In the Laboratory
A Unified Kinetics and Equilibrium Experiment: Rate Law, Activation Energy, and Equilibrium Constant for the Dissociation of Ferroin Simeen Sattar Physics Program, Bard College, Annandale-on-Hudson, New York 12504, United States
[email protected] Kinetics is an important topic in the general chemistry curriculum, challenging for students regardless of their past experience. The difficulty of this topic stems from the range and number of concepts, encompassing determination of the rate law by different methods, activation energy, and the relationship between the rate law and reaction mechanism. Innumerable welltested experiments are available to illustrate all facets of these topics. Equilibrium customarily follows kinetics and is often introduced in terms of reversible kinetics. Establishing the form of the equilibrium constant expression and studying the effects of perturbations on the equilibrium are typical experiments. After many years of using one experiment for the determination of a rate law, a second experiment for the determination of an activation energy, and a third experiment for the determination of an equilibrium constant, it was felt that the variety of chemical systems distracted students from understanding the underlying concepts. An experiment that combines the different topics in kinetics and equilibrium by focusing on a single chemical system was developed. The reaction is a classic example from analytical and coordination chemistry, the dissociation of tris(1,10-phenanthroline)iron(II), or ferroin, in acid solution: FeðphenÞ3 2þ ðaqÞ þ 3H3 Oþ ðaqÞ / Fe2þ ðaqÞ þ 3phenHþ ðaqÞ þ 3H2 OðlÞ
ð1Þ
Experimental Overview In the first week, students establish the rate law for the reaction with respect to both ferroin and acid. In the second week, they determine the activation energy for the reaction. In the third and fourth weeks, they determine the equilibrium constant. In the fifth week, students determine the base dissociation constant for phenanthroline, linking the core experiments to acid-base equilibria, the most common application of equilibrium in general chemistry. The equilibrium constant and rate laws for the dissociation and formation reactions for eq 1 were first reported by Lee, Kolthoff, and Leussing in 1948 (1, 2). They found that the dissociation reaction is first-order in Fe(phen)32þ and zero-order in acid for sulfuric acid concentrations in the range 0.005-0.5 M and Kc = (1.7 ( 0.7) 10-6 at 25 °C.1 These authors also determined the acid dissociation constant of phenHþ. The reaction rate increases dramatically with temperature, as the activation energy is relatively high. Values from 125 kJ/mol (σ = 2 kJ) (3) to 134 ( 2 kJ/mol (4) have been reported.
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Kinetics experiments at the general chemistry level involving this system have been described in this Journal and in at least one commercially published laboratory manual (5-7). In all these cases, the reaction is conducted in excess acid concentration, and in two cases at least, the reaction is presented to students as following first-order kinetics (5, 7). Although we have made many small changes to increase decision-making by students, our principal innovation in the kinetics portion of the experiment is to have students also determine the reaction order with respect to acid concentration in the first week of the experiment. Our second innovation is to follow the kinetics study with a determination of the equilibrium constant for the same system. Our third innovation is to use phenanthroline to illustrate the determination of a pKb via pH titration. Although not integral to the suite of experiments, it works well in terms of timing, because the topic of weak acids and bases follows closely on the heels of the general introduction to chemical equilibrium. Kinetics: Rate Law and Activation Energy For the kinetics experiment, students first run the reaction using the concentrations chosen by Nitz et al. (7): [Fe(phen)32þ]0 = 7.5 10-5 M and [H2SO4]0 = 0.50 M. Next, the reaction is run with the same initial ferroin concentration but 1/10 the initial sulfuric acid concentration.2 These two experiments are conducted in a thermostatted bath at 40 °C allowing ample time to follow the reaction for about two half-lives within a 2.5 h laboratory period. Inspection of their numerical data reveals to students the two main features of the kinetics. First, the half-life of the reaction is approximately constant in any given run; second, the half-life does not change much even when the acid concentration is reduced by a factor of 10. Although students are prepared from classroom discussion to interpret the constancy of the half-life in a single run as indicative of first-order kinetics, the constancy of the half-life despite the change in acid concentration is unexpected and puzzling. A laboratory discussion can guide students to reason that concentration independence corresponds to zero-order kinetics. Some students choose to make the plots of absorbance, logarithm of the absorbance, and reciprocal absorbance versus time during the laboratory period (Figure 1). The linearity of the second plot compared to the nonlinearity of the first and third is evident. The similarity of the calculated slopes of the first-order plots at the two different acid concentrations gives students another way to understand zero-order dependence; compare the two data sets in Figure 1B. Thus, the instructive value of this experiment is enhanced by not revealing at the outset that reaction 1 is first-order with
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In the Laboratory
Figure 2. Arrhenius plot of student data and best-fit line for the dissociation of ferroin. Four sets of data are included to show the typical variation. An unweighted linear least-squares fit of all the data gives Ea = 127 ( 15 kJ/mol.
