Mechanism and reaction rate of the Karl-Fischer titration reaction. Part II. Rotating ring-disk electrode measurements

Mechanism and reaction rate of the Karl-Fischer titration

reaction. Part II. Rotating ring-disk electrode measurements

Citation for published version (APA):

Verhoef, J. C., & Barendrecht, E. (1977). Mechanism and reaction rate of the Karl-Fischer titration reaction. Part

II. Rotating ring-disk electrode measurements. Journal of Electroanalytical Chemistry, 75(2), 705-717.

https://doi.org/10.1016/S0368-1874(77)80056-7

DOI:

10.1016/S0368-1874(77)80056-7

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Published: 01/01/1977

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MECHANISM AND REACI’.ION RATE OF THE KARLFJSCHER

ti~R~770N REACTION

PART ti. ROTATING RING-DISK ELECTRODE MEASUREMENTS *

.-

J.C. VERHoEF

Labordory

of

E. BARENDRECHT

Laboratory of Electrachemisky. University of Technology. P-0. Box 513. Eindhocen (T& Nethorloxds)

(Received 19th 3&y 1976)

ABSTRACT

A platinum disk-platinum ring electrode was used to investigate the kinetics of the oxidation of the monomethyt sultite ion (which is the oxidizable species in the Karl- Fischer reagent) by triiod:de and iodine, generated with controlled current at the disk electmde. The experimental conditions were such, that the technique for measurement of hoac :eneous pseudo-first order reactions could he used. The results are in reasonable agree&, rl with thaw of the poteniiometric investigations as de&bed in part I. The reac- tion rate constant~of triiodide is approxim&Iy 600 l2 mol-* s-l; for iodine the rate constant is approximately 7 X 106.

IIUTRODUCI’ION ,

In part I [l] the oxidation of a methanolic sulfur dioxide solution by elec- trolytically generated triiodide and iodine has been studied by means of potentiometry. In the potentiometric experiments, the distance between the generating electrode and the indicator electrode ti_ large (ca. 3 cm). compared to the distance between the .&Sk electrode and the ring electrode (ca, O-O1 em):Moreover, the potentiometric experiments are typically zero-current experiments; in the experiments with the ring-disk electrode, the current through the ring electrode is measured (at constant ring potential); while the current through the disk electrode is controlfed_- It was found that at pH v&G up to 5, log readion rate c&stant increases linearly adith pH, while at higher.pH:dum the r&e:cxnistan$ is invariant:-Fro+ this; we concluded

: th&rht sulfur dioxide;its&,

but a base, the monomethyl sulfite-ion, is the

,-,- 2 :- ,. -. _{~ ~:_}

oxidizable species_ It is formed from methanol and sulfur diosider

’

SO2 -I- C&CM = CH,SO, + H’

(1)

& = CCH3So- * c&/c,

₃

_{2 =}

mol l-l (at 25°C)

The oxidation of this base by iodine and triiodide in the presence of water

appeared to be first

order in each of the reactants: I2 and 6, Hz0

CH,SC?,

As long as the pH was fixed, addition of pyridine had no influence, s6 that

pyridine does not play a role in the mechanism.

&cause of the equilibrium between iodine and triiodide [ 2):

I, + I- = 1;

(2)

K, =c,,lc~.~

2.3

X

lo4 1 molmi (at 25°C)

there are always two oxidizing species, triiodide and iodine, with different

reaction rate constants, k,, and kl,

respectively.

part I

that the third order reaction rate, ki

, based on the simultaneous

_‘L _{3 =k,, +}

_kIZ/Ksc,-

₍₃₎

Therefore, a plot of

k, vs.

l/c,-

gives a straight line with intercept

kI,

dope kI, lK,.

THEORY OF MEASUREMENT

In the measurements of homogeneous kinetics with the rotating ring&Sk

electrode, triiodide (and iodine) are generated at the disk electrode with con-

trolled

from an iodide solution_ The concentration of the iodide is so

large, that at useful currents (say, less than 500 PA) and useful rotating speeds

(say, more than

10

RPS) the limiting current is never reached.

