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Kinetics of decomposition of the fluorosulphate ion in aqueous solution
J. inorg,nucl.Chem.,1968,Vol.30, pp. 1237to 1243. PergamonPress. PrintedinGreat Britain
KINETICS OF FLUOROSULPHATE
DECOMPOSITION OF THE ION IN AQUEOUS SOLUTION
M. M. JONES and W. L. L O C K H A R T Department of Chemistry, Vanderbilt University Nashville, Tennessee 37203 (Received 9 August 1967) A b s t r a c t - T h e rate of decomposition of the fluorosulphate ion(SO3F-) has been determined in aqueous solution under conditions ranging from 4 M hydrochloric acid to 5 M sodium hydroxide. The empirical rate law found for this process is: --d[SO.~F-] dt
{k[H+l + kn~°+ kl[OH-] }[SO:~F-]'
The activation energies for all steps can be estimated, and elementary processes consistent with such a rate law are presented. INTRODUCTION
THE FLUOROSULPHATEion (SO3F-) has previously been reported to decompose rapidly in strong mineral acid, and much more slowly in base [1]. The stoichiometries of the respective reactions are: SO3F- + H20 SO3F- + 2 O H -
) HSO4- + HF
~ SO4 = + H20 + F-.
Previous rate studies on these processes have examined the reaction under conditions in which the pH was uncontrolled [2] or over a relatively narrow range of sodium hydroxide concentrations [3]. These studies reported the existence of a rate law with three terms: (l) a water term (2) a term with a first order dependence on hydrogen ion concentration and (3) a term with a first order dependence on hydroxide ion concentration. The present work was undertaken to provide more precise data over a wider range of acid and base concentrations and to utilize more convenient techniques
for following this reaction by the determination of the released fluoride. EXPERIMENTAL Materials. Potassium fluorosulphate (KSOaF) was the source of the fluorosulphate ion for all kinetic runs. It was prepared from the ammonium salt obtained from Ozark-Mahoning Co. of Tulsa, Oklahoma (lot no. R-5-122). This salt, as received, was dissolved in methanol, filtered, and the solution evaporated to dryness. The residue was dissolved in a small amount of water and added to an ice cold aqueous solution containing a slight excess of potassium hydroxide. The potassium fluorosulphate precipitates immediately. It was filtered quickly, and washed with a large volume of 95 per cent ethanol. It was dried with air and stored under a vacuum over anhydrous calcium chloride for several days. Lumpy material was crushed daily, and the final product was a fine white powder. It was analyzed by heating I. W. Traube, J. Hoerenz and F. Wunderlich, Bet. 52B, 1272 ( 1919). 2. I. G. Ryss and T. A. Gribanova, Zh. Fis. Khim. URSS 29, 1822 (1955); Chem. ,4bstr. 50, 9121h (1956). 3. I. G. Ryss and A. Kh. Drabkina, Kinetika i Kataliz, 7, 319 (1966). Chem..4 bstr. 65, 3082b (1966). 1237
1238
M . M . J O N E S and W. L. L O C K H A R T
weighed portions in. plalinum crucibles at a dull red heat for 15 min and then to constant weight furnace at 600°C. Under these conditions the fluorosulphate reacts with moisture as follows: 2KSO3F + H20 ---* K2SO4+ SO3
1' + 2 H F 1'.
Care must be taken during heating as the material tends to creep out of the crucible. The crucible contents were weighed as potassium sulphate (K2SO4). This material contained no residual fluoride when tested for its presence. The three samples of KSO3F used in this work had purities of 99.11, 98.15 and 98.20 per cent; this was taken into consideration when preparing solutions. The reagent used for fluoride in solution was a modification of that used by Johnson and Jones [4]. It was prepared by adding 7-1000 g of Eastman White Label 7-iodo-8-hydroxyquinoline-5-sulphonic acid (ferron) to a two-litre volumetric flask containing 40 ml of 4.3 M sodium acetate with a litre of water and mixed thoroughly until all of the solid dissolved: Fifty ml of 0-2 M FeC13, containing sufficient sulfuric acid to prevent hydrolysis of Fe(llI), were added to form a green solution of the 2 : 1 ferron-Fe(IIl) complex. The pH of the solution (after dilution to 21.) was 4.2 at 25°C, and it was filtered before use. This sequence of addition must be observed to obtain rapid solution of the ferron and prevent formation of ferric hydroxide. Neither de-iodination of the ferron nor precipitation of ferric hydroxide were observed at the p H described, and the solution appeared to be stable indefinitely. Method. To begin a kinetic run, aliquots of hydrochloric acid or sodium hydroxide were thermostatted in polyethylene flasks, arrd measured amounts of a solution of KSOaF were added such that desired final concentrations of HCI, N a O