The Effect of Temperature and Ionic Strength on the Oxidation of

Laboratory Experiment pubs.acs.org/jchemeduc

The Effect of Temperature and Ionic Strength on the Oxidation of Iodide by Iron(III): A Clock Reaction Kinetic Study Jurica Bauer,*,†,‡ Vladislav Tomišić,† and Petar B. A. Vrkljan§ †

Laboratory of Physical Chemistry, Department of Chemistry, Faculty of Science, University of Zagreb, Horvatovac 102 a, 10000 Zagreb, Croatia § XVIII Gymnasium, Zagreb, Croatia S Supporting Information *

ABSTRACT: A laboratory exercise has recently been reported in which the students use the initial rates method based on the clock reaction approach to deduce the rate law and propose a reaction mechanism for the oxidation of iodide by iron(III) ions. The same approach is used in the exercise proposed herein; the students determine the dependence of the reaction rate on ionic strength and temperature in a straightforward manner. The previously proposed mechanism is further supported by the results, the rate-determining step is identified, and the activation parameters Ea, Δ⧧H, and Δ⧧S are determined for the overall reaction of the first two steps of the mechanism. The significance of such kinetic studies in elaborating reaction mechanisms is clearly demonstrated to the students.

KEYWORDS: High School/Introductory Chemistry, Upper-Division Undergraduate, Inorganic Chemistry, Laboratory Instruction, Physical Chemistry, Hands-On Learning/Manipulatives, Kinetics, Mechanisms of Reactions, Thermodynamics

an indicator for I3− ions (2, pp 51−55). The complex Fe(S2O3)+ is purple and the starch−pentaiodide complex is blue. The reaction is started by mixing a colorless acidic solution of iron(III) nitrate with a colorless solution containing sodium thiosulfate, potassium iodide, potassium nitrate,13 and starch. The solution immediately turns purple. The color gradually fades until the solution becomes colorless. At that very moment, the solution suddenly turns dark blue. The time elapsed from the mixing of the two solutions to the sudden color change to blue, Δt, is measured. The reaction, eq 1, is first order with respect to iron(III) ions and second order with respect to iodide ions, as expressed by eq 2.1 The exercise presented here is designed for use in an undergraduate physical chemistry laboratory course. The exercise could be done by students individually or in groups. Two 4-h laboratory sessions are needed: one for the study of the ionic strength effect and the other for the study of the temperature effect. The setup, the experiment, and the report can be completed in each laboratory session. The aim of the exercise is to examine the dependence of the rate of iodide oxidation by iron(III) ions (eq 1) on temperature and ionic strength and to get more detailed insight into the reaction mechanism.

T

he student laboratory exercise presented here is an extension of the experiment described in our earlier publication.1 In that experiment the oxidation of iodide by iron(III)

2Fe3 +(aq) + 3I−(aq) → 2Fe2 +(aq) + I3−(aq) (1) is transformed into a clock reaction. The students use the initial rates method to study the kinetics of the reaction, obtain the rate law,

[S2O32 −]0 = k[Fe3 +]0 [I−]0 2 (2) Δt where Δt is the time to the observed color change, and propose a reaction mechanism. In the present work, a study of the dependence of the rate of the above reaction on ionic strength and temperature using the same approach is described. Clock reactions2−4 are commonly used to illustrate chemical kinetics because such systems are easily monitored by means of the initial rates method. Rate laws are deduced from the experimental results and the reaction mechanisms are discussed.1,5−7 Clock reactions are also conveniently used to demonstrate the dependence of reaction rates on temperature3,4,7,8 as well as on ionic strength. The corresponding results may give insight into the reaction mechanism.7,9−12 The oxidation of iodide by iron(III) ions in an acidic medium (eq 1) is a reaction that can easily be transformed into a clock reaction using thiosulfate as a limiting reagent and starch as v0 =

© 2012 American Chemical Society and Division of Chemical Education, Inc.

