the transform of the current. The diffusion coefficients of 2 and Ox are assumed to be equal and are represented by D. For linear sweep voltammetry, the current varies in a complex fashion, but it can be approximated by a series of linear current segments as previously demonstrated (5):
The terms bj are the slopes of the individual segments. The term a0 is the current a t the beginning of the first segment. Experimental conditions can be arranged in linear sweep voltammetry so that the initial current, a0 is zero. The current function of Equation 3 with a0 = 0 is transformed, combined with Equation 2, and inverted to yield Equation 4.
kb
Imbeau and Saveant have already indicated how the semiintegral method could be applied to such systems under conditions of complete kinetic control of the current ( I ) . Lawson and Maloy have treated the EC and ECE complications by calculating numerical working curves of the diffusion controlled semiintegral for double potential step experiments (2). The range of usefulness for the method presented in this communication is the same as Nicholson and Shain's method ( 3 ) of nonlinear curve fitting but possesses the advantage of simplicity of use and allows correction for uncompensated resistance. Furthermore, this method does not require precalculated working curves.
THEORY The necessary equations are most easily derived from consideration of chronopotentiometric theory under conditions of semiinfinite linear diffusion. For the reaction mechanism given by Equation 1, the concentration a t the electrode surface is obtained by taking the inverse Laplace transform indicated by Equation 2 ( 4 ) r
__
K
-
l+K
where C* is the sum of the concentrations of 2 and Ox in the solution bulk, K is the equilibrium constant for the equilibrium between 2 and Ox, and L is the sum (kf kb).
+
where
and
(7) The second term inside the braces of Equation 4 is equivalent to the semiintegral for the diffusion-controlled electron transfer (6). For the diffusion-controlled case as well as for the mechanism considered here, the concentration of Red a t the electrode surface is given by Equation 7. The term x ( t ) in Equation 4 contains the kinetic information. Unfortunately, because of the form of the kinetic term, direct analysis cannot be made. Values for L and the equilibrium constant must both be guessed and Equation 4 evaluated with these parameters, then the results compared with theory. The desired numbers are determined by a two-step approach. First L is adjusted until the ratio C,,(O,t)l C r e d ( O , t ) behaves in Nernst fashion. This behavior is determined by plotting potential vs. the second log term of Equation 8 and adjusting L until the plot is a straight line with slope RTInF.
ANALYTICAL CHEMISTRY, VOL. 47,
NO.
13, NOVEMBER 1975
2267
i 20
-
.I6
-
,I2
-
08
-
.04
r
W
,
I2
Figure 3. Nernst plot for the current-voltage curves of Figure 2 0
R, = 0 ohms, m Ru = 2500 ohms
Figure 1. Nernst plot for theoretical current-potential curve The values of parameters employed are K = 0.01, (kf f kb) = 43300 sec-'. De, = Drd = 1.0 X cmz sec-'. The various values of kf f k b tried are given below. 55000 sec-l, A 47000 sec-l, 0 42100 sec-', V 40000 sec-'
I
6
-0.6
-0.7
E1 is the intercept obtained by plotting Equation 8 with an incorrect (guessed) K , and E112 is the sum of the first two terms on the right side of Equation 8. The true equilibrium constant is K . Finally, the true value of L can be extracted from the product K2L, which was determined in the first step.
EXPERIMENTAL VERIFICATION The cadmium-nitrilotriacetic acid system, which has been studied by Shuman and Shain, is a good example of a homogeneous reaction which precedes a reversible electron transfer (7). In acetate buffers, the system shows two reduction waves. The second wave is the direct, irreversible reduction of the complex. The more positive wave involves the reversible electron transfer:
-0.0
Cd2+
POTENTIAL, V.
Figure 2. Current-voltage curves in the region of the first wave The more positive curve was taken with no added uncompensated resistance. The more negative curve was recorded with 2500 ohms resistance added. C' = l.OmM, A = 0.0224cm2, scan rate = 0.10 V sec-l, pH 3.20
+ 2e- + Cd(ama1)
This step is preceded by a two-path homogeneous dissociation of the complex. ki
CdNTA-
+
Cd2+ NTA3k-1
RT RT COA0,t) E = E o + -In (D,,d/D)1/2 -In (8) nF nF m ( t)/nFADlI2 The determination of L is illustrated in Figure 1 for a theoretical current-voltage curve for which K = 0.01 and L = 4.33 X lo4. Equation 8 is plotted for four values of L to determine which value yields a straight line with the correct slope. In this case, the guessed value of K is taken as the correct value. The value of L which produces the correct behavior is about 3% below the expected L . This discrepancy apparently arises from the approximations made in evaluating x ( t ) .I t was felt that this bias in calculating L would be less than the uncertainty introduced by experimental error. A simple algorithm was devised to compare the computed slope obtained from the plot of Equation 8 to the expected slope of RTInF; and from the difference, calculate a better value of L . In this manner, satisfactory results for L were obtained over the whole range of kinetic parameters tabulated by Nicholson and Shain ( 3 ) . The procedure described above actually yields the true value of the product K2L; thus, the determined value of L is affected by the guessed K . The correct value for the equilibrium constant can be obtained from E1 the potential axis intercept of the plot of Equation 8. RT K' K E1 = Ell2 +-In- RT -ln(9) nF l + K ' nF 1 + K
+
2268
(10)
CdNTA-
hz + H+ h=Cd2+ + HNTA2-
(11) (12)
-2
Reaction 11 is much slower than the acid-assisted path of Reaction 12. The PbNTA- complex, which was also studied, would be expected to behave in a similar manner.
EXPERIMENTAL Linear sweep voltammetry experiments with CdNTA- were carried out with a three-electrode controlled potential circuit of conventional design. The current-voltage curves were recorded on a Hewlett-Packard 7001A X-Y recorder. Experiments with PbNTAwere carried out with a Princeton Applied Research Model 170 Electrochemistry System. The syringe type hanging mercury drop electrode was a Metrohm E410. The counter electrode was a platinum wire and the reference electrode was a saturated calomel electrode with ionic contact made through an intermediate salt bridge containing the solution being studied. The resistance between the reference electrode tip and the indicator electrode was estimated to be less than 50 ohms and was thus neglected. Nitrilotriacetic acid (NTA) was obtained as the disodium salt monohydrate (Aldrich, Gold Label). A polarogram of Cd(I1) in the presence of this NTA showed the impurity wave previously noted by Shuman and Shain. The NTA was purified in the manner described by them ( 7 ) .Stock solutions were prepared by determinant weighings. Solutions for the experiments were prepared by taking appropriate aliquots of the stock solutions to give l.OmM Cd(I1) or Pb(II), 0.04M NTA, 0.1M sodium acetate, 1.OM KN03, and acetic acid to give the desired pH. All experiments were carried out a t 25 "C. Data from the current-voltage curves were digitized by hand, and the computations were carried out on an RCA 70/6 or an IBM 370 computer.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
Table I. Rate and Equilibrium Parameters for CdNTADH
2.90 3 .oo 3.10 3.14 32 0 3.50 3.65 3.90 4 .OO
kf, sec-1
127 125 95.4 88.0 84.5 57.1 43.6 31.3 18.6
K
0.10 0.097 0.076 0.064 0.059 0.046 0.045 0.028 0.028 SCAN RATE, V l S E C
Table 11. Rate and Equilibrium Parameters for PbNTADH
3.30 3.42 3 -48 3.54 3.59 3.69 3.85 3.89
kf, rec-1
K
100 81 68 60 45 44 29 20
0.0096 0.0082 0.0071 0.0098 0.0052 0.0050 0.0035 0.0034
Flgure 4. Rate parameter, vI@L, a$ a function of scan rate at pH 3.20
0 Ru = 0 ohms, W R, = 2500 ohms
I 140
"
-
"
"
I
100 120
RESULTS AND DISCUSSION Linear sweep experiments were carried out a t various p H values over a range of scan rates from 0.025 V/sec to 0.25 V/sec. A typical current-voltage curve for CdNTA- in the region of the first wave a t pH 3.20 is shown in Figure 2. Also included is the current-voltage curve obtained with 2500 ohms of uncompensated resistance deliberately added in series with the indicator electrode. The results of the semiintegral analysis for these two curves are shown in Figure 3 as a plot of potential vs. RT/nF In (Coz(O,t)/(m(t)/ nFAD1/2). In each case, the initial guess of the equilibrium constant was 0.05, and the initial guess of the kinetic parameter, L , was 2.0 x lo3 sec-l. For the curve obtained with negligible uncompensated resistance, the product was found to be 2262 sec-l; for the curve with 2500 ohms added resistance, L was found to be 2067 sec-l. The reasonably close agreement between the two values demonstrates the ability of the semiintegral method to correct for uncompensated resistance. Correction for the effect of uncompensated resistance was made by subtracting algebraically the ohmic voltage drop from the applied potential point by point. The fact that the points for both the case of negligible resistance and that with 2500 ohms resistance fall on the same line indicates that K for both cases is the same. From Equation 8, the true value of K was found to be 0.059. In practice, the value of L a t each pH was found by plotting the term v/K2L as a function of the scan rate, v. The slope of this plot yielded an average value of the product K2L. The slope method was employed to detect any unexpected dependence of K 2 L on scan rate. Figure 4 illustrates such a plot for experiments run at pH 3.20. Again, points obtained in the presence of 2500 ohms added resistance are included. The equilibrium constant was calculated from Equation 9 with a value of E1 taken as the average of the values of the intercept a t the various scan rates. Finally, the value of L could be determined, and then kf, the forward rate constant, obtained from K and L. Results of all experiments are included in Table I. Also the values of kf are plotted as a function of hydrogen ion activity in Figure 5 . The slope of this plot yields the value of the acid assisted dissociation rate constant as 9.0 f 0.6 x
20 OO
0
0.2
0.4
0.8
Flgure 5.
0.8
1:o
1.;
Id Forward rate constant as a function of hydrogen ion con["] Id
X
centration 0 R, = 0 ohms, W R, = 2500 ohms
104M-l sec-l. From the intercept, the value of the firstorder rate constant is found to be 25 f 5 sec-l. The secondorder rate constant is somewhat lower than the value of 4.1 X 105M-l sec-l determined by Shuman and Shain using Nicholson's method (7). At the same time, the first-order constant is about five times greater than the maximum value assigned by them. Since the values of the product K 2 L are in reasonable agreement with those of the previous workers, the probable cause of the discrepancies among the rate constants is the larger equilibrium constants found in this work. The values are 1.5 to 2.0 times larger than those determined by Shuman and Shain. It is not possible to determine which set of equilibrium constant values is more accurate since both give the expected behavior with change in pH. The equilibrium values presented in this communication are subject to uncertainty of about 3 mV in determination of the intercept potential, EI. This uncertainty would cause a range of f10% of the computed value of K . Dissociation of the PbNTA- complex was also investigated. As expected, linear sweep voltammetry proved that PbNTA- behaves in a manner identical to the Cd(I1) complex. Rate and equilibrium parameters for the PbNTAdissociation are listed in Table 11. The dissociation constants, K , show the expected dependence on pH. A plot of the rate constants as a function of hydrogen ion activity is linear. The slope of the plot indicates a secondorder, acid-assisted dissociation rate constant of 2.1 f 0.1 X 105M-' sec-l. The intercept of the plot is -3 f 4 sec-l.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
2269
Thus we assume that the first-order dissociation of the PbNTA- is essentially negligible.
LITERATURE CITED 11) (2j (3) (4)
.
,
J. C. lmbeau and J. M. Saveant. J. Nectroanal. Chem.. 44. 169 11973). R. Joe Lawson and J. T. Maloy,'Anal. Chem. 46, 559 (1974). R. S. Nicholson and Irving Shain, Anal. Chem., 36, 706 (1964).
J. W. Ashley and C. N. Reilley. J. Nectroanal. Chem., 7, 253 (1964). (5)J. H. Carney and H. C. Miller, Anal. Chem., 45, 2175 (1973).
(6) K. B. Oldham, Anal. Chem., 44, 196 (1972). (7) Mark S.Shuman and Irving Shain, Anal. Chem., 41, 1818 (1969).
RECEIVEDfor review May 20, 1974. Resubmitted July 2, 1975. Accepted August 4, 1975. This work was supported in part bv The Research Foundation of The City Universitv bf New York under grant number 10754N. Part of this work was carried out at the Department of Chemistry, University of Alabama, University, Ala.