H and KSO3F were achieved. Analysis for free fluoride was carried out on I0 ml aliquots from these mixtures. For hydrochloric acid runs, the 10 ml aliquots were discharged into 4.4 M sodium acetate in 100 ml volumetric flasks. The amount of sodium acetate was such that upon dilution to 100ml, the pH of the solution at 25°C was between 3.0 and 4.0. This essentially quenches the reaction. T h e same procedure was used for sodium hydroxide runs except the 6.0 M acetic acid served as the quench reagent. At the higher concentrations of N a O H (3.00-5.00 M), hydrochloric acid was added after the l0 ml aliquot to reduce the pH. In these cases, the flask was also cooled for 30 sec with running tap water. The fluoride reagent was then added in a 5 mi portion, the contents were diluted to 100 ml and the per cent transmittance measured at 620 mtz to the nearest 0-25 per cent. The presence of fluoride bleaches the color of the ferron-Fe(III) complex and this bleaching is related to the amount of free fluoride. The concentration of acetate in the 100 ml volumetric flask must be kept below 2.4 M, as the sensitivity of the method rapidly decreases as the acetate concentration increases. Calibration data were obtained for each concentration of HCI and NaOH used, by following the same procedure as for a kinetic run but with measured amounts of 0.1000 M N a F to give a concentration range of 0-0-01 M fluoride. Since the absorbance of these solutions does not follow Beer's law with respect to fluoride, the values for per cent transmittance and fluoride concentration were fitted to a power series equation with eight constants by means of a computer. This equation is
x =A+By+Cy2+Dy~+...Hy 7 where x is the concentration of free fluoride, y is the per cent transmittance, and A to H are constants. The output was a table from which the concentration of fluoride could be read directly. RESULTS
Kinetics o f decomposition in acid solutions. R a t e d a t a w e r e t a k e n o v e r a r a n g e of up to 40-80 per cent of total reaction for the concentrations of hydrochloric acid used. The amount of hydrochloric acid was such that the hydrogen ion concentration could be considered constant during the course of a given experiment. Under conditions of constant hydrogen ion concentration, the rate law has the form --d{[SO3F-]} dt = k°bs" { [ S O 3 F - ] }. 4. w . L. Johnson and M. M. Jones, lnorg. Chem. 5, 1345 (1966).
Kinetics of decomposition of the fluorosulphate ion
1239
All kinetic runs were carried out in duplicate and rate constants were calculated f r o m the integrated f o r m of the rate law. D a t a for a typical run are given in T a b l e 1. Table I. D a t a for a typical run ( [HCI] = 4.00 M; T e m p . = 30°C) T i m e , min 10z[SO.~F-], M
0.0 5.00
30.0 3.78
52.5 2-92
85.0 2.19
135.0 1.36
T h e first-order d e p e n d e n c e on the fluorosulphate concentration is found for all the concentrations of fluorosulphate used. T h u s for initial fluorosulfate concentrations (all in 4 M HC1 at 30 °) of 0.0250, 0-0500, and 0.100 M, the o b s e r v e d first order rate constants were 1.58±0.11 × 10 -4 s e c - ' , 1-66___0-08 × 10 -4 s e c - ' and 1.66_+0.08 × 10 -4 s e c - ' , respectively. All rate constants given here or later are averages of 7 - 1 0 values. Rate constants for the concentration range of hydrochloric acid used are shown in T a b l e 2. Table 2. Pseudo-first order rate c o n s t a n t s at varying hydrochloric acid concentrations (Temp. = 30°C)
[HCI], M 106koh~., sec '
0.500 9.01±0-79
1-00 17.0±1-0
2.00 40-2±2.5
4.00 166±8.0
T h e variation of the rate constant with temperature, in 4.00 M hydrochloric acid is as follows: T° kobs.(Sec-') 105
20 ° 4.72±0.23
30 ° 1 6 . 6 ± 0.80
40 ° 40.9±2.4.
Kinetics of decomposition in basic solution. Rate data were taken o v e r a range of up to 3 0 - 5 0 per cent of total reaction for the lower concentrations of sodium hydroxide (0.250-1.50 M) so that as the reaction p r o c e e d e d the hydroxide ion concentration could be considered essentially constant. T h e rate law under conditions of constant hydroxide concentration is -d{[SO3F-]} dt = kobs.{[SO3F-]}. All kinetic runs were carried out in duplicate, and rate constants were calculated f r o m the integrated f o r m of the rate law. D a t a for a typical run are given in T a b l e 3. T h e first-order d e p e n d e n c e on the fluorosulphate concentration is found o v e r the range of fluorosulphate concentrations studied. Thus, for a series of runs in Table 3. D a t a for a typical run ( [ N a O H ] = 3-00 M; T e m p . = 25°C) T i m e , hr 10~[SO3F-], M
0.0 5-00
10-5 3-37
21-5 2.23
34-5 1.28
46.5 0.783
1240
M.M.
