The application of double potential-step chronocoulometry to the study of catalytic reactions : the Ti(III)-hydroxy lamine reaction

ELECTROAMAI.YTICAL

THE

CHEMISTRY

APPLICATION

OF

AP\ID II%TERF_*CI&

DOUBLE

CHRONOCOULOMETRY TO THE Ti(II1) -HYDROXYLAMINE

PETER

JAMES

LINGXI‘NE

Gales and CreZli?t Laboratories

_44ND

=-v

ELECXROCHE-MISTRY

POTENTIIAL-STEP

THE

STUDY OF REACTION”

JOSEPH

of Chemistry.

H.

CATALYTIC

RE-4CTIONS:

CHRISTIE

CaEifovnG

Ixstitzrte

of TechrzoLog>e, Pasaderza,

CnZifomz;z

(U4S.A.)

(Recei-i-edFebruaq

rqth, rg66)

IKKRODUCTI03i

The originally

oxidation and most

of Ti(II1)

by hydrosylamine

in the presence

of oxalic

acid was

polarographically by RI&XX AXD ICORYTAI. These authors obtained a rate constant at ~5” of ~z_z-+ 1-5 l/mole set and an activation energy of 7.9 “r;calfmole. This value of the rate constant was subsequently confirmed polarographka-lly by DELXHAY, &~A~AX AND BERZIKS~. BL~~EKAXDX(ORYT_LL~ alsodetermin ed the rate constant by mixing hydroxylamine and TifIII) solutions and following the rate of disappearance of Ti(III) polarographically_ The rate constant obtained under these conditions was qz.o~o.z l/mole setBLX~EK AKD KORYTA concluded that their results were consistent with the previously-proposed mechanism of Dxvrs, EV_L~KS AND HIGGINSON~I Ti(IV)

+ e+

Ti(II1)

+

-XI& 03zIic

acid

thoroughly

+

Ti(II1)

TNH~OH oxalic

serves

FISCHER,

studied

.?% Ti(IV)

acid %%

as a radicd DRXCK_%

-I- Ho_O +

-NH2

products scavengers_

SXD

FISCHER•

VXQ

hax7e

potentiome~y at low concentrations of hy~oxyl~ne where the catalytic reaction is relatively slow and rate

cocstant SXVEAW~

for the study

of 45_9-1_0_4 _4XD

l/mole

studied this system by chrono(5-10 rnr;) under conditions of second order. They obtained a

sec. have

vwSELILoL~

of this reaction_

(Ii

They

e-x~ploy-ed

obtained

a rate

Linear

sweep

constant

chronoamperometry

of qz_ot_1_7

l/mole

sec.

In the case of a controlled-potential experiment such as polarography. the presence of a catalytic reaction simply means that a larger current is flowing at -any given time and the precision tithwhich this larger current can be measured is not affected. But in the case of a controlled-current experiment such as chronopotentiometry, the presence of a catalytic reaction greatly decreases the rate of potent&I change of the indicator electrode, especially in the vicinity of the transition time, aud * Conl23+iaIl

X0. 333g_

228

P. J_ LINGXXE,

thusrendersthe this reason we

determination ofthetransition timesubstantially expect chronopotentiometry to be a poorer ted

J_ H. CHRISTIE

more

than

difficult_For a controlled-

potential technique for the study of fast catalytic reactions. This is borne-out by the investigation of DEL-WY, &JAm-ax

These

authors found

quite a low

value of z4l/mole

AXD BERZIXS~. set for the rate constant (recal-

culated from their value at 30~ using an activation energy of 7-9 kcal/mole) in a chronopotentiometric study of the Ti(III)-hydroxylamine reaction. They concluded that

they

had obtained an incorrect value

of

the

rate constant because

of the

poor

definition of the chronopotentiometric

transition times. were able to circumvent some

CHRISTE AKD LAUER~ difficultiesby the use of reverse-current chronopotentiometry. Under these conditions, the forward time is a quitewell-definedquantity- Since the shapeoftheTi(II1) oxidationwaveis essentially unaffected by the catalytic reaction, a normal potential inflection is obtained at the transition time

for the reverse

wave_

CHRISTIE

ASD

LXUER

obtained

a value

of

32_0-&2.0 l/mole set for the rate constant (recalculated from their value atz7"S using an activation energy of 7.9 kcal/mole). HERMAN AND BXRD~ consideredtheapplicationofcyclicchronopotentiometry to the studyofthe Ti(III)-hydroxylamine inconsistent Mth a single rate constant complicated than previously =sumed_ justlfied5.

reaction_ Their experimental results were and they suggested that the s_ystemis more This conclusion may not be completely

CKRISTI@ has recently investigated the application of double potential-step chronocoulometrytothestudyofelectrodereactions_ Inthispaperweundertakethe application of the double-step chronocoulometric technique to the study of the Ti(III)-hydroxylamine reaction. RESULTS

