Communication pubs.acs.org/jchemeduc
Kinetics of the Rapid Reaction between Iodine and Ascorbic Acid in Aqueous Solution Using UV−Visible Absorbance and Titration by an Iodine Clock Arthur E. Burgess*,† and John C. Davidson‡ †
School of Contemporary Sciences, University of Abertay Dundee, Bell Street, Dundee DD1 1HG, United Kingdom Perth Tuition Centre, Auld Bond Road, Perth PH1 3FX, United Kingdom
‡
ABSTRACT: An iodine clock is the basis for studying the kinetics of the fast reaction between iodine and ascorbic acid in aqueous solution. UV−visible absorbance, where the molar absorptivity of the triiodide ion is high, is equated with the total concentration of iodine, through the equilibrium, I2 + I− ⇌ I−3 , established when the iodine clock is concluding its steady-state titration of ascorbic acid. Persulfate ion is the primary oxidant catalyzed by the iodide ion, which produces the iodine titrant and is recycled. A method testing the second-order rate equation, R1 = k[iodine][ascorbic acid], uses the coefficient of variation, CV. This locates equivalence, enabling [ascorbic acid] to be measured and contributes to a procedure where rate of reaction, R1, at different concentrations of iodine and ascorbic acid determines an average value of the overall rate constant, k. In combination with results from another source, the rate constants of the two individual forms of iodine reacting with ascorbic acid also are determined and show that the triiodide ion is five times more active than I2 at an ambient temperature of 20 °C. KEYWORDS: Second-Year Undergraduate, Physical Chemistry, Inquiry-Based/Discovery Learning, Aqueous Solution Chemistry, Equilibrium, Kinetics, Oxidation/Reduction, Reactions, Spectroscopy, UV-Vis Spectroscopy
A
continuously being recycled, its concentration remains constant, so, at an unchanged temperature, by choosing [persulfate] ≫ [ascorbic acid] the rate of titration becomes practically constant.
scorbic acid (vitamin C) is readily oxidized, a feature that serves as a useful property for its titration in aqueous solution. A halogen, bromine, or iodine is frequently the oxidation titrant of choice and methods used include conventional titrimetry,1 constant-current coulometry,2 and kinetic methods of analysis.3 A kinetic titration, often demonstrated, is the iodine clock,4−6 where iodine is generated in situ by an iodide ion oxidant such as the persulfate (peroxydisulfate) ion. Iodide, characteristically, acts as a catalyst, so the persulfate, as a primary oxidant, has a suitable reaction pathway for quantitative oxidation of a titrand such as ascorbic acid. Although persulfate is a powerful oxidant in its own right, its kinetic activity with ascorbic acid, under normal room temperature conditions, is much too slow to be of significance; hence, the more kinetically active iodide is introduced as a catalyst. Concentration conditions can be chosen so the catalyst, smoothly and homogeneously, produces iodine (I2, I−3 ) to titrate ascorbic acid equally smoothly and homogeneously while simultaneously recycling to the former reduced state of iodide:
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MEASURING THE CONCENTRATION OF IODINE There are two convenient instrumental ways for measuring the concentration of iodine generated by an iodine clock: (i) By recording the changes in the potential of a bright platinum indicator electrode and calibrating these with standard solutions of iodine. This is the method adopted by Rao et al.7 to measure the concentration of total iodine (mainly as triiodide) for their studies of the kinetics of aqueous iodine with vitamin C. (ii) By absorbance spectrophotometry, with a method previously described in this Journal8 for the determination of the constant, K, of the triiodide equilibrium with iodine and iodide. This method makes use of the high molar absorptivity, ε = 2.76 × 104 cm−1 L mol−1 , of triiodide at 352 nm9 to measure the rising concentration of total iodine as the iodine clock approaches the time its kinetic titration of ascorbic acid is concluding. The concentration of triiodide, [I−3 ], can be measured by absorbance, A, using the Beer−Lambert law,10 where l is the path length of the cell
S2 O82 − + 2I− → 2SO4 2 − + I 2
C6H8O6 + I 2 → C6H6O6 + 2H+ + 2I−
and S2 O82 − + 3I− → 2SO4 2 − + I−3 C6H8O6 +
I−3
+
[I−3 ] =
−
→ C6H6O6 + 2H + 3I
(1)
When [I−3 ] and [I2] are in equilibrium through
The rate at which this kinetic titration proceeds depends predominantly on temperature and the concentration product of persulfate with iodide, [persulfate][iodide]. While iodide is © XXXX American Chemical Society and Division of Chemical Education, Inc.
