This last expression allows one to determine the maximum increase in the column length that will improve the peak capacity. If the increase in length is such that the RHS of Equation 25 is larger than the left hand side, the peak capacity will deteriorate. The reduction in n is due to the decrease in the ratio of the retention times which overpowers the increase in the plate number. The initial value of t,/ta determines the maximum allowable increase in the column length. Capillary columns, consequently, are less flexible in terms of the allowed increase in length than packed columns. Once the required length is found, the temperature that will yield the time normalization can be calculated (27). Similar to the case of resolution under time normalization, there is an optimum length increase that maximizes the peak capacity. That maximization occurs when x is equal to (tn/tA)e-**
Other Factors Influencing n. Horvath and Lipsky (28) have suggested that n can be improved by keeping the width of the peaks constant via temperature programming in GC or via gradient elution in LC. In this case the retention time of the last component is given as fA (n - 1)w = tn (26) where n is the number of peaks and w is their width. Equation 26 can be rearranged and solved for n
+
,-
n=1+-
l/NA
(;
-
1)
4 N A is the number of plates as obtained from the inert peak. When n is much greater than unity, Equation 27 reduces to the (28) C. G. Horvath and S. R. Lipsky, ANAL. CHEM.,39, 1893 (1967).
peak capacity expression given by Horvath and by Lipsky (28). The improvement in the peak capacity, under these conditions, is due to the fact that n depends linearly on t,/tA and not logarithmically as in Equation 6. Whenever possible temperature programming or gradient elution should be attempted as a means of increasing the number of resolvable peaks. Parameters such as support particle size and radius of tubing (in capillary columns) will affect the peak capacity. These factors are complicated due to secondary effects such as the change in the stationary phase thickness and thus in the /3 value of the column. If, however, the /3 value is kept constant, then an increase in the particle size or tube diameter will frequently reduce N,,, (Ij and consequently will be detrimental to n. The peak capacity can be an important measure of the efficiency of a chromatographic system. In cases where the number of resolvable peaks, n, is small-Le., exclusion chromatography-it is very useful to know the methods by which n can be improved. In the case where the mixture to be analyzed has many components-ie., petroleum analysisan understanding of the factors that might improve the resolution of all the components in the shortest possible time is essential. As with the conventionally used resolution, increasing the plate number does not necessarily mean an increase in n. A careful evaluation of experimental results must be made in order to pursue the correct road to increased peak efficiency. RECEIVED for review March 30, 1970. Accepted June 19, 1970.
Electrochemical Reduction of Phenol Red J. K. Senne’ and L. W. Marple2 Department af Chemistry, Iowa State University, Ames, Iowa 50010
The reduction of phenol red has been investigated by polarography, cyclic voltammetry, and controlled potential coulometry. Reduction occurs in two steps, with the product of the first step undergoing a subsequent chemical reaction. The product of the chemical reaction was shown to be identical to that formed by a direct two-electron reduction of phenol red. A mechanism for the reduction is proposed which involves the formation and disproportionation of a free radical intermediate. The apparent temperature independence of the second order rate constant is discussed in light of the proposed mechanism.
cein, the reduction mechanisms appear to be incompletely understood. The electrochemical behavior of these compounds was of interest to us, and it was felt that an investigation of sulfonephthalein reductions would be most instructive. We began with phenol red, the simplest of the sulfonephthaleins, which has the structure
ELECTROCHEMISTRY of the phthaleins, sulfonephthaleins, and fluoresceins has been investigated in only a few instances (1-5) and, with the exceptions of phenolphthalein and fluores-
Present address, University of Alberta, Edmonton, Alberta, Canada. 2 Present address, Syntex Research Center, Stanford Industrial Park, Palo Alto, Calif. (1) I. M. Kolthoff and J. J. Lingane, “Polarography,” 2nd ed., Vol. 11, Interscience,New York, N. Y., 1952, pp 722-726. (2) M. Suzuki, J. Electrochem. SOC.Japan, 22, 220 (1954). (3) P. Delahay, Bull. SOC.Chim. France, 348 (1948). I . Chinese Chem. Soc. (Taiwan), 9, (4) K. Pang and S. F. Lin, . 100 (1962). ( 5 ) E. K. Wang and H. C. Sung, Chutig Kuo K O Hsuen Yuatz Yitig Yung Hua Hsueh Yen Chiu So Chi K’an, 13, 18 (1965); Chem. Abstr., 64, 13761e (1966). 1
Polarographic reduction yielded two well-defined waves of unequal height. The ratio of the wave heights was independent of pH and temperature, Thus, there is necessarily a kinetic complication in the electroreduction other than a chemical reaction prior to electron transfer as occurs in the reduction of phenolphthalein (I). This paper reports the results of polarographic, cyclic voltammetric, and controlled potential coulometric studies of phenol red reduction. The data suggest that a free radical is formed uia a one-electron transfer and that the radical disproportionates to starting material and completely reduced product.