XND

DISCUSSION

Our solutions areinitialIy free of Ti(II1) and the concentration of hydroxylamineissufficicntlylarge(roo-zoomF) thattherate ofreactionis well described by a pseudo first-orderrate eIertrode,issuchthatno

constar,t, K('NHaOH). Eo, currentflowsthroughthe

whichissufficientiycathodicthatthereduction

theinitial-potentialoftheindicator cell.ThepotentialissteppedtoE1 of Ti(IV)

is diffusionlirnited. After a

time. t. thepotentialoftheelectrodeissteppedtoEs~vhichissuKicientlyanodicthat the

otidation

of Ti(III) is diffusion l&nit&_

Ignoring the effects of double-layer total faradaic charge ares

charging,

the faradaic

currents

and

the

Ti(III)-HYDRoXYL_sMINE

TRE

where

82 = K( -NHsOH)

,

concentration of Ti(IV). extreme values of fltf_

Fxg. (II),

I. Experimental fit*1_3_ The

D

REXCTIO~

is assumed

TV

Figure

equal

I reproduces

1-t and Q-t traces for extreme current. charge. and time scales

to

Q(z)

E

D, and *CO is the bulk I-t

values of flth_ (I). fl tl= are identical in I and

Forming the ratio of the charge due to the due to the reduction of Ti(IV), we obtain

Q(=) -Q(t)

DTi[m,

experimental

(2figr+,E)erf

oxidation

and

traces

for

o (no hydroxylamine) II.

;

of Ti(II1)

Q-t

to the

charge

f2E-t

I _ 1 -

3

(2)

-

Note that this ratio is independent of the numerical value of D. of the electrode area, and of the bulk concentration of Ti(IV). calculated from eqn. (2)) ‘us. The curve illustrated in Fig. 2 is a plot of @&+I, #Pt_ In the limiting case of no catalytic reaction (KS+). the simple diffusion-limited reaction becomes very fast (k-co). no value of 0.586 is obtained 8. As the catalytic charge G recovered on the reverse step and the ratio goes to zero. We have calculated an extensive table of b”t a5-a function of IQb/Q=j (copies can be obtained from the authors)_ This table was used for the evaluation of /P from the experimental data_ which

A- striking advantage of any integral technique lies a correction-for double-layer charging can be effected_ J. EZecCroanaE.

in the simplicity with In the present case we Chem.,

13 (x967)

2~7--235

P. J __LINGANE,

230

J. H_

CHRISTIE

write

whereQ,and&arethe tively and

esperimentally~observedvalues

41 and

50 represent

the charge

required

ofQ

to charge

att=t

and

the double

21;

layer

respecfor the

forward (cathodic) and backward (anodic) steps, respectively. The asterisks signify that the measured quantities have been corrected for double-layer charging. In the present investigation, qfand qb were deterrninedby repeatingthe experiment in solutionsidenticalwiththosebeinginvestigated but which containedno titanium_ I

I 0.6

I

I

-

I

o-o

o-a

O-0

I

I

I

I.6

2.4

32

4-o

B2y

Fig.

2. Plot

T-!BLE

of IQb/Q,l

us. 82~

talc

from

(2).

1

2.0 mF 35_0°

Ti(IV).

0.20

F oxalic

16.8 II-7

440-O 21=&o

go-0 +z.o

acid,

pH

The results of double of hydrkylamineare

determinations-~-The o-50 -ad 0.60 PC, smaller

than

I-I,

E.

=

-TOO

mV,

EL

=

-60600 mV,

EI =

ooo mV.

o-57 0.5s 0.58 O-576

absence

=

o-57 0.58

7-81 5-5 6 4-03

21.0

1_7%

eqn.

f

0.002

potential-step chronocoulometric tixperirnents in the given-in Table r; each entry is the average of four

Vah~es of _Qf -and @, determined respectively_ The average vz&e

the theqretical

value

of 0.5S6.

for-the sa%e step intervals, are of~~/*Qb/?QII is 01576 +nd is sbme

The reason

for this small

discrepancy

THE

Ti(IIT)-HYDRoXYL_%MINE

TABLE 2-omF

mv,

2

Ti(IV),o.ZoFoxalic EZ = ooo mV

15 o" 412.0 ZIO_O 93-o

acid,pH=

16.5 10.4 6-4

25.oQ -402_0t

25.8 r5_I 7-6 5.2 3-6

207-O

79-o 4I_0 20_0t

84.0 44-O

35.o0 92.0 43-9 20.0

* zb f +

0.021 o-19 0.07I 0033

Average

7.90 8 6 8.q 8.1 8.4 8-35

2 & f + + 2

0-15 0.14 0.065 o-12 0.13 o-092

Average

S-14 -8.6 8.4 S-37

f f f 5

0.081 0.19 0.11 o.oS6

0.32

3-17 1.78 0.65 o-33

o.=j16

0.17

0.220 o-357 o-447

1.70 0.72 036

O-195 o-3=3

201 o-95 042 Average

0_4’Cj

in theaverage.