A εl
A
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I 2 + I− ⇌ I−3
(iii) a brief interlude between the other two periods, when steady-state conditions no longer apply, where the concentration of iodine is beginning to rise more rapidly and a declining concentration of ascorbic acid is being exceeded by that of the iodine. All three periods operate under the same controlling rate, R, of the persulfate−iodide reaction. However, R is a sum of two other rates: R1, the rate of iodine that reacts with ascorbic acid and R2, the rate of iodine that is not reacting but being released freely into solution:
then, [I 2] =
[I−3 ] K[I−]
(2)
and the concentration of total iodine, [iodine], can be measured by absorbance using [iodine] = [I−3 ] + [I 2] =
[I−3 ](K[I−] + 1) K[I−]
(3)
R = R1 + R 2
to give −
[iodine] =
A(K[I ] + 1) εlK[I−]
(5)
In the initial period when R1 ≫ R2, then R = R1 and is known as the steady-state approximation.13 In the final period, R2 ≫ R1, then R = R2 and R2 can be used to measure R. It is in the intervening period when R1 and R2 are comparable that both can be readily measured. In their redox study of iodine reacting with vitamin C in aqueous solution, Rao et al.7 concluded that the reaction rate law is second-order, being first-order in both the concentration of iodine and vitamin C (ascorbic acid). It follows that the rate law, under the present conditions, is given by
(4)
It may be thought that, for a study of aqueous iodine− ascorbic acid kinetics, [iodine] could be extrapolated back to zero time where the initial concentration of ascorbic acid could be determined by the usual iodine clock procedures. This may seem an obvious ploy but is seriously flawed; another approach is required to obtain experimental data that can be verified. While iodine is being kinetically generated and ascorbic acid is being titrated, very low concentrations of both [I−3 ]and [I2] apply, making equilibrium between them extremely unlikely, even though their kinetic interchange with [I−] is very fast.11 Under steady-state conditions, a quasi-equilibrium exists until, nearing the conclusion of the iodine clock titration, iodine begins to increase in concentration, which is marked by its sudden color appearance and usually visually enhanced by the blueing of a soluble starch indicator,12 but omitted here. This increasing concentration of iodine enables equilibrium between [I−3 ], [I2], and [I−] to be fully attained and [iodine] measured by absorbance (Figure 1).
R1 = k[iodine][ascorbic acid]
(6)
where k is the second-order rate constant for the reaction of iodine with ascorbic acid. It is in the brief time-zone that this equation can be tested and a value of k determined.
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TESTING THE RATE EQUATION AND DETERMINING k A method was devised to test the rate equation and simultaneously determine a value of k. Within the intervening brief period of the iodine clock when [iodine] is rising and [ascorbic acid] falling, the two concentrations, for an instant, will become the same: [iodine] ≡ [ascorbic acid]
To locate this instant, or more realistically the time that shows the closest fit, the rate equation is tested repeatedly over a set of times, within the time-zone, to obtain a range of k values with sample standard deviation, SD, using MS Excel. Results of a typical data set are given in Table 1. The data from all of the times tested are summarized and shown for test-comparison in Figure 2 and Table 2, from which the coefficient of variation, CV, is calculated. This is a procedure used to normalize each set of data14−16 and enables sets of data having different averages to be compared simply by dividing each individual SD with its respective average:
Figure 1. Iodine clock titration of ascorbic acid: concentration of iodine nearing and after equivalence.
CV =
■
SD Average
(7)
The resulting CV then becomes a dimensionless comparator with the smallest locating the time of closest fit (the minimum of the curve shown in Figure 2). This is the set of results from Table 1 that has an average for k at 20 °C of 2.3 × 105 L mol−1 s−1, SD = 0.14 × 105 L mol−1 s−1 so CV = 0.14/2.3 = 0.06. The briefness of the time-zone limits the range of times over which the rate equation can be tested, but is sufficient to confirm the rate law obtained by Rao et al.7 and make comparison with their results.