The

potential

of the ring electrode is set at such a value, that all of the triiodide that suc-

ceeds to reach the ring, immediately is reduced to iodide.

ring-disk electrode [ 31,

follows, that if no triiodide reacts on its way

from the disk to the

the collection efficiency, N,,

a-constant, indepen-

dent of the rotation speed,

the disk current and the iodide concentration.

No is defmed as the absolute value of the ratio of the (cathodic) ring current

to the

(anodic) disk current. It can be measured and also cat&&ted. No is

only

a function of two parameters 01 and 0:

I

(Y

= (r2/rI)3

-1

₍₄₎

D = (rs /rl I3 -

(5)

No =1 -F(~/@+p~‘~{l

--F(a)}-(1

+a +-@)2'3X

X 11

-FCb/P)(~ +a +P1Ill

_{.- (6)}

where rl

,

the radius of the disk, the in&r radius of -the ringand

the outer radius of the ring, respectively. and the function P is given by

(71

If, on its way from the disk to the ring, some of the triiodide is reduced by the monomethyl sulfite, a smaller portion of it

will

sures then a collection factor, NL, that is

constant, but depends on the

rotation speed

reaction rate constant

disk current.

In the literature two cases have been described:

(i) a

(ii) a (pseudo-) second order reaction, when the consumption of mono- methyl sulfite is so fast, that near the disk electrode its concentration be- comes small and it has therefore to be transported from the bulk of the solu- tion by diffusive convection [5I.

It depends on the magnitude of k, , the pseudo-second order rate constant, whether the reaction proceeds as a pseudo-first order or as a pseudo-second order reaction, With changing the water concentration we can vary the pseudo- second

order rate constant, since

k, =

Therefore, at high water concentrations we have 2 pseudo-second order regime,

where both the concentrations of triiodide and methyl sulfite vary (assuming that the water concentration remains constant)_ At low water concentrations, the reaction rate is slow enough to consider the methyl sulfite concentration as practically constant. In both cases we suppose that the methyl sulfite con- centratien is much lower than the water concentration_ When tk methyl sulfite concentration becomes very low, one would expect to find a second order regime. The value of k, , however, decreases equally:

kl = k2cCH3S07

so

that the methyl sulfte concentration

remains practically constant.

(9)

In a first order measuring technique the collection factor is a function of

the

Nk , for which:

0

d Nk =

f(k,l&) <No

In a.second order measuring technique the collection factor is zero at low disk currents and increases at higher disk currents. The asymptote oi the plot of & vs; iD has a slope JJYO .and intersects the disk current axis in a point where .- + _. ~_

N,i, = 1.88 X 105 X ~~3r12nD2~3u~‘16w’~zc~~jsoj-

(All symbols have their usual significance; w is expressed Ike rad s-l)- In most of the experiments the wa&r concentra’ioo was~smaLl enough (usxaily less than 0.1 M) to establish a pseudo&& order regime_ Then the ratio of Nk 60 N, is a function of X, where

X = 2.60 (Y/D) *‘3&I jw) (12) No analytical function, describing the dependence of the ratio of Nk to No on h, has proved to be possibIe. However, approaimate analytical expressions are found that satisfy well gver certair. ranges of values of h. For A < 1.7, use is made of an approximate collection efficiency:

N; = (fl’)2’3(1 - e(~‘)l/~) - ;(a’ + p’) {l - F(a’@‘) 1 _(i3) with a’ = 3 ln(r,/r,) and 8’ = 3 ln(rs/rz) ₍₁₄₎ while P(x) is given by (7).

From this, an approximate kinetic collection factor is calculated:

N,:=N; - (~1)2/3 [I-*@) + O-160 @‘)“‘” \/A tanh +-0.879 T2X (15) The S~III~~ term T2 only depends on the electr~e dimensions, and is set out

in the literature [6]_ When a’ = p’, CC, equals 0.115 (q’)‘j3 _ The approximz- tion is corrected for by putting

& =

+

- tanh2d/x)(N,,i~~ - l)lNL

₍₁₆₎

-.-

: ,-

oh----, . ..~ . . ,-

-For h < 0.15, it is better to calculate Ni in a somewhat different way:

N; = N&i -ip’)2’3 (0.3’12 X - 0.146 X2) + (/3’)4’3 (0.160 X - 0.059 h2)

-0.879

₍₁₇₎

However, when calculating X from a measured NiJN,, value, the increase in

a&racy is small if (17) is used instead of (15).

