Mechanism and reaction rate of the Karl-Fischer titration
reaction. Part I. Potentiometric measurements
Citation for published version (APA):
Verhoef, J. C., & Barendrecht, E. (1976). Mechanism and reaction rate of the Karl-Fischer titration reaction. Part I. Potentiometric measurements. Journal of Electroanalytical Chemistry, 71(3), 305-315.
https://doi.org/10.1016/S0022-0728(76)80017-4
DOI:
10.1016/S0022-0728(76)80017-4
Document status and date: Published: 01/01/1976 Document Version:
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J Electroanal Chem., 71 ( 1 9 7 6 ) 3 0 5 - - 3 1 5 305 © Elsevier S e q u o i a S.A., Lausanne - - Printed in T h e N e t h e r l a n d s
MECHANISM A N D REACTION RATE OF THE KARL-FISCHER TITRATION REACTION
PART I. POTENTIOMETRIC M E A S U R E M E N T S
J . C V E R H O E F
Laboratory of Analytical Chem~try, Free Unwersity, de Boelelaan 1085, Amsterdam (The Netherlands)
E. B A R E N D R E C H T
Laboratory of Electrochemistry, Technzeal University, P.O. Box 513, Eindhoven (The Netherlands)
( R e c e i v e d 17th N o v e m b e r 1975)
A B S T R A C T
T h e r e a c t i o n rate o f t h e c o u l o m e t r i c variant o f t h e Karl-Fischer t i t r a t i o n r e a c t i o n (in which 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 t r i i o d i d e is used as o x i d a n t instead o f iodine) has b e e n measured in m e t h a n o l . T h e r e a c t i o n is first o r d e r in water, sulfur d i o x i d e and t r i i o d i d e , respectively. F o r p H < 5 t h e r e a c t i o n rate c o n s t a n t decreases l o g a r i t h m i c a l l y w i t h decreas- ing pH. A d d i t i o n o f p y r i d i n e solely influences t h e p H ( b y fixing it t o a value o f a b o u t 6) and has no direct i n f l u e n c e on t h e r e a c t i o n rate. A linear r e l a t i o n exists b e t w e e n t h e reac- tion rate c o n s t a n t and t h e reciprocal value o f t h e i o d i d e c o n c e n t r a t i o n , f r o m w h i c h we can calculate t h e individual r e a c t i o n rates for t h e o x i d a t i o n by i o d i n e and triiodide, re- spectively. While t h e r e a c t i o n rate c o n s t a n t for t r i i o d i d e is relatively small (k 3 ~ 350 12 tool - 2 s--l), t h e r e a c t i o n rate c o n s t a n t for i o d i n e is m u c h larger (k 3 ~ 1.5 x 107 12 tool - 2 s-~).
I N T R O D U C T I O N
A m o n g the many m e t h o d s for the determination of water that are available [1] the titrimetric m e t h o d as introduced b y Karl Fischer [2] in 1 9 3 5 has sur- passed all others in simplicity and applicability. Although the titration accord- ing to Karl Fischer is used n o w a d a y s as a routine determination, one still has not succeeded to unravel completely the reaction mechanism [3--7].
The mechanism that Fischer originally p r o p o s e d stems from the benzene ex- periments, for in his publication he assumes that one mole o f iodine is equiva- lent to t w o moles o f water:
306
Later investigations by Mitchell and Smith [ 3] showed t h a t in alcoholic solu- tions one mole of iodine is equivalent to one mole of water. They proposed the following two-step overall mechanism
P y ' i 2 "e PF.SO 2 + I ~ + H20 --~ 2 I ~ ' H I + (2)
/!o,
(3)
G
N\ + CHHOHIn the second step the pyridine sulfu~rioxide is solvolysed by methanol (that must be present in a very large excess over water, otherwise this too will so]vo- lyse the pyfidine sulfurtnoxide).
The vast majority of publications [8--18] on the Karl-Fischer reagent deals with technical problems of handling and keeping the reagent, with various ap-
plications, with possible substitutes or alterations of the reagent and with mea-
suring techniques. Little has been published on the mechanism of t h e reaction. Since the investigations of Mitchell and Smith some authors tried to investigate the possible intermediates and especially the role of pyridine. To our knowl- edge, no publications so far have considered the role of the pH in t h e reaction mechanism.
