In the Laboratory
A Stopped-Flow Kinetics Experiment for Advanced Undergraduate Laboratories: Formation of Iron(III) Thiocyanate Charles R. Clark Chemistry Department, University of Otago, P.O. Box 56, Dunedin, New Zealand Few kinetic experiments are both relevant in the mechanistic sense and capable of being carried out in the time available in the undergraduate laboratory. The primary requirement is that the student be able to collect and process sufficient data over a 3- to 4-hour period that subsequent analysis provides a meaningful description of the reaction pathways. One system that we have developed with this criterion in mind involves the reaction of iron(III) with thiocyanate ion in aqueous solution. This classical metal ion substitution reaction has been extensively investigated using rapid-mixing (1–4), T-jump (5, 6), flash-photolysis (6), and P-jump (7) methods. The pathways leading to formation of the dark red iron(III)-thiocyanato complex are consequently well understood. The reaction scheme is outlined in Figure 1. The system is particularly amenable to a stopped-flow spectrophotometric study because reactant concentrations can be adjusted to give half-times of milliseconds to seconds appropriate to the technique. Despite the apparent complexity of the reaction scheme, only one process is observed on this time scale. This is because the proton transfer steps (via Ka1 and Ka2) are diffusion controlled and are consequently much more rapid than those involving either complex formation or decay. As the experiments can be arranged so that pseudo-first-order kinetics are followed, the resulting absorbance–time traces are correspondingly simple to analyze. When the known values of Ka1 (8) and Ka2 (9) are combined with the primary kinetic data the values of the rate constants k1, k{1, k2 , and k{2 may be determined. The formation constant of the iron(III)–thiocyanato complex (Kf = k1 /k{1) is also defined by the kinetic results. Furthermore, since the reactants are essentially colorless, while the products are strongly colored, it is a simple matter to use the absorbance data obtained in the kinetic experiments for a more direct spectrophotometric evaluation of Kf. The reaction thus illustrates many of the important features of metal ion substitution chemistry and the data can be obtained rapidly and analyzed in a straightforward manner. When a carefully designed experimental protocol
Figure 1. The reversible formation of iron(III)-thiocyanato complexes.
1214
is coupled with the use of rapid data acquisition and computational methods of analysis, this system is able to be defined well within the allowed time. In the experiment described here this definition is achieved using data obtained from just 15 kinetic runs. The study owes much to previous investigations (3, 4), and for the last three years it has been successfully incorporated into a laboratory course at 3rd-year level. It complements an earlier investigation described in this Journal (6) where relaxation methods were employed. Experimental Details
Reagents Distilled water is used in all preparations. The following stock solutions should be prepared in advance and filtered through Celite: 1. 1.00 M HClO4 , from dilution of a standardized concentrated solution of perchloric acid to 1.00 dm3. 2. A standardized ferric ion solution—ca. 0.2 M iron(III)—prepared from Fe(ClO4 )3?xH 2O and made up to be exactly 0.400 M in HClO4. This corresponds to about 25 g of Fe(ClO4 )3?xH2 O dissolved in 1.00 M HClO4 (100.0 cm3 ) with dilution to 250.0 cm3. Because the water content of solid ferric perchlorate is variable, it is not a simple matter to make up the solution to a particular iron(III) concentration. If analysis shows it to lie in the range 0.17 to 0.23 M no adjustment is necessary. 3. 2.00 M NaClO 4 , prepared by dissolving NaClO4?H2O (280.92 g) in water and diluting to 1.00 dm3 . 4. A solution approximately 1.5 × 10 {4 M in NaSCN1 and 1.00 M in NaClO 4. The stock solutions are stable for many weeks. The iron(III) stock solution is conveniently standardized by atomic absorption spectroscopy. In the preparation of the iron(III) reagents used in kinetic determinations the stock solutions are more readily dispensed using adjustable pipets (0.200–1.00 cm3 , 1.00– 5.00 cm3 capacity) fitted with disposable tips rather than conventional all-glass graduated pipets. (C AUTION: Perchloric acid solutions are corrosive and should not be pipetted by mouth. On completion of the experiment all acid residues should be combined and neutralized by the careful addition of solid sodium carbonate. The resulting solution should then be disposed of in a manner dictated by local regulations.)
