Summary-The rate constant k of the reaction of ascorbic acid with &6- ... the rate constant is 56.5 x lo3 1. mole-'. set- ' and the overall standard deviation is 0.6 x ...
Talanta. Vol. 23, pp. 27-30.
Pergamon
Press, 1976. Printed in Great Britain
COMPARATIVE KINETIC STUDY FOR RATE CONSTANT DETERMINATION OF THE REACTION OF ASCORBIC ACID WITH 2,6-DICHLOROPHENOLINDOPHENOL M. I.
KARAYANNIS
Laboratory of Analytical Chemistry, University of Athens, 104 Solonos Str., Athens, Greece (Received 15 October 1974. Accepted 18 February 1975) Summary-The rate constant k of the reaction of ascorbic acid with &6-dichlorophenolindophenol (DCPI) in oxalic acid solutions is determined, by stopped-flow techniques. Four different methods are used to evaluate the results. The values and errors are compared statistically. The average of the rate constant is 56.5 x lo3 1. mole-‘. set- ’ and the overall standard deviation is 0.6 x lOa 1. mole-‘. set-’ or 1.0% relative. The pH-dependence of the rate constant suggests that DCPI reacts with undissociated ascorbic acid.
The reaction of ascorbic acid and 2,6-dichlorophenolindophenol has been widely applied for the assay of ascorbic acid in various biological and food samples. The stoichiometry of the reaction was first proposed by Tihnans,’ the products being dehydroascorbic acid and the leuco-compound of the indophenol. The reaction is very fast and first-order in respect to each of the participants. To our knowledge no kinetic study of the reaction has been undertaken in order to determine the second-order rate constant. In the present investigation we have applied stopped-flow techniques to determine the rate constant and to study the effect of pH on the reaction. Oxalic acid solutions were used as reaction media, these being solvents commonly used for the extraction and isolation of ascorbic acid from natural or biological samples. EXPERIMENTAL Apparatus
A Durrum stopped-flow spectrophotometer, model D131, was used. The course of the reaction was displayed on the screen of a storage oscilloscope (Tektronix R 564 B) and photographed with a “Polaroid” camera (Tektronix C-12). Reagents
The solutions of ascorbic acid and 2,6-dichlorophenolindophenol (DCPI) were standardized volumetrically, with a 5-ml burette and class-A glassware. All runs were performed at 27”, the temperature being thermostatically controlled. All solutions were prepared in distilled water from p.a. grade reagents. Ascorbic acid solutions were prepared from a O.lOOOM stock solution in 0.05 M oxalic acid. The buffers used were hydrochloric acid-potassium chloride for OH 1.3-2.0, 0.1 M potassium hydrogen phthalate-0.1 M hydrochloric acid (or 0.1 M sodium hydroxide) for pH 2.26.0, 0.1 M potassium dihydrogen phosphate-O.1 M sodium hydroxide for pH 6.0-7.5. Solutions of DCPI were prepared from a I.0 x 10m3M stock solution in a 210mg/l.
sodium bicarbonate solution. The DCPI solutions were standardized titrimetrically against prestandardized solutions of ascorbic acid, or photometrically on a Beckman DK double-beam spectrophotometer with a l-cm cuvette. The molar absorptivity was taken to be 8.60 x lo3 1. mole-‘. cm-’ at 522 nm’. Procedure
The stopped-flow spectrophotometer was calibrated for zero and lCOO/O transmittance with water in the observation cell. All measurements were performed at 522nm which is the isosbestic point for DCPI at various pH values.’ In all experiments the light-path was adjusted to give a signal of 800mV with water in the observation cell (T = 1). The course of reaction was followed with the storage oscilloscope and the trace on the screen was photographed with a “Polaroid” camera. Evaluation of the experimental data
All concentrations of ascorbic acid and DCPI given in the tables and diagrams are the actual values in the reacting mixtures at zero time after mixing. In order to avoid systematic errors which may have been introduced during the experimental work, or appear during the evaluation of the data, four different techniques were applied for the calculation of the second-order rate constant k. The analytical conditions in each case were adjusted in such a way as to ensure the applicability of the treatment used. Method A. For the bimolecular reaction A + B A Products the rate law is given by the equation -dA
p’
dt
= t
-dB dt
= k,J$,
where k, the rate constant, applies to a particular set of reaction conditions such as temperature, ionic strength and pH. If a spectrophotometric method is used and the transmittance T of the reacting mixture is monitored as the reaction progresses, the following mathematical expressions are valid, provided that the reactant B is the only absorbing species at the wavelength used: log;= 27
0
-r,.b.B,
(2)
M. I. KARAYANNIS
28
where
IO3 1. mole-‘. set-’ 57.2 57.2 56.1 54.6 56.2 Mean k = 56.2 s, = 1.3 .rk = 0.6
by mixing aqueous unbuffered solutions of ascorbic acid with buffered solutions of DCPI. This procedure was followed to avoid prolonged exposure of the ascorbic acid to an alkaline environment, where it auto-oxidizes. The results of these experiments are shown in Fig. 3. RESULTS
AND DISCUSSION
Tables l-4 list the results of the evaluation of the experimental data according to methods A, B, C, and D as described above. In most of the cases shown in Table 1 the values of k were calculated by measuring dV/dt at V = 300mV on the reaction curve, where Q has its maximum value. In some cases where
the starting concentration of DCPI was lower than 2.0 x 10m5M, the slope dV/dt was measured at V > 360 mV where Q < 294.3 mV and the linear part of the reaction curve is shorter. Both experimental conditions have their advantages and disadvantages, which are discussed elsewhere.3 Column 2 of Table 1 lists the values of k corrected for a parameter Y
Y=l-~+~ 0
0
appearing as a result of the substitution of A, for A, in equation (3). These are the “apparent” values of the rate constant k. A second correction was applied to the “apparent” values for the contribution of species other than DCPI, in the absorbance of the
Effect of pH on the reaction rate constant k The effect of pH was studied in four different experiments which were performed with various concentrations of the reagents DCPI and ascorbic acid. The pH range 1.1-6.0 was covered by mixing buffered solutions of ascorbic acid with solutions of DCPI in sodium bicarbonate (NaHCO, 210mgJ.). The pH range 6G7.5 was covered Table 3. Values of k determined according to Method C DCPI, 1O-6 M 5 29 38 39 68 100
k, lo3 I.mole-l.sec-’
57.5 55.8 57.0 57.1 57.3 55.8 Mean k = 56.8 at = 0.8 Sk = 0.3
I 0
I
I 2
I 3
I 4
@‘Oh
5
6
7
]
.3
PH
Fig. 3. Dependence of the rate constant k on the pH of the reaction mixture.