AVerage

3.17 3-3 344 3-32

1.30 0.69

O-134 0.2I3 o-371 o-457

11.8 6.8 4-o

f Neglected

1.o.0.204 Fhydroxylamine,&

0.262 3_362 0461

16_78-g 59

210.0

TAELE

23=

REACTION

=

-IoomV,E+

=

-6600

0.32 0.3I -F_0.7' f 0.26

22.0

&

22.4

&

21.8 22.0

see text.

3

2.0 mE; Ti(Iv). 0.20 F oxahc -600 mV, EZ = 000 mV

acid, pH

=

1-1, 0.102

F

p

hydroxylamine,

t (mice)

Qr f&l

'Qb/'Qf

fi’t

25.00 4I4-0 220.0 go.0

22.4 13.6

O-203 0.300

I.90 r-03

7-S 5-I

O-430 O-500

0.42

t-67

43-o

0.2I

22.0t

3-7

0547

0.085

4-8 f 4.2 * 4.70 f

.

4-60

21-O

IO-I

6-3 4-4

o-293 0.404 o-489

: j- yeglectedin

I.08

12.5

&

12.2

f

0.24

II-Z- f I'_? f

I-04 O-50 -0.25 -Average the avey+,seetext:

&

0.52 Average

45-o0 37-o_ X9.0 8.6

-& o.org

4-71 zt o-079

Average 35-o" S6_0 42-O

(SEC-l)

o-049

O-I3 0.35 0.040

0.28 0.28 0.24

0.23

28.0 ma I-6 -27-o -& 2.0 29.0 +!z I-I 27-g --f 0.92

ECU=

-100

rnv, EL =

P_ J. LIXGANE,

233

J_ H. CHRISTIE

was varied from - IOO to + zoo mV were performed and results similar to those of Table I were obtained_ \%‘e conclude that the reduction of Ti(IV) and the oxidation of Ti(II1) are diffusionlimited at -600 and ooo mV US. S.C.E., respectively; all subsequent

experiments employed these step potentials. The data obtained in the presence of 0.1 and 0.2 F hydroxylamine edinTables z and3_ Eachentryistheaverageofatleastfourexperirnents. fidence

intervals

listed

correspond

to the

standard

deviation

of the

are present-

mean.

Thecon-

Values

of

qf and qb were determined for the same step interval for the various solutions and only small variations were observed among them_ Therefore, 4~ and @ were taken to be c-50 and 0.60 PC in all solutions. Variation of qY and qb with temperature was not investigated. For any given temperature and hydroxylamine concentration, 8’ should be independent of t. In certain experiments performed with unrecrystallized oxalic acid (which appeared to contain a trace of reducible impurity), B2 was observed to increase dramatically with decreasing values of z at any given temperature and concentration of hydroxylarnine. The constancy of ,9* over a wide range of values of t appears to be a sensitive and useful diagnostic test for impurities and othcirregularities in the system and for the correctness of 40 and yl_ In performing the experiments, it was necessary to decide over what range to vary /?“t_ We have rejected all val les of /?z corresponding to values of the ratio I*Qb/*efl less than 0.2 or greater than o-s_ XVhere available, such values have beers included in Tables 2 and 3 and it is evident that including them in the averages would not

have

altered

the rate

constant

substantially_

,.a -

Fig. 3_ Plot of log RT US. T- 1 for 'he (e).u.I; (0). 0.2 FNH~OH

evaluation

of Rz~

and

of the

_%rrhenius

activation

energy-

The slope of the working curve (Fig. z) has a value of about 6 in the vicinity of p2t = I_ Therefore, an error of about I”/~ in the ratio of i*@/*@[ in this region results in an error of about 6% in the rate constant_ The precision for the determination of r and QzIis not better than I o/o and so xi-e are somewhat surprised, and gratified, by 3 the low standard deviations associated with the experimental determination bf pz.The activation energy was deterrnin ed from the pldt in Fig. 3. Since the stand-

THE Ti(IIIf-HYDROXYLAWIXE

REACTION

233

ard deviationsassociated=vith thevarious values oftherate constant vary by only a factor of three, all of the data pairs were weighted equal157 in the calculation of the least-squares slope and intercept_ The results are 43_4+r_x