Journal of Chemical Education • Vol. 74 No. 10 October 1997
In the Laboratory Apparatus The experiment requires access to a stopped-flow spectrophotometer equipped with a suitable data acquisition system. The reactions described here were followed using a Durrum D110 instrument in conjunction with a Northstar Horizon computer. The cell path length was 2.0 cm. Drive syringes were thermostatted to 25.0 °C. Olis software was used for data acquisition and for the evaluation of rate constants (On Line Instrument Systems Inc., Bogart, GA 30622).
which on rearrangement and integration gives:
ln
[FeSCN]eq [FeSCN]eq – [FeSCN]
= k f [Fe]T + k r ⋅ t
Because FeSCN is the only absorbing species present to any significant extent, the reaction mixture absorbance, A, is given by the expression A = εFeSCN ? [FeSCN] ? ,
The Rate Law Treatments for obtaining the rate law of a reversible reaction are available (10, 11); our approach closely follows that for the general case. Less detailed treatments dealing specifically with the iron(III)–thiocyanate system have also been given (3, 4). We use a simplified nomenclature in which charges and coordinated water molecules on the reacting species are omitted. According to the pathways of Figure 1, the rate of change of concentration of thiocyanate ion is described by an expression containing terms governing both its disappearance and appearance: { d [SCN]/dt = k1[Fe][SCN] + k 2[FeOH][SCN] – k{1[FeSCN] – k{2 [Fe(OH) SCN]
(1)
This is equivalent to eq 2 when the concentrations of the hydroxo complexes are eliminated by use of the appropriate acid dissociation constants, Ka1 and Ka2 : {d [SCN]/dt = (k 1 + k2Ka1 / [H+]) [Fe][SCN] – (k{1 + k -2K a2/[H +])[FeSCN]
(2)
Expression 2 is simplified by defining rate constants for the forward and reverse reactions, kf = k1 + k2 Ka1/ [H+], kr = k{1 + k{2Ka2 /[H+]. Further, the experiments are set up such that [H+] is constant during any particular kinetic run and the iron(III) concentration is always in large excess over [SCN{]. We can then write: { d [SCN]/dt = k f[Fe]T[SCN] – kr[FeSCN]
(3)
where [Fe]T represents the total concentration of iron(III). The concentration of thiocyanate ion at any time t may be expressed in terms of x, where x represents the displacement from the equilibrium concentration, [SCN]eq. Thus: [SCN] = [SCN]eq + x
(4)
From the stoichiometry of the reaction:2 [FeSCN] = [FeSCN]eq – x
(5)
At equilibrium { d[SCN]/dt = 0, with the consequence that kf[Fe] T[SCN]eq = kr[FeSCN]eq . If we use eqs 4 and 5 to substitute for the concentrations of free and bound thiocyanate into eq 3 we get the simple relationship: { dx/dt = (kf[Fe]T + k r) ? x
(6)
Substituting for x in eq 6 from eq 5 gives: d[FeSCN]/dt = (kf[Fe] T + kr ) ? ( [FeSCN]eq – [FeSCN] ) (7)
(8)
(9)
Using expression 9 to substitute for [FeSCN] and [FeSCN]eq in eq 8 gives
ln
A eq A eq – A
= k f [Fe]T + k r ⋅ t
(10)
