In the Laboratory
A Simple Electrochemical Approach to Heterogeneous Reaction Kinetics K. J. Drok and I. M. Ritchie* A. J. Parker Cooperative Research Centre for Hydrometallurgy, Murdoch University, Murdoch, Western Australia 6150 G. P. Power Alcoa of Australia, Kwinana, Western Australia 6167
The study of kinetics in undergraduate courses is largely restricted to homogeneous systems, and usually to reactions in solution. The reason for this is undoubtedly related to the ease with which reaction mixtures can be prepared and the progress of the reaction followed by solution analysis. On the other hand, there is a major experimental hurdle that must be overcome before the kinetics of a reaction between a solid and a solution can be established satisfactorily. The problem is simply stated: all reactants in solution must be transported to the reacting surface before reaction can take place, but ways in which this can be achieved reproducibly are few and far between. Experimentally, the most convenient method of achieving reproducible mass transport is to have the solid sample in the form of a disk that can be rotated about its axis with one face exposed to the reactant solution. Figure 1 is a schematic diagram showing such a rotating disk system. The mathematics of mass transfer to a disk rotating in a solution under conditions of laminar flow was first developed by the famous Russian physical chemist Levich (1). The field in which rotating disks have been most widely adopted is electrochemistry, and a number of companies now market rotating disk electrodes in a variety of metals. However, the use of rotating disks is not restricted to electrochemists. Any of the many important solid–solution reactions are best studied by this technique. Thus we find rotating disks have been used in such diverse applications as the dissolution of tooth enamel (2), the leaching of fertilizers (3), and the slaking of lime (4 ). To teach the elements of the kinetics of heterogeneous reactions, the simplest approach is to measure the rate of a diffusion-controlled reaction at a rotating disk by following the loss of reactant from solution or appearance of product in solution. However, the rate of change of reactant and product concentration is slow, and so it is difficult to complete the experiment in a half-day laboratory session. A much more rapid method based on chronopotentiometry (the measurement of potential as a function of time) is described. The system chosen for study is the dissolution of copper by iron(III) in strong chloride solutions. Because a range of chlorocomplexes is involved (e.g., FeCl2+, FeCl3, and FeCl4᎑), the dissolution reaction is written Cu + Fe → Cu + Fe III
I
II
(1)
It is known that the rate of this reaction is controlled by the speed at which iron(III) is transported to the dissolving copper surface (5). The reaction is therefore carried out using a copper sample in the form of a rotating disk. In addition to *Corresponding author.
Brush contact
Shaft (brass)
Insulator (plastic) Disk (gold)
Fluid flow lines Figure 1. Schematic of rotating disk electrode, showing laminar fluid flow.
an investigation of the iron(III)/copper reaction at a rotating disk, a way of studying the same reaction using a fixed sample with solution stirring is presented. This allows laboratories that do not possess a rotating disk system to carry out the experiment. It also illustrates the merits of using a rotating disk system rather than other forms of solution stirring. This experiment is suitable for a senior chemistry laboratory class. In order to carry it out successfully, students should be familiar with the material presented in the following section dealing with the principle of the method. Unfortunately, there are relatively few text books to which students can be referred for further information. Most either contain nothing at all or are too detailed in their treatment. One exception to this is the text on Physical Chemistry by Atkins (6 ), which contains both a brief description of a rotating disk and a more detailed discussion of mixed potentials (called corrosion potentials by Atkins) than is attempted here. Students completing the experiment should obtain a better understanding of: • • •
• •
the importance of solid/solution reactions; the importance of mass transport as a possible ratedetermining step in heterogeneous reactions; the importance of the rotating disc geometry in achieving reproducible hydrodynamics, and therefore reproducible mass transfer at the reacting surface; the utility of the Levich equation for describing the kinetics of a diffusion-controlled reaction; and the difference between equilibrium and mixed potentials.