As99

=

E,

= 17_2+1_1

where

the

vaIue

of

l/mole set kca_l/mole

confidence KPS

intervals

confirms

the

now

correspond

polarographic

value

to

the

of

B~AZEK

g5:&

confidence

level_

AXD KORYTA~

chronopotentiomet~c value of FIXHER et &?.a_ Theactivationenergy deterrninedinthisstudyislargerbyafactoroftwo thevalueof7.9 kcal/ mole found by BL_+EK AXD KORYT-~1. We were unable

and

This the

than to resolve

this large disagreement by repeating their calculations a-fid therefore we have re-determined t’ne activation energy polarographically. The polarographically and double potential-step chronocoulometrically-d&e-tied rate constants are plotted in Fig_ 3_ The slope of the polarographic line corresponds to an kcal/mole and is in excellent agreement with the value potential-step technique.

activation determined

energy of 17.3 by the double

Double potential-step chronocoulometry compares very favorably with polarography for determining the kinetic parameters of catalytic reactions. This technique can probably be used to measure values of p” of at least 7coo-zoo see-I, well into the polarographic range. /32z can be varied over a far wider range than is possible xvith ‘polarography and this flexibility makes possible the useful diagnostic test for systematic irregularities described above_ Although the experiments were easily performed, obtaining the data from Polaroid prints 1s somewhat tedious, but it is evident that the -experiments could be modified in any of a variety of ways so as to obtain Qr and Qer directly in digital form and thereby increase the ease and simplicity of the experimentl”. ESPERIMEhTTAL

Fisher technical-grade ter and

then

dried

KzTiO(GO&

to constant

weight

- z H20 was twice recrystaliized from waat 60% relative humidity. Solutions were

prepared by weight and were allowed to equihirate 2-1 h before use. Solutions tigated prior to such equilibration appeared to contain two reducible species.

~~nc~odt impurity

xvhich was

AR

H&QO~ - 2 H&

removed

by a single

contained small recrystallization-

inves-

amourzts of some oxidizing The salt was dried for 2 h

at so0 and weighed as the dihydrate.

>99% putity,was recxystalMatheson, Coleman-and Bel! (NHzOH) - HzSOe, lized from an &o/0 ethanol-water solution and d&d for I h at TOES_Stock solutions

P. J. Llh’G_4NE,

231

were standardized by titration withperm_g~ateaccordiTlg~~o &LzZ_~ andthetiterofthesesolutionschangedlessthano.~o~odnring-the experiments-

J_ H. CHmSTIE

&e-method of BRAY courseofthese

MeYczcYy

Ik%llinckrodt

AR

mercurywasemployedintheexperirnentstiththehanging

mercury

drop- The DME experiments Bethlehem Apparatus Cd.,Hellertown, edto

be less than

employ&l triply-distilled mercury from the Pa.; totalnon-volatileimpurities werereport-

0.025 p-p-m_

AU solutions were prepared from triply-distilled water and de-aerated with Matheson “prepurified” nitrogen ( c S p.p_m_ oxygen) -which was further deoxygeuatedby passage through a vanadous &shingtower prior ro entry into the cell. The

electronic circuitry is shown

schematically

in Fig_ 4 and

is analogous

to

LMJER AND OSTERYOUNG~O. Neiay z controls the reverse step and is fired by a xrariable delay timing circuitrf_ The supporting equipment is essentially as previously descnbedl”. The measured rise time of the potentiostat is less than 20 ,usec. The area of the hanging mercury drop was 0.0407 cm2 at zs”_

that of CHFUSTIE.

WEIIKING

7”E”

‘R’ T

POTZNTlOSTAT Aux I

[ I

CURRENT

Relay

MEASURING

AMP.,

2

tiCZA1002 INTEGRATOR

HGZAIOOZ

Fig. -4- Block diagram of the solid-state operational amplifiers The

employing G. electronic appmtus and C. =P. Glare 9c Co_ mercury-tietted

polarographicset-upernployedtheequipm&rtshownin

A.

PhiZbrick relays_

Researches

Fig:dandathree-

electrode cell; the output of the current-measuring amplifier was fed to a Sargent SR recorder aiid the maximum polarographic currents were r_ecorded at - 500, 2 600 and _poo mVvs.S.C.E.Underourconditions,th~ecatalytic~--tcurvewasobservedtobe a->/3_orderparabolaandthecatalyticcurrentwas mercury head: Therate constant was calculated

observedtobeindependentofthe accord>o KOUTECK~~~.

THE

Ti(III)-HYDROXYLAMINE

Thecellwas -f-O.ZO.

REACTION

235

thermostattedatthestatedtempertitures

withaprecisionofabout

2xCKKOWLEDGEIvIEXT Wewishto

thank Army tion

withProfessorF_

acknowledgehelpfuldiscussions

C_ AXSON

and

to

him for providing splendid research facilities under the auspices of the Office of Research (Durham)_ We are especially indebted to G. LAUER for his collaboraon

certain

preliminary

experiments,

for desi,ting

the

experