Mechanism and reaction rate of the Karl-Fischer titration reaction. Part IV. First and second order catalytic currents at a rotating disk electrode

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Mechanism and reaction rate of the Karl-Fischer titration

reaction. Part IV. First and second order catalytic currents at a

rotating disk electrode

Citation for published version (APA):

Verhoef, J. C., Cofino, W. P., & Barendrecht, E. (1978). Mechanism and reaction rate of the Karl-Fischer titration reaction. Part IV. First and second order catalytic currents at a rotating disk electrode. Journal of

Electroanalytical Chemistry, 93(1), 75-80. https://doi.org/10.1016/S0022-0728(78)80240-X

DOI:

10.1016/S0022-0728(78)80240-X Document status and date: Published: 01/01/1978

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J. Electroanal. Chem., 93 (1978) 75--80 75 © Elsevier Sequoia S.A., Lausanne - - Printed in The Netherlands

Short c o m m u n i c a t i o n

MECHANISM AND R E A C T I O N R A T E O F THE 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 IV. F I R S T AND SECOND O R D E R CATALYTIC C U R R E N T S AT A R O T A T I N G DISK E L E C T R O D E

J.C. V E R H O E F * and W.P. COFINO

Laboratory of Analytical Chemistry, Free University, De Boelelaan 1083, Amsterdam (The Netherlands)

E. BARENDRECHT

Laboratory of Electrochemistry, University o f Technology, P.O. Box 513, Eindhoven (The Netherlands)

(Received 16th May 1977; in revised form 9th F e b r u a r y 1978)

The oxidation of the m o n o m e t h y l sulfite ion b y iodine and triiodide (which is the basic reaction in a Karl-Fischer titration) has been investigated with a potentiometric technique [ 1] and with the rotating ring<lisk electrode [ 2] in Parts I and II, respectively. Both m e t h o d s d e m a n d a rather high iodide concentration. In the potentiometric m e t h o d , the potential o f the indicator electrode must be only a function o f the triiodide concentration and therefore the iodide concentration must remain constant. In the ring-disk electrode m e t h o d , the current through the disk electrode must only be controlled b y the galvanostat and m a y n o t be limited b y diffusion phenomena.

No such d e m a n d exists for the m e a s u r e m e n t o f limiting currents at a rotating disk electrode; on the contrary, it is necessary to have a small iodide concentration. As has been pointed o u t in Part I, the overall third order rate constant, k3, is a function o f the iodide concentration:

k 3 = (k3,i~-" K s c I _ + k s , 1 2 ) / ( 1 + K s c I _ ) ( 1 )

where k 3 . _ _• _. _{, 1 3} and k3,i2 are the individual third order rate constants for triiodide and lodme, respectively, and Ks is the stability constant of the triiodide ion [3]:

Ks = cig/ci-"

ci2 = 2 X 104 1 tool -1 (2) Because o f the small iodide concentration used, the term

Ksc~-

will be in the order o f one and the simplification t h a t led to eqn. (28) of Part I is n o t allowed. However, k3,x2 is m o r e than f o u r orders o f magnitude larger than k3 ig [the average values from (1) and (2) are: 8 X 106 12 mo1-2 s - 1 and 5 X 1 0 ~ 12 mo1-2 s -1, respectively], so that, as long as c i - is relatively small, the

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76

therm k3.i~ • Ksc I_ is negligible with respect to k3,i2 and we m a y write:

k3 ~ ks,12/(1 + Ksci-) (3)

We e x p e c t therefore rather high values o f the overall third order rate constant, which are virtually only due to the contribution of the rate constant o f iodine.