JChemEd.chem.wisc.edu • Vol. 75 No. 9 September 1998 • Journal of Chemical Education
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In the Laboratory
The method used to measure the rate of loss of copper is a type of chronopotentiometry in which the potential of the electrode is measured as a function of time (7 ). A thin film of copper of known number of moles is first plated onto an inert electrode, such as gold. This is achieved by electrodeposition using a constant current, Ip, for an appropriate period of time, tp. If the copper is deposited from a copper sulfate solution, the number of moles of copper, n, plated out is n = ηI p tp /2F
(2)
where η is the current efficiency and F is the faraday. η can be determined experimentally, and if care is taken, it can be shown to be close to unity in the present experiment. A value of 1.00 has therefore been assumed. The inert electrode with its thin film of copper is then immersed in the reactant solution containing iron(III), and its potential is recorded against a suitable reference electrode as a function of time using a chart recorder or a computer. A typical trace is shown in Figure 2. At the start of the trace, and until all the copper film has been consumed, the potential recorded is the mixed (or reaction) potential. The concept of mixed potentials is one that many students will not have come across before, and so a brief explanation is given here. A more detailed discussion is given in the paper by Power and Ritchie (8). Consider first an inert electrode such as a platinum electrode dipping in a solution containing iron(II) and iron(III) ions. If the platinum electrode is at equilibrium in the solution (i.e., no external current is flowing into or out of the electrode), the rate of transfer of electrons as a result of the oxidation of iron(II) FeII → FeIII + e
(3)
will be exactly balanced by the rate of loss of electrons from the platinum electrode as a result of the reduction of iron(III). FeIII + e → FeII
(4)
However, there is no net reaction, as is clear from the sum of eqs 3 and 4: FeIII + FeII → FeII + FeIII
(5)
The potential of the electrode at which the two half reactions (3 and 4) are in dynamic equilibrium is known as the equilibrium potential. Consider now the case of a copper electrode dipping in an iron(III) solution. The oxidation half reaction is Cu0 → CuI + e
(6)
and the reduction half reaction is, as before, the reduction of iron(III) to iron(II) (eq 4). As in the case discussed above, the potential assumed by the copper electrode is the one at which the rate of transfer of electrons to the copper electrode as a result of reaction 6 is exactly balanced by the rate of loss of electrons as a result of reaction 4. This potential is known as the mixed potential because the two half-reactions comprising the overall reaction are not the reverse of each other, as is the case with reactions 3 and 4. Thus when we add together eqs 6 and 4, we get the overall reaction 1 for the dissolution of copper in an iron(III)-containing solution. 1146
Potential
Principle of the Method
Time
td
Figure 2. Schematic diagram showing a typical chronopotentiogram for the dissolution of copper by iron(III) ions.
It is clear that the mixed potential will be different from the iron(III)/iron(II) equilibrium potential because different half reactions, which proceed at different rates, are involved. In fact, it can be shown that the mixed potential for a reaction will be somewhere between the equilibrium potentials of the constituent half reactions (the E °’s for reactions 6 and 4 are 0.166 V [9] and 0.77 V [10], respectively). This means that the mixed potential for the iron(III)–copper reaction will be below the equilibrium potential for the iron(III) iron(II)couple. Thus, when all the copper on the inert electrode used in this experiment is consumed, the electrode potential will no longer be equal to the mixed potential, but will rise until it reaches the equilibrium potential for an inert electrode in an iron(III)/iron(II) solution. This is the basis of the chronopotentiometric method. The time taken to dissolve the copper film, td, is then the time between the start of the reaction, when the electrode is immersed in the reactant solution, and the point where the potential rises sharply. The average reaction rate, r (in mol m᎑2s᎑1), is given by r = n/At d
(7)
where A is the copper area. The geometric area is less than the actual area as a result of surface roughness. However, in the particular case of the iron(III)–copper reaction, whose rate is controlled by the slow transport of iron(III) ions to the copper surface, the reaction area is equal to the geometric area when the copper is in the form of a rotating disc (11). Combining eqs 2 and 7 yields td = (I p/2AFr)t p
(8)
Hence a plot of td against tp, for a constant set of reaction conditions, should be a straight line through the origin. The slope, which is characteristic of the rate of dissolution, is given by m = Ip/2AFr
(9)
Since the slow step in the dissolution reaction is the transport of iron(III) ions to the copper surface, the reaction is diffusion controlled and the flux, j, of iron(III) ions to the electrode surface is equal to the rate of copper dissolution. j=r
(10)
When the copper sample is in the form of a rotating disk, the hydrodynamics of the system are well known, and the flux is given by the Levich equation: j = 0.62D2/3 ν ᎑1/6ω 1/2 C
Journal of Chemical Education • Vol. 75 No. 9 September 1998 • JChemEd.chem.wisc.edu
(11)
In the Laboratory
