Mechanism and reaction rate of the Karl-Fischer titration
reaction. Part III. Rotating ringdisk electrode measurements
-comparison with the aqueous system
Citation for published version (APA):
Verhoef, J. C., Kok, W. T., & Barendrecht, E. (1978). Mechanism and reaction rate of the Karl-Fischer titration reaction. Part III. Rotating ring-disk electrode measurements - comparison with the aqueous system. Journal of Electroanalytical Chemistry, 86(2), 407-415. https://doi.org/10.1016/S0022-0728(78)80014-X
DOI:
10.1016/S0022-0728(78)80014-X
Document status and date: Published: 01/01/1978
Document Version:
Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)
Please check the document version of this publication:
• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.
• The final author version and the galley proof are versions of the publication after peer review.
• The final published version features the final layout of the paper including the volume, issue and page numbers.
Link to publication
General rights
Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain
• You may freely distribute the URL identifying the publication in the public portal.
If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement:
www.tue.nl/taverne
Take down policy
If you believe that this document breaches copyright please contact us at: openaccess@tue.nl
providing details and we will investigate your claim.
J. Electroanal. Chem., 86 (1978) 407--415 407 © Elsevier Sequoia S.A., Lausanne -- Printed in The Netherlands
M E C H A N I S M A N D R E A C T I O N R A T E O F T H E K A R L - F I S C H E R T I T R A T I O N R E A C T I O N
P A R T III. R O T A T I N G R I N G - D I S K E L E C T R O D E M E A S U R E M E N T S - - C O M P A R I S O N W I T H T H E A Q U E O U S S Y S T E M
J.C. VERHOEF and W.Th. KOK
Laboratory o f Analytical Chemistry, Free University, de Boelelaan 1083, Amsterdam (The Netherlands)
E. BARENDRECHT
Laboratory of Electrochemistry, University of Technology, P.O. Box 513, Eindhoven (The Netherlands)
(Received 13th December 1976; in revised form 14th March 1977)
ABSTRACT
A platinum disk-platinum ring electrode was used to investigate the oxidation of sulfur dioxide by iodine and triiodide in aqueous solutions. Contrary to methanolic solutions, where the monomethyl sulfite ion is the only oxidizable species, in aqueous solutions both the hydrogen sulfite ion and the sulfite ion can be oxidized. The reaction rate was generally so high, that the method for measurements of homogeneous second order reactions had to be used. At pH values > 5, the reaction proceeded too fast to be measured reliably. In a solution "diluted" with ethanol (50% of weight), however, the reaction rate was within the range where a rotating ring-disk electrode can be applied to measure fast homogeneous reactions. At very low pH values both the first order calculation technique and the second order method could be used. The results with both methods were in fair agreement.
INTRODUCTION
T h e o x i d a t i o n o f a m e t h a n o l i c sulfur d i o x i d e s o l u t i o n b y e l e c t r o l y t i c a l l y g e n e r a t e d iodine a n d t r i o d i d e has b e e n studied b y means o f p o t e n t i o m e t r y [1] a n d b y m e a n s o f a g a l v a n o d y n a m i c t e c h n i q u e f o r t h e m e a s u r e m e n t o f p s e u d o - first o r d e r r e a c t i o n s with t h e r o t a t i n g ring-disk e l e c t r o d e [2]. It was f o u n d t h a t t h e m o n o m e t h y l sulfite ion is t h e oxidizable species. This ion is f o r m e d f r o m m e t h a n o l a n d sulfur d i o x i d e :
SO2 + C H s O H ~ C H s S O ~ + H + (1)
B o t h i o d i n e a n d triiodide can oxidize t h e m o n o m e t h y l sulfite, b u t the r e a c t i o n rate c o n s t a n t o f t h e iodine (k3 ~ 107 12 mo1-2 s - 1 ) is m u c h larger t h a n t h a t o f t h e t r i i o d i d e ion (k 3 ~ 5 0 0 12 mo1-2 s - l ) . The r e a c t i o n is first o r d e r in each o f t h e r e a c t a n t s : C H a S O 3 , H 2 0 a n d I2 ( t o g e t h e r with I 3 ) at relatively small w a t e r c o n c e n t r a t i o n s . When CH20 e x c e e d s 1 M, r e a c t i o n b e c o m e s s e c o n d o r d e r in
408
H 2 0 . This is m o s t p r o b a b l y caused b y t h e f o r m a t i o n o f h y d r o g e n sulfite f r o m sulfur dioxide and water:
SO2 + H20 ~ HSO~- + H ÷ (2)
Then, the h y d r o g e n sulfite ion reacts f u r t h e r with iodine or triiodide and a n o t h e r water molecule.
In this part we have focussed o u r a t t e n t i o n o n the reaction b e t w e e n sulfur d i o x i d e and iodine when t h e water c o n c e n t r a t i o n is very high, viz. in aqueous solutions. T h e reaction rate is n o w much higher than in m e t h a n o l i c solutions. There- fore, we had t o use a calculation t e c h n i q u e f o r the m e a s u r e m e n t o f homogene- ous pseudo-second o r d e r reactions. An i m p o r t a n t difference is t h a t the m o n o - m e t h y l sulfite c a n n o t dissociate, while t h e h y d r o g e n sulfite can:
HS03 ~ H ÷ + SO~- (3)
Therefore, depending on the pH of the solution and the dissociation constants of the sulfurous compounds, the solution will contain sulfur dioxide, hydrogen sulfite or sulfite. The oxidation rates of these compounds with iodine and tri- iodide were investigated.
THEORY OF MEASUREMENT
Basically, the m e a s u r e m e n t o f reaction rates with a rotating ring-disk elec- t r o d e is t h e same for a second o r d e r reaction and f o r a first o r d e r reaction. The main differences exist in the galvanograms obtained and the evaluation o f the results.
As is shown in Part II [2], the typical iR v s . iD curves f o r a first o r d e r reac- tion are straight lines t h r o u g h the origin with a slope Nk, f o r which:
0 < Yk = f(kl/¢O) < No (4)
while t h e typical galvanograms for a second o r d e r reaction are curved. In a t h o r o u g h s t u d y b y Albery et al. [3,4], the m e a s u r e m e n t o f second o r d e r reac- tion rate constants is based on the so-called t i t r a t i o n curves, i.e. galvanograms where t h e reaction rate is very high c o m p a r e d t o t h e diffusion rate. T h e differ- ence b e t w e e n the t i t r a t i o n curves and the e x p e r i m e n t a l iR vs. i D curves enables us t o calculate t h e rate constant. In the case o f a very fast reaction b e t w e e n the iodine and triiodide f o r m e d at t h e disk electrode and t h e sulfurous com- p o u n d s t r a n s p o r t e d f r o m t h e bulk o f t h e solution b y convective diffusion, no iodine and triiodide can e n t e r into the solution, unless the disk c u r r e n t gen- erates a flux o f iodine and triiodide, larger than the t r a n s p o r t limited flux o f sulfurous c o m p o u n d s t o the electrode. Assuming t h a t the diffusion coefficients o f t h e various species involved in the r e a c t i o n are equal, the fluxes o f the t w o reactants (in o u r case, iodine and triiodide and t h e sulfurous c o m p o u n d s , respectively) match, if the disk c u r r e n t equals a distinct value M, where
M = 0.62 7rr 2 n F D 2/3 v - 1 1 6 ¢o 1/2 Coo (5)
The symbols have the same significance as in Part II; co, d e n o t e s the bulk con- c e n t r a t i o n o f t h e sulfurous c o m p o u n d s .
409 iodide can exist, b u t outside this region, only the sulfurous c o m p o u n d s can. The width of the b o u n d a r y between the iodine region and the sulfurous region depends on the reaction rate: the slower the reaction, the more diffuse the boundary.
The "middle" of the b o u n d a r y (where the concentrations of the iodine and triiodide and of the sulfurous c o m p o u n d s are equal) is just on the inside edge of the ring if i D is set on a critical value b y adjusting so that:
i n , k = M / { 1 -- F(a)} (6) where a = ( r 2 / r l ) 3 -- 1 (7) and x/3 (1 + al/a)s 3 ! /20~ 1/3 -- 1~ 1 F(a) = ~ - - a r c t a n ] + (8) ~ - n In l + a 31r \ ~ 3 4
For a very fast reaction, no iodine and triiodide can reach the ring and the ring current will be zero, as long as iD ~< iD$. If the reaction is not very fast, how- ever, some iodine and triiodide can penetrate into the sulfurous region, so that at iD = iD,k, some iodine and triiodide penetrate across the inner edge of the ring. Then, there will be a ring current iR.k:
lia,k l = 0.21 ~rr~nFDv -112 co s12 k 2 1 (9) All'we have to do, is to find the critical disk current and to measure the critical ring current at that point, in order to obtain the second order rate constant, k2.
One also can make use of the critical collection efficiency, Nk. Dropping the absolute value symbols for the sake of convenience, we can calculate with (5), (6) and (9)
Nk - !e,k _ 0.34 r ~ D 1Is {1 -- F ( a ) } w
Zv~ r~ v 1/s k2 c ~ ( 1 0 )
At high disk currents, the galvanogram approaches the a s y m p t o t e that can be described with
iR = NOiD -- ~2/S M (11)
where
= (rs/r1)3 _ ( r 2 / r l ) s (12)
An extrapolation of the ia v s . i D curve to iR = 0, therefore, should give the
value of M, but, especially at high rotation speeds or small reaction rate con- stants, the extrapolation is very unreliable. Instead, one could use (5) to calcu- late M, b u t c= may differ at the end of a series of experiments from the initial value. Moreover, D stands for the diffusion coefficient of all species involved in the reaction, and some error is made if the diffusion coefficient of the triiodide ion is used. Therefore, it is usually preferable to follow a somewhat more ela- borate procedure to find M.
It is possible to calculate the titration curve. If the disk current is such, that the reaction b o u n d a r y is placed on the ring at rj, where
4 1 0
r2 ~< rj ~< r 3 (13)
then, o n e can define a p a r a m e t e r flj :
~j = (rj/rl) 3 -- (r2/rl) 3 (14)
F o r rj = r2, ~j = 0 and for rj = r3, ~j = ~, With this ~j c o r r e s p o n d s a kinetic col- lection factor, Nj:
Nj = iR,j/iD,j
= 1 - - F(a/~j) -- (1 + a ) ( 1 + a + ~j)-- 1/3X [1 -- F { ( 1 + a + f l j ) . a/,Gj} ] (15)
and a disk current, given b y :
(iDj/M) -1 = 1 -- F ( a ) - - ~ 1 / 3 ( 1 + a + f l j ) - - l / 3
X [ 1 - - F { ( 1 + ~ + ~ i ) " {2/~j}] (16)
E q u a t i o n s (15) and (16) describe a theoretical titration curve for a particular e l e c t r o d e . A l t h o u g h it it n o t possible to eliminate fli f r o m (15) and (16) t o find
iDj/M
as a f u n c t i o n o f Ni, one can easily obtain a graphical relationship b y cal- culatingiD,j/M
and N i for several/~j values (0 < flj < fl) and plotting the results (Fig. 1). T o o b t a i n M, we calculate the N i values (0 < Nj ~< No) for several p o i n t s o f an e x p e r i m e n t a l galvanogram. Then, we p l o t t h e c o r r e s p o n d i n g e x p e r i m e n t a l iDj values against the theoretical iD,i/M values t h a t we find with the aid o f Fig. 1. A line t h r o u g h the origin and the p o i n t s o f the p l o t has a slope M. A t high r o t a t i o n speeds and l o w rate constants, the d i f f e r e n c e b e t w e e n t h e t i t r a t i o n curve and the e x p e r i m e n t a l galvanogram is the largest and there- fore the points near the origin diverge f r o m a straight line.10 i[ FS 6
T
2C / / • / 1 6 / ././ £ o 4 i J ~ i i io o~o o~o o~o o ~ ' ~
- N j :~ w C ~ / ' l O ~ m o l " l rps
F i g . 1. C a l c u l a t e d d e p e n d e n c e o f iD,i/M o n N i f o r e l e c t r o d e n o . 1.
Fig. 2. D e p e n d e n c e o f t h e k i n e t i c c o l l e c t i o n f a c t o r , N k , o n t h e r a t i o ¢o/c~ ( e q n . 1 0 ) , w a t e r -
411
If M is found, one can calculte c~ with (5), if D and v are known. This saves a titration afterwards. One also can find D if c~ is known. The critical disk cur- rent can now be calculated with (6). Like ~, the factor 1 -- F(~) is an electrode parameter and is easily calculated. Some approximations, implied in the theory, demand t h a t certain conditions must be met. For usual values of D and ~, it is necessary that
w/k2c~
< < 5 (17)and
(r 3 - - r2)/r 2 > O.06(W/k2c~) 315 ( 1 8 )
(A more precise formulation of these conditions can be found in the literature [ 5 ] .) These conditions mean, t h a t the rate constant of the reaction must n o t be too low and t h a t the width of the ring must be large. These demands are quite opposite to those for a first order method. Figure 2 illustrates the validity of eqn. (10). At higher
w/coo
values the condition of eqn. (17) is broken.E X P E R I M E N T A L
Distilled water and ethanol {Baker, A.R.) were used as solvents. The same reagents as described in the previous parts were used; for buffering also use was made of succinic acid (Merck, P.A.), malonic acid (Merck, P.A.), a m m o n i u m hydroxide (Baker, A.R.) and a m m o n i u m chloride (Baker, A.R.).
The same procedure is followed and the same equipment is used as is
described in Part II. Only another electrode with a wide ring was needed for the second order method. The characteristics of the electrode used are given in Table 1. All experiments were performed at 25 + 0.3°C.
R E S U L T S A N D D I S C U S S I O N
We have tested our equipment by measuring the bromination of allyl alcohol in an aqueous solution. The rate constant of this reaction has been measured by Albery et al. [4], using the ring-disk electrode and by Bell and Atkinson [6],
T A B L E 1
Characteristics o f t h e electrodes no. 1 and 2
Characteristics 1 2 r l ] m m 2.017 2.011 r 2 / m m 2.147 2.100 r 3 / m m 3.028 2.201 0.2061 0.1387 /~ 2.1773 0.1723 F(~) 0.4659 0.4143 N 0 ( t h e o r . ) 0.4634 0.1595 N o ( e x p . ) a 0.465 0.157
412 T A B L E 2 V a l u e s o f k 2 for t h e b r o m i n a t i o n o f allyl a l c o h o l at d i f f e r e n t b r o m i d e c o n c e n t r a t i o n s N u m b e r o f e x p e r i m e n t s in p a r e n t h e s e s 10 - 5 X
k2/1
tool - 1 s - 1 CBr-- = 0.1 M CBr-- = 0.2 M CBr-- = 0.3 M CBr-- = 0.4 M Our e x p e r i m e n t s 3.06 ( 8 ) 1.92 ( 7 ) 1.39 ( 4 ) 1.42 ( 8 ) A l b e r y e t al. [ 4 ] 2.76 ( 6 2 ) 1.95 ( 3 2 ) 1.62 ( 2 8 ) 1.42 ( 2 2 ) Bell and A t k i n s o n [ 6 ] 3.09 2.26 - - 1.51using low-concentration potentiometry. As is shown in Table 2, the results o f our measurements are in fair agreement with those o f the other investigators. In Fig. 3, a typical galvanogram is shown for a second order reaction. The asymp- tote is drawn according to eqn. (11), after M has been calculated with the procedure outlined above. It is clear, that simply drawing a tangent to the gal- vanogram would have given an erroneous result. Usually, a low rotation speed is used to find M, because in that case, according t o (9), the critical ring current is l o w and there is little difference between the (experimental) galvanogram and the (theoretical) titration curve. For the calculation o f the rate constant, how- ever, it is advantageous to use the higher rotation speeds and to expand the ring current scale (Fig. 4).
20C 16C ~ 12C 4C 2O 15 l j 0.4 0.6 0.8 0 0.2 0 Q2 0.4 . iD/mA ~ i o / m A 40 80 8 0 r p $ I
I
Fig. 3. T y p i c a l s e c o n d order galvanogram. E l e c t r o d e no. 1 in w a t e r - e t h a n o l ( 5 0 - - 5 0 ) , co = 20
rps, c I - = 0.5 M, Cso 2 ( t o t a l ) = 1.58 raM, p H = 2.1, E R = - - 0 . 2 V vs. SCE.
413 ..¢ A
f .
I o G Jf
l v b ,,, pHFig. 5. Reaction rate constant as a function of pH. (a) 0.5 M NaI in water; (b) 0.5 M NaI in the water-ethanol mixture.
We can obtain the rate constant f r o m the critical ring c u r r e n t with (9) or f r o m the collection efficiency with (10), if we know v and D. The viscosity coefficient was measured with an Ubbelohde viscosimeter; for an aqueous solu- tion o f 0.5 M NaI, we f o u n d u = 8.7 X 10 -7 m 2 s - i : The diffusion coefficient was f o u n d , using eqn. (5). For t h a t purpose, M was calculated with the proce- dure described above. Before and after the experiment, co. was determined b y an iodometric titration and the mean value was used for the calculations. We f o u n d for D a value o f 9.8 X 10 - i ° m s s - i . The pH d e p e n d e n c e o f the reaction rate in water is shown in Fig. 5a. The points in this Figure represent the mean o f several measurements with different sulfur dioxide concentrations at a given pH value. Up t o pH = 1.7, the logarithm o f the reaction rate c o n s t a n t increases linearly with the pH. In the range from pH = 2.3 to pH = 5.2, the rate constant does n o t vary. At c r - = 0.5 mol 1 - i , we f o u n d log k s = 7.21 + 0.08. At pH values larger than 5.2, the reaction rate increases again, b u t the reaction pro- ceeds t h e n t o o fast for accurate measuring.
As in methanolic solvents, it appears t h a t n o t sulfur dioxide itself b u t a sul- furous base is oxidized. In water, this is the h y d r o g e n sulfite ion. The first dis- sociation constant o f sulfurous acid (pKia = 1.8 [7] ) corresponds very well with the inflexion p o i n t o f the log k s v s . pH curve. The increase of the reaction rate at pH values larger than 5.2 must be attributed to the f o r m a t i o n o f the sulfite ion ( p K ~ = 6.9 [7]), assuming t h a t it reacts faster than the h y d r o g e n sulfite ion.
To investigate the reaction with the sulfite ion, we have tried to lower the reaction rate b y " d i l u t i n g " the water with ethanol (50% o f weight). We used e t h a n o l instead o f m e t h a n o l because more data for ethanol-water mixtures are known. Moreover, this replacement does n o t alter significantly the relevant properties o f the system.
The reaction rate decreased b y a b o u t two orders o f magnitude, so that the oxidation o f t h e sulfite ion could be measured with the rotating ring-disk elec- trode. The viscosity coefficient and the diffusion coefficient were measured as with water as solvent: v = 2.5 X 10 --s m s s - i and D = 4.1 X 10 - i ° m 2 s - 1 . The dissociation constants o f sulfurous acid in the water-ethanol m i x t u r e (that also contained 0.5 M sodium iodide) were determined f r o m a titration with sodium
414 "T d] 0 E o )< aid j • p H = l O o ~ ~ ~ • cI:" / I tool-' Fig. 6. R e a c t i o n r a t e c o n s t a n t in w a t e r - e t h a n o l ( 5 0 - - 5 0 ) as a f u n c t i o n o f t h e i o d i d e c o n c e n - t r a t i o n at p H = 1.0 a n d p H = 3.3. h y d r o x i d e : PKla = 2.3 + 0.1 and PK2~ = 7.0 + 0.2.
The glass electrode-pH meter combination was calibrated with a 0.01 M per- chloric acid solution and a 0.5 M acetic acid +0.5 M sodium acetate solution. The dissociation constant of the acetic acid was taken from the literature (5.84
[8]). In the pH range from 2.3 to a b o u t 5, the prevalent sulfurous species is the hydrogen sulfite ion. The rate constant of its oxidation in a 0.5 M iodide solu- tion is given by log k2 = 5.35 + 0.08 (Fig. 5b). At pH values larger t h a n 7.5 the prevalent sulfurous c o m p o u n d is the sulfite ion, for which we f o u n d log k2 = 6.40 + 0.18.
