1214 Journal of Chemical Education • Vol. 74 No. 10 October 1997

In the Laboratory

Few kinetic experiments are both relevant in themechanistic sense and capable of being carried out in thetime available in the undergraduate laboratory. The pri-mary requirement is that the student be able to collect andprocess sufficient data over a 3- to 4-hour period that sub-sequent analysis provides a meaningful description of thereaction pathways. One system that we have developed withthis criterion in mind involves the reaction of iron(III) withthiocyanate ion in aqueous solution. This classical metal ionsubstitution reaction has been extensively investigated us-ing rapid-mixing (1–4), T-jump (5, 6), flash-photolysis (6), andP-jump (7) methods. The pathways leading to formation of thedark red iron(III)-thiocyanato complex are consequentlywell understood. The reaction scheme is outlined in Figure 1.

The system is particularly amenable to a stopped-flowspectrophotometric study because reactant concentrationscan be adjusted to give half-times of milliseconds to secondsappropriate to the technique. Despite the apparent complex-ity of the reaction scheme, only one process is observed onthis time scale. This is because the proton transfer steps(via Ka1 and Ka2) are diffusion controlled and are conse-quently much more rapid than those involving either com-plex formation or decay. As the experiments can be arrangedso that pseudo-first-order kinetics are followed, the result-ing absorbance–time traces are correspondingly simple toanalyze. When the known values of Ka1 (8) and Ka2 (9) arecombined with the primary kinetic data the values of therate constants k1, k{1, k2, and k{2 may be determined. Theformation constant of the iron(III)–thiocyanato complex(Kf = k1/k{1) is also defined by the kinetic results. Further-more, since the reactants are essentially colorless, while theproducts are strongly colored, it is a simple matter to usethe absorbance data obtained in the kinetic experiments fora more direct spectrophotometric evaluation of Kf.

The reaction thus illustrates many of the importantfeatures of metal ion substitution chemistry and the datacan be obtained rapidly and analyzed in a straightforwardmanner. When a carefully designed experimental protocol

A Stopped-Flow Kinetics Experiment for AdvancedUndergraduate Laboratories: Formation of Iron(III)ThiocyanateCharles R. ClarkChemistry Department, University of Otago, P.O. Box 56, Dunedin, New Zealand

is coupled with the use of rapid data acquisition andcomputational methods of analysis, this system is able tobe defined well within the allowed time. In the experimentdescribed here this definition is achieved using data ob-tained from just 15 kinetic runs. The study owes much toprevious investigations (3, 4), and for the last three years ithas been successfully incorporated into a laboratory courseat 3rd-year level. It complements an earlier investigationdescribed in this Journal (6) where relaxation methods wereemployed.

Experimental Details

ReagentsDistilled water is used in all preparations. The follow-

ing stock solutions should be prepared in advance and fil-tered through Celite:

1. 1.00 M HClO4, from dilution of a standardizedconcentrated solution of perchloric acid to 1.00dm3.

2. A standardized ferric ion solution—ca. 0.2 Miron(III)—prepared from Fe(ClO4)3?xH2O andmade up to be exactly 0.400 M in HClO4. Thiscorresponds to about 25 g of Fe(ClO4)3?xH2O dis-solved in 1.00 M HClO4 (100.0 cm3) with dilu-tion to 250.0 cm3. Because the water content ofsolid ferric perchlorate is variable, it is not asimple matter to make up the solution to a par-ticular iron(III) concentration. If analysis showsit to lie in the range 0.17 to 0.23 M no adjust-ment is necessary.

3. 2.00 M NaClO4, prepared by dissolvingNaClO4?H2O (280.92 g) in water and diluting to1.00 dm3.

4. A solution approximately 1.5 × 10 {4 M inNaSCN1 and 1.00 M in NaClO4.

The stock solutions are stable for many weeks. Theiron(III) stock solution is conveniently standardized byatomic absorption spectroscopy.

In the preparation of the iron(III) reagents used in ki-netic determinations the stock solutions are more readilydispensed using adjustable pipets (0.200–1.00 cm3, 1.00–5.00 cm3 capacity) fitted with disposable tips rather thanconventional all-glass graduated pipets. (CAUTION: Perchlo-ric acid solutions are corrosive and should not be pipettedby mouth. On completion of the experiment all acid resi-dues should be combined and neutralized by the careful ad-dition of solid sodium carbonate. The resulting solutionshould then be disposed of in a manner dictated by localregulations.)