where Aeq represents the absorbance of the system at equilibrium. Equation 10 predicts that a plot of { ln(A eq – A) versus t will be linear with slope (kf[Fe]T + kr). The latter quantity is defined as the observed first-order rate constant, kobs. That is, kobs = (k1 + k 2K a1/[H +])[Fe]T + k {1 + k{2Ka2 /[H+] (11) Procedure and Results It is generally best for students to work in pairs. They should first prepare the three sets of iron(III) solutions described in Table 1.3 The reagents in series A are made up to be 0.20 M in H+ concentration, while members of the B and C series are 0.40 M and 0.60 M in [H+], respectively. Within each series the iron(III) concentration varies over the same range: ca. 0.005 to 0.04 M. Each solution is made up to a volume of 10.00 cm3 and each contains sufficient NaClO4 to maintain ionic strength at 1.00 M. This stage of the experiment generally takes 30 to 40 minutes to complete. Before commencing the stopped-flow investigation it is informative for students to gain a feeling for the rapidity of the reaction they are about to examine. This can be achieved through simple test tube experiments by mixing NaSCN solution (ca. 5 × 10{3 M) with an approximately equal volume of acidified, dilute ferric ion solution. Even for concentrations of iron(III) down to 5 × 10{3 M the formation of the thiocyanato complex appears to be instantaneous. A thorough familiarity with the operation of the spectrophotometer flow system is also important. If the valves controlling the transfer of reagents from reservoir to drive syringes are opened in the wrong sequence premature mixing of the reagents may result. Such an occurrence will almost certainly require the preparation of replacement solutions. A 10 cm3 volume of iron(III) solution is sufficient to flush a drive syringe between runs, and is enough for several replicate determinations. The solutions of Table 1 are separately mixed in the stopped-flow reactor with an equal volume of NaSCN solution (ca. 5 × 10{4 M ) and the complexation reaction is monitored at 450 nm. For best results the reactants should be thermostatted in the drive syringes for at least 1 min before initiating the reaction. The increase in absorbance is followed over five reaction half-lives (5 t 1/2) with the “infinity” absorbance reading (i.e. Aeq) being recorded after at least
Vol. 74 No. 10 October 1997 • Journal of Chemical Education
1215
In the Laboratory Table 1. Stock Solution Volumes for Preparation of Iron(III) Reagentsa Solution Designation
0.2 M Fe(ClO4)3 & 0.40 M HClO4 (cm3)
1.0 M HClO4 2.0 M NaClO4 (cm3) (cm3)
A1
0.25
1.90
3.85
A2
0.50
1.80
3.70
A3
1.00
1.60
3.40
A4
1.50
1.40
3.10
A5
2.00
1.20
2.80
B1
0.25
3.90
2.85
B2
0.50
3.80
2.70
B3
1.00
3.60
2.40
B4
1.50
3.40
2.10
B5
2.00
3.20
1.80
C1
0.25
5.90
1.85
C2
0.50
5.80
1.70
C3
1.00
5.60
1.40
C4
1.50
5.40
1.10
C5
2.00
5.20
0.80
a
Each reagent is made up to a volume of 10.00 cm 3 with water.
Table 2. Absorbance Changes and First-Order Rate Constants at 25 °Ca Reaction Designation
[Fe]T (M)
[H+] (M)
∆A
k obs (s{1)
k calcb (s{1)
A1
0.00221
0.10
0.116
2.96
3.03
A2
0.00442
0.10
0.193
3.62
3.56
A3
0.00884
0.10
0.292
4.66
4.63
A4
0.0133
0.10
0.346
5.65
5.69
A5
0.0177
0.10
0.388
6.76
6.76
B1
0.00221
0.20
0.117
2.02
2.03
B2
0.00442
0.20
0.194
2.42
2.41
B3
0.00884
0.20
0.293
3.23
3.19
B4
0.0133
0.20
0.356
4.00
3.96
B5
0.0177
0.20
0.390
4.71
4.73
C1
0.00221
0.30
0.118
1.72
1.69
C2
0.00442
0.30
0.195
1.96
2.03
C3
0.00884
0.30
0.298
2.71
2.71
C4
0.0133
0.30
0.356
3.39
3.38
C5
0.0177
0.30
0.395
4.04
4.06
At ionic strength 1.00 M and [SCN{] = 0.75 × 10{4 M. When considering the iron(III) and hydrogen ion concentrations it must be remembered that each reactant solution is diluted by a factor of two in the stopped-flow experiment. b Calculated using eq 11 and the values of rate and equilibrium constants given in the text.