For X > 1.7, Nk/No is calculated with

N,JN,, = exp[--urcc + b

where

0.776 X1”

trode dimensions, are tabulated in the literature [S] .

A plot of N,/N, vs. A for ttio different electrodes is shown in Fig. 1. Al-

though it looks cumbersome to calculate the points of *he plot, it is easily done by using a programmable desk calculat:lr or a computer_ For that matter, it only

has to be done once for a single electrode. gnce 9 &J,C has been made,

it is easy to find k, from a measured NJN, v&e_

EXPERIMENTAL

Reagents and procedur=

The reagents used in this investigation are esse&ially the same as those used in part

I. The procedure also is the same for the

25.0 + 0;3”C (unless otherwise stzted).

The electrodes-were cl&&l before the experiments by

polishing

alumina (0.1 pm, Fischer Scientific Co.), then rinsing with, successively,

water, ethanol and methanol and finally by enodic polishing (in a separate

WOO,

Apparatus

Two exchangeable ring-disk electrodes have been used, both developed and manufactured in our laboratory. The ring

and the disk were made of platinum

and the electrode holy was made of Kel-F. The electrodes were mount&

in

such ti way that the system

was air-sealed

(O--S5 rps). Pr&semeasurements of the

tit&on speed were performed

holes at the,edge. .- _

.~~e~d&inferrup&tielightb&

-&‘ph@&+&&. me pulse frequen~:..waS m~‘tvith

a Hewlett-Packard,

model 5304 A, counter. The electrodes were co&olled by a -Tacussel, model &pad, bipotentiostat/galvanostat, with independent control of the disk and ring potentials (in the potentiost&.mode), or the disk

current

se1 signal generator (model GSTP). Recordings were made on a Hewlett- Packard model 7046 A XY recorder.

RESULTS AND DISCUSSION

The characteristics of the two electrodes are tabulated in Table 1. Although, according to the theory of the ringdisk electrode, the collection efficiency should be constant at different rotation speeds, we found z smaI1 .lariation

of

NO (only a few

No and

No values.

Generally, the water and/or sulfur dioxide concentration was chosen such,

that

In this range the best accu-

racy was obtained (see Fig. 1). In order to calculate a kl value from an experi-

mental A value, one needs to know the viscosity coefficient of the solution,

v,

be known very accurately, since only (u/D)“~ has to be known. We used

a Ubbelohde viscometer to measure the viscosity of the solutions (V = 9.41

X 10m7 m2 s-l for a solution with ionic strength 0.5 at 25°C). The diffusion’

coefficient of the triiodide ion is 1.09 X lO+ m2 s-l 121, ,S that (v/D)“~

Characteristics of the electrodes No. 1 and 2

Chrrractcristia 1 2 rl /mm 2.027 2.011 J-2 /mm 2.175 2.100 r3 Imm 2.461 2.201 % 0.2354 0.1387 f 0.2114 0.5542 0.3706 0.1299 0.1723 0.1409 No (theor_) 0.2679

0.1595

ArO

(exp_) *

G 0.1956 03374

;

7-2 0.010 0.004

-

1.6

-

&A

Fig. 2. Typical i, vs. i, curves for different mo!e fractions of water. ER = a.2 V vs. SCE; w = 20 rps; cl- = 0-5 ~\f; cso2 (total) = 7.4 mhf; pH = 2.0;xHz0 = 0 (I), 0.15 (II), 0.24 (III), 0.29 (IV), 0.34 (V), 0.46 (VI).

equals 9.52. This val de W,‘IS fairly independent of the temperature and the composition of the solut;on.