where D is the diffusion coefficient of the iron(III) ions, ν is the kinematic viscosity of the reactant solution, ω is the disk rotation speed, and C is the bulk iron(III) concentration. If the sample is not in the form of a rotating disk, eq 11 is replaced by j = j (D, ν , s, g)C (12) where s is a factor depending on the stirring of the solution and g is a factor depending on the geometry of the sample and the containing vessel. The functional dependence of the quantities inside the brackets is, in general, not known. From eqs 10 and 11, it is clear that a plot of r against ω 1/2 should be a straight line through the origin of slope 0.62D 2/3 ν ᎑1/6C. Similarly, a plot of r against C should be another straight line through the origin of slope 0.62D 2/3 ν ᎑1/6 ω 1/2 . If D and ν are known from separate measurements, it will be possible to calculate the slopes of these two lines and compare them with the experimental values. However, if the sample is not in the form of a rotating disk, only concentration will be directly proportional to the rate and the slope of this line will not be calculable. The dissolution rate is expected to depend on stirring, but not in any simple way. While the chronopotentiometric method has much to commend it in terms of its simplicity, it should be noted that it is only applicable to diffusion-controlled reactions. If the reaction is chemically controlled, the substrate electrode can affect the apparent reaction rate (12). Description of Apparatus and Techniques Any of the commercial rotating disk systems are satisfactory for this experiment. For example, Pine Instrument Company markets a series of rotator systems retailing from about U.S. $2400. A gold electrode is recommended, although platinum is satisfactory. If a rotating disc electrode is not used but the solution is stirred separately, then the inert electrode need not be circular in cross section. As long as only one flat surface of constant area is in contact with the plating solution, fairly reproducible results are possible. Prior to the plating, the electrode should be washed with nitric acid and then rinsed carefully. Occasionally, it may be necessary to abrade the electrode surface gently with 1200 wet silicon carbide paper. The composition of the plating solution is not critical; a solution containing about 0.2 M copper sulfate and 0.1 M sulfuric acid gives satisfactory results. However, it is necessary to purge the solution of any oxygen present by bubbling nitrogen through it for 15–20 minutes. Suitable deposits of copper can be prepared by using plating currents of the order of 1 mA. A power supply capable of delivering constant currents of this magnitude is needed for this purpose. A battery in series with a large variable resistor and the plating cell is a satisfactory substitute. The counter electrode should be a copper wire. During plating, the solution should be stirred to achieve a uniform electrodeposit. If the electrode is a rotating disk, this is most conveniently achieved by rotating the electrode at a moderate speed, say 100 rpm. When the electrode has been copper plated, it needs to be removed from the plating solution, rinsed quickly, and transferred to the reactant solution. Failure to do this will result in the loss of copper by aerial oxidation, leading to spuriously high reaction rates. The composition of the reactant solution is not critical. The solution used to obtain
the results described in this paper contained 0.01 M iron(III) ammonium sulfate in 4 M sodium chloride and 0.1 M hydrochloric acid. Dissolution solutions containing different iron(III) concentrations were prepared by serial dilution of the original iron(III) solution with 4 M sodium chloride and 0.1 M hydrochloric acid. The volume of reactant solution must be known with reasonable accuracy (for mechanical stirring to be as reproducible as possible); 50.0 mL was used in the experiments described here. To minimize the oxidation of copper by dissolved oxygen, it was necessary to degas all reactant solutions by purging with nitrogen for 10–15 minutes immediately before use. In the interests of completing the experiments in the minimum time, it is advisable to degas all other solutions while the first experiment is under way. When using a rotating disk, stirring of the solution is provided by rotation of the disk itself. Experiments have shown (13) that the hydrodynamics of the system are relatively insensitive to such factors as the position of the disk with respect to the walls of the containing vessel. However, if some other method of stirring is employed, very considerable care must be taken to ensure that the positions of the copper-plated electrode, stirrer, and reference electrode with respect to the containing vessel are reproduced as exactly as possible between each experiment. To obtain the results described here, a stationary disk electrode was mounted directly above a 2-cm magnetic stirring bar in a 100-mL beaker. The stirring rate was kept at a maximum in order to minimize the random movements of the stirring bar. The potential of the copper-plated electrode in the iron(III) solution is measured relative to a reference electrode whose position in the solution is not critical provided it does not interfere with the fluid flow. The best choice of reference electrode is a calomel electrode in a saturated solution of potassium chloride (SCE). However, a silver wire that has been electrochemically oxidized in a chloride solution, or even a silver wire, provides a satisfactory alternative. The change in potential of the copper-plated electrode with time is readily recorded using a chart recorder or a computer connected through either an analog-to-digital converter card or a highimpedance multimeter with an RS232 serial interface port. Normal laboratory safety precautions are called for during these experiments. None of the chemicals used are particularly hazardous, but the plating and dissolution solutions are both acidic and care should be taken that these do not come into contact with the skin. Electrical equipment should always be treated with care. The currents passed when plating copper under the conditions stated above are small, but it should be noted that the electrochemical cell should always be off before attempting to touch any electrode. When using a rotating disc, as with any moving equipment, caution must be exercised so that loose clothing, hair, etc. does not get caught in the moving parts. Results A suggested series of student experiments is given below. An analysis of each experiment is encouraged so that students can elucidate the effect of the studied variable on dissolution rate and compare their results with what is predicted from theory. A comparison between the rotating disc system and the mechanically stirred system should be encouraged where possible.