Published: January 27, 2012 540

dx.doi.org/10.1021/ed2002972 | J. Chem. Educ. 2012, 89, 540−544

Journal of Chemical Education

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Laboratory Experiment

THE EXPERIMENT The experiments are conducted in a thermostated cell described elsewhere1 (Figure 1 in the Supporting Information). A total of 55 mL of solution A (containing Na2S2O3, KI, KNO3, and starch) is placed in the cell and 5 mL of solution B (containing Fe(NO3)3 and HNO3) is placed in the syringe. Solution A is stirred by a magnet. Solution B is injected into solution A and a stopwatch is started at that point. Time is recorded at the moment the solution suddenly turns dark blue. The experiment is conducted three times for each temperature and ionic strength.

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HAZARDS Concentrated nitric acid is both a strong acid and a powerful oxidizing agent. Contact with the skin can result in severe burns. The vapor irritates the respiratory system, eyes, and other mucous membranes. Iron(III) nitrate and potassium nitrate are strong oxidizing agents and skin irritants. Contact with combustible materials can cause fire. Sodium thiosulfate may cause irritation to skin, eyes, and respiratory tract.

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Figure 1. Dependence of Δt on ionic strength according to eq 3: [Fe(NO3)3]0 = 3.0 mmol L−1; [KI]0 = 0.02 mol L−1; [Na2S2O3]0 = 0.48 mmol L−1; (•) experimental; () calculated by means of eq 5.

rate-determining step is the reaction of the FeI2+ complex with the second I− ion according to the previously proposed mechanism: 1

RESULTS AND DISCUSSION

Ionic Strength

The first experiment involves examination of the effect of ionic strength on the reaction rate. The ionic strength is varied while the initial concentrations of all reactants and the temperature are kept unchanged. Ionic strength is adjusted with HNO3. The experiments are performed at ionic strength values ranging from approximately 0.05 to 0.20 mol L−1 for which the extended Debye−Hückel law and Brønsted−Bjerrum equation are approximately valid and commonly used (14, pp 163−166, 884−885, 15). The data obtained are submitted to linear regression analysis according to the Brønsted−Bjerrum equation, which, for the system studied, can be written as

− log Δt = C + 2ADHzAzB

K1 Fe3 +(aq) + I−(aq) ⇌ FeI2 +(aq) k2 FeI2 +(aq) + I−(aq) → Fe2 +(aq) + I2−(aq) k3

2I2−(aq) → I3−(aq) + I−(aq) (6) Considering the mechanism (eq 6) and applying the steadystate approximation for I 2−, eq 2 can be rewritten as 1

v=

Ic

(3)

where ADH denotes a constant from the Debye−Hückel law, zA and zB are the charge numbers of the reacting ions, and Ic is the ionic strength. The constant C is defined as

C = log

v=

k 0[Fe3 +]0 [I−]0 2 [S2O32 −]0

v=

Ic 1+

Ic

1 k 2[FeI2 +][I−] 2

(8)

which clearly depicts the reaction between ions FeI2+ and I− as the rate-determining step in the mechanism (eq 6). Because I− ions are present in excess, under the reaction conditions, eq 8 can be rewritten as

(4)

where k0 is the reaction rate coefficient at Ic = 0. The typical results of the data analysis are given in Figure 1 and by

− log Δt = −0.42 − 2.17

(7)

From the mechanism (eq 6) and the rate law (eq 7), one can derive the Brønsted−Bjerrum equation for the system where the slope of the line is predicted to be −5.11 (see the Supporting Information).17 The experiment, however, gives the slope of −2.17. This seeming discrepancy deserves a closer look. From the definition of the concentration equilibrium constant, K1 = [FeI2+]/{[Fe3+][I−]}, and eq 7, it follows

Ic 1+

1 K1k 2[Fe3 +][I−]2 2

1 k 2[FeI2 +][I−]0 2

(9)

The slope of −2.17 (eq 5) indicates that the change in the ionic strength influences only k2 in eq 9 and not [FeI2+]. This may seem counterintuitive as the value of the concentration equilibrium constant K1 is ionic strength dependent. As a consequence of the change in K1, the equilibrium concentration of Fe3+ ions will also change with ionic strength. If, however,