Figure 2. A comparison between observed (points) and calculated (line) absorbance changes on reaction of iron(III) with thiocyanate ion in acidic solution.
Duplicate data recorded for three or four runs allows reproducibility to be tested, but does not markedly extend the time required. Under the conditions employed in this study the iron(III)–thiocyanato product is never fully formed, with ca. 20% conversion at the lowest [Fe]T and 66% at the highest. The approach to equilibrium is always first order, however, irrespective of the difference between the initial and final states. Table 2 gives ∆A values and pseudo-first-order rate constants (kobs ) obtained in a typical study. Included in Table 2 are computed values of the firstorder rate constants, kcalc, obtained from a least squares fit of the data to eq 11. This analysis uses literature values (8, 9) for Ka1 (2.04 × 10{3 M) and Ka2 (6.5 × 10{5 M), which give best fit values4 of k1 =109(10) M {1s {1, k{1 = 0.79(0.10) s{1, k2 = 8020(800) M{1s{1, and k{2 = 2630(230) s{1 . The kinetically determined value of the formation constant for iron(III)– thiocyanate is therefore 109/0.79 M {1 = 138(29) M{1. The absorbance data in Table 2 are treated with the knowledge that [Fe(OH2)5 SCN]2+ is the only absorbing species present at equilibrium. If Alim represents the limiting absorbance corresponding to the situation where all the SCN{ is converted to [Fe(OH2 )5SCN]2+, then the concentration ratio [Fe(OH2)5SCN]2+ /[SCN{] is simply ∆A/(Alim – ∆A). Therefore, the expression for determining the formation constant from the spectrophotometric data is
Kf =
a
∆A [Fe]T A lim – ∆A
which on rearrangement gives
∆A = 10 t1/2. This requires data collection times ranging from 0.5 s (for solution A5) to 2.0 s (for solution C1), with each reaction having a post-collection delay time of up to 3 s prior to recording Aeq. The change in absorbance observed on reaction is designated as the positive quantity, ∆A. If the kinetic data are stored directly onto diskette this phase of the experiment usually requires about 5 min per estimation.
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(12)
A limK f [Fe]T 1 + K f [Fe]T
(13)
For a particular iron(III) concentration inspection of Table 2 shows that, as expected, ∆A is independent of [H+] over the range of interest. Least squares fitting of the averaged ∆A values to eq 13 gives Alim = 0.590(0.012) and Kf = 112(5) M{1 . There is excellent agreement between ob-
Journal of Chemical Education • Vol. 74 No. 10 October 1997
In the Laboratory
Table 3. Selected Rate and Equilibrium Data for Iron(III)–Thiocyanate System at 25 °C Ionic Strength (M)
k1 (M-1s-1)
k {1 (s{1)
Kf (M{1)
k2 (M{1s{1)
Method and Ref.
0.5
130 (40)
—
—
1.3(0.2) × 104
T-jump and flash photolysis (6 )
—
2.6(0.2) ×
—
104
0.5
150 (50)
0.5
90 (5)
1.6 (0.2)
1.0
97 (3)
0.75 (0.03)
1.0
—
—
1.0
109 (10)
0.79 (0.10)
138 (29)
8.0(0.8) × 103
1.0
—
—
112 (5)
—
56 (10) 129 (7) 134
— 9.6(0.5) × 103 —
P-jump (7 ) Stopped-flow (4 ) Stopped-flow (3 ) Spectrophotometric (14 ) Stopped-flow, this work Spectrophotometric, this work
served and calculated data as shown by the comparison given in Figure 2. Similarly, the agreement between the spectrophotometrically and kinetically determined values of the formation constant is also satisfactory, but it is the latter result that is the less certain owing to a relatively large error in k{1 . The k{1 term never dominates under any condition. Its maximum contribution occurs for reaction C1, where it accounts for 46% of the observed rate. Table 3 compares values of rate and formation constants obtained over the course of a number of studies. The present results compare very favorably with those derived from a study (3) that involved 162 kinetic runs and a data collection time of 7 hours.