The consumption of the triiodide formed at the disk eIectrode occurs by a pseudo-first order reaction unless the water concentration becomes high (Fig. 2). At low water concentrations, the

iR vs. iD curves are

caustxi

found in other solvents, e.g. water and acetonitrile [7]_

The complex has a~ma_Cmum absorbance at 354 nm, while at this wave- length neither-iodide noz :W dioxide show any appreciable absorbance_ The’stability constant, KC, and the absorptivity, E, of the sulfur dioxide-iodide complex can be found from a plot of l/A (absorbance) vs. l&o, ,-since at relatively large csol [ 81:

(Cl_ ~+ &&,

-)[A

= i&~~~

+ I/E

(18)

We

Kc 6 u+,;~-&,Q$-- k

i.24.-+

O-13,1

indication in an ordinary Karl-Fischer titration, for even at pH a 7, the solu-

tion contains usually enough of the complex to colqr it yellow (although at

this pH only a very small part of the total amount of sulfurous compounds is present as the iodide complex).

For the calculation of the reaction rate, one n&ds to know both the part of the total (analytical)

sulfur dioxide concentration

that is present as the

monomethyl sulfite ion, and the part of the total (analytical) iodide concen-

tration that is present as iodide, because we can only measure the total iodide and sulfur dioxide concentrations. Let the total sulfur dioxide

and iodide

concentrations be a and b, respectively:

= = CSO- + _* CSO~~- -i cCHjSOj WV

b = cl- + cso2r- + Cr, Gw

Since very little iodine is present we may neglect the equilibrium between iodine and iodide (Z), so that the term cl3 may be omitted from (20). Then, one can derive

cl- = {B + [B2 + 4K,b(K,/c, + + 1)]1’2 )/2K, where

(21)

B = K,(b -a) - (K&J+ f 1)

md cH+ is put equal to 10VpH, while

%HJSO~ = a _

K,/(K,

+

K,c,-))

(22)

Except for the term &cl-, (22)

is equivalent to eqn. (20) of part I. Often,

all sulfur

pK,,

dioxide is present as such, and,

especially at high iodide concentrations; the formation of the complex is irn- portant_ If the iodide concentration decreases considerably.as a result of the formation of the complex, the reaction rate increases (c.f. part I

and below),

so

that the effects cancel out to

some extent. Anyhow, where n&id,

a cor-

rection for the formation of the complex has been-made.

We measured the reaction order with respect to sulfur dioxide and water at pH = 5.0 and at pH =

6.6 (Fig. 3). Either

the water

concentration

or the

order in water as well as in sulfur

dioxide. At increasing water concentrations

the stoichidmetry of the Karl-Fischer reagent increases

from’one mole I-I&3

tion between the reaction rate andthe water concentr+on

could.be &I-

linear. In Fig. 4, the logarithm of the ps+doke&ond.orde? reactiod’rate &tin-’

stant (i.e. the measured pseudo-first order

rate_tinstank~cJi&d,by

the sulf;u

Fig. 3. First order reaction rate constant as a function of change in concentration. (a! pH = 5.0, (m) CH20 = 129 mM. (0) cso2 = 10.9 mAI; (b) pH c 6.6. (s! cHzo = 75 m&f. (0: cso2 = 8.6 m&I.

dioxide concentration) is plotted vs. the logarithm of the water concentra- tion. Up to ca_ 1 M Ha0 the slope of the curve is 1, while at higher concen- trations it increases to a vahre of about 2. Probably, bisulfite is formed:

SO2 +

Hz0

whereafter this hisulfite reacts with iodine or triiodide and a second water molecule: hence a stoichiometric factor that increases from 1 (only methyl sulfite formed) ‘Jo 2 (mainly bisulfite formed)_ In order to have a known and constant stoichiometric factor, it is therefore necessary to keep the water

~-. .-I r 1 0 2 4 6 0 10 PH p

Fig. 5_ Reaction rate constant as a function of pH. (a) Calculated for cso2 +cCHJwy;

fb) calculated for cCH,si)j Only. (0) q- = 1 i+f, (0) cl- = 0.07 &f_

it

seems easy to

condition one must bear in mind that, owing to

the small molar weight of water, it amounts to only about 2% of water in

methanol;

The reaction rate of the Karl-Fischer reaction has been metired as a func-

tion of the pH for a small and for a large iodide concentration (Fig. 5). When

we calculate

the reaction

rate constant for the total sulfur dioxide coucen-

tration (Le. for cso2 + c,,,,,~

),

find a pE-dependent rat& constant_ This

indicates that not sulfur dioxide, but the monomethyl sulfite ion

is the oxi-

dizable species, Calculations for the consumption of only

this species result

in

pH-independent rate con&ants, in complete agreement with the results of

the

potentiometric experiments.

.-

At various pH values we measured the.deperidence of the reaction rate on

the iodide concentratifin (Fig. 6)_ The plots of k3 vs. f/q-- are straight lin&.

in accordance with (3). At pH = 6-5, the values of the rate constant for the

total sulfur dioxide practically coincide with those for the monomethyl suk

fite alone. From the intercept at this pH -we find.

h,, =

6142 801’ mole2 SC’

and

from the slope:

_

kI,/Ks =

316 2 5 1 mol-1 s?

With

2.3 X 10’ 1 mol-’ (2), we calculate:

k,,=(7.27?

0.12)

1CJ6 l2 mol-* k-’

I

-Y ’

-. 1 :,

:,I_ .

These results are in reasonable agreement with the

&h~es-

&I part J:fYz~.-

.~

k5 =

346 f 93 and kI = (8.83 + 0.32) x I@_

mm.

The

tempera&e d&endex& of &e%ea&iofi &.e& &oti.&:ljS&?;

A&,

increasing temperature both the interceptsl_&d- th&&q~~6f]the~~&i i& ~.:_. .:--

crease-

A

plot of the logarithm of .the-intercept&and .&he slo@++&v&~.~~~~-~

- . . - y : _- .-.. , ,; -z : ‘_ ._ .’ -; . . -,__.. ;_ :_-.:-~._ -‘._..~. _>. I :. -_ .- . . : -:.< -. ;-..7.,.:. . . _:‘, ~~,, _i;

values.

Fig_ 8 (a and b, respectively)_ The temperature dependence of the slope of

the lines,of

7 is atmost the same as the temperature dependence of the

stability constant of triiodide 121, so that the reaction rate with iodine

is almost temperature independent (Fig. 8, c)_

‘: ._ REFERENCES

J.C. VerhoeC and & Barendrecht, J; Elec&xnal. Chem., 71 (1976: ?%I_ J.C. Vetibef, W.H. Voo& agd E_ Barendxht; to. be published.

w.4. Albe& and S_~Brucken.steia~ Trans. F&day Sot., 62 (1966) 1920.

W-J_ Albery and S.-Bruckenstein, Trans. Faraday Sot.. 62 (1966) 1946; W.J_ Albery, ibid..-63 (1967) 1771: WJ. Albery, ML. Hitchman and J. Ulstrup, ibid., 64 (1968) 2831; W-J. Albery, J-S. Drury-and ML. Hitchman, ibid., 67 (1971) 2162.

W.J:Albery;~S. Bruckenstein and D.C_ Johnson. Trans. Faraday Sot., 62 (1966) 1938; W-J. AIbery arid S. Bruckenstein. ibid., 62 (1966) 2584; W.d. Albery, M.L. Hitchman

and J- ULstrup, ibid.. 65 (1969) !lOl.

W.J- Albery and M.L. Hitchman. Ring-Disc Electrodes. Oxford University Press. London, 1971: -.

A. Salama, S-B. Salarna, M.-Sobeir and Saad -arif, J. Chem. Sot. (A), (1971) 1112. H.A. Benesi and J_ Hildebrand, J. Amer. Chem. Sot_, 71 (1949) 2503.

E. Eberius, Wassecbestimmung mit Karl-Fischer L&ung, Veriag Chemie, Weinheim, 2e Aufl-, 1958. pp_ 36-49.