J O N E S and W. L. L O C K H A R T
1.00 M NaOH at 25°, initial fluorosulphate concentrations of 0.0500, 0.100, and 0.200M gave observed first order rate constants of 12.2___0.21× 10-7 sec -1, 12.6___ 0.61 × 10-7 sec -1, and 11-7 --- 0.50 × 10-7 sec -1, respectively. The hydroxide ion dependence of the rate and its temperature variation are shown in Table 4. Table 4. P s e u d o first-order rate c o n s t a n t s for the decomposition of fluorosulphate in basic solution (Initial KSO3F conc. = 5.00 × 10 -~ M)
[NaOH] M 0.250 0.500 1.00 1.50 2.00 3.00 4.00 5-00
I 0rkobs., sec -1 T e m p . = 15°C
3.67___0.17 10.3 21.4 44.8 98.8
±0.95 ±1-4 ±3-8 ±4.5
T e m p . = 25°C
T e m p . = 35°C
3.55__- 0.20 5.87___ 0.12 12.2 ___ 0.21 25-5 ___ 0.77 43.0 ± 3.7 108 ± 3.6 218 +_-12 532 ±33
10.0___ 0.70 39.1___ 2.1 111 228 477 1048
± 6.4 ±14 ±26 ----_77
All rate c o n s t a n t s are averages of 6 - 1 0 values. DISCUSSION
Because of the high electrolyte concentrations in the media in which this reaction was studied, it was not feasible to determine the order of the reactions with respect to [H ÷] or [OH-] by using the nominal stoichiometric concentrations of these species. To circumvent this problem, activity corrections and suitable indicator functions were used. The indicator functions are similar to or related to the Hammett acidity function, but are dependent upon the charges on the species involved. For the acidic reaction the probable rate determining step is H + + SO3F- ~ [HSO3F] where the transition state has no net charge. In this case the activity corrections were applied as described below. For the reaction in base, the probable rate determining step is O H - + SO3F- ~ [HOSO3F2-]. Here the transition state has a doubly negative charge and the appropriate indicator function is H~_ as determined for concentrated solutions of sodium hydroxide. For concentrated solutions of hydrochloric acid, it is necessary to make allowance for the variation of activity coefficients. If the rate law is Rate = k[HSO3F] then use of the ionization constant expression for HSO3F allows this to be written as
Rate = k__~ ° _ ~ ~-y0[H+I[SO3F-I, k •[H+][SO3F_] ~/+y7
Kinetics of decomposition of the fluorosulphate ion
1241
since y0 ~ (Y+T-) l/z- If we assume that the activity coefficient of HSO3F in hydrochloric acid can be approximated by the activity coefficients of the hydrochloric acid itself, then one would expect that kobs. =
k ~ y o [ H +]
and the value of kobs./yo[H+] should be approximately constant. The values below in Table 5 show that this is so. Table 5. Acid dependence of rate and activity correction [HCI] M 0.5 1.0 2.0 4.0
Yo
(kob~,/yo[H+]) 10'~
0-752 0-804 1-014 1.875
2.4 2.1 2.0 2.2
From the data in Table 4 and activity coefficients for hydrochloric acid at other temperatures [5], the activation energy for the acid catalyzed process was found Lo be 20.6 kcal/mole. Rate laws of the same form have been reported for oxygen exchange[6] of aqueous sulphate and the hydrolysis of fluoroborate (BF4-)[7], hexafluorogermanate (GeF6=)[8], and sulfamate (SO3NH2-)[9]. Mechanisms which fit this rate law include the following: Mechanism A. (Bimolecular) SO3F-+H +,
K
' HSO3F
HSO3F + HzO --~ H2SO4 + H F H2SOa
fast ~ H++HSO4_.
Mechanism B. (Dissociative) SO3F-+H +, HSO3F SO3+ H20 H2SO 4
fast
K
'HSO3F
k~SO3+HF fast
> H2SO 4
~ H + + HSO4-.
Fluorosulphuric acid (HSO3F) is a well characterized compound [ 10] and a reasonable intermediate for either mechanism. 5. H. S. Harned and B. B. Owen, In The Physical Chemistry of Electrolytic Solutions, 3rd Edn, p. 469. Reinhold, New York (1958). 6. T. C. Hoering and J. W. Kennedy, J. Am. chem. Soc. 79, 56 (1957). 7. M. Anbar and S. Guttman, J. phys. Chem. 64, 1896 (1960). 8. A. E. Gebala and M. M. Jones, Unpublished results, Vanderbilt University. 9. S. H. Maron and A. R. Berens, J. Am. chem. Soc. 72, 3571 (1950). 10. J. H. Simons (Editor), Fluorine Chemistry, Vol. 1. pp. 167-171. Academic Press, New York (1950).