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I
I
1
-.4
I
-.6
I
1
-.8
I
1
-1.0
I
I
-1.2
I
I
-1.4
I
1
-1.6
1
I
I
I
I
-1.8
,POTENTIAL, VOLTS VS. S.C.E.
Figure 1. Polarogram of millimolar phenol red in 0.1M phosphate buffer (pH 7.0), 0.1M KCI, and 0.015% Triton x-100
I
-.4
I
-.6
I
-.8
I
-1.0
I
-1.2
1
-1.4
I
-1.6
POTENTIAL, VOLTS VS. S.C.E.
Figure 2. Cyclic voltammogram of phenol red. Solution conditions same as in Figure 1. Scan rate was 0.25 V/sec
EXPERIMENTAL Apparatus. Polarograms were recorded with a Leeds and Northrup Electro-Chemograph Type E. The cell for both polarographic and cyclic voltammetric studies was the following:
DMEl1KCl(s,t, j 1 KCl(ee.t,, HgC1*, Hg Ultrafine sintered-glass frits separated the three compartments. Solutions were deaerated with commercial prepurified nitrogen. A two compartment H-cell was used in controlled potential coulometric studies. The working electrode (cathode) was a mercury pool of approximately 7 cmz area which was stirred continuously during electrolysis. The other compartment contained a bright platinum flag electrode in contact with the same buffer and supporting electrolyte as used in the cathode compartment. Contact with the anode compartment was made through a fine sintered-glass frit. The potential of the cathode was monitored against a n external SCE, contact being made through a 3% agar salt bridge containing saturated KC1. The potentiostat for the three electrode system was constructed from a Heath Model EUW19 Operational Amplifier System (6), and had a current capability of 20 mA at 1 5 0 V. The associated coulometer was of the hydrogen-nitrogen type described by Page and Lingane (7). Electrolysis was assumed complete when the current through the cell reached the background level, as determined by pre-electrolysis of the buffer and supporting electrolyte. Cyclic voltammograms were obtained on an instrument designed and built by Dennis Johnson of Iowa State University. A D M E with a drop time on the order of 15 sec was used with a scan rate of 0.25 V/sec. Unless otherwise specified, all solutions contained millimolar phenol red, 0.1M KCl, 0.1M phosphate buffer (pH 7.0), and 0.015% Triton X-100. All potentials are referred to the SCE. Studies of polarographic wave heights as a function of concentration were done in a water bath at 25 f 0.3 O C . All other data, except where temperature was the variable under study, were taken at room temperature. Chemicals. Phenol red (Hartman-Leddon Co.) was purified by elution from an alumina column. The impure material was placed on the column as a slurry in 95 % ethanol. (6) H. V. Malmstadt, C . G. Enke, and E. C . Toren, Jr., “Electronics for Scientists,” W. A. Benjamin, New York, N. Y., 1963, p. 371. (7) J. A. Page and J. J. Lingane, Anal. Chim. Acta, 16,175 (1957). 1148
Using a 20:20:60 by volume mixture of water, concd ammonium hydroxide, and 95% ethanol as eluent, several colored impurities were eluted, followed by the phenol red. The phenol red was precipitated by addition of hydrochloric acid, redissolved in dilute NaOH, precipitated again, and dried at 110 O C for several hours. This material was 97% pure (acid-base titration) and contained about 0.7 % water (Karl Fischer titration) and 0.8 % alumina (by ignition). Phenolsulfonephthalein was prepared by the reduction of phenol red with zinc dust (8). Phenolphthalein (Mallinckrodt, N. F. powder) and thymol blue (Hartman-Leddon) were used without further purification. RESULTS AND DISCUSSION
A typical polarogram of phenol red is shown in Figure 1. Because the complete reduction of phenol red requires the transfer of two electrons (as shown by controlled potential coulometry), the inequality in the wave heights means that more than a simple two-step reduction is involved. Polarograms of this type are often observed in the reduction of organic acids where the equilibrium between the acid and its conjugate base is established slowly and the two species are reduced a t different potentials. This cannot be the case here, however, since changes in p H do not affect either the relative or total wave heights, but serve only to shift the half-wave potential of the first wave in accordance with the equation =
