Communication pubs.acs.org/jchemeduc
A Kinetic−Equilibrium Study of a Triiodide Concentration Maximum Formed by the Persulfate−Iodide Reaction Arthur E. Burgess*,† and John C. Davidson‡ †
School of Contemporary Sciences, University of Abertay Dundee, Bell Street, Dundee, DD1 1HG, United Kingdom Kip McGrath Educational Centre, Highland House, St. Catherine’s Road, Perth, PH1 5YA, United Kingdom
‡
ABSTRACT: The presence of triiodide, I3−, throughout the lifetime of a persulfate−iodide reaction with persulfate in excess, is controlled by an opposing effect of falling iodide concentration and rising iodine concentration. This brings triiodide to a concentration maximum, [I3−]max, which can be studied by UV−visible spectroscopy using absorbance measurements taken over an extended iodine clock time-scan. Equilibrium and conservation equations can be combined so that, together with [I3−]max, a value of the constant K for the equilibrium established between iodine, iodide, and the triiodide complex ion can be obtained.
KEYWORDS: Upper-Division Undergraduate, Analytical Chemistry, Laboratory Instruction, Physical Chemistry, Aqueous Solution Chemistry, Equilibrium, Kinetics, Oxidation/Reduction, Reactions, UV−Vis Spectroscopy
I
odide oxidation to iodine is the basis of an iodine clock reaction with persulfate (peroxydisulfate), typically the oxidant, and a small quantity of an iodine scavenger, usually sodium thiosulfate, added to make a time-delay before the colorful appearance of iodine provides a measure for the initial reaction rate:1,2 S2O82 − + 2I− → 2SO24 − + I2 2S2O32 − + I2 → S4 O62 − + 2I−
A variation uses ascorbic acid as the iodine scavenger,3,4 which is oxidized by 1:1 stoichiometry to dehydroascorbic acid: C6H8O6 + I2 → C6H6O6 + 2H+ + 2I− Figure 1. Time-scan at λ = 352 nm with [S2O82−]0 = 50 mM, [I−]0 = 500 μM, and [ascorbic acid]0 = 50 μM near 20 °C.
Generally, starch is added to visually enhance the first trace of iodine that appears and marks the time-measure for the iodine clock. The study presented herein augments the kinetic determination of the clock reaction and follows the continuing development of iodine in the persulfate−iodide solution, so no starch is added. The major complex of dissolved iodine in iodide solution is triiodide, I 3− , formed through the equilibrium:5
reaction. Later, with persulfate in excess, the growth of triiodide absorbance lessens appreciably, comes to a maximum, Amax, at point b, then goes into decline. A study of this maximum provides insight about the relationship between the iodine and iodide concentrations at the triiodide maximum [I3−]max that provides a method of evaluating the equilibrium constant K.
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I2 + I− ⇌ I− 3
UV−VISIBLE ABSORBANCE TIME-SCAN A typical reaction time-scan, similar to an initial-rate study but extending over a longer period with persulfate in excess, was started by quickly mixing equal volumes, kept at 20 ± 0.5 °C, of
The deepening yellow color of triiodide, I3−, is measured by UV−visible absorbance spectroscopy. The increase of triiodide concentration is shown by the steeply rising part of the absorbance curve (Figure 1), which starts just beyond point a, that indicates the close approaching time-measure for the clock © 2012 American Chemical Society and Division of Chemical Education, Inc.
Published: March 15, 2012 814
dx.doi.org/10.1021/ed200055t | J. Chem. Educ. 2012, 89, 814−816
Journal of Chemical Education
Communication
equations with respect to t. Differentiating the equilibrium equation, (eq 1) gives
potassium persulfate (100 mM) and a solution containing potassium iodide (1000 μM) and ascorbic acid (100 μM). A portion of the mixture was transferred into a 1 cm quartz cell at the same temperature. The cell was tapped to dislodge any air bubbles and then placed in the sample beam of a Shimadzu 1650 UV−visible spectrophotometer. The wavelength λ was set at 352 nm (see Figure 2), which is where triiodide strongly
− d([I2][I−]) d[I ] 1 d[I3 ] d[I−] = = [I−] 2 + [I2] K dt dt dt dt
When [I3−] = [I3−]max, the triiodide concentration maximum, d[I3−]/dt = 0, and [I−]
d[I2] d[I−] = −[I2] dt dt
(3)
Differentiating the conservation equation (eq 2), and noting [I−]0 is constant, gives d[I−] d[I−]0 d[I ] d[I−] =0= +2 2 +3 3 dt dt dt dt
So, at the triiodide maximum when the rate of triiodide formation is zero, (d[I3−]/dt = 0), the rate of iodine formation equals half the rate of iodide removal: d[I2] 1 d[I−] =− dt 2 dt
Combining eq 4 with eq 3 gives the relationship between iodine and iodide at [I3−]max:
Figure 2. Color development (inset) during a persulfate oxidation of iodide and the accompanying absorbance spectrum.