T H E O R Y
To measure the reaction rate of the titration reaction it is most convenient to m o n i t o r the triiodide concentration. In a buffered solution with a relatively large excess of water, sulfur dioxide and iodide, only the triiodide concentra- tion will vary. If we assume the reaction to be first order in triiodide, the de- crease in the triiodide c o n c e n t r a t i o n per unit o f time is proportional to its instantaneous c o n c e n t r a t i o n (concentrations are used instead of activities t h r o u g h o u t ) :
dcr3 ~dr = - - k 1 ci~ (4)
S o
In ci~ = In c°- 3 - - k i t
(5)
where ci~, kl and c°~ are, respectively, the actual triiodide concentration, the
3 . . . .
pseudo-first order reaction rate constant and the mlhal truodlde c o n c e n t r a h o n . According to Nernst's law, the potential of an inert electrode in a solution of iodide and triiodide is given by:
E = E °' + ( R T / 2 F ) l n ( c r a / ( c r ) 3) + Ej (6) where E 0, is the formal standard redox potential and Ej the j u n c t i o n potential.
307
When the iodide concentration is relatively large, one can write instead of (6):
E = E °'' + ( R T / 2 F ) In ci~ (7)
where
E °'' = E °' + Ej ~ ( 3 R T / 2 F ) In c F F r o m (5) and (7) follows:
E = E °'' + ( R T / 2 F ) In cO - - ( R T / 2 F ) k i t (8) A plot of E vs. t gives a straight line with a slope
(dE/dt) = - - ( R T / 2 F ) k l (9)
and an intercept
Et=o = E °'' + ( R T / 2 F ) In cO- 3 (10)
Cedergren [6] has shown that a platinum electrode can be used successfully as a monitoring electrode for the triiodide concentration, but he has n o t taken advantage o f the logarithmic characteristic o f t h e electrode. This, indeed, makes it possible to obtain directly the reaction rate c o n s t a n t and obviates the tedious way o f first making a calibration curve. F r o m (9) it follows that it is n o t necessary to k n o w the initial triiodide concentration, c °.
If the sulfur dioxide concentration is n o t relatively large with respect to the triiodide concentration, t h e reaction becomes pseudo-second order (as- suming that the reaction is first order both in I~- and SO2). Then:
dci~ ~dr = --k2Cso2Ci§ (11)
with
d c ~ / d t = d c s o J d t So
In ci~ = In(c°Jc°02) + In Cso 2 + (c~ -c°02)k2t (12)
where c~ and c o so2 are the initial triiodide and sulfur dioxide concentrations,
respeCtively.
Ifc°o2 >> cO, t h e n Cso2 ~ C°o2 and (12) simplifies to (5), with k l = C°o2k2.
Combination J f (7) and (12) gives:
R T . cO R T R T
+ ~ - In ( c ~ - - C°o2 ) h 2 t (13)
3 0 8
The tangent in any p o i n t o f the
E--t
curve has a slope:dE/dt = --(RT/2F)(c°o: - - c ~ + cI~ )k2
(14)that varies with the triiodide concentration and therefore with time. However, the initial slope has a value
(dE/dr)0
= --(RT/2F)c°o2k2
(15)that is equal to the slope in the first order case, with kl =
C°o~k2.
In the case that the water concentration t o o is small, the reaction is third order (assuming that the reaction is first order in H 2 0 as well). Then, one can derive, that the initial slope o f the
E--t
curve has the value(16)
(dE/dt)o
= --( R T/2F ) c°o2 C°2ok 3
This result is the same as (9) with:
0 0
k l = Cs02 CH20 k 3 (17)
At 25°C the factor
( R T / 2 F )
equals 12.85 mV. The (third order) reaction rateconstant, ks, is obtained b y dividing the experimentally f o u n d initial slope of
__ 0 0
the E--t
curve by a factor 12.85Cso2CH:o.E X P E R I M E N T A L
Apparatus
The experiments have been carried o u t at 25 + 0.5°C in a cell as shown in Fig. 1. The main c o m p a r t m e n t (35 ml) contained the generator electrode (anode) and the indicator electrode. The c o u n t e r electrode (cathode) compart- m e n t (13 ml) and the reference electrode c o m p a r t m e n t (9 ml) were c o n n e c t e d to the main c o m p a r t m e n t b y means of glass frits. The experiments were carried o u t in a glove b o x (Mecaplex, model GB 3 1 1 1 / 1 ) with nitrogen c o n t i n u o u s l y p u m p e d through (via silica gel a n d 3 A molecular sieve filters). Small a m o u n t s of triiodide were generated b y a Delta Elektronika current source, model CST 100 (max. capacity 100 mA at 45 V). The potential of the indicator elec- trode vs. the reference electrode was measured with a PAR, model 135, elec- t r o m e t e r and recorded on a Kipp, model BD8, fiat bed recorder. The charge through the cell was measured with a Wenking current integrator, m o d e l SSI 70. The pH of the solution was measured with a Metrohm c o m b i n e d glass elec- trode and a Philips digital p H meter, model PW 9408.
