1055
Anal. Chem. 1986, 58,1055-1057
Differential Scanning Potentiometry Ruben H. Manzo* and Ernestina Luna Departamento de Farmacia, Facultad de Ciencias Quimicas, Uniuersidad Nacional de Cdrdoba, Sucursal 16, CC61, 5016 Cdrdoba, Argentina
Differential scannlng potentiometry (DSP) is based on the function ApH, which arises from the difference of pH between the reference scanning (strong acld AH-strong base MOH) and the sample scannlng, in which a small amount of a weak base, B, is added to AH before the titration. This method, among other properties, allows for the tltration in aqueous systems of very weak bases; thus, the equation ,,,'ApH dVMm = aC, holds for bases as weak as sulfaniiamlde (pK, = 2.36).
1
The limitation of the classic method of aqueous acid-base potentiometry to titrate very weak acids or bases is well-known (1). This fact is a consequence of the high buffer capacity, p, originated by an appreciable concentration of either hydroxyl or hydrogen ions, which masks the equivalence point of a titration a t pHs far away from neutrality. This limitation can be overcome by the differential scanning potentiometry (DSP) developed here, which among other properties, enhances considerably the capacity of aqueous systems to titrate weak acids or bases. Several attempts of introducing differential techniques were reported in the early stages of development of potentiometric titrimetry (1-3). Later on, the use of two glass electrodes to take differential pH measurements has been also reported (4-6); however, DSP is based on a different strategy. THEORY Let us consider the theoretical titration curves of Figure 1. Curve R corresponds to the titration of 20 mL of a solution containing 1.5 mequiv of a strong acid, AH, with a solution of a strong base, MOH, while curve P was calculated for the same system in which before titration 0.5 mequiv of a weak hypothetical base, B with pKa = 4.00, was added. The different shape of curves P and R can be seen as a consequence of the different buffer capacities exhibited by the reference PR and the problem Pp solutions during the titration. The mathematical expressions for P in such systems are well-known (7) and given in eq 1 and 2.
[BH'I + [BI In the equations, [M+]refers to the cation of the titrating base, MOH. ApH Function. The difference between the pH of the systems P and R a t the same titrated fraction is a convenient way to account for the different behavior of P and R during the titration. (3) ApH = (PHP - PHR)constanttitratedfraction Equation 4 relates eq 3 with eq 1 and 2. 1 -~=A- -P-H = - -~- P H P ~ P H R 1 (4) d[M'] d[M'] d[M+] PP PR As it will be shown later, ApH is a useful magnitude to account for the relevant variations in the properties of the combined systems during the titration. 0003-2700/86/0358-1055$0 1.50/0 _. -'
Table I. Experimental and Theoretically Derived Areas Part a: Simulated Sytemsa amt of B, mmol 0.1 0.2 0.3 0.4 0.5 0.3 0.3 0.3 0.3 0.3
PKn 4.00 4.00 4.0 4.00 4.00 4.75 4.20
3.60 2.97 2.36
A (ApH-mL)
2.60 5.21 7.78 10.36 12.89 9.99 8.34 6.64 4.38 3.26
Part b: Experimental Systemsb 0.1 0.2 0.3 0.4 0.5
0.2 0.4 0.6 0.8
4.76 (I) 4.76 (I) 4.76 (I) 4.76 (I) 4.76 (I) 2.36 (11) 2.36 (11) 2.36 (11) 2.36 (11)
2.60 5.68 8.21 10.98 14.49 1.48 2.89 4.17 5.30