[I−] = 2[I2]
absorbs (molar absorptivity ε = 2.76 × 104 L mol−1 cm−1), iodine only weakly (ε = 189 L mol−1 cm−1), and iodide not at all,5−7 as is the case with persulfate. This spectrophotometer had no ancillary temperature controller for the cell-holder, but the surplus mixed solution was measured and remained close to 20 °C throughout the scanning period.
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I3−
absorbance at 352 nm,
A max = εl[I− 3 ]max
(6)
I3−
where, at a wavelength of 352 nm, molar absorptivity for is ε = 2.76 × 104 L mol−1 cm−15−7 and cell length is l = 1 cm, [I3−]max is obtained. The corresponding values for [I−] and [I2] are calculated from eqs 2 and 5 (Table 1). These values are Table 1. Amax and Corresponding [I3−]max, [I−], and [I2] Using Different [I−]0 for the Persulfate−Iodide Reaction
A time-scan (Figure 1) shows light absorbance by triiodide in a persulfate−iodide reaction under a restricted concentration of iodide by choosing the oxidant to be in excess. This condition brings about the formation of iodine while iodide is being depleted to the extent that at some point the rising concentration of triiodide, which is dependent on both iodine and iodide concentrations, goes into decline and a maximum concentration of triiodide is reached. Consideration of this maximum allows the equilibrium constant K to be determined, as follows. Two relationships pertaining to the triiodide concentration maximum must apply during the reaction time: • The formation of triiodide from iodine and iodide, which sharply marks the conclusion of the iodine scavenger reaction, is sufficiently rapid8 to keep [I3−] ∝ [I2][I−]. This relationship with the equilibrium constant K gives the equilibrium equation
a
[I−]0a/μM
Amax
[I3−]max/μM
[I−]/μM
[I2]/μM
1000 800 700 600 500 400
1.520 1.038 0.774 0.632 0.454 0.305
55 38 28 23 16 11
418 344 308 266 225 184
209 172 154 133 113 92
[K2S2O8]0 = 50 mM and the reaction temperature is at 20 °C.
then adjusted for the absorbance of I2, which, although of appreciably lower molar absorptivity at 352 nm (ε = 189 L mol−1 cm−15−7) than I3−, have reached proportionately much higher concentrations at Amax (Table 2). Analysis of the adjusted values using eq 1 gives a mean for K of 600 L mol−1 with a standard deviation of the sample of 24 L mol−1; K = 600 ± 24 L mol−1 near 20 °C. This compares to Keq = 500 using thermodynamic data obtained from visible spectroscopy by Schmidt and Heiman.5 They determined ΔHO̵ = −34.2 ± 5.1 kJ mol−1 and ΔSO̵ = −65 ± 16.4 J K−1 mol−1 over the temperature range 296.2−332.2 K. The thermodynamic Keq at 293 K, though slightly outside of their temperature range, is calculated by
(1)
• The sum of iodine atom concentrations throughout the reaction is equal to the initial iodide concentration, [I−]0. The mass-balance or conservation equation is [I−]0 = [I−] + 2[I2] + 3[I− 3]
(5)
Using the Beer−Lambert law for
EQUILIBRIUM CONSTANT FROM ABSORBANCE
− [I− 3 ] = K[I2][I ]
(4)
ΔGO̵ = ΔH O̵ − T ΔSO̵ = −RT ln K eq
(2)
Information about the changes with time, t, that affect each component concentration is obtained by differentiating these
Note that Keq increases in value as temperature decreases. 815
dx.doi.org/10.1021/ed200055t | J. Chem. Educ. 2012, 89, 814−816
Journal of Chemical Education
Communication
Table 2. Amax Corrected for the Absorbance of I2 and the Adjusted [I3−]max, [I−], and [I2] for the Persulfate−Iodide Reaction [I−]0a/μM
Amax − AI2b
[I3−]max/μM
[I−]/μM
[I2]/μM
1000 800 700 600 500 400
1.481 1.006 0.745 0.607 0.433 0.288
54 36 27 22 16 10
420 346 310 267 226 185
210 173 155 134 113 93
triiodide to be determined and compared to other reported values. Different concentration conditions can be chosen for the persulfate−iodide reaction and measurements made of Amax over a range of constant temperatures. Also, similar reactions that generate I3− may be made for a kinetic−equilibrium study using this absorbance maximum method; a table of iodide oxidants can be found in ref 12.