The m e t h o d for measuring the rate constant of the reaction o f iodine with the m e t h y l sulfite ion:

(electrode) 2 I - - * I2 + 2 e - (4)

(solution) I2 + CHaSO~ -~ 2 I - + products (5)

is that developed for catalytic currents. The t h e o r y for first order catalytic currents at a rotating disk-electrode b y Levich [4] and Hale [5] shows, that a very good approximation o f the exact solution for

q = ik/i d (6)

(i.e. the ratio o f the catalytic current in the presence of methyl sulfite and the diffusion current in the absence of it) is given b y

q = x/~/tanh x/~ (7)

with

= 2.60 (v/D) 1Is k l / ~ (8)

i.e. the dimensionless pseudo-first order rate constant used in Part II. The relative a m o u n t of methyl sulfite c o n s u m e d near the electrode determines whether a pseudo-first order or a second order calculation must be applied. It can be shown [6] that this a m o u n t depends on the relative magnitude o f the catalytic current, q, and the ratio i o d i d e : m e t h y l sulfite in the bulk of the solution:

0 ~ ~_

CRSo~/CRso. ~ 1 - - p ( q - - 1) (9)

where

p = 0.5 c~_/C~so_ ~ (10)

The coefficient 0.5 in eqn. (10) stems from the coefficient 2 in eqns. (4) and (5); the superscripts 0 and ~o denote, respectively, the electrode surface and the bulk o f the solution.

It is possible [6] to obtain a relation

q = f(k, p ) (11)

b y means o f series expansion of the differential equations o f the catalytic sys- tem. We prefer, however, the digital simulation technique as described b y Feld- berg [7]. The results o f applying this technique are shown in Fig. 1.

F o r p = 0 there is an infinite excess of methyl sulfite and the catalytic reaction is first order. The results o f the digital simulation for this case are equal to those obtained b y Hale [ 5].

EXPERIMENTAL

The reagents used and the procedure applied in this investigation were grosso m o d o the same as those m e n t i o n e d in the previous Parts. The disk electrode

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~.0 3.8 77 36 it Q2 0 -2 -1 0 1 2 3 log ),. ~, Fig. 1. D e p e n d e n c e o f q o n ~ a n d p , c a l c u l a t e d w i t h t h e m e t h o d o f digital s i m u l a t i o n .

used was actually the disk o f the ring-disk electrode no. 2 in Part II (rl = 2.011 mm); the ring was n o t connected. The electrode was controlled by a Tacussel PItT 30-01 p o t e n t i o s t a t with a UAP 4 pulse u n i t t h a t contained the potential control and the current m e a s u r e m e n t amplifiers. More details are given in ref. 6.

R E S U L T S A N D D I S C U S S I O N

The usual way to measure rate constants of h o m o g e n e o u s reactions by means of catalytic currents is to select such conditions, t h a t a pseudo-first order regime is established. In the present case, this means t h a t the concentration of water and sulfur dioxide must be m u c h larger t h a n the concentration of iodide. A relatively large water c o n c e n t r a t i o n causes no problem, as long as it becomes n o t t o o large (cf. Part II). A m o d e r a t e l y large sulfur dioxide concentration, however, deforms the voltammograms [6], so t h a t it becomes very dif- ficult to obtain a useful limiting current plateau, especially at pH values larger t h a n pKa, where m o s t of the sulfur dioxide is converted into the m e t h y l sulfite ion [1]

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7 8 80 c 6C "~'4C 0 I 2 0 ~ o o 05 i 1.5 ~, CSO 2 /10 ,3 tool I -I

Fig. 2. D e p e n d e n c e o f t h e rate c o n s t a n t o n t h e sulfur d i o x i d e c o n c e n t r a t i o n , c~-- = 2 x

1 0 - 4 M , co = 2 5 r p s . ( a ) p H = 2 . 6 , C H 2 0 = 0 . 2 2 5 M ; ( b ) p H = 4 . 1 , C H 2 0 = 0 . 1 1 1 M ; ( c ) p H = 7 . 1 , C H 2 0 = 0 . 0 7 5 M.

At l o w pH values, however, a large excess o f sulfur dioxide can be used {e.g. a fiftyfold excess at pH = 2.6), so that t h e n first order measurements can be made.