to give an absorbance of ca. 0.5–0.8 on complete conversion to [Fe(OH2 )5SCN]2+ (ε = 4980 dm3 mol{1 cm {1 at 450 nm [6]).
Other Considerations
1. Below, J. F.; Connick, R. E.; Coppel, C. P. J. Am. Chem. Soc. 1958, 80, 2961–2967. 2. Trimm, H. H.; Ushio, H.; Patel, R. C. Talanta 1981, 28, 753– 757. 3. Mieling, G. E.; Pardue, H. L. Anal. Chem. 1978, 50, 1333– 1337. 4. Funahashi, S.; Adachi, S.; Tanaka, M. Bull. Chem. Soc. Jpn. 1973, 46, 479–483. 5. Cavasino, F. P.; Eigen, M. Ric. Sci. Rend. Sez. A 1964, 4, 509–522. 6. Goodall, D. M.; Harrison, P. W.; Hardy, M. J.; Kirk, C. J. J. Chem. Educ. 1972, 49, 675–678. 7. Wendt, H.; Strehlow, H. Z. Electrochemistry 1962, 66, 228– 234. 8. Martinez, P.; van Eldik, R.; Kelm, H. Ber. Bunsenges. Phys. Chem. 1985, 89, 81–86. 9. Lister, M. W.; Rivington, D. E. Can. J. Chem. 1955, 33, 1572–1590. 10. Cox, B. G. Modern Liquid Phase Kinetics; Oxford: New York, 1994; p 23. 11. Espenson, J. H. Chemical Kinetics and Reaction Mechanism, 2nd ed.; McGraw-Hill: Singapore, 1995; p 46. 12. Grant, M.; Jordan, R. B. Inorg. Chem. 1981, 20, 55–60. 13. Gibson, Q. H.; Milnes, L. Biochem. J. 1964, 91, 161–171. 14. Martinez, P.; van Eldik, R. Ber. Bunsenges. Phys. Chem. 1985, 89, 728–734.
Several extensions to this investigation are possible. The higher order complexes [Fe(OH 2 ) 4 (SCN) 2 ] + and [Fe(OH2)3(SCN)3] have been described (9), and kinetic studies relating to their formation can similarly be carried out using low iron(III) and high SCN- concentrations. Also, by referring to the appropriate rates of water exchange (12), students will gain insight into the mechanisms of substitution available to iron(III) species in aqueous solution. Tracing the development of rapid-mixing devices can add an interesting historical dimension to the study. The iron(III)–thiocyanate kinetic study reported by Connick et al. (1) provides a good starting point. In this case reactant solutions were separated by moveable baffles and a single kinetic run would consume 30 to 45 cm3 of each reagent. Subsequently, Gibson and Milnes (13) described the construction and use of the modern stopped-flow spectrophotometer. Notes 1. The SCN { concentration is dictated by the spectrophotometer cell path length. It need not be known exactly, but it should be constant throughout the experiment and sufficient
2. This relationship follows because the concentration of [Fe(OH2) 4(OH)SCN]+ is always small (< 0.1% of total product) relative to that of [Fe(OH2)5SCN] 2+. Students may therefore find it surprising that the former species does make its presence felt in the kinetic sense. 3. The successful outcome of the study depends to a large degree on the care taken in making up these solutions. 4. Values given in parentheses represent errors corresponding to two standard deviations.
Literature Cited
Vol. 74 No. 10 October 1997 • Journal of Chemical Education
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