30
M. I.
KARAYANNIS
reacting mixture. This has a negative effect on the slope dV/dt which entails negative error in the final value of the slope kQ. The correction is based on the following considerations. In equation (3) magnitude (Abs) refers to the absorbance due to DCPI. We found that at 522nm dehydroascorbic acid abbreviated DAA) also absorbs, having a molar absorptivity eDAA= 526 1.mole- 1.cm- ‘. This value is about 6”/, of eDCP,.If the contribution of DAA to the absorbance calculated from the oscilloscope pictures is considered, equation (3) must be replaced by dV _ k (Abs):. V dt-
.-Em
(10)
where (Abs)? is the instantaneous absorbance of the reacting mixture. Equation (10) contains all corrections applied for the calculation of the k values given in column 3 of Table 1. Equation (10) shows that the Q values for each V must be corrected for the factor 1 - ED,JED~PI,which has the value 0.939 for this particular case. The standard deviations of the means are calculated according to the equation s, =
Z(k - ki)’
(11)
i N(N - 1) and the standard deviations for the method by using the equation Sk =
Methods A and C give better reproducibility than methods B and D. This is obvious, since the measurement of the slope dV/dt in method A is accurate, because of the relatively long part of the reaction curves that is used. Method B requires the measurement of dV/dt at different points of a curved trace such as that shown in Fig. 2, which is less accurate. The method of determining k,,,, by the infinite-time method involves many points on the reaction curves and consequently the values obtained are accurate. This enhances the accuracy of method C. Methods B and D require the computation of the product A& of two small numbers, one of which is read from the trace and the other is computed by using equation (6). The probable error in B, affects the accuracy of A, as well as that of the product A,& thus introducing larger errors. We have calculated the weighted average of the mean k values by using the relation6 (13) where wi is the number of degrees of freedom for the ith method. The value of this average is k =
56.5 x lo3 1. mole-‘. set- ‘. The error associated with this average value was calculated by conventional methods of analysis of variance. The variance of the average k was calculated according to the equation6
s;=--Csfw. CWi
(14)
The result of this calculation is sk = O-6 x lo3 1. mole- ‘. set- ’ which is taken as the overall error for the average k. Referring to Fig. 3, the S-shaped curve is reminiscent of titration curves and can be explained by the hypothesis that the main species participating is the product of a protolytic reaction. This suggests that the effect of [H’] on the reaction rate is indirect. Hydrogen ions do not participate directly in the reaction, but control the concentration of the reacting species in the mixture. Ascorbic acid acts as a weak diprotic acid with dissociation constants &I = 6.17 x lo-’ and K, = 1.62 x lo-” (pK,, = 4.21, pK,* = 11.79) at 20”.$ If we consider only the first dissociation, the experimental data can be explained by the hypothesis that the active species is undissociated ascorbic acid. The solid line in Fig. 3 is a theoretical curve which was derived by multiplying the value k = 59.0 x lo3 1. mole- ‘. set-’ (extrapolated value of the experimental curve), by the ratio of the concentration of the acid form to the analytical concentration of ascorbic acid, at each pH. The two lines of Fig. 3 do not overlap fully at higher pH. Two explanations can be given for this disagreement. First, the experimental value pK,, = 4.25 deviates from the theoretical (4.21) at higher pH values because of the effect of ionic strength. As stated above the measurements were carried out in buffers of relatively high ionic strength. Alternatively, the ascorbate ion may react with DCPI in a similar manner to ascorbic acid, but with a different rate constant, thus altering the overall value of the rate constant k. Both explanations can be justified by the experimental results. Acknowledgement-The author acknowledges the assistance of Miss Lela Nanou and Miss Dina Athanasopoulou during the experimental work and the contribution of Miss Yuli Tsoutsoura in preparing Fig. 3. REFERENCES
J. Tilmans, Z. Unters. Lebensmittel, 1927, 54. 33. J. McD. Armstrong, Biophys. Acta, 1964, 86. 194. M. I. Karayannis, Anal. C&n. Acta 1975, 76. 121. M. G. Fleck. Chemical Reaction Mechanisms. D. 36. Holt, Rinehait and Winston, New York, 1971.’ A 5. M. Nord, Chem. Ind., 1949, 64. 280. 6. R. R. Sokal and F. J. Rohlf, Biometry, p. 178. Freeman, San Francisco, 1969. 7. L. Erdey and G. Svehla, Ascorbinometric Titrations, p. 10. Akadkmiai Kiad6, Budapest, 1973. 1. 2. 3. 4.