1242
M . M . J O N E S and W. L. L O C K H A R T
Both mechanisms predict a leveling off of the rate when all of the fluorosulfate is protonated. Such an effect was not observed over the hydrochloric acid concentration range used in this work. This indicates that fluorosulfuric acid is a very strong acid, a fact which is known from independent studies [ 11 ]. If values for the ionization constant of fluorosulfuric acid are assumed and calculations performed to determine the fraction[12] present as fluorosulfuric acid, it is found that the ionization constant must at least be of the order of 100 to account for the fact that no leveling offin the rate was observed. The role of the hydrogen ion as a catalyst is probably two-fold. First, the reduction in charge to form a neutral species (HSO3F) would facilitate nucleophilic attack by water. Second, the attachment of the proton would be expected to occur on the fluoride with a weakening of the sulfur-fluorine bond. This would enhance the ability of hydrofluoric acid (HF) to act as a leaving group. For the rates of the reactions run in sodium hydroxide solutions, an analogous procedure was used, based upon an indicator function for strongly basic media, H~_, given by Yigal [ 13]. This corresponds to a reaction in which a doubly charged anion is formed in the transition state: SOzF- + O H - ---> [HOSO3F2-]. In this case a plot of log kobs. VS. H2_ is a straight line of unit slope over the range of sodium hydroxide concentrations used. In order to obtain H~_ values for this plot it is necessary to assume that ( H 2 - - H _ ) values are the same for sodium hydroxide as those given by Yigal for potassium hydroxide. It is then possible to simply add this difference to the H_ values given for sodium hydroxide to obtain the desired H2- values. These are summarized as follows: [NaOH]g-moles/l. 0.250 H~_ 13.60
0.50 13.95
1.00 14.33
1.50 14.55
2.00 14.81
3.00 15.08
4.00 15.45
5.00 15.80.
This plot is then consistent with the rate determining step given above being the only important one in strongly basic solutions. The rate in concentrated base is thus -d[SOzF-] -- k[SOzF-][OH-]. dt A mechanism which will give this rate law is one which considers the decomposition of fluorosulfate as the displacement of a weak base, fluoride, by the stronger base, hydroxide ion. Data on related compounds support this interpretation. Chlorosulfuric acid (HSOaCI) is rapidly hydrolyzed by water but fluorosulphuric acid[10] is not. Chloride is, of course, a much weaker base than fluoride. Sulphamate may be boiled [9] in neutral or alkaline solution without decomposition. Here, the amide ion (NH2-) is a stronger base than hydroxide or water and is, therefore, not displaced by them. Likewise, the oxygen exchange in sulphate ion 11. J. Barr, R. J. Gillespie and E. A. Robinson, Can.J. Chem. 39, 1266 (1961). 12. H. A. Laitinen, ChemicalAnalysis, p 36. McGraw-Hill, New York (1960). 13. G. Yigal, J. phys. Chem. 71, 1040 (1967).
Kinetics of decomposition of the fluorosulphate ion
1243
[6] is s u p p r e s s e d in basic solutions. T h e e m p t y d-orbitals on the sulphur a t o m can serve as the a c c e p t o r site for the incoming base. T h e reaction steps for this term of the rate law would be SO3F-+ OH- ~ HSO4-+ OH-
HSO4-+
F-
fast ~ H 2 0 + S O a =.
In s u m m a r y , the experimental data are consistent with three processes o v e r the entire range of conditions (1) the attack of S O 3 F - by a proton (2) the attack of S O a F - by a hydroxide ion and (3) the attack of S O 3 F - by a w a t e r molecule. T h e w a t e r reaction is such a slow process that it does not show up at all in more c o n c e n t r a t e d solutions whether they are acidic or basic. F r o m the log kobs. VS. H2_ plot, kn,o can be estimated to be 2.15 × 10 -7 sec -1, in excellent agreement with the value of 2.1 x l0 -7 reported previously [2]. Because of the lack of data to construct H2- scales at t e m p e r a t u r e s other than 25 °, it is not possible to reduce the data at such t e m p e r a t u r e s other than approximately. I f one makes the assumption that H2- values at 25 ° can also be used at other temperatures, it is possible to estimate activation p a r a m e t e r s for these processes. With this assumption, the activation energy for the reaction in b a s e is 20.2 kcal.
Acknowledgements-The financial support of the United States Atomic Energy Commission is gratefully acknowledged. Thanks are due also to Mr. James E. Hix for writing the computer program and Dr. Andrej Kodjak of the Vanderbilt Department of Germanic and Slavic Languages for a translation of Ref. [2].
KINETICS OF FLUOROSULPHATE
DECOMPOSITION OF THE ION IN AQUEOUS SOLUTION
M. M. JONES and W. L. L O C K H A R T Department of Chemistry, Vanderbilt University Nashville, Tennessee 37203 (Received 9 August 1967) A b s t r a c t - T h e rate of decomposition of the fluorosulphate ion(SO3F-) has been determined in aqueous solution under conditions ranging from 4 M hydrochloric acid to 5 M sodium hydroxide. The empirical rate law found for this process is: --d[SO.~F-] dt
{k[H+l + kn~°+ kl[OH-] }[SO:~F-]'
The activation energies for all steps can be estimated, and elementary processes consistent with such a rate law are presented. INTRODUCTION
THE FLUOROSULPHATEion (SO3F-) has previously been reported to decompose rapidly in strong mineral acid, and much more slowly in base [1]. The stoichiometries of the respective reactions are: SO3F- + H20 SO3F- + 2 O H -
) HSO4- + HF
~ SO4 = + H20 + F-.
Previous rate studies on these processes have examined the reaction under conditions in which the pH was uncontrolled [2] or over a relatively narrow range of sodium hydroxide concentrations [3]. These studies reported the existence of a rate law with three terms: (l) a water term (2) a term with a first order dependence on hydrogen ion concentration and (3) a term with a first order dependence on hydroxide ion concentration. The present work was undertaken to provide more precise data over a wider range of acid and base concentrations and to utilize more convenient techniques
for following this reaction by the determination of the released fluoride. EXPERIMENTAL Materials. Potassium fluorosulphate (KSOaF) was the source of the fluorosulphate ion for all kinetic runs. It was prepared from the ammonium salt obtained from Ozark-Mahoning Co. of Tulsa, Oklahoma (lot no. R-5-122). This salt, as received, was dissolved in methanol, filtered, and the solution evaporated to dryness. The residue was dissolved in a small amount of water and added to an ice cold aqueous solution containing a slight excess of potassium hydroxide. The potassium fluorosulphate precipitates immediately. It was filtered quickly, and washed with a large volume of 95 per cent ethanol. It was dried with air and stored under a vacuum over anhydrous calcium chloride for several days. Lumpy material was crushed daily, and the final product was a fine white powder. It was analyzed by heating I. W. Traube, J. Hoerenz and F. Wunderlich, Bet. 52B, 1272 ( 1919). 2. I. G. Ryss and T. A. Gribanova, Zh. Fis. Khim. URSS 29, 1822 (1955); Chem. ,4bstr. 50, 9121h (1956). 3. I. G. Ryss and A. Kh. Drabkina, Kinetika i Kataliz, 7, 319 (1966). Chem..4 bstr. 65, 3082b (1966). 1237
1238
M . M . J O N E S and W. L. L O C K H A R T
weighed portions in. plalinum crucibles at a dull red heat for 15 min and then to constant weight furnace at 600°C. Under these conditions the fluorosulphate reacts with moisture as follows: 2KSO3F + H20 ---* K2SO4+ SO3
1' + 2 H F 1'.
Care must be taken during heating as the material tends to creep out of the crucible. The crucible contents were weighed as potassium sulphate (K2SO4). This material contained no residual fluoride when tested for its presence. The three samples of KSO3F used in this work had purities of 99.11, 98.15 and 98.20 per cent; this was taken into consideration when preparing solutions. The reagent used for fluoride in solution was a modification of that used by Johnson and Jones [4]. It was prepared by adding 7-1000 g of Eastman White Label 7-iodo-8-hydroxyquinoline-5-sulphonic acid (ferron) to a two-litre volumetric flask containing 40 ml of 4.3 M sodium acetate with a litre of water and mixed thoroughly until all of the solid dissolved: Fifty ml of 0-2 M FeC13, containing sufficient sulfuric acid to prevent hydrolysis of Fe(llI), were added to form a green solution of the 2 : 1 ferron-Fe(IIl) complex. The pH of the solution (after dilution to 21.) was 4.2 at 25°C, and it was filtered before use. This sequence of addition must be observed to obtain rapid solution of the ferron and prevent formation of ferric hydroxide. Neither de-iodination of the ferron nor precipitation of ferric hydroxide were observed at the p H described, and the solution appeared to be stable indefinitely. Method. To begin a kinetic run, aliquots of hydrochloric acid or sodium hydroxide were thermostatted in polyethylene flasks, arrd measured amounts of a solution of KSOaF were added such that desired final concentrations of HCI, N a O H and KSO3F were achieved. Analysis for free fluoride was carried out on I0 ml aliquots from these mixtures. For hydrochloric acid runs, the 10 ml aliquots were discharged into 4.4 M sodium acetate in 100 ml volumetric flasks. The amount of sodium acetate was such that upon dilution to 100ml, the pH of the solution at 25°C was between 3.0 and 4.0. This essentially quenches the reaction. T h e same procedure was used for sodium hydroxide runs except the 6.0 M acetic acid served as the quench reagent. At the higher concentrations of N a O H (3.00-5.00 M), hydrochloric acid was added after the l0 ml aliquot to reduce the pH. In these cases, the flask was also cooled for 30 sec with running tap water. The fluoride reagent was then added in a 5 mi portion, the contents were diluted to 100 ml and the per cent transmittance measured at 620 mtz to the nearest 0-25 per cent. The presence of fluoride bleaches the color of the ferron-Fe(III) complex and this bleaching is related to the amount of free fluoride. The concentration of acetate in the 100 ml volumetric flask must be kept below 2.4 M, as the sensitivity of the method rapidly decreases as the acetate concentration increases. Calibration data were obtained for each concentration of HCI and NaOH used, by following the same procedure as for a kinetic run but with measured amounts of 0.1000 M N a F to give a concentration range of 0-0-01 M fluoride. Since the absorbance of these solutions does not follow Beer's law with respect to fluoride, the values for per cent transmittance and fluoride concentration were fitted to a power series equation with eight constants by means of a computer. This equation is
x =A+By+Cy2+Dy~+...Hy 7 where x is the concentration of free fluoride, y is the per cent transmittance, and A to H are constants. The output was a table from which the concentration of fluoride could be read directly. RESULTS
Kinetics o f decomposition in acid solutions. R a t e d a t a w e r e t a k e n o v e r a r a n g e of up to 40-80 per cent of total reaction for the concentrations of hydrochloric acid used. The amount of hydrochloric acid was such that the hydrogen ion concentration could be considered constant during the course of a given experiment. Under conditions of constant hydrogen ion concentration, the rate law has the form --d{[SO3F-]} dt = k°bs" { [ S O 3 F - ] }. 4. w . L. Johnson and M. M. Jones, lnorg. Chem. 5, 1345 (1966).
Kinetics of decomposition of the fluorosulphate ion
1239
All kinetic runs were carried out in duplicate and rate constants were calculated f r o m the integrated f o r m of the rate law. D a t a for a typical run are given in T a b l e 1. Table I. D a t a for a typical run ( [HCI] = 4.00 M; T e m p . = 30°C) T i m e , min 10z[SO.~F-], M
0.0 5.00
30.0 3.78
52.5 2-92
85.0 2.19
135.0 1.36
T h e first-order d e p e n d e n c e on the fluorosulphate concentration is found for all the concentrations of fluorosulphate used. T h u s for initial fluorosulfate concentrations (all in 4 M HC1 at 30 °) of 0.0250, 0-0500, and 0.100 M, the o b s e r v e d first order rate constants were 1.58±0.11 × 10 -4 s e c - ' , 1-66___0-08 × 10 -4 s e c - ' and 1.66_+0.08 × 10 -4 s e c - ' , respectively. All rate constants given here or later are averages of 7 - 1 0 values. Rate constants for the concentration range of hydrochloric acid used are shown in T a b l e 2. Table 2. Pseudo-first order rate c o n s t a n t s at varying hydrochloric acid concentrations (Temp. = 30°C)
[HCI], M 106koh~., sec '
0.500 9.01±0-79
1-00 17.0±1-0
2.00 40-2±2.5
4.00 166±8.0
T h e variation of the rate constant with temperature, in 4.00 M hydrochloric acid is as follows: T° kobs.(Sec-') 105
20 ° 4.72±0.23
30 ° 1 6 . 6 ± 0.80
40 ° 40.9±2.4.
Kinetics of decomposition in basic solution. Rate data were taken o v e r a range of up to 3 0 - 5 0 per cent of total reaction for the lower concentrations of sodium hydroxide (0.250-1.50 M) so that as the reaction p r o c e e d e d the hydroxide ion concentration could be considered essentially constant. T h e rate law under conditions of constant hydroxide concentration is -d{[SO3F-]} dt = kobs.{[SO3F-]}. All kinetic runs were carried out in duplicate, and rate constants were calculated f r o m the integrated f o r m of the rate law. D a t a for a typical run are given in T a b l e 3. T h e first-order d e p e n d e n c e on the fluorosulphate concentration is found o v e r the range of fluorosulphate concentrations studied. Thus, for a series of runs in Table 3. D a t a for a typical run ( [ N a O H ] = 3-00 M; T e m p . = 25°C) T i m e , hr 10~[SO3F-], M
0.0 5-00
10-5 3-37
21-5 2.23
34-5 1.28
46.5 0.783
1240
M.M.