Figure 1. The reversible formation of iron(III)-thiocyanatocomplexes.

Vol. 74 No. 10 October 1997 • Journal of Chemical Education 1215

In the Laboratory

ApparatusThe experiment requires access to a stopped-flow spec-

trophotometer equipped with a suitable data acquisitionsystem. The reactions described here were followed using aDurrum D110 instrument in conjunction with a NorthstarHorizon computer. The cell path length was 2.0 cm. Drivesyringes were thermostatted to 25.0 °C. Olis software wasused for data acquisition and for the evaluation of rate con-stants (On Line Instrument Systems Inc., Bogart, GA30622).

The Rate Law

Treatments for obtaining the rate law of a reversiblereaction are available (10, 11); our approach closely followsthat for the general case. Less detailed treatments dealingspecifically with the iron(III)–thiocyanate system have alsobeen given (3, 4). We use a simplified nomenclature in whichcharges and coordinated water molecules on the reactingspecies are omitted.

According to the pathways of Figure 1, the rate ofchange of concentration of thiocyanate ion is described byan expression containing terms governing both its disap-pearance and appearance:

{ d [SCN]/dt = k1[Fe][SCN] + k2[FeOH][SCN] – k{1[FeSCN] – k{2 [Fe(OH) SCN]

(1)

This is equivalent to eq 2 when the concentrations of thehydroxo complexes are eliminated by use of the appropri-ate acid dissociation constants, Ka1 and Ka2 :

{d [SCN]/dt = (k1 + k2Ka1/ [H+]) [Fe][SCN] – (k{1 + k-2Ka2/[H+])[FeSCN]

(2)

Expression 2 is simplified by defining rate constants for theforward and reverse reactions, kf = k1 + k2Ka1/ [H+], kr = k{1+ k{2Ka2 /[H+]. Further, the experiments are set up such that[H+] is constant during any particular kinetic run and theiron(III) concentration is always in large excess over [SCN{].We can then write:

{d [SCN]/dt = kf[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 beexpressed in terms of x, where x represents the displace-ment 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 thatkf[Fe]T[SCN]eq = kr[FeSCN]eq . If we use eqs 4 and 5 to sub-stitute for the concentrations of free and bound thiocyan-ate into eq 3 we get the simple relationship:

{ dx/dt = (kf[Fe]T + kr) ? x (6)

Substituting for x in eq 6 from eq 5 gives:

d[FeSCN]/dt = (kf[Fe]T + kr) ? ( [FeSCN]eq – [FeSCN] ) (7)

which on rearrangement and integration gives:

ln

[FeSCN]eq

[FeSCN]eq – [FeSCN]= k f [Fe]T + k r ⋅ t (8)

Because FeSCN is the only absorbing species presentto any significant extent, the reaction mixture absorbance,A, is given by the expression

A = εFeSCN ? [FeSCN] ? , (9)

Using expression 9 to substitute for [FeSCN] and[FeSCN]eq in eq 8 gives

ln

Aeq

Aeq – A= k f [Fe]T + k r ⋅ t (10)

where Aeq represents the absorbance of the system at equi-librium. Equation 10 predicts that a plot of { ln(Aeq – A) ver-sus t will be linear with slope (kf[Fe]T + kr). The latter quan-tity is defined as the observed first-order rate constant, kobs.That is,

kobs = (k1 + k2Ka1/[H+])[Fe]T + k{1 + k{2Ka2/[H+] (11)

Procedure and Results

It is generally best for students to work in pairs. Theyshould first prepare the three sets of iron(III) solutions de-scribed in Table 1.3 The reagents in series A are made up tobe 0.20 M in H+ concentration, while members of the B andC series are 0.40 M and 0.60 M in [H+], respectively. Withineach series the iron(III) concentration varies over the samerange: ca. 0.005 to 0.04 M. Each solution is made up to avolume of 10.00 cm3 and each contains sufficient NaClO4 tomaintain ionic strength at 1.00 M. This stage of the experi-ment generally takes 30 to 40 minutes to complete.

Before commencing the stopped-flow investigation it isinformative for students to gain a feeling for the rapidity ofthe reaction they are about to examine. This can be achievedthrough simple test tube experiments by mixing NaSCN so-lution (ca. 5 × 10{3 M) with an approximately equal volumeof acidified, dilute ferric ion solution. Even for concentra-tions of iron(III) down to 5 × 10{3 M the formation of thethiocyanato complex appears to be instantaneous.

A thorough familiarity with the operation of the spec-trophotometer flow system is also important. If the valvescontrolling the transfer of reagents from reservoir to drivesyringes are opened in the wrong sequence premature mix-ing of the reagents may result. Such an occurrence will al-most certainly require the preparation of replacementsolutions. A 10 cm3 volume of iron(III) solution is sufficientto flush a drive syringe between runs, and is enough forseveral replicate determinations.

The solutions of Table 1 are separately mixed in thestopped-flow reactor with an equal volume of NaSCN solu-tion (ca. 5 × 10{4 M ) and the complexation reaction is moni-tored at 450 nm. For best results the reactants should bethermostatted in the drive syringes for at least 1 min beforeinitiating the reaction. The increase in absorbance is fol-lowed over five reaction half-lives (5 t1/2) with the “infinity”absorbance reading (i.e. Aeq) being recorded after at least

1216 Journal of Chemical Education • Vol. 74 No. 10 October 1997

In the Laboratory

10 t1/2. This requires data collection times ranging from 0.5s (for solution A5) to 2.0 s (for solution C1), with each reac-tion having a post-collection delay time of up to 3 s prior torecording Aeq. The change in absorbance observed on reac-tion is designated as the positive quantity, ∆A. If the kineticdata are stored directly onto diskette this phase of theexperiment usually requires about 5 min per estimation.

Duplicate data recorded for three or four runs allows repro-ducibility to be tested, but does not markedly extend thetime required.

Under the conditions employed in this study theiron(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 finalstates. Table 2 gives ∆A values and pseudo-first-order rateconstants (kobs) obtained in a typical study.

Included in Table 2 are computed values of the first-order rate constants, kcalc, obtained from a least squares fitof 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 givebest 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 kineticallydetermined 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 theknowledge that [Fe(OH2)5SCN]2+ is the only absorbing spe-cies present at equilibrium. If Alim represents the limitingabsorbance corresponding to the situation where all theSCN{ is converted to [Fe(OH2)5SCN]2+, then the concentra-tion ratio [Fe(OH2)5SCN]2+/[SCN{] is simply ∆A/(Alim – ∆A).Therefore, the expression for determining the formationconstant from the spectrophotometric data is

K f = ∆A[Fe]T Alim – ∆A

(12)

which on rearrangement gives

∆A =AlimK f [Fe]T1 + K f [Fe]T

(13)

For a particular iron(III) concentration inspection ofTable 2 shows that, as expected, ∆A is independent of [H+]over the range of interest. Least squares fitting of the aver-aged ∆A values to eq 13 gives Alim = 0.590(0.012) andKf = 112(5) M{1. There is excellent agreement between ob-

etaRredrO-tsriFdnasegnahCecnabrosbA.2elbaT52tastnatsnoC °Ca

noitcaeRnoitangiseD

]eF[ T)M(

H[ +])M(

∆Ak sbo

s( {1)k clac

b

s( {1)

1A 12200.0 01.0 611.0 69.2 30.3

2A 24400.0 01.0 391.0 26.3 65.3

3A 48800.0 01.0 292.0 66.4 36.4

4A 3310.0 01.0 643.0 56.5 96.5

5A 7710.0 01.0 883.0 67.6 67.6

1B 12200.0 02.0 711.0 20.2 30.2

2B 24400.0 02.0 491.0 24.2 14.2

3B 48800.0 02.0 392.0 32.3 91.3

4B 3310.0 02.0 653.0 00.4 69.3

5B 7710.0 02.0 093.0 17.4 37.4

1C 12200.0 03.0 811.0 27.1 96.1

2C 24400.0 03.0 591.0 69.1 30.2

3C 48800.0 03.0 892.0 17.2 17.2

4C 3310.0 03.0 653.0 93.3 83.3

5C 7710.0 03.0 593.0 40.4 60.4

aAt ionic strength 1.00 M and [SCN{] = 0.75 × 10{4 M. When consideringthe iron(III) and hydrogen ion concentrations it must be remembered that eachreactant solution is diluted by a factor of two in the stopped-flow experiment.

bCalculated using eq 11 and the values of rate and equilibrium constantsgiven in the text.