-0.19 - 0.069 p H
between p H 2.5 and 10.6. The half-wave potential of the second wave is - 1.20 V and is pH-independent. Reversibility. A plot of E GS. log [i/(ilim - i)] for the first wave is linear, with a slope of 0.058 + 0.003 (average of four determinations between pH 4.7 and 13.0). This is very near the theoretical value of 0.059 for a reversible one-electron transfer. Since a plot of half-wave potential US. p H gives experimentally a straight line with a slope of 0.069 volt per p H unit, one hydrogen ion is involved in the reduction. The wave due t o the second electron transfer yields slopes considerably greater than 0.059, and is apparently irreversible. These findings were confirmed by cyclic voltammetric experiments on phenol red (Figure 2). The anodic and (8) W. R. Orndorff and F. W. Sherwood, J . Amer. Clzem. Soc., 45, 486 (1923).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 11, SEPTEMBER 1970
TEMPERATURE, "C MOLAR CONCENTRATION OF PHENOL' R E D x 103 Figure 3. Limiting polarographic currents as a function of phenol red concentration. Other solution conditions same as in Figure 1 A 0
---
First wave Second wave Total wave Theoretical one-electron wave
cathodic peaks for the first electrode process indicate reversible formation of an intermediate compound with some degree of stability. However, the cathodic peak area is significantly larger than the anodic. This may be due to the disappearance of the intermediate by chemical reaction or possibly by diffusion away from the electrode during the reverse scan since a rather slow sweep rate was employed. The second wave lacks an anodic peak and is irreversible. Diffusion Coefficient and Temperature Effects. Limiting currents of the first, second, and total waves as a function of phenol red concentration are shown in Figure 3. The total wave height is proportional to concentration, but the limiting current of the first wave curves upward with higher concentrations, while that of the second wave drops off. The diffusion coefficient of phenol red was calculated from the Ilkoviz equation. From the total wave height and assuming a two-electron transfer, a value of 5 . 3 x 10-8 cm2/sec was obtained. This is close to the value of 5.2 x 10-6 cm2/sec obtained for phenolphthalein (I). In addition, the total current is proportional to the square root of the height of the mercury in the reservoir. Thus, the overall reduction is diffusion controlled. Since kinetic complications are obviously involved, the polarographic behavior of phenol red might be expected to be unusually temperature dependent. This was not found to be the case, however (Figure 4). The temperature coefficients of the first, second, and total wave heights were all within 1.62 to 1.79 % per degree, and were linear over the range from 0 to 43 OC. Reductions which are diffusion controlled normally have temperature coefficients on the order of 1 to 2 % per degree while those controlled by kinetic factors are generally much higher. A possible explanation for this anomaly will be discussed later in light of the proposed mechanism. Controlled Potential Coulometry. The reduction of phenol red was shown to involve two electrons by controlled potential
Figure 4. Limiting currents as a function of temperature. Solution conditions same as in Figure 1 0
First wave
A Second wave 0 Total wave
Table I. Controlled Potential Coulometry of Phenol Red Applied potential, Trial volts us. SCE PH n - 1 .40 (Second wave) 7.2 2.21a - 1.40 (Second wave) 7.2 2.17 -0.90 (First wave) 7.2 2.20 -0.90 (First wave) 7.2 2.16 -0.90 (First wave) 9.0 2.02b - 1 .OO (First wave) 9.0 2.05 - 1.40 (Second wave) 8.9 2.02c -0.90 (First wave) 8.9 2.04 a Trials one through four were made in 0.1M potassium chloride, 0.1M sodium phosphate, and 0.015% Triton X-100. * Trials five and six were made in 0.1M potassium chloride, 0.05M ammonium sulfate-ammonium hydroxide buffer, and 0.015 % Triton X-100. Trials seven and eight were made in solutions similar to those used in five and six except that no Triton X-100 was present.