(5)

Because ADH = 0.511 for aqueous solutions at 25 °C (15, 16, pp 251−261), from eqs 3 and 5 it follows that zAzB = −2.12. The zAzB value obtained indicates that the 541




(which holds if K1°[I−]0 is large enough), eq 15 can be simplified affording

the standard equilibrium constant

K1° =

a FeI2 + a Fe3 +a I−

(10)

v0 =

where ai = γi[ci/(mol L−1)], (and therefore K1 as well) is large enough, the concentration of FeI2+ does not change significantly with the change of ionic strength under the conditions used. Using the value of K1° = 3.9 × 103 derived from the literature value of the concentration equilibrium constant K1,18 one can easily calculate [FeI2+] under the experimental conditions (from the definition of K1° and by using Debye− Hückel law to estimate activity coefficients γi, one can calculate K1 at a given ionic strength and use that value to calculate [FeI2+] under the reaction conditions). This shows that [FeI2+] changes up to 7% on changing the ionic strength from 0.05 to 0.20 mol L−1 (see the simulation in the Supporting Information). Thus, by changing the ionic strength, under the experimental conditions used, only its effect on k2 is observed, as indicated by the result (slope of −2.17). This will be the case as long as the product K1[I−]0 is large enough. The above considerations can be further clarified as follows. From the definition of K1 and under the reaction conditions, [FeI2+] can be expressed as [FeI2+] = K1[Fe3+][I−]0 and [Fe3+] can in turn be expressed as [Fe3+] = [Fe3+]0 − [FeI2+] − [Fe2+] ≈ [Fe3+]0 − [FeI2+] (as the initial rate is monitored, Fe2+ ions are present only in minute concentrations). From these two equations, one can write

[FeI2 +] =

K1[Fe3 +]0 [I−]0 1 + K1[I−]0

Temperature

The second experiment involves examination of the effect of temperature on the reaction rate. The temperature is varied while the initial concentrations of all reaction participants are kept unchanged. Ionic strength is set to Ic = 1.0 mol L−1 with KNO3 and HNO3. The data obtained are submitted to linear regression analysis according to the Arrhenius equation for the system considered

(11)

− ln Δt = ln A − ln

Ic

(12)

the concentration equilibrium constant can be expressed as a function of the ionic strength

K1 = K1°·10−6ADH{

Ic / (1 + Ic )}

[S2O32 −]0 [Fe

3+

]0 [I−]0 2

−

Ea 1 R T

(18)

with A and Ea being the Arrhenius pre-exponential factor and the activation energy, respectively (14, pp 807−809). The typical results of linear regression analysis of the collected data are given in Figure 2 and by

Ic 1+

(17)

With ADH = 0.511 for aqueous solutions at 25 °C (15, 16, pp 251−261), the logarithmic form of eq 17 is expected to give the slope of −2.04. The result of −2.17 is in agreement with the one predicted by this equation. This result therefore confirms the proposed mechanism (eq 6) with the reaction between ions FeI2+ and I− as the rate-determining step. The validity of the assumption used to simplify eq 15 into eq 17 can be easily verified by using K1° = 3.9 × 103 18 and [I−]0 = 0.02 mol L−1 used in the experiment (see the Supporting Information). To summarize this part, the slope of the line obtained from the study of the dependence of the reaction rate on ionic strength is ≈ −2 and not ≈ −5 because of the conditions used (excess of iodide) and the method used to follow the kinetics (the initial rates method). With these in mind, it is clear that the result is in accord with the reaction mechanism.