Figure 1. Filled circles show the zero- (A), first- (B), and second-order (C) plots for [Fe(phen)32þ]0 = 7.5 10-5 M and [H2SO4]0 = 0.50 M at 40 °C; open circles in (B) are for [H2SO4]0 = 0.05 M. In (B), k = (1.2 ( 0.1) 10-3 s-1 (continuous line, 0.5 M H2SO4) and k = (1.1 ( 0.3) 10-3 s-1 (dashed line, 0.05 M H2SO4). Student data are shown.
respect to Fe(phen)32þ and not ignoring the acid independence of the reaction. From the moment rate laws are introduced, students are impatient to understand their significance. Consequently, they are deeply satisfied to discover the connection between the observed rate law and reaction mechanism. The reason for the emphasis on determining rate laws and why they cannot be deduced from the coefficients in the balanced reaction are clear at last. In the present reaction, eq 1, the discrepancy between the rate law
Fe(phen)22þ and protonation of phenanthroline and that these steps must be rapid by comparison with reaction 2 (2, 6). Among the smaller changes we made to the published procedures are that the class collectively records a spectrum of Fe(phen)32þ and determines the appropriate wavelength for monitoring the reaction (510-512 nm). A recommendation is made to sample the reaction solution (in the 40 °C bath) at 3 min intervals to start with and adjust the time as the reaction proceeds. Students are surprisingly reluctant to deviate from strict regularity, but eventually admit the sense of lengthening the time intervals. This experience illuminates what it means for a reaction to slow down with time more effectively than classroom discussion and graphs. In the second week of the kinetics experiment, when students run the reaction in baths at 30, 50, and 60 °C, they are asked to rely on the previous week's experience and their understanding of the effect of temperature on reaction rates to choose appropriate time intervals. The reaction is fast enough at 50 and 60 °C for students to repeat the runs in case their initial choices of time intervals are too long. As the temperature is raised from 30 to 60 °C, the half-life of the reaction decreases precipitously from about 90 to 1 min. An Arrhenius plot typical of those obtained by students is shown in Figure 2. Activation energies obtained by students are in good agreement with literature values. Dissociation Constant for Ferroin The equilibrium constant for reaction 3, the reverse of reaction 1, is determined in the third and fourth weeks of the experiment: Fe2þ ðaqÞ þ 3phenHþ ðaqÞ þ 3H2 OðlÞ / FeðphenÞ3 2þ ðaqÞ þ 3H3 Oþ ðaqÞ
Rate ¼ k½FeðphenÞ3 2þ and stoichiometric coefficients can be profitably discussed in class. The discrepancy immediately indicates that the reaction cannot occur in one step. Students can be led to develop a mechanism starting with the rate-determining step: FeðphenÞ3 2þ ðaqÞ f FeðphenÞ2 2þ ðaqÞ þ phenðaqÞ
ð2Þ
With this first step, the remainder of the mechanism falls into place for students. Students readily conjecture that the steps needed to give the overall reaction are stepwise dissociation of 458
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ð3Þ
Our experimental design is similar to that for the popular iron(III)-thiocyanate equilibrium constant determination (8-10). Students prepare solutions with known initial millimolar concentrations of the reactants in 0.50 M H2SO4. Consequently, the hydrogen ion concentration is essentially fixed. The equilibrium ferroin concentration is determined spectrophotometrically and used to calculate the equilibrium concentrations of the reactants. Reactant concentrations close to those used in the 1948 study are employed (1). Sulfuric acid is treated as a strong monoprotic acid, as it was for the first kinetics experiment.
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In the Laboratory
formic acid. As a very weak base (pKb = 9.14) with low solubility in water, the phenanthroline titration curve poses more of an experimental and interpretive challenge. A typical student titration curve is shown in Figure 3. Students use a simple two-point finite difference formula to locate the inflection point in the titration curve and obtain good agreement with the literature values. Some students continue the titration beyond the expected second equivalence point and are surprised by its absence. This can become an additional topic of discussion in the laboratory or during class. Hazards
Figure 3. Titration curve for 20 mL of 0.01 M phenanthroline titrated with 0.022 M HCl (filled circles, left axis). Slope of the titration curve, |ΔpH|/Δvolume HCl (open circles, right axis). The peak maximum corresponds to a pKb of 9.3. Dashed curves serve to guide the eye.