electrolysis of solutions at -1.4 V. This potential corresponds to the limiting current of the total wave (Figure 1). Electrolysis at more positive potentials might be expected to yield values of n substantially less than two, but this was not the case. Table I summarizes the results. The major product from a controlled potential reduction of phenol red at -1.4 V was isolated and purified. The infrared and NMR spectra were identical to those of the product obtained from a similar reduction at -0.90 V. Also, this compound was shown to be spectrally identical to that obtained by the reduction of phenol red with zinc dust. The facts that n = 2 at all potentials sufficiently negative to cause reduction and that the same product is obtained at all potentials means that the product of the first electron transfer undergoes disproportionation. Reduction Mechanism. On the basis of the above observations, the following mechanism is proposed for the reduction of phenol red :
ANALYTICAL CHEMISTRY, VOL. 42, NO. 11, SEPTEMBER 1970
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OH
cHO
H
6
O
W
-
0
m ma Reactions 1 and 2 constitute the first polarographic wave. Species I is protonated to form the oxonium ion, Ia (9), which is reversibly reduced to the free radical 11. Disproportionation of some I1 regenerates Ia (or I) which, being in the vicinity of the electrode, recycles through Reaction 1. This results in enhancement of the first wave beyond that expected for a normal one-electron reduction. The reason for the nonlinear dependence of the first wave on concentration is now apparent, since the rate of Reaction 2 will be proportional to the square of the concentration of 11. This mechanism also accounts for the controlled potential electrolysis data in that the final product of exhaustive reduction will always be phenolsulfonephthalein (IIIa). At potentials more negative than about -1.2 V, the free radical is reduced (Reaction 3). The process is irreversible and yields species 111, which immediately gains a proton from the solvent. A means of obtaining second order rate constants from polarographic data for reactions of this type has been derived by Orleman and Kern (IO) who showed that a plot of i/id us. id (where i is the observed limiting current of the first wave and id is the normal diffusion controlled current) should be linear with a slope proportional to the rate constant. Plots of this type for phenol red showed appreciable scatter and the rate constant could not be estimated with any certainty. Since I1 is a free radical, it might be expected to disproportionate quite rapidly. It is therefore somewhat surprising that two waves are present, for if I1 reacted rapidly with itself, only one wave would be seen. If, on the other hand, it reacted slowly two waves of equal height would appear. Since an intermediate situation prevails, an appreciable temperature
(9) I. M. Kolthoff, “Acid-Base Indicators,”translated by C. Rosenblum, Macmillan Co., New York, N. Y., 1937. (10) E. F. Orleman and D. M. H. Kern, J. Amer. Chem. SOC.,75, 3058 (1953). 1150
Table 11. Controlled Potential Coulometry of Phenolphthalein and Thymol Blue Applied potential, Compound volts us. SCE PH n Phenolphthalein - 1.50 (Second wave) 10.85 2.03“ Phenolphthalein -1.10 (First wave) 10.85 2.16 Thymol blue - 1.40 (Second wave) 7.10 1.89b Thymol blue 7.10 1.90 - 1.40 (Second wave) Thymol blue -0.80 (First wave) 7.10 1.74 Phenolphthalein was reduced in a solution of 0.2M potassium chloride and 0.4M sodium carbonate adjusted to pH 10.85 with hydrochloric acid. bThymol blue was reduced in a solution of 0.2M potassium chloride and 0.4M potassium dihydrogen phosphate adjusted to pH 7.1 with potassium hydroxide.
dependence of the first wave would be expected. Only a small temperature dependence is observed, most of which can be accounted for by increased mass transfer to the electrode at higher temperatures. A situation which illustrates the “expected” behavior is the disproportionation of U(V) to U(1V) and U(V1) in acidic solution. An increase in temperature results in a marked increase in the rate of disproportionation (and therefore the limiting current) as observed polarographically ( I I). One reason the temperature dependence of the first wave is not so large as expected may be as follows. Since I1 is a very bulky and sterically hindered species, it is reasonable to assume that electrons may be transferred only when the radicals are correctly oriented with respect to each other at the moment of collision. In this way, only a certain fraction of the collisions would be effective. Increasing the temperature would merely increase the number of collisions (and the number of effective collisions in nearly the same proportion), and a large temperature dependence would not be seen. Both phenolphthalein (pH 9 or above) and thymol blue are reduced in two steps of equal height.
PHENOLPHTHALEIN
THYMOL BLUE
Controlled potential reductions of these compounds, performed in a manner similar to that used with phenol red, indicate that the product of the first electron transfer of both of these compounds may also disproportionate, though at a rate too slow to be observed polarographically (Table 11). The products of reduction were not isolated but were assumed to be phenolphthalein and thymolsulfonephthalein. The nonintegral values of n obtained probably mean that other reactions occur in competition with disproportionation. Thus, it seems possible that the reduction of most phthaleins and sulfonephthaleins may proceed by the same mechanism. Further investigations of other members in these series would seem profitable. ACKNOWLEDGMENT
The authors express their appreciation to Harvey Diehl for helpful suggestions. RECEIVED for review March 3,1970. Accepted May 18,1970. (11) I. M. Kolthoff and W. E. Harris, ibid., J . Amer. C h m . SOC., 68, 1175 (1946).
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