OAreas calculated for a set of simulated experiments, first with increasing amounts of base of pK, = 4.00 and second with equal amounts of bases of decreasing strength. *Areasobtained experimentally with sodium acetate (I) and sulfanilamide (11). Profile ApH vs. V M OThe ~ variation of ApH as a function of VMoH is shown in Figure 2. At the starting point [H'Ip < [H+]Rbecause a fraction of H+p is involved in the protonation of the sample B. Under such conditions, the term [H'] is the major contributor to /3 in both P and R (eq 1 and 2); hence, having P the lower [H'] has also a lower P; consequently, according t o eq 4, ApH also increases in the first phase of the titration. The second phase, which begins with the first inflection, is characterized by a progressive contribution to Pp of the third term on the right member of eq 2. Such contribution reaches a maximum at pHp = pKa, to decrease as B becomes progressively deprotonated. The shape of the profile depends on both the amount and strength of B. With regard to the last, it should be noted that a plot such as Figure 2, of a titration of an hypothetical base of pKa = 7, would exhibit a bell-shaped profile. For weaker bases, however, the shape becomes unsymmetrical like that of the figure. On the other hand, the smaller the amount of B, the closer curves P and R of Figure 1 will be, and P will approach R when CB approaches zero. Relationship between (ApH/ VMoH)and CB. Since ApH against VMoH has properties of a derivative function, it is reasonable to expect a simple relationship between it in the integrated form and CB. On this ground, the area, A , under the curve (Figure 2) was calculated for a set of simulated experiments in which CB was adequately varied (Table I, part a). From the results quoted there, a linear correlation between A and the concentration (or amount) of B is found (correlation 1 in Table 11),which is conveniently expressed as (5) 0 1988 American Chemical Society
1056
ANALYTICAL CHEMISTRY, VOL. 58, NO. 6, MAY 1986
2'5 2.0
t t
' 0
2
4
6
8
10
12
14
16
18
'MOH *
Figure 3. Simulated (solid line) and experimental (0)tilrations of 0.3 2
0;
4
6
8
10
'MOH
12
14
16
mequiv of
18
ml
Figure 1. Reference (R) and problem (P) curves of a titration of a hypothetical base of pK, = 4.00.
2'5 2.0
I.
readings were taken at VMOH intervals of 0.2 or 0.1 mL as appropriate. Stable readings were obtained within 20-40 s after the addition of a portion of titrating solution. Samples were introduced into the AH solution either as a weighed amount or through a measured volume of a solution containing it. Sodium acetate (I) (analytical grade) and sulfanilamide (11) (mp = 164-165 OC,water) (9)were used as samples. The volume of every (P or R) solution was completed to 20 mL with distilled water before titration. To calculate A from a set of ApH values, a program based on the trapezium approach was used. The equations used to generate pHR and pHp values in simulated experiments are given in the Appendix.
RESULTS AND DISCUSSION In order to test experimentally eq 5 , two bases of different strengths were selected: I (pK, = 4.76) (10) and I1 (pK, =
2.36) (11). 'MOH
m'
Flgure 2. Variation of ApH during the titration of a hypothetical base = 4.00.
of pK,
Table 11. Correlations According to Equations 5 and 6. correlation function correlated system slope intercept r no points 6points
891.
1
A vs. B"
2 3 A vs. pK, A vs. I"
simulated simulated experimental 2.82 29.08 25.74 -0.33 0.05 -3.48 1.000 0.999 1.000 5 6 5 0.29 0.02 0.06 0.93 0.08 0.03
4
A vs. 11" experimental 6.37 0.27 0.999 4 0.10
0.22
"Amount of base in mmol.
A relationship, based on the definite integral of a titration curve, which resembles eq 5, has been used previously (8). Relationship between A and the Strength of B. To gain information concerning this point, the areas corresponding to equal concentrations of a set of hypothetical bases of decreasing pK, were calculated (Table I, part a). The results quoted there also show a linear relationship between A and the pK, of B (correlation 2, Table 11), which can be expressed by A = bpK,
+C
(6)
Equations 5 and 6 would be potential tools for a variety of analytical purposes.
EXPERIMENTAL SECTION A conventional pH meter with a standard combined glass/ silver-silver chloride electrode was used. Two separate conventional titrations, one for R and the other for P, were carried out as described in the theoretical section; pH
Table I, part b, reports the areas obtained with scannings of samples of increasing amounts of I and 11, respectively. The corresponding correlations with eq 5 are reported in Table I1 (correlations 3 and 4). As can be seen there, the regression parameters indicate a good quality of linear correlation in both cases. The intercepts, having values near zero, which are below experimental errors, are also in agreement with eq 5. On the other hand, the sensitivity of the response ( A ) to the changes in CB,which is expressed by the slopes, qualitatively fills the prediction of eq 6. In order to compare experimental results with those theoretically derived, an experimental together with a simulated scanning, both corresponding to the titration of 0.3 mequiv of I, were plotted in Figure 3. T o simulate the experiment, the thermodynamic pK, was corrected for the ionic strength of the titration medium, which is about 0.08; hence, a pK, value of 4.57 is generated by using the appropriate f H + and fAd)- calculated through Debye-Huckel equation (12). No other correction for ideality departure was made. The figure shows a close adherence between theoretical and experimental profiles in the first stages of the titration. Under those conditions, nearly all the factors that affect the activity coefficients, and the p H measuring system, acquire a similar value in both P and R, and so are largely cancel'ed. However, near the stoichiometric point, where pp and particularly OR dramatically fall, the ideality departure becomes more evident. The analysis of the results reported in Tables I and I1 indicates some analytical advantages of DSP over conventional titrimetry. First, it can be used to titrate a base as weak as 11, whose determination in aqueous systems is not possible by the classical methodology; besides, although a determination of the lower limit of quantitation is outside the scope of this paper, it is easily apparent the potentiality of DSP to titrate very low concentrations of a strong base like I.
1057
Anal. Chem. 1986, 58, 1057-1062
LITERATURE CITED
APPENDIX The following.~ equations were taken from ref 13
1
VMOHMMOH - VAHMAH (H+)- K , = 0 VAH+ VMOH
(H+)2+
1
(7)
VMOHMMOH + KBH+ (H+)' + VBH + VMOH KBH+MMOH VMOH- KBH+MBH+VBH+ VBH + VMOH K w K ~=~0+(8)
(H+)3+
VMOH= -VBH+((H+)~ + KBH+(H')' - {Kw+ KBH+MBH+](H+) - KwKBH+/ (H+)3+ (KBH+ + MMoHKH+)~+ (KBH+MMoH- K,l(H+) - KwKBH+J(9) In eq 8 and 9 V B ~refers + to the volume of the solution under titration after having finished the first phase, and MBH+refers to'the corresponding concentration of B. Registry No. Sulfanilamide, 63-74-1;sodium acetate, 127-09-3.
Watters, J. I.I n "Treatise on Analytical Chemistry", 1st ed.; Kolthoff, I . M., Elving, P. J., Eds.; Wiley: New York, 1975; Part I,Vol. 11, Chapter 114. Cox, D. C. J . A m . Chem. SOC.1925, 4 7 , 2138. Furman, N. H. Ind..€ng. Chem. Anal. Ed. 1930, 2 , 213. Luzzana, M.; Perreila, M.; Rossi-Bernardi, L. Anal. Biochem. 1971, 4 3 , 556. Busch, N.; Freyer, P. Anal. Biochem. 1977, 79, 212. Busch, N.; Freyer, P.; Szameit, H. Anal. Chem. 1978, 50(14), 2166. Fleck, G. M. "Equilibrios en disoiucibn", Ira ed.; Editorial Alhambra S. A,: Madrid, Espafia, 1967; p 99. Matsushita, H.; Ishikawa, N. Nippon Kagaku Kaishi 1976, ( l l ) , 1710. "Vogel'sTextbook of Practical Organic Chemistry", 4th ed.; Longman: New York, 1978; p 651. Martin, N. A,; Swarbrick, J.; Cammarata, A. "Physical Pharmacy", 2nd ed.; Lea & Febiger: Philadelphia, PA, 1969; p 194. "The Merck Index", 10th ed.; Merck & Co., Inc., 1983; p 1280. Westcott, C. Clarck "pH Measurements"; Academic Press: New York, 1978; p 158. Fleck, G. M. "Equilibrios en disolucibn", Ira ed.; Editorial Alhambra S. A,: Madrid, Espafia, 1967; p 71.