Reagents
All methanol used was Baker analytical grade, dried by distillation after re- fhLxing with magnesium. S o d i u m iodide (Merck or Baker, A.R.) and sodium
10 ) k
I
t 309 6 1Fig. 1. Coulometric cell. (1) Pt gauze generator electrode, 4 cm2; (2) Pt indicator electrode; (3, 4) salt bridge and saturated calomel reference electrode in methanol; (5) Pt wire counter electrode; (6) P3 glass frits; (7) stirring magnet; (8) stop cocks; (9) t h e r m o m e t e r ; (10) vent. acetate (Baker, A.R., anhydrous) were dried at ca. 150°C for at least 24 h. Sulfur dioxide (Matheson, anhydrous gas) was used without further purifica- tion. Dried pyridine (Merck), tetramethyl ammonium hydroxide (EGA, ca. 3 M solution in methanol) or sodium hydroxide (Baker, A.R.) together with glacial acetic acid (Baker, A.R.), monochloroacetic acid (Baker, A.R.), di- chloroacetic acid (Baker), trichloroacetic acid (Baker, A.R.), salicylic acid (Baker, A.R.), hydrogen chloride (Baker, gaseous) or perchloric acid (Baker, A.R.) were used for buffering, also without further purification. As the pKa of acetic acid in methanol is 9.7 [21], sodium acetate can be used instead of sodium hydroxide at lower pH values in order to keep the water concentration small.
Typical concentrations of the reagents used are: iodide 0.5 M, sulfur dioxide 10--100 mM, water 30--100 mM, buffer 0.1 M + 0.1 M conjugated acid--base couple.
Procedure
Before each experiment the cell was overfilled with a few milliliters of the buffered sodium iodide solution. After sulfur dioxide was added, the pH was readjusted, if necessary, to the desired value with perchloric acid, sodium acetate, etc. The excess cell content was used for a preliminary water deter- mination by the classical Karl-Fischer method. The result served to calculate
3 1 0
the a m o u n t o f water to be added for the a d j u s t m e n t of a desired water con- centration. Then, a generating current of approximately 100 mA was allowed to flow through the cell until the potential o f the indicator electrode reached a value o f a b o u t 100 mV vs. SCE. After each experiment 10 ml of t h e cell c o n t e n t was used for an accurate d e t e r m i n a t i o n o f the final water concentra- tion and 5 to 10 ml was used for an iodometric d e t e r m i n a t i o n of t h e final sulfur dioxide c o n c e n t r a t i o n (addition of a small excess of an aqueous iodine solution and a subsequent back t i t r a t i o n with sodium thiosulfate}. Then, the pH was checked: a shift less t h a n 0.05 pH u n i t was considered as acceptable. In order to obtain the actual concentrations at the beginning o f each experi- ment, the current integrator readings were used to correct for c o n s u m p t i o n of sulfur dioxide and water during the experiments.
R E S U L T S A N D D I S C U S S I O N
The response time of the indicator electrode and the time o f mixing of the triiodide f o r m e d determine t h e m a x i m u m possible rate of potential decrease. First order reaction rates to a p p r o x i m a t e l y 2 s - 1 (i.e. a b o u t 25 mV potential decrease per second) were still reliable; at higher first order reaction rates t o o low values were always f o u n d . Further, potential decrease rates less t h a n 0.1 mV s - 1 were n o t reliable because o f drift o f the system and, moreover, made the measurements very time consuming. A potential change o f more than 50 mV was usually obtained. A typical potential--time curve is shown in Fig. 2. A t time to the current source was switched on and at tl switched off. As can be seen, the descending part of t h e E--t curve is c o m p l e t e l y straight. Only when one of the concentrations of t h e constituents of t h e reagent was very small (or the buffering was insufficient) t h e linearity of the E--t curve was poor, b u t t h e initial slope was always well measurable.