The reaction rate is d e p e n d e n t on the iodide concentration. In Fig. 6 this dependence is shown for the water-ethanol mixture. As has been pointed o u t in the previous parts, the intercept of the k2 vs.
1/cr--
curve equals ki~-, the rate constant for the triiodide ion, while the slope of the curve equalski2/Ks,
the rate c o n s t a n t for iodine, divided by the stability constant of the triiodide ion. At pH = 3.3, where practically all the sulfur dioxide is converted into hydrogen sulfite, we f o u n d :kT~- = (2.09 + 0.15) × 1051 mo1-1 s -1
and
ki2/Ks =
(2.44 + 0.25) X 104 s -1We have measured K s in the water-ethanol mixture, following the voltammetric m e t h o d of Guidelli and Piccardi [9], and f o u n d :
K s = (7.10 + 0.50) X 103 1 mo1-1
so t h a t
ki2 = (1.73 + 0.29) X 108 1 mo1-1 s -1
It has n o t been possible to measure the dependence of the rate constant on the iodide concentration at pH > 6 , because at decreasing iodide concentrations the reaction rate increases so much, t h a t it c a n n o t any longer be measured with sufficient reliability.
415
to measure its rate with the first order m e t h o d as described in Part II, as well as with the second order method.
A thin gap-thin electrode had to be used for the (pseudo-) first order meth- od. The calculated ~ vs. Nk plot for this electrode is shown in Part II (electrode no. 2).
With the first order method, we found at pH = 1 2 and c i - = 0.5 M:
k2 = (1.71 + 0.26) × 104 1 mo1-1 s -1
The result of the second order m e t h o d was: k2 = (1.67 + 0.25) × 104 1 mo1-1 s -1
This close agreement is a good indication for the reliability of both methods. In Part II, it was shown, t h a t with methanol as solvent and a t low pH values, the formation of the relatively weak complex SO2I- had to be accounted for. The stability constant of this complex in water (0.38 1 mo1-1 [10]) and in the water-ethanol mixture (ca. 0.2 l mo1-1, measured spectroscopically in the way described in Part II) is so low, t h a t no corrections had to be made.
C O N C L U S I O N
In aqueous solutions, n o t sulfur dioxide, but the hydrogen sulfite ion and the sulfite ion are oxidized by triiodide and iodine, the sulfite ion having a higher rate constant than the hydrogen sulfite ion. Iodine reacts much faster than triiodide. So, there is a fair similarity between the reactions in aqueous solutions and in methanol.
The second order ring-disk m e t h o d extends the range of rate constants t h a t can be measured with the first order technique.
Employing both methods, it was possible with our system to measure a con- tinuous range of second order rate constants from less than 10 1 mo1-1 s -1 up to 3 X 107 1 mo1-1 s -1, using the same equipment. Only the electrodes for a first order m e t h o d and a second order m e t h o d are different.
REFERENCES
1 J.C. Verhoef and E. Barendrecht, J. Electroanal. Chem., 71 (1975) 305. 2 J.C. Verhoef and E. Barendrecht, J. Electroanal. Chem., 75 (1977) 705.
3 W.J. Albery, S. Bruckenstein and D.C. J o h n s o n , Trans. Faraday Soc., 62 (1966) 1938. 4 W.J. Albery, M.L. Hitchman and J. Ulstrup, Trans. Faraday Soc., 65 (1969) 1101.
5 W.J. Albery and M.L. H i t c h m a n , Ring-Disc Electrodes, Oxford University Press, London, 1971. 6 R.P. Bell and J.R. A t k i n s o n , J. Chem. Soc. (1963) 3260.
7 Handbook of Chemistry and Physics, C.R.C. Press, Cleveland, Ohio, 53th edn., 1972. 8 E. Grunwald and B.J. Berkowitz, J. Amer. Chem. Soc., 73 (1951) 4939.
9 R. Guidelli and G. Piccardi, Electrochim. Acta, 12 (1967) 1085. 10 S.B. Salama and S. Wazif, J. Chem. Soc., Dalton Trans., (1971) 151.