By taking into account the definition of the standard equilibrium constant and the extended Debye−Hückel law (14, pp 163−166),

log γi = − ADHzi 2

1 k 2,0[Fe3 +]0 [I−]0 ·10−4ADH{ Ic / (1 + Ic )} 2

− ln Δt = 37.2 − 12.0 × 103(1/T )

(19)

(13)

The reaction rate coefficient, k2, can be expressed by the Brønsted−Bjerrum equation (14, pp 884−885, 15)

k 2 = k 2,0· 10−4ADH{

Ic / (1 + Ic )}

(14)

with k2,0 defined as the reaction rate coefficient at Ic = 0. Bearing in mind that the initial reaction rate is followed, from eqs 9−14 it follows

v0 =

1 k 2,0· 10−4{ Ic / (1 + Ic )}[Fe3 +]0 [I−]0 2 ×

K1°· 10−6ADH{ Ic / (1 + Ic )}[I−]0 1 + K1°· 10−6ADH{ Ic / (1 + Ic )}[I−]0

(15)

Equation 15 is an expression for the dependence of the initial reaction rate, v0, on ionic strength, provided that the iodide is present in excess. If

K1°·10−6ADH{ Ic / (1 + Ic )}[I−]0 ≫ 1

Figure 2. Temperature dependence of Δt according to eq 18: [Fe(NO3)3]0 = 8.5 mmol L−1; [KI]0 = 8.0 mmol L−1; [Na2S2O3]0 = 0.20 mmol L−1; [KNO3]0 = 0.9 mol L−1; [HNO3]0 = 0.1 mol L−1; (•) experimental; () calculated by means of eq 19.

(16) 542




Physical quantities Δ⧧H and Δ⧧S are therefore hard to interpret in terms of the elementary steps of the mechanism (eq 6).

From Figure 2 and eqs 18 and 19, it follows that A = 5.1 × 1018 L2 mol−2 s−1 and Ea = 99.7 kJ mol−1. The value of the activation energy is in excellent agreement with the literature values, for example, 100 kJ mol−1 19 and 102 kJ mol−1.20 The data obtained are also submitted to linear regression analysis according to the Eyring equation for the system considered (14, pp 880−884),

− ln(T Δt ) = ln − ⧧

[Fe3 +]0 [I−]0 2 [S2O32 −]0

+ ln

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CONCLUSION Earlier a laboratory exercise was proposed in which the students use the initial rates method based on the clock reaction approach to deduce the rate law and propose a reaction mechanism for the oxidation of iodide by iron(III) ions.1 Here an extension of that exercise is reported in which the students determine the dependence of the reaction rate on ionic strength and temperature using the same approach. The first study further supports the proposed mechanism (eq 6) and identifies the reaction between FeI2+ and I− ions as the rate-determining step, whereas the latter study reveals the activation quantities Ea, Δ⧧H, and Δ⧧S for the overall reaction of the first two steps of the mechanism. The clock reaction approach allows for the experiments to be carried out easily affording valuable information about the reaction studied. It also allows the students to experience the initial rates method first hand. In that way, they can study the dependence of the reaction rate on ionic strength and temperature in a straightforward manner. Another important feature of the work presented here is that the thorough study of the dependence of the reaction rate on ionic strength clearly shows its significance in elaborating reaction mechanisms. The study of the temperature dependence of the reaction rate has also been simplified and used as a high school students’ miniproject in teaching chemical kinetics in the classroom (five six-student groups, 90 min period). Having carried out the appropriate experiments, the students determine the activation energy and the pre-exponential factor from eq 18 and a plot similar to the one shown in Figure 2.

kB Δ⧧S + h R

Δ⧧H 1 R T

(20)

⧧

where Δ H and Δ S are the activation enthalpy and entropy, respectively, and kB and h are the Boltzmann and Planck constants, respectively. The typical results of linear regression analysis are given in Figure 3 and by

− ln(T Δt ) = 30.5 − 11.7 × 103(1/T )

(21)

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ASSOCIATED CONTENT

S Supporting Information *

Instructions and discussion questions for students; instructions for instructors; an Excel file of the simulation used. This material is available via the Internet at http://pubs.acs.org.

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Figure 3. Temperature dependence of Δt according to eq 20. [Fe(NO3)3]0 = 8.5 mmol L−1, [KI]0 = 8.0 mmol L−1, [Na2S2O3]0 = 0.20 mmol L−1, [KNO3]0 = 0.9 mol L−1, [HNO3]0 = 0.1 mol L−1; (•) experimental, () calculated by means of eq 21.