NOTES
Anion Exchange Sorption Behavior of Benzoic Acid and Its Derivatives Kil Sang Lee, Dai Woon Lee, and Won Lee Department of Chemistry and Natural Science Research Institute, Yonsei University, Seoul, Korea
The aliphatic and aromatic organic acids have often been chosen as the typical solutes to study the sorption and elution mechanism in anion exchange system (1-8). It is generally known that aromatic carboxylic acids are adsorbed by both ion-exchange and molecular sorption on the anion exchange resins. In the molecular sorption of organic acids, the most important factor seems to be the interaction between the nondissociated acid molecule and the resin matrix. However, there are many other complicated factors which influence the sorption behavior of the acids. An extensive review about the sorption and elution mechanism of carboxylic acids was given by Jandera and Chur6Eek (9). The purpose of the present work was to study the sorption behavior of benzoic acid derivatives from the relationship between their distribution coefficients and their acid strengths which are closely related to their chemical structures. Therefore, this sorption behavior will be useful in predicting the elution position and the sorption degree of the related compounds.
EXPERIMENTAL Materials. The chloride form of a strongly basic anion exchange resin, Dowex 1-X8(100-200 mesh) was used throughout this work. The procedure for purifying the resin was described previously (IO, 11). In the water-methanol media, the concentration of methanol indicates the percentage by volume. Benzoic acid, its derivatives, potassium chloride, and methanol which were used in this work were all of analytical reagent grade. Weight Distribution Coefficients ( D ) . The weight distribution coefficients of the benzoic acid derivatives were measured by a batch method. Fifteen milliliters of water-methanol medium containing 0.025 mmol of the acid were added to 0.5 gram of resin in a 50-ml glass-stoppered shaking flask. The flask was mechanically shaken for an hour and allowed to stand for several hours. An aliquot taken from the supernatant liquid was then analyzed spectrophotometrically a t the absorption maxima of the acids. The D values were calculated from the relation described in the previous paper (8). All experiments were carried out a t 20 & 1 "C.
RESULTS AND DISCUSSION Weight Distribution Coefficients (log D ) of Benzoic Acid Derivatives on the Resin. In order to investigate the 2270
sorption behavior and the relationship between chemical structure and the distribution data, log D values of the acids were measured in the water-methanol media. The results are given in Table I. The dissociation constants given in Table I are taken from a handbook (12) as a rough guide to the interpretation of the results since we presumed a correlation between pK, and log D . Because the log D values were measured a t the natural pH of the solution, each acid would be present partly in the molecular and partly in the anionic form. Therefore, this sorption is likely to proceed by an anion exchange mechanism and the molecular sorption. The molecular soprtion mechanism, in turn, may be due to van der Waals' interaction between the aromatic matrix of the resin and the benzene ring of the acid, and the ion-dipole interaction between the resin and the acid molecule. On the other hand, the distribution coefficients measured in alkaline medium were extremely large as may be observed from the comparison of log D values at two media: H20-50% MeOH and alkaline H20-50% MeOH (pH 10). This result seems resonable from the viewpoint of the dissociation of the acid in alkaline medium. It is in agreement with a previous result on Amberlyst A-26 ( 1 ) in which the effect of pH on the sorption of benzoic and o-nitrobenzoic acids was studied. In addition, it is reasonable to expect that the increase of log D value by the pH change is more pronounced in the case of the derivatives which have relatively high pK, values than in the case of more acidic derivatives (Table I). For example, the increased log D value is 0.18 for o-chlorobenzoic acid (pK, 2.94) and 1.32 for p-chlorobenzoic acid (pK, 3.98). T o obtain more information about the sorption of the acids, the log D values in the KC1-MeOH medium were measured. In the KC1-MeOH medium, where the anion exchange sorption must be reduced because of the presence of the excess chloride ion, all log D values of the acids in 0.1 M KC1-10% MeOH medium were decreased compared to the log D values for H20-10% MeOH medium. I t is also observed that the decrease of log D value by the addition of potassium chloride, contrary to the effect of pH, was more
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