The order of the reaction with respect to sulfur dioxide and water has been investigated by changing only one concentration and keeping all o t h e r param- eters constant. The results are shown in Fig. 3 f r o m which it appears t h a t the
75 > E Le 25 I}to tl I \~ 20 ~b do eo ~o ~/S
Fig. 2. Typical potential---time c u r v e . CH2 o = 2 9 m M , c s o 2 = 1 0 r a M , c l- = 0 . 5 M , p H = 5 . 0
3 1 1 3 0 '~ o E 2O ~ o ~0 o ~ ~b ~ 2'o c H2 o . c s% / 10-~ tooL2 ?2
Fig. 3. Initial rate o f potential change as a f u n c t i o n o f change in c o n c e n t r a t i o n at pH = 6 . 0
and c 1- = 0 . 5 M . (©) Variation o f CH20, w i t h C s o 2 = 1 0 m M _+ 1 0 % ; ( A ) v a r i a h o n o f c s 0 2 ,
with C H 2 0 = 5 0 m M -+ 1 0 % .
reaction is first order in both sulfur d i o x i d e and water. To investigate the pH d e p e n d e n c e o f the reaction, the pH was varied over a wide range, from pH = 2 to pH = 11 (Fig. 4, a). The points in this Figure are the mean values o f several measurements with different sulfur d i o x i d e and water c o n c e n t r a t i o n s at a certain pH value.
In acid solutions up to ca. pH = 5 t h e logarithm o f the reaction rate con- stant increases linearly with the pH. In the range from pH = 5.5 to pH = 8 the reaction rate has a c o n s t a n t value: log k3 = 3.12. This value agrees well with the value f o u n d by Cedergren [6] : k 3 = 1 2 0 0 -+ 2 0 0 , i.e. log k3 = 3 . 0 8 -+ 0.08. It appeared that addition o f pyridine to a buffered s o l u t i o n (and readjustment of the pH, if necessary) has n o influence o n the reaction rate (Table 1). A solu-
4
0
o ' ~ ' ~ ' @ ' @ ' ~b ' ~
pH •
Fig. 4. R e a c t i o n rate c o n s t a n t as a f u n c t i o n o f the pH. (a) Measured reaction rate; (b) re- calculated for m o n o m e t h y l sulfite.
3 1 2 T A B L E 1 V a l u e s o f log k 3 a t d i f f e r e n t p H values a n d d i f f e r e n t p y r i d i n e c o n c e n t r a t i o n s
Cpy/m.M
log h 3 a t p H = 5 . 0 p H = 6 0 p H = 7 0 0 2 . 7 5 3 . 1 5 3 . 1 6 10 2 . 7 5 3 . 1 2 3 . 1 8 30 2 . 7 8 3 . 1 3 3 14 100 2 . 8 3 3.17 3 15tion t h a t is buffered with pyridine (to a value of pH ~ 6) gives the same results as a solution t h a t is buffered with a n o t h e r buffer reagent, e.g. dichloroacetate or salicylate. This makes it clear, t h a t in solutions where the pyridine concen- tration is in excess, because o f the good buffering capacities of pyridine, the reaction rate does n o t vary with increasing pyridine concentrations, since a plateau is already reached in the reaction rate constant--pH curve [6,7].
At pH = 8.5 the reaction rate increases again with pH, b u t to a m u c h lesser e x t e n t t h a n in the pH range < 5. Possibly, the f o r m a t i o n of i o d o n i u m hydrox- ide or i o d o n i u m m e t h o x i d e t h a t occurs at this pH value [19] is the cause of this effect.
The shape of the log ha vs. pH curve suggests t h a t n o t sulfur dioxide itself, but a sulfurous base is oxidized. Although sulfites and bisulfites are practically insoluble in methanol, a sulfur dioxide solution can be titrated with a methanol- ic t e t r a m e t h y l a m m o n i u m h y d r o x i d e solution w i t h o u t the f o r m a t i o n of a precip- itate. Recrystallization of the (CHa)4N+SOaCH3 formed, however, renders it insoluble. Only the pyridine--sulfur dioxide a d d u c t is soluble, b u t this is prob- ably n o t a salt. F r o m the titration curve one can calculate an apparent dissocia- tion c o n s t a n t for the reaction
2 CHaOH + SOz ~ CHaOH~ + SOaCH~
(18)
K a = CCHaO~2
CSO3CH~/C802
We f o u n d for pKa a value of 6.02 + 0.02, i n d e p e n d e n t of the water concentra- tion, so t h a t the f o r m a t i o n o f bisulfite according to
CHaOH + H 2 0 + SO2 # CHaOH~ + HSOa
(19)
+ c
K'a = CcH 30H~ nso~/Cso2
Cn~o
is unlikely. In a 0.5 M sodium iodide solution we f o u n d a larger value for K: pKa = 5.10.