RECEIVED for review May 13,1985. Accepted November 11, 1985. Support of this work was from CONICET and CONICOR (Grants 560/84 and 340/84, respectively).
Electrochemical Reduction of Dioxygen to Perhydroxyl (HO,.) Aprotic Solvents That Contain Brmsted Acids
in
Pablo Cofr6 and Donald T. Sawyer*
Department of Chemistry, Texas A&M University, College Station, Texas 77843
I n acetonltrlle (MeCN) and dlmethylformamlde the effect of proton sources (HC104 and PhOH) on the electrochemistry of 0, at platlnum (PI) and glassy carbon (GC) electrodes has been studied by rotated ring-disk and cyclic voltammetry. With weak Brernsted acids (H20 and PhOH) the reverslble reduction of 0, to O,-. Is followed by protonation to form HO,. A-). For stronger acids perhydroxyl (O,-. 4-HA at GC there Is dlrect formation of HO,. (0, HA eH02'(ads) A-), which chemlsorbs to the electrode surface and dlsproportlonates to 0, and H202;wlth excess protons a HA eH202 second electron transfer occurs (HO,.,,,,, 4- A'-). For strong acids In MeCN direct reduction of the proton occurs at PI (H+ eprlor to electron transfer to 0,; the chemisorbed hydrogen atoms react wlth O2 ("(ads) + O2 H02'(ads) '/2H202 + '/202)*
-
+
+
+
+
+
+
+
+
-
-
-+
+
The electrochemistry of dioxygen (0,) is one of the most extensively studied processes (1-4), but a reasonable understanding of the electron-transfer mechanism for its reduction has been gained only during the past 2 decades through the use of dipolar aprotic solvents (5-14). Thus, in acetonitrile (MeCN) and dimethylformamide (DMF) the reduction of O2 is a reversible one-electron process (15) 0 2
+ e- + 0 2 - - EMecN0' =
-0.90 V vs. SCE
(1)
The resulting superoxide ion is stable in the absence of proton sources but rapidly disproportionates upon protonation (16)
HOy
+ HO2.
-
HzOz + 0
2
(2)
Although the effect of protons on the electrochemistry of O2 has been noted in several previous studies (15, 16),there has not been a systematic characterization of the electrontransfer reduction for O2 in the presence of Bronsted acids. Superoxide is a natural intermediate that is produced in biological respiration and metabolism; its protonated form, H02., can initiate lipid peroxidation and autoxidation ( 17). This occurs because H02. can oxidize substrates with allylic functions via hydrogen-atom abstraction (e.g., 1,4-cyclohexadiene (1,6CHD)). The present study has been directed, in part, to ascertain whether direct production of H02. by electron transfer to O2 in biomembranes is feasible and a potential biohazard. The effect of solvent and electrode material on the electrochemical reduction of oxygen in the presence of Bronsted acids is the primary focus of the study. Rotated ring-disk voltammetry has been the primary technique for the investigation, because the product species that are generated via reduction of O2 at the disk can be characterized a t the ring electrode within a few milliseconds.
EXPERIMENTAL SECTION Instrumentation. The rotated ring-disk measurements were made with a Pine Instruments Co. Model PIR rotator with either Pt-Pt or GC-GC ring-disk electrodes. The parameters of the electrodes were as follows: Pt-Pt electrode, rI = 0.382 cm, r2 = 0.399 cm, r3 = 0.422 cm, N = 0.178; GC-GC electrode, r1 = 0.382 cm, r2 = 0.416 cm, r3 = 0.556 cm, N = 0.418. Potential control was provided by a Pine Instruments Co. Model RDE 3 dual potentiostat. The sample solutions and electrode assembly (including a Pt auxiliary electrode in a separate tube with a medium-porosity fritted-glass disk at the end and a Ag/AgCl reference electrode in a luggin capillary (15))were contained in a 150-mL beaker with a Leeds and Northrup plastic cell top. 1986 American Chemical Society