JChemEd.chem.wisc.edu • Vol. 75 No. 9 September 1998 • Journal of Chemical Education
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In the Laboratory
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600
❍
500
❍
td / s
400
❍
300
●
❍ ●
200
❍ ● ●
100
0
●
❍ ❍ ● 0
50
100
150
200
250
300
tp / s Figure 3. Effect of plating time on dissolution time for dissolution of copper by iron(III) ions. Ip = 1 mA, C = 10 mol m᎑3, ω = 400 rpm, A = 1.66 × 10 ᎑5 m 2. Black circles represent the rotating disk electrode measurements; open circles, the stationary electrode measurements.
4
● rate / (10-4 mol m-2 s-1)
The effect of plating time on dissolution time was investigated and results for both the rotating disk system and the stationary electrode with the solution stirred by a magnetic stirring bar are shown in Figure 3. As can be seen, both electrode geometries give results that can be described by straight lines through the origin, in accordance with eq 8. Figure 3 also shows that the scatter of results is appreciably greater for the system in which stirring is carried out by a magnetic stirring bar than for the rotating disk system. Furthermore, the reproducibility becomes even worse when the magnetic stirring bar is rotated more slowly, presumably because the fluctuations of the fluid become greater. However, changes in the disk rotation speed make little difference in the reproducibility of the results obtained using this geometry. These results reflect the more reproducible solution hydrodynamics in a rotating disk system. The effect of stirring on dissolution rate is shown in Figure 4 for the case of a rotating copper plated disk. In this figure, the dissolution rate is plotted as a function of the square root of the disk rotation speed, this being the expected relationship for a diffusion controlled reaction in accordance with eq 11. The fact that the plot is a straight line through the origin confirms that the dissolution reaction is diffusion controlled. The slope of the line, which has a value of 3.64 × 10᎑5 mol m ᎑2rad᎑1/2s᎑1/2, should be equal to 0.62D 2/3 ν ᎑1/6C. If the kinematic viscosity of the fluid is known, the diffusion coefficient can then be calculated. A value of 1.357 × 10᎑6 m2s᎑1 for the kinematic viscosity of the reactant solution was obtained by assuming that the solution was only 4 M in sodium chloride and interpolating from the tables in the Handbook of Chemistry and Physics (10). An exact value for this quantity is not required because ν enters the expression for the slope as only the minus one-sixth power. Using this value for the kinematic viscosity of the solution, the diffusion coefficient for iron(III) in 4 M sodium chloride can be calculated as being 4.9 × 10᎑10 m2s᎑1. The literature values for the diffusion coefficient of iron(III) vary markedly with solution composition, and some representative values are given in Table 1. The variation in these values, showing the dependence of diffusion coefficient on ionic strength and composition of the solution, means that a true comparison of the calculated diffusion coefficient with a literature value cannot be made. However, the calculated value is obviously a reasonable estimate. While it was noted that the dissolution rate increased with the setting of the magnetic stirring bar in the case of the stationary electrode, no attempt was made to correlate the rate with the rotation speed of the stirring bar. The effect of iron(III) concentration on dissolution rate is shown in Figure 5 for the case of a copper plated rotating disk. As is clear from this diagram, the rate is directly proportional to the iron(III) concentration. This is the expected relationship for a diffusion controlled reaction in accordance with eq 11. Also shown in Figure 5 is the corresponding plot for the dissolution of a fixed copper sample, the solution being stirred by a magnetic stirring bar. In accord with eq 12, this plot is also a straight line through the origin, although the greater scatter in the experimental points is again evident. To a certain extent, the emphasis of the experiment will be determined by the attitude of the teacher. If the experi-
3
● ●
2
● ● 1
0 0
2
4 6 ω1/2 / rad1/2s-1/2
8
10
Figure 4. Effect of rotation speed on dissolution time for dissolution of copper by iron(III) ions. Ip = 1 mA, tp = 120 s, A = 1.66 × 10᎑5 m2, C = 10 mol m᎑3.
ment is primarily an exercise in understanding heterogeneous kinetics and the use of rotating discs, the chronopotentiometric method will be seen as simply a means to that end. Under these circumstances a high level of understanding of mixed potentials will not be expected. Good students in such a class might carry out additional experiments such as increasing the viscosity of the reactant solution and observing its effect on the dissolution rate. On the other hand, if the experiment is part of a course in electrochemistry, a fuller treatment of mixed potentials will be required of the class. In this event, some of the better students might like to explore how the mixed potential varies with disc rotation speed and iron(III) concentration.