313
sulfur dioxide solution can be considered as to contain a m o d e r a t e l y weak monobasic acid. If the analytical sulfur dioxide concentration (i.e. the total concentration of sulfurous products as it is determined by i o d o m e t r y ) is C-so 5, then one can easily derive that
Cso2 = CCH3SO-3 (1 + CH+/Ka) (20)
in which CH+ is the concentration of the solvated proton. The reaction rate
v = dCl-3/dt = k 3 c i ~ CH20 CSO: (21)
can n o w be written as:
v = k'acrz CH2 o CCH 3SO~ (22)
where
k~ = k 3 (1 + CH+/Ka) (23)
If we may interchange the activity and the concentration of the solvated pro- ton, then at CH÷ >> 10--PKa:
log k' = 3 l o g k 3 pH + pKa while at CH÷ ~ 10--PK~: log k ' = 3 l o g k 3
(24)
(25) Recalculation of the reaction rate for the m o n o m e t h y l sulfite ion with (23), (24) or (25) shows, that kh is independent of the pH (Fig. 4, b).
We have studied the effect of change of the iodide concentration. Triiodide is in equilibrium with iodine and iodide:
K = ci~/ci2 c I- (26)
If b o t h triiodide and iodine oxidize the sulfurous base with reaction rates ki~ and k h , then one can easily derive, that
k 3 = (ki§ K c I- + ki2 ) / ( 1 + K c F ) (27)
If the iodide concentrations are chosen so that
K c r >> 1
we may simplify (27) to
314
0
E
%
• . c~'_ / L m o t '
Fig. 5. Reaction rate constant as a function of the iodide concentration at pH = 6.5.
A plot of ka vs. 1/c I- gives a straight line with intercept k1~ and slope k h / K (Fig. 5).
We find
i 8 - - _ _ i 8 + . _ . o r even
k~ = (3.46 + 0.93) × 102 and k h / K = (3.84 +- 0.14) × 102
Triiodide is very stable in m e t h a n o l and therefore the value of K is very large. A value of K = 2.3 × 104 is given in the literature [19] (respectively [20]/> 4 × 104); with this value we find ki: = 8.8 × l 0 s.
The large difference in reaction rate of iodine and triiodide is remarkable. We could think of a reaction intermediate
O - - S - - O C H 3
I - " " - I+-- LO--S--OC 3J
that would be m u c h easier f o r m e d with iodine than with triiodide. This inter- mediate then is h y d r o l y s e d by water to form h y d r o i o d i c acid and m o n o m e t h y l - sulfate. If it is also very slowly solvolysed by m e t h a n o l , this would be a possible explanation for the slow decrease in titer of a Karl-Fischer reagent.
CONCLUSION
Since t h e publication of the m o n o g r a p h y by Mitchell and Smith [3], all authors have more or less accepted a mechanism for the Karl-Fischer titration reaction in which pyridine plays an i m p o r t a n t role. F r o m our experiments,
315 h o w e v e r , it a p p e a r s t h a t p y r i d i n e s o l e l y a c t s as a b u f f e r a n d t h a t a t a f i x e d p H a d d i t i o n o f p y r i d i n e h a s n o i n f l u e n c e o n t h e r e a c t i o n r a t e .
T h e s p e c i e s o x i d i z e d is n o t s u l f u r d i o x i d e , b u t a s u l f u r o u s b a s e , t h e m o n o - m e t h y l sulfite ion. A t p H v a l u e s larger t h a n a b o u t 6 p r a c t i c a l l y all s u l f u r d i o x i d e is c o n v e r t e d i n t o t h i s b a s e , so t h a t t h e r e a c t i o n r a t e h a s a m a x i m u m value. T h i s r e a c t i o n r a t e is c o m p o s e d o f t w o c o n t r i b u t i o n s : o x i d a t i o n b y t h e s l o w r e a c t i n g t r i i o d i d e t h a t is p r e s e n t in v e r y large e x c e s s a n d o x i d a t i o n b y t h e f a s t r e a c t i n g i o d i n e o f w h i c h v e r y little is p r e s e n t . S i n c e a t l o w i o d i d e c o n c e n t r a t i o n s t h e i o d i n e c o n c e n t r a t i o n is larger, t h e u s u a l a n a l y t i c a l t e c h n i q u e (in w h i c h t h e c o n t e n t o f o n e vessel is u s e d f o r several s u b s e q u e n t t i t r a t i o n s ) is, f r o m t h e v i e w - p o i n t o f p e r f o r m i n g a r a p i d t i t r a t i o n , less f a v o r a b l e .
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