)III(norIfonoitaraperProfsemuloVnoituloSkcotS.1elbaTstnegaeR a

noituloSnoitangiseD

OlC(eFM2.0 4)3 &OlCHM04.0 4

mc( 3)

OlCHM0.1 4mc( 3)

OlCaNM0.2 4mc( 3)

1A 52.0 09.1 58.3

2A 05.0 08.1 07.3

3A 00.1 06.1 04.3

4A 05.1 04.1 01.3

5A 00.2 02.1 08.2

1B 52.0 09.3 58.2

2B 05.0 08.3 07.2

3B 00.1 06.3 04.2

4B 05.1 04.3 01.2

5B 00.2 02.3 08.1

1C 52.0 09.5 58.1

2C 05.0 08.5 07.1

3C 00.1 06.5 04.1

4C 05.1 04.5 01.1

5C 00.2 02.5 08.0aEach reagent is made up to a volume of 10.00 cm3 with water.

Figure 2. A comparison between observed (points) and calculated(line) absorbance changes on reaction of iron(III) with thiocyan-ate ion in acidic solution.

Vol. 74 No. 10 October 1997 • Journal of Chemical Education 1217

In the Laboratory

served and calculated data as shown by the comparisongiven in Figure 2. Similarly, the agreement between thespectrophotometrically and kinetically determined values ofthe formation constant is also satisfactory, but it is the lat-ter result that is the less certain owing to a relativelylarge error in k{1. The k{1 term never dominates under anycondition. Its maximum contribution occurs for reaction C1,where it accounts for 46% of the observed rate. Table 3 com-pares values of rate and formation constants obtained overthe course of a number of studies. The present results com-pare very favorably with those derived from a study (3) thatinvolved 162 kinetic runs and a data collection time of 7hours.

Other Considerations

Several extensions to this investigation are possible.The higher order complexes [Fe(OH2)4(SCN)2]+ and[Fe(OH2)3(SCN)3] have been described (9), and kinetic stud-ies relating to their formation can similarly be carried outusing low iron(III) and high SCN- concentrations. Also, byreferring to the appropriate rates of water exchange (12),students will gain insight into the mechanisms of substitu-tion available to iron(III) species in aqueous solution.

Tracing the development of rapid-mixing devices canadd an interesting historical dimension to the study. Theiron(III)–thiocyanate kinetic study reported by Connick etal. (1) provides a good starting point. In this case reactantsolutions were separated by moveable baffles and a singlekinetic run would consume 30 to 45 cm3 of each reagent.Subsequently, Gibson and Milnes (13) described the con-struction and use of the modern stopped-flow spectropho-tometer.

Notes

1. The SCN{ concentration is dictated by the spectropho-tometer cell path length. It need not be known exactly, but itshould be constant throughout the experiment and sufficient

52tametsySetanaycoihT–)III(norIrofataDmuirbiliuqEdnaetaRdetceleS.3elbaT °ChtgnertScinoI

)M(k1

M( 1- s 1- )k

{1

s( {1)Kf

M( {1)k2

M( {1s{1).feRdnadohteM

5.0 )04(031 — — )2.0(3.1 × 01 4 (sisylotohphsalfdnapmuj-T 6 )

5.0 )05(051 — — )2.0(6.2 × 01 4 (pmuj-P 7 )

5.0 )5(09 )2.0(6.1 )01(65 — (wolf-deppotS 4 )

0.1 )3(79 )30.0(57.0 )7(921 )5.0(6.9 × 01 3 (wolf-deppotS 3 )

0.1 — — 431 — (cirtemotohportcepS 41 )

0.1 )01(901 )01.0(97.0 )92(831 )8.0(0.8 × 01 3 krowsiht,wolf-deppotS

0.1 — — )5(211 — krowsiht,cirtemotohportcepS

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]).

2. This relationship follows because the concentration of[Fe(OH2)4(OH)SCN]+ is always small (< 0.1% of total product) rela-tive to that of [Fe(OH2)5SCN]2+. Students may therefore find it sur-prising that the former species does make its presence felt in thekinetic sense.

3. The successful outcome of the study depends to a largedegree on the care taken in making up these solutions.

4. Values given in parentheses represent errors correspond-ing to two standard deviations.

Literature Cited

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: NewYork, 1994; p 23.

11. Espenson, J. H. Chemical Kinetics and Reaction Mecha-nism, 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.