IODINE CLOCK TIME-ZONES There are three distinctive time-zones or periods for an iodine clock: (i) an initial period of steady-state reaction conditions, when iodine is below a concentration level that is visually discernible; (ii) a final period, when iodine is clearly visible and the yellow color is intensifying; B
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Table 1. Assessing the Rate Equation R1 = k[Iodine][Ascorbic Acid] Using [Iodine] ≡ [Ascorbic Acid] at Time t = teq = 405 s t/s
[iodine]/nMa
[ascorbic acid]/nMb
R1/nmol L−1 s−1 c
k/105 L mol−1 s−1 d
403 403.5 404 404.5 405 405.5 406 406.5 407 407.5 408 408.5 409 409.5 410 410.5 411 411.5
692 704 716 730.5 745 763 781 807 833 864 895 932.5 970 1014 1058 1110 1162 1220
1012 944 876 810.5 745 683 621 567 513 464 415 372.5 330 294 258 230 202 180
136 133.5 131 127.5 124 116 108 103 98 91.5 85 78.5 72 64 56 50
2.05 2.13 2.21 2.30 2.38 2.39 2.36 2.41 2.44 2.46 2.45 2.45 2.42 2.34 2.19 2.13
a There is a minor contribution to absorbance by [I2] of 0.023A (due to its molar absorptivity of 189 cm−1 L mol−1 at 352 nm) and obtained by combining [I2] = A/27600 l K [I−] (from eqs 1 and 2) with 189 l [I2] (from the Beer−Lambert law), where K = 600 L mol−1 at 20 °C and [I−] = 0.5 mM. Absorbance is then amended to 0.977A and the total concentration of iodine obtained from eq 4. bThe concentration of ascorbic acid, [ascorbic acid], is obtained at the time of equivalence, teq = 405 s from [iodine], then at teq − 0.5 s by adding 80 nM to [iodine] and at teq + 0.5 s by subtracting 80 nM from [iodine] and pro rata for each 0.5 s. For example, at teq − 0.5 = 404.5 s, [ascorbic acid] = 730.5 + 80 = 810.5 nM and at teq + 0.5 = 405.5 s, [ascorbic acid] = 763 − 80 = 683 nM. At teq + 2(0.5) = 406 s, [ascorbic acid] = 781 − 2(80) = 621 nM. cThe rate of iodine reaction with ascorbic acid, R1, is obtained from −Δ[ascorbic acid]/Δt, so at t = 403.5 s, where t2 = 404 s and t1 = 403 s, R1 = −(876 − 1012)/1 = 136 nmol L−1 s−1. dThe rate constant k is calculated from eq 6, so at t = 403.5 s [iodine] = 704 nM, [ascorbic acid] = 944 nM, R1 = 136 nM s−1 to give k = 2.05 × 105 L mol−1 s−1. Average for k at 20 °C is 2.32 × 105 L mol−1 s−1, SD = 0.14 × 105 L mol−1 s−1, so CV = 0.06 (from eq 7).
Table 2. CV Data for Assessing the Location of t = teq at Times from 404 to 406.5 s teq
Average k/105 L mol−1 s−1 a
404 404.5 405 405.5 406 406.5
3.72 2.91 2.32 1.96 1.70 1.52
SD/105 L mol−1 s−1
CVb
1.08 0.40 0.14 0.18 0.22 0.24
0.29 0.14 0.06 0.09 0.13 0.16
c
a
The set of times over which k is averaged is the same as in Table 1. CV = SD/Average k. cTwo outliers are disregarded at t = 410.5 and 411 s. b
Figure 2. Coefficient of Variation, CV: a method for locating the time nearest [iodine] ≡ [ascorbic acid] that gives the best-fit to R1 = k[iodine][ascorbic acid] and for determining k. The minimum locates equivalence at t = 405 s when the average for k at 20 °C is 2.32 × 105 L mol−1 s−1; SD = 0.14 × 105 L mol−1 s−1 so CV = 0.06 (from eq 7 and Tables 1 and 2).