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AUTHOR INFORMATION
Corresponding Author
a [K2S2O8]0 = 50 mM and the reaction temperature is at 20 °C. bThe absorbance of I2, ε = 189 L mol−1 cm−1, is measured at 352 nm.
*E-mail:
[email protected].
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ACKNOWLEDGMENTS Evelyn McPhee is thanked for her able technical support, Maurice Lindsay for his photograph of the I3− color formed in a persulfate−iodide solution and John D. Burgess for his assistance with the figures.
Klassen, Marchington, and McGowan9 determined K at 24 °C to be 600 ± 30 L mol−1 and they cite eight other reports that put K in the range of 650−760 L mol−1 (presumably at 25 °C) for low concentrations of I2 with no added salts. It is evident that determinations of K vary widely and that ionic strength is important in this reaction involving ionic species. Consequently, the value obtained by measuring the concentration components from Amax at moderate ionic strength (due mainly to the oxidant) is acceptable. The simplicity of this approach augments clock reaction experiments and provides a basis for a more extensive study of K under different concentration conditions that includes ionic strength. Also, given the availability of a spectrophotometer incorporating a temperature-controlled cell holder, measuring the enthalpy change of triiodide formation over a limited temperature range is possible. Contrary to a view that a large K value indicates an equilibrium position favoring triiodide as the major form of iodine,5 the results show that, even at [I3−]max, this is not necessarily the case when the participants are at low concentrations.
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REFERENCES
(1) Moews, P. C.; Petrucci, R. H. J. Chem. Educ. 1964, 41, 549−551. (2) Carpenter, Y-y.; Phillips, H. A.; Jakubinek, M. B. J. Chem. Educ. 2010, 87, 945−947. (3) Wright, S. W. J. Chem. Educ. 2002, 79, 40A. (4) Vitz, E. J. Chem. Educ. 2007, 84, 1156. (5) Schmidt, E.; Heiman, P. J. Phys. Chem. Lab. 2005, 9, 37−41. (6) Mamane, H.; Ducoste, J. J.; Linden, K. G. Appl. Opt. 2006, 45, 1844−1856. (7) Rahn, R. O.; Stefan, M. I.; Bolton, J. R.; Goren, E.; Shaw, P.-S.; Lykke, K. R. Photochem. Photobiol. 2003, 78, 146−152. (8) Turner, Flynn, Sutin, and Beitz investigated the kinetics of the triiodide equilibrium by a laser temperature-jump method and obtained formation and reverse rate constants of (6.2 ± 0.8) × 109 L mol−1 s−1 and (8.5 ±1.0) × 106 s−1, respectively, at 25 °C. Turner, D. H.; Flynn, G. W.; Sutin., N.; Beitz, J. V. J. Am. Chem. Soc. 1972, 94, 1554−1559. (9) Klassen, N. V.; Marchington, D.; McGowan, H. C. E. Anal. Chem. 1994, 66, 2921−2925. (10) Skoog, D. A; Leary, J. J. Principles of Instrumental Analysis, 4th ed.; Saunders College Publishing: Fort Worth. TX, 1992; Chap. 8, pp 167−168 . (11) Potassium Persulfate ICSC Data. http://www.inchem.org/ documents/icsc/icsc/eics1133.htm (accessed Jan 2012). (12) Harris, D. C. Quantitative Chemical Analysis, 3rd ed.; Freeman: New York, 1991; Chap. 16, p 415.
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IODINE CLOCK REACTION WITH A PHOTOMETRIC END POINT The feasibility of marking the removal of the iodine scavenger by a sharply defined photometric end point (point a in Figure 1) and continuing the absorbance measurements to locate Amax (point b in Figure 1) has been illustrated. The aim was to extend the conditions suitable for iodine clock kinetics to an equilibrium study. Freshly prepared solutions of ascorbic acid and sodium thiosulfate were both convenient delaying agents for a well-defined photometric end point;10 however, the presence of a time-delaying iodine scavenger was unnecessary to take peak maximum measurements and could be excluded. Iodide oxidation by persulfate provides a suitable basis to make a kinetic−equilibrium study. Nevertheless, persulfate salts are powerful oxidants and appropriate precautions are necessary.11 Persulfate solutions also degrade over time and fresh preparation of both this reagent and of iodide is recommended.
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CONCLUSIONS The strong UV−visible absorbance of triiodide offers opportunities to observe and measure an unusual change that occurs to an equilibrium participant during a chemical reaction and augments familiar iodine clock kinetic experiments and calculations using persulfate oxidation of iodide. Measuring Amax allows a value of the constant K for the formation of 816
dx.doi.org/10.1021/ed200055t | J. Chem. Educ. 2012, 89, 814−816