The d e p e n d e n c e o f the reaction rate o n the (formal) sulfur d i o x i d e concen- tration and o n the water c o n c e n t r a t i o n is s h o w n in Figs. 2 and 3, respectively. Clearly, the reaction is first order, b o t h in sulfur d i o x i d e and in water. At high currents (high reaction rates), some passivation o f the electrode occurs, so that t h e reaction rate and the reagent c o n c e n t r a t i o n are n o longer proportional.

b 0 01 f c I d2 d3 CH2 0 / m o I F ~ Oh Fig. 3. D e p e n d e n c e o f t h e rate c o n s t a n t o n t h e w a t e r c o n c e n t r a t i o n , c~-- = 2 x 1 0 - 4 M , c ~ o 2 = 1 x 1 0 --4 M , ¢o = 2 5 r p s . ( a ) p H = 4 . 1 , ( b ) p H = 7 . 2 .

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79 2

T

3 I i i I i t i i I i 0 2 ~ 6 8 10 pH

Fig. 4. Dependence of the third order rate constant on the pH, at c I - = 2 x 10 - 4 M. T h e t h i r d o r d e r rate c o n s t a n t s h o w s a s i m i l a r d e p e n d e n c e o n t h e p H ( F i g . 4 )

as in the previous parts, indicating t h a t n o t sulfur dioxide b u t the m e t h y l sulfite ion is the oxidizable species. The points in Fig. 4 are the mean values o f several measurements with different r o t a t i o n speeds and concentrations of water and sulfur dioxide. The average value o f the rate constant is (2.6 -+ 0.2) X 106 12 mo1-2 s -1, at a bulk concentration o f iodide o f 2 X 10 --4 M. At the limiting current the iodide concentration varies from zero near the electrode to the bulk value at some distance from the electrode. It seems reasonable to estimate an average (effective) iodide concentration of approximately half the bulk concentration, and with this effective iodide concentration we calculate with eqn. (3) the third order rate constant for iodine:

k 3 , i 2 = 7.8 × 1 0 6 12 mo1-2 s -1.

This value agrees fairly well with the values previously f o u n d (8.8 × 106 in Part I, 7.3 X 106 in Part II). It is n o t possible with the present m e t h o d to measure any c o n t r i b u t i o n to the reaction rate by triiodide. The only effect of the f o r m a t i o n o f triiodide is t h a t some of the iodine is taken away. In the previous parts, triiodide was the p r e d o m i n a n t species, but, because o f the large rate constant of iodine, the presence of even a small a m o u n t of this species had a marked effect on the overall rate constant, so t h a t b o t h the individual rate constants of iodine and triiodide could be determined.

We have tested the influence o f pyridine on the reaction rate. With t h e pH fixed at a value of pH = 7, addition of pyridine (even to a concentration o f 1 M, i.e. a fivethousandfold excess over iodide) does not, within experimental error, affect the reaction rate. This is in agreement with previous observations. ACKNOWLEDGEMENT

Mr. C. Kaas is gratefully acknowledged for carying o u t m a n y of the experi- ments.

REFERENCES

1 J.C. Verhoef and E. Barendrecht, J. Electroanal. Chem., 71 ( 1 9 7 6 ) 305. 2 J.C. V e r h o e f a n d E. Barendrecht, J. Eleetroanal. Chem., 75 ( 1 9 7 7 ) 705.

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3 J.C. Verhoef and E. Barendrecht, E l e c t r o c h i m . Acta, in press.

4 V.G. Levich, P h y s i c o c h e m i e a l H y d r o d y n a m i c s , Prentice-Hall, E n g l e w o o d Cliffs, N.J., 1962. 5 J.M. Hale, J. Electroanal. Chem., 8 ( 1 9 6 4 ) 332.

6 J.C. Verhoef, Thesis, Vrije Universiteit, A m s t e r d a m , 1977, Ch. 6.

7 S.W. Feldberg, in A.J. Bard (ed.), E l e c t r o a n a l y t i c a l Chemistry, Vol. 3, Marcel Dekker, New York, 1969, p. 199.