J O N E S and W. L. L O C K H A R T
1.00 M NaOH at 25°, initial fluorosulphate concentrations of 0.0500, 0.100, and 0.200M gave observed first order rate constants of 12.2___0.21× 10-7 sec -1, 12.6___ 0.61 × 10-7 sec -1, and 11-7 --- 0.50 × 10-7 sec -1, respectively. The hydroxide ion dependence of the rate and its temperature variation are shown in Table 4. Table 4. P s e u d o first-order rate c o n s t a n t s for the decomposition of fluorosulphate in basic solution (Initial KSO3F conc. = 5.00 × 10 -~ M)
[NaOH] M 0.250 0.500 1.00 1.50 2.00 3.00 4.00 5-00
I 0rkobs., sec -1 T e m p . = 15°C
3.67___0.17 10.3 21.4 44.8 98.8
±0.95 ±1-4 ±3-8 ±4.5
T e m p . = 25°C
T e m p . = 35°C
3.55__- 0.20 5.87___ 0.12 12.2 ___ 0.21 25-5 ___ 0.77 43.0 ± 3.7 108 ± 3.6 218 +_-12 532 ±33
10.0___ 0.70 39.1___ 2.1 111 228 477 1048
± 6.4 ±14 ±26 ----_77
All rate c o n s t a n t s are averages of 6 - 1 0 values. DISCUSSION
Because of the high electrolyte concentrations in the media in which this reaction was studied, it was not feasible to determine the order of the reactions with respect to [H ÷] or [OH-] by using the nominal stoichiometric concentrations of these species. To circumvent this problem, activity corrections and suitable indicator functions were used. The indicator functions are similar to or related to the Hammett acidity function, but are dependent upon the charges on the species involved. For the acidic reaction the probable rate determining step is H + + SO3F- ~ [HSO3F] where the transition state has no net charge. In this case the activity corrections were applied as described below. For the reaction in base, the probable rate determining step is O H - + SO3F- ~ [HOSO3F2-]. Here the transition state has a doubly negative charge and the appropriate indicator function is H~_ as determined for concentrated solutions of sodium hydroxide. For concentrated solutions of hydrochloric acid, it is necessary to make allowance for the variation of activity coefficients. If the rate law is Rate = k[HSO3F] then use of the ionization constant expression for HSO3F allows this to be written as
Rate = k__~ ° _ ~ ~-y0[H+I[SO3F-I, k •[H+][SO3F_] ~/+y7
Kinetics of decomposition of the fluorosulphate ion
1241
since y0 ~ (Y+T-) l/z- If we assume that the activity coefficient of HSO3F in hydrochloric acid can be approximated by the activity coefficients of the hydrochloric acid itself, then one would expect that kobs. =
k ~ y o [ H +]
and the value of kobs./yo[H+] should be approximately constant. The values below in Table 5 show that this is so. Table 5. Acid dependence of rate and activity correction [HCI] M 0.5 1.0 2.0 4.0
Yo
(kob~,/yo[H+]) 10'~
0-752 0-804 1-014 1.875
2.4 2.1 2.0 2.2
From the data in Table 4 and activity coefficients for hydrochloric acid at other temperatures [5], the activation energy for the acid catalyzed process was found Lo be 20.6 kcal/mole. Rate laws of the same form have been reported for oxygen exchange[6] of aqueous sulphate and the hydrolysis of fluoroborate (BF4-)[7], hexafluorogermanate (GeF6=)[8], and sulfamate (SO3NH2-)[9]. Mechanisms which fit this rate law include the following: Mechanism A. (Bimolecular) SO3F-+H +,
K
' HSO3F
HSO3F + HzO --~ H2SO4 + H F H2SOa
fast ~ H++HSO4_.
Mechanism B. (Dissociative) SO3F-+H +, HSO3F SO3+ H20 H2SO 4
fast
K
'HSO3F
k~SO3+HF fast
> H2SO 4
~ H + + HSO4-.
Fluorosulphuric acid (HSO3F) is a well characterized compound [ 10] and a reasonable intermediate for either mechanism. 5. H. S. Harned and B. B. Owen, In The Physical Chemistry of Electrolytic Solutions, 3rd Edn, p. 469. Reinhold, New York (1958). 6. T. C. Hoering and J. W. Kennedy, J. Am. chem. Soc. 79, 56 (1957). 7. M. Anbar and S. Guttman, J. phys. Chem. 64, 1896 (1960). 8. A. E. Gebala and M. M. Jones, Unpublished results, Vanderbilt University. 9. S. H. Maron and A. R. Berens, J. Am. chem. Soc. 72, 3571 (1950). 10. J. H. Simons (Editor), Fluorine Chemistry, Vol. 1. pp. 167-171. Academic Press, New York (1950).
1242
M . M . J O N E S and W. L. L O C K H A R T
Both mechanisms predict a leveling off of the rate when all of the fluorosulfate is protonated. Such an effect was not observed over the hydrochloric acid concentration range used in this work. This indicates that fluorosulfuric acid is a very strong acid, a fact which is known from independent studies [ 11 ]. If values for the ionization constant of fluorosulfuric acid are assumed and calculations performed to determine the fraction[12] present as fluorosulfuric acid, it is found that the ionization constant must at least be of the order of 100 to account for the fact that no leveling offin the rate was observed. The role of the hydrogen ion as a catalyst is probably two-fold. First, the reduction in charge to form a neutral species (HSO3F) would facilitate nucleophilic attack by water. Second, the attachment of the proton would be expected to occur on the fluoride with a weakening of the sulfur-fluorine bond. This would enhance the ability of hydrofluoric acid (HF) to act as a leaving group. For the rates of the reactions run in sodium hydroxide solutions, an analogous procedure was used, based upon an indicator function for strongly basic media, H~_, given by Yigal [ 13]. This corresponds to a reaction in which a doubly charged anion is formed in the transition state: SOzF- + O H - ---> [HOSO3F2-]. In this case a plot of log kobs. VS. H2_ is a straight line of unit slope over the range of sodium hydroxide concentrations used. In order to obtain H~_ values for this plot it is necessary to assume that ( H 2 - - H _ ) values are the same for sodium hydroxide as those given by Yigal for potassium hydroxide. It is then possible to simply add this difference to the H_ values given for sodium hydroxide to obtain the desired H2- values. These are summarized as follows: [NaOH]g-moles/l. 0.250 H~_ 13.60
0.50 13.95
1.00 14.33
1.50 14.55
2.00 14.81
3.00 15.08
4.00 15.45
5.00 15.80.
This plot is then consistent with the rate determining step given above being the only important one in strongly basic solutions. The rate in concentrated base is thus -d[SOzF-] -- k[SOzF-][OH-]. dt A mechanism which will give this rate law is one which considers the decomposition of fluorosulfate as the displacement of a weak base, fluoride, by the stronger base, hydroxide ion. Data on related compounds support this interpretation. Chlorosulfuric acid (HSOaCI) is rapidly hydrolyzed by water but fluorosulphuric acid[10] is not. Chloride is, of course, a much weaker base than fluoride. Sulphamate may be boiled [9] in neutral or alkaline solution without decomposition. Here, the amide ion (NH2-) is a stronger base than hydroxide or water and is, therefore, not displaced by them. Likewise, the oxygen exchange in sulphate ion 11. J. Barr, R. J. Gillespie and E. A. Robinson, Can.J. Chem. 39, 1266 (1961). 12. H. A. Laitinen, ChemicalAnalysis, p 36. McGraw-Hill, New York (1960). 13. G. Yigal, J. phys. Chem. 71, 1040 (1967).
Kinetics of decomposition of the fluorosulphate ion
1243
[6] is s u p p r e s s e d in basic solutions. T h e e m p t y d-orbitals on the sulphur a t o m can serve as the a c c e p t o r site for the incoming base. T h e reaction steps for this term of the rate law would be SO3F-+ OH- ~ HSO4-+ OH-
HSO4-+
F-
fast ~ H 2 0 + S O a =.
In s u m m a r y , the experimental data are consistent with three processes o v e r the entire range of conditions (1) the attack of S O 3 F - by a proton (2) the attack of S O a F - by a hydroxide ion and (3) the attack of S O 3 F - by a w a t e r molecule. T h e w a t e r reaction is such a slow process that it does not show up at all in more c o n c e n t r a t e d solutions whether they are acidic or basic. F r o m the log kobs. VS. H2_ plot, kn,o can be estimated to be 2.15 × 10 -7 sec -1, in excellent agreement with the value of 2.1 x l0 -7 reported previously [2]. Because of the lack of data to construct H2- scales at t e m p e r a t u r e s other than 25 °, it is not possible to reduce the data at such t e m p e r a t u r e s other than approximately. I f one makes the assumption that H2- values at 25 ° can also be used at other temperatures, it is possible to estimate activation p a r a m e t e r s for these processes. With this assumption, the activation energy for the reaction in b a s e is 20.2 kcal.
Acknowledgements-The financial support of the United States Atomic Energy Commission is gratefully acknowledged. Thanks are due also to Mr. James E. Hix for writing the computer program and Dr. Andrej Kodjak of the Vanderbilt Department of Germanic and Slavic Languages for a translation of Ref. [2].