Journal of Chemical Education • Vol. 75 No. 9 September 1998 • JChemEd.chem.wisc.edu
In the Laboratory
rate / (10-4 mol m-2 s-1)
2.5
●
2.0
●
❍
1.5
❍
● 1.0
❍ ● ❍
0.5
0❍ ● 0
2
4
6
8
10
The experiment can be readily completed in a half-day practical session if stock solutions (copper sulfate plating solution and 0.01 M iron(III) ammonium sulfate solution) are provided and the reactant solutions are degassed at the earliest possible opportunity.
-3
[Fe(III)] / mol m
Figure 5. Effect of iron(III) concentration on dissolution time for dissolution of copper by iron(III) ions. Ip = 1 mA, tp = 120 s, A = 2.01 × 10᎑5 m2, ω = 400 rpm. Black circles represent the rotating disk electrode measurements; open circles, the stationary electrode measurements.
Acknowledgment We gratefully acknowledge funding from the Parker Centre for this work. The Parker Centre was established and is supported under the Australian government’s Cooperative Research Centre Program. Literature Cited
In either case, the experiment is an excellent one for assessing the experimental skills of the students. Students who are experimentally adept get results similar to Figures 3 and 5 with high correlation coefficients and relatively low D values. Overview This experiment introduces students to elementary heterogeneous kinetics. In particular, it develops the concept of diffusion control, which is a common type of ratedetermining step in solid–solution reactions. The reaction chosen for study was the dissolution of copper metal in an iron(III) solution containing an excess of chloride ions. Because this is a redox reaction, it can be studied using electrochemical methods. Chronopotentiometry was used to determine the time taken for an electrodeposited copper film of known number of moles to dissolve. It is shown that heterogeneous reactions can be conveniently studied if the solid sample is in the form of a rotating disk. With such a sample, there is good agreement between measured and calculated reaction rates when the reaction is under diffusion control. However, if a fixed sample of solid is used and the solution is stirred by means of a magnetic stirring bar, the reproducibility is appreciably worse and there is no theoretical treatment from which the reaction rate can be calculated.
1. Levich, V. G. Physicochemical Hydrodynamics; Prentice-Hall: Englewood Cliffs, NJ, 1962. 2. Linge, H. G.; Nancollas, G. H. Calcif. Tissue Res. 1973, 12, 193– 208. 3. Barton, A. F. M.; McConnel, S. R. J. Chem. Soc. Faraday Trans. 1 1974, 70, 2355–2361. 4. Ritchie, I. M.; Xu, B. A. Hydrometallurgy 1990, 23, 377–396. 5. Power, G. P.; Staunton, W. P.; Ritchie, I. M. Electrochim. Acta 1982, 27(1), 165–169. 6. Atkins, P. W. Physical Chemistry, 5th ed.; Oxford University Press: Oxford, 1994. 7. Barth, H.; Gans, W.; Knacke, O. In Proceedings of the International Symposium on Hydrometallurgy, Chicago, 1973; Evans, D. J. I.; Shoemaker, R. S. Eds.; American Institute of Mining, Metallurgical, & Petroleum Engineers: New York, 1993; Chapter 40, p 1081. 8. Power, G. P.; Ritchie, I. M. J. Chem. Educ. 1983, 60, 1022–1026. 9. Muir, D. M. The Application of Thermodynamics to Extractive Metallurgy with Chloride Solutions–a Review; Warren Spring Laboratory Report LR425(ME); Stephen Austin and Sons: Hertford, 1984. 10. CRC Handbook of Chemistry and Physics, 60th ed.; Weast, R. C.; Astle, M. J., Eds.; CRC: Boca Raton, FL, 1979. 11. Opekar, F.; Beran, P. J. Electroanal. Chem. 1976, 69, 1–105. 12. Zheng, J.; Khan, M.; La Brooy, S. R.; Ritchie, I. M.; Singh, P. J. Appl. Electrochem. 1996, 26, 509–514. 13. Gregory, D. P.; Riddiford, A. C. J. Chem. Soc. 1956, 3756–3764. 14. Self-Diffusion in Electrolyte Solutions; Mills, R.; Lobo, V. M. M., Eds.; Physical Sciences Data 36; Elsevier: Amsterdam, 1989.
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