Iron(II) sulfate, ferroin, and 1,10-phenanthroline may irritate the eye and skin. In addition, as 1,10-phenanthroline is toxic to aquatic life, it should not be released into the environment. Sulfuric acid and hydrochloric acid are corrosive and can be dangerous to the eyes and skin; safety goggles must be worn. Summary
In the first week of this experiment, students prepare the “equilibrium” solutions by diluting stock solutions of FeSO4 and phenanthroline with 0.50 M H2SO4. They also prepare standard solutions for making the calibration curve. Students must decide how to make all required solutions. As the reaction is slow to equilibrate at room temperature, absorbance measurements are recorded in the second week. In the second week, students record the absorbances of the equilibrium and standard solutions. They also observe the effect of temperature on equilibrium by immersing one of their equilibrated solutions in a warm water bath. Interpretation of the fading of the red color vis-a-vis the sign of ΔrH provokes a surprising amount of debate among students, even though Le Ch^atelier's principle has been previously discussed in the classroom with accompanying demonstrations. A Beer's law plot is constructed from class data during the laboratory period. Students complete at least one calculation of the equilibrium constant during the laboratory period and are encouraged to use a spreadsheet (a template is not provided) rather than a calculator. For many students, this is the most elaborate spreadsheet calculation they have done, so the time is well spent. In the next few days, students submit their calculated equilibrium constants to the instructor for verification. A spreadsheet containing all the calculated values is then made available to all students. (Students transform the equilibrium constants for the formation reaction 3 to that for the dissociation reaction, eq 1). The larger pool of results permits students to assess the accuracy and precision of class results for Kc. Order-of-magnitude agreement with the literature value with a similar relative uncertainty is obtained, for example, Kc = (2.7 ( 0.8) 10-6.
The dissociation of tris(1,10-phenthroline)iron(II) in acid solution has proven to be a versatile system for general chemistry students to investigate. We have extended a published experiment in which students determined the rate law with respect to only the complex ion and activation energy to include determination of the order with respect to acid and the equilibrium constant. The simplicity of the rate law is an attractive feature of this reaction for instructors who choose to introduce reaction mechanisms into their course. In the final experiment, the base dissociation constant of the ligand is determined; this serves as a natural bridge to the topic of acids and base equilibria that follows the general introduction to chemical equilibrium.
Base Dissociation Constant for Phenanthroline
Literature Cited
Acknowledgment I thank my students in Basic Principles of Chemistry II in 2008 and 2009 for the use of their data and Robert Olsen for a critical reading of the manuscript. I am grateful to the reviewers for their valuable suggestions. Notes 1. This is the “concentration equilibrium constant” not the “activity equilibrium constant” whose value is (4 ( 2) 10-7 (1). 2. Students are instructed to assume H2SO4 is a strong monoprotic acid at both 0.50 and 0.05 M. This assumption is examined when the topic of polyprotic acids arises in class. It is found to be correct for the 0.50 M solution, but the nominally 0.05 M solution is closer to 0.06 M in [Hþ].
Determination of dissociation constants for weak acids and bases by pH titration is a common experiment accompanying the topic of weak acids and bases in the classroom. For the fourth and final experiment in this suite, students are given the problem of determining the pKb for phenanthroline (along with the pKa for a weak acid). Students are expected to devise their own procedure (titration curves have been discussed in the classroom by this time). Phenanthroline is a good choice to contrast with acetic or
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1. Lee, T. S.; Kolthoff, I. M.; Leussing, D. L. J. Am. Chem. Soc. 1948, 70, 2348. 2. Lee, T. S.; Kolthoff, I. M.; Leussing, D. L. J. Am. Chem. Soc. 1948, 70, 3596. 3. Burgess, J.; Prince, R. H. J. Chem. Soc. 1963, 5752. 4. Basolo, F.; Hayes, J. C.; Neumann, H. M. J. Am. Chem. Soc. 1954, 76, 3807. 5. Twigg, M. V. J. Chem. Educ. 1972, 49, 371.
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In the Laboratory 6. Edwards, J. O.; Edwards, K.; Palma, J. J. Chem. Educ. 1975, 52, 408. 7. Nitz, O. W.; Ondrus, M. G.; Melton, T. Laboratory Manual for Introductory Chemistry; Wm. C. Brown: Dubuque, IA, 1993. 8. Marcus, S.; Sienko, M. J.; Plane, R. A. Experimental General Chemistry; McGraw-Hill: New York, 1988. 9. Slowinski, E. J.; Wolsey, W. C.; Masterton, W. L. Chemical Principles in the Laboratory, 6th ed.; Saunders: Fort Worth, TX, 1996.
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10. Nelson, J. H.; Kemp, K. C. Laboratory Experiments; Pearson Prentice Hall, Upper Saddle River, NJ, 2009.
Supporting Information Available Instructors' notes; instructions for students. This material is available via the Internet at http://pubs.acs.org.
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