results emerges. Thus, corresponding to the second-order rate equation, eq 6: R1 = (k1[I−3 ] + k 2[I 2])[ascorbic acid]
(8)
where k1 and k2 are, respectively, the individual rate constants for the reaction of I−3 and I2 with ascorbic acid. Then, including
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[iodine] = [I−3 ] + [I 2] =
DETERMINING THE RATE CONSTANTS FOR [I−3 ] AND [I2] REACTING WITH ASCORBIC ACID It is apparent that the overall rate constant k determined by the present study and that by Rao et al.7 is obtained with very different concentrations of iodide (0.5 mM compared to 40 mM). In the latter case, iodine forms predominantly as the triiodide ion. It can be inferred that triiodide is the more reactive oxidant of ascorbic acid, which leads to a different overall k. When scrutinized, a clearer interpretation of the
[I−3 ](K[I−] + 1) K[I−]
(9)
rearranged to [I−3 ] =
K[I−] [iodine] K[I−] + 1
(10)
and [iodine] = [I−3 ] + [I 2] = [I 2](K[I−] + 1)
(11)
rearranged to C
dx.doi.org/10.1021/ed400579m | J. Chem. Educ. XXXX, XXX, XXX−XXX
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1 [iodine] K[I ] + 1 −
Communication
nmol L−1 s−1. So, at teq + 1 = 406 s, some of this iodine had reacted to decrease the concentration of ascorbic acid and some added to increase the concentration of iodine in solution. Let x be this increase, then
(12)
this gives R1 =
k1K[I−] + k 2 [iodine][ascorbic acid] K[I−] + 1
x = [iodine]teq + 1 − [iodine]teq (13)
and
then, comparing eq 13 with eq 6 k K[I−] + k 2 k= 1 − K[I ] + 1
[ascorbic acid]teq + 1 = [iodine]teq − (160 − x)
[ascorbic acid]teq + 1 = [iodine]teq + 1 − 160
(20)
So, simply by subtracting 160 nM from [iodine] at 406 s, we obtained [ascorbic acid] at this time, 781 − 160 = 621nM (see Table 1). In a similar way, at teq − 1 = 404 s, [ascorbic acid] = [iodine] + 160 = 716 + 160 = 876 nM. This enabled [ascorbic acid] to be obtained starting from [iodine] at equivalence and applied pro rata to the reaction times within the brief time-zone
k = 2.3 × 105 = (0.3k1 + k 2)/1.3
giving (15)
Repeating the calculation, using k = 5.7 × 105 L mol−1 s−1 at 20 °C and [I−] = 40 mM from Rao et al.7 (energy of activation is 53.1 kJ mol−1; k = 8.18 × 105 L mol−1 s−1 at 25 °C), the main oxidizing reaction is the same, ionic strength is comparable, but the concentration of iodide is considerably greater so most of the iodine is present as triiodide, then k1 = 5.9 × 105 L mol−1 s−1
(19)
Substituting for x in eq 19 gives
(14)
Consequently, with k = 2.3 × 105 L mol−1 s−1; K = 600 L mol−1 and [I−] = 0.5 mM
k 2 = 3.0 × 105 − 0.3k1
(18)
(16)
and k 2 = 1.2 × 105 L mol−1 s−1
(17)
This confirms triiodide to be the more reactive form of iodine that oxidizes aqueous ascorbic acid (vitamin C) in the iodine clock reaction and also explains how k, when determined under very different concentrations of iodide, can differ.
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Figure 3. Concentration change of iodine and ascorbic acid through the brief time-zone with equivalence at t = 405 s.
SUMMARY OF THE REACTION Shimadzu 1650 spectrophotometer and reagents are as described in ref 8, except that the cell path length was changed from 1 to 10 cm and more frequent readings were recorded. Procedure and reagent concentrations ([S2O2− 8 ]0 = 50 mM, [I−]0 = 0.5 mM) were the same and [ascorbic acid]o was determined from equivalence.
when the reaction rates R1 and R2 were comparable. These changes to [ascorbic acid] and [iodine] are shown in Figure 3. Rate of Iodine Reaction with Ascorbic Acid, R1 in the Brief Time-Zone
Rate of Iodine Generation, R
The rate of iodine reaction with ascorbic acid, R1 at time t, was obtained from −Δ[ascorbic acid]/Δt, by using the concentrations of ascorbic acid at t ± 0.5 s. So, at t = 405 s, where t2 = 405.5 s and t1 = 404.5 s, R1 = −(683 − 810.5)/1 = 127.5 nmol L−1 s−1 (see Table 1).
The rate of the concentration of iodine being generated, R, was obtained from R2 when the iodine clock was freely releasing iodine into solution and its rate of increasing concentration was linear. In this study, at 20 °C, R2 = R = 160 nmol L−1 s−1 (see Figure 1) with a correlation coefficient of 0.9999.17
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CONCLUSIONS An opportunity is described to investigate the kinetics of iodine reaction with ascorbic acid in aqueous solution without resorting to a specialist rapid-reaction technique.18 This fast reaction, essential to iodine clock demonstrations and laboratory exercises in chemical kinetics, can be readily studied by conventional UV−visible spectrophotometry. Absorbance at a fixed wavelength of 352 nm can be used to measure [I−3 ] and, through equilibrium with [I2] and [I−], also measure the total concentration of iodine, [iodine], forming in solution during the brief time interval as the iodine clock concludes its titration of ascorbic acid. This continues into the final period when [iodine] is being generated free from reaction with ascorbic acid enabling rate, R, to be readily measured.