Corresponding Author

*E-mail: [email protected].

⧧

From Figure 3 and eqs 20 and 21, it follows that Δ S = 105 J K−1 mol−1 and Δ⧧H = 97.2 kJ mol−1. From eqs 2 and 7, it is obvious that the observed rate coefficient is

k 1 1 k = k 2K1 = k 2 1 2 2 k −1

Present Address ‡

Stratingh Institute for Chemistry, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands.

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ACKNOWLEDGMENTS This work was supported by the Ministry of Science, Education and Sports of the Republic of Croatia (Project No. 1191191342-2960). The authors warmly thank Mladen Biruš and Nikola Kallay for helpful discussions.

(22)

From eq 22 and the Eyring equation, it follows that the activation enthalpy and entropy obtained are

Δ⧧H = Δ⧧H1 + Δ⧧H2 − Δ⧧H −1 ⧧

⧧

⧧

⧧

Δ S = Δ S1 + Δ S2 − Δ S−1

AUTHOR INFORMATION

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(23)

REFERENCES

(1) Bauer, J.; Tomišić, V.; Vrkljan, P. B. A. J. Chem. Educ. 2008, 85, 1123−1125. (2) Shakhashiri, B. Z. Chemical Demonstrations; The University of Wisconsin Press; Madison, WI, 1992; Vol. 4, pp 3−86. (3) Carpenter, Y.; Phillips, H. A.; Jakubinek, M. B. J. Chem. Educ. 2010, 87, 945−947. (4) Sattsangi, P. D. J. Chem. Educ. 2011, 88, 184−188. (5) Creary, X.; Morris, K. M. J. Chem. Educ. 1999, 76, 530−531. (6) Vitz, E. J. Chem. Educ. 2007, 84, 1156−1157.

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where the subscripts of the thermodynamic functions refer to the forward or reversed steps in eq 6. The values of the enthalpy and entropy for the equilibrium of the FeI2+ complex formation could not be found in the literature, so the activation parameters for the rate-determining step cannot be calculated. 543




(7) Copper, C. L.; Koubek, E. J. Chem. Educ. 1998, 75, 87−89. (8) Shurvell, H. F. J. Chem. Educ. 1966, 43, 555−556. (9) Orvis, J. A.; Dimetry, B.; Winge, J.; Mullis, T. C. J. Chem. Educ. 2003, 80, 803−805. (10) Watkins, K. A.; Olson, J. A. J. Chem. Educ. 1980, 57, 158−159. (11) Nóbrega, J. A.; Rocha, F. R. P. J. Chem. Educ. 1997, 74, 560− 562. (12) Jonnalagadda, S. B.; Gollapalli, N. R. J. Chem. Educ. 2000, 77, 506−509. (13) Potassium nitrate is only used in the study of the effect of temperature on the reaction rate but not in the study of the effect of the ionic strength. (14) Atkins, P. W., De Paula, J. Physical Chemistry, 8th ed.; Oxford University Press: Oxford, 2006. (15) de Levie, R. J. Chem. Educ. 2005, 82, 885−888. (16) Bockris, J. O’M., Reddy, A. K. N. Modern Electrochemistry, Vol 1: Ionics, 2nd ed.; Kluwer Academic Publishers: New York, 2002. (17) Fudge, A. J.; Sykes, K. W. J. Chem. Soc. 1952, 119−124. (18) Novoselov, R. I.; Ptitsyn, B. V. Russ. J. Inorg. Chem. 1965, 10, 1241−1243. (19) Austin, J. M.; Groenewald, T.; Spiro, M. J. Chem. Soc., Dalton Trans. 1980, 854−859. (20) Creeth, A. M.; Spiro, M. J. Chem. Soc., Faraday Trans. 1991, 87, 977−985.

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The Effect of Temperature and Ionic Strength on the Oxidation of

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