Determining the Initial Concentration of Ascorbic Acid
The initial concentration of ascorbic acid, [ascorbic acid]o, was determined from the time t = 0 s to equivalence at teq = 405 s, and the rate of the titration reaction from, R = 160 nmol L−1 s−1 = −Δ[ascorbic acid]/Δt = −(745 − [ascorbic acid]o)/(405 − 0), so [ascorbic acid]o = 65.5 μM. As teq is near the beginning of the brief period following the end of the steady state, the rate of the titration remained practically constant. Determining Concentration of Ascorbic Acid in the Brief Time-Zone
By locating the time to equivalence, teq = 405 s, then [ascorbic acid] was determined to be the same as [iodine] at this time (see Table 1). The rate of iodine being generated was R = 160 D
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(15) How to use excel to calculate coefficient of variation. http:// www.ehow.co.uk/how_7304187_use-excel-calculate-coefficientvariation.html (accessed Dec 2013). (16) Håkanson, L. The Role of Characteristic Coefficients of Variation in Uncertainty and Sensitivity Analyses, with Examples Related to the Structuring of Lake Eutrophication Models. Ecol. Modell. 2000, 131, 1−20. (17) Correlation coefficient, 2006, http://goldbook.iupac.org/ C01347.html (accessed Dec 2013). (18) Caldin, E. F. Fast Reactions in Solution; Blackwell: Oxford, 1964; pp 1−13. (19) Ascorbic acid (A7506) - Product Information Sheet - Sigma.
Equivalence allows [ascorbic acid] to be measured and a range of kinetic data obtained. Assessing these data, using the coefficient of variation (CV = SD/Average), locates the time nearest to equivalence between the concentrations of iodine and ascorbic acid, which confirms the rate equation and obtains a value of the reaction rate constant. Also, triiodide ion can be shown to be the more active form of iodine reacting with ascorbic acid in aqueous solution at room temperature and the individual rate constants for triiodide and I2 in the reaction can be determined. Other opportunities to study rapid reaction kinetics may be found with iodine clock titrations of readily oxidized titrants such as the thiosulfate ion in aqueous solution. A significant feature of this methodology is the use of equivalence as a fundamental property to measure the conclusion of the kinetic titration by an iodine clock and it contrasts with subjective methods of end point detection for reductants such as ascorbic acid, which are susceptible to oxidation by atmospheric oxygen in dilute aqueous solution19 and introduce additional uncertainty for calibration with standard solutions.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Harris, D. C. Quantitative Chemical Analysis, 3rd ed.; Freeman: New York, 1991; pp 410−413. (2) Evans, D. H. Coulometric Titration of Cyclohexene with Bromine. J. Chem. Educ. 1968, 45, 88. (3) Mark, H. B.; Rechnitz, G. A. Kinetics in Analytical Chemistry; Wiley: New York, 1968; pp 70−72. (4) Moews, P. C.; Petrucci, R. H. The Oxidation of Iodide Ion by Persulfate Ion. J. Chem. Educ. 1964, 41, 549−551. (5) Wright, S. W. Tick Tock, a Vitamin C Clock. J. Chem. Educ. 2002, 79, 40A. (6) Vitz, E. A Student Laboratory Experiment Based on the Vitamin C Clock Reaction. J. Chem. Educ. 2007, 84, 1156. (7) Rao, T. S.; Murhe, M. M.; Dabke, R. B.; Harikrishna, T. Study of Rapid Reactions by the Steady-State Principle: Kinetics of the Reaction between Vitamin C and Iodine in Aqueous Solution. Curr. Sci. 1990, 59, 370−372. (8) Burgess, A. E.; Davidson, J. C. A Kinetic-Equilibrium Study of a Triiodide Concentration Maximum Formed by the Persulfate-Iodide Reaction. J. Chem. Educ. 2012, 89, 814−816. (9) Rahn, R. O.; Stefan, M. I.; Bolton, J. R.; Goren, E.; Shaw, P.-S.; Lykke, K. R. Quantum Yield of the Iodide-Iodate Chemical Actinometer: Dependence on Wavelength and Concentration. Photochem. Photobiol. 2003, 78, 146−152. (10) Beer−Lambert law (or Beer−Lambert−Bouguer law), 2006, http://goldbook.iupac.org/B00626.html (accessed Dec 2013). (11) Turner, D. H.; Flynn, G. W.; Sutin, N.; Beitz, J. V. Laser Raman Temperature Jump Study of the Kinetics of the Triiodide Equilibrium. J. Am. Chem. Soc. 1972, 94, 1554−1559. (12) Yu, X.; Houtman, C.; Atalla, H. A. The Complex of Amylose and Iodine. Carbohydr. Res. 1996, 292, 129−141. (13) Steady state (stationary state) also contains definition of: steady state approximation (treatment), 2006, http://goldbook.iupac.org/ S05962.html (accessed Dec 2013). (14) STEPS Statistics Glossary. http://www.stats.gla.ac.uk/steps/ glossary/presenting_data.html (accessed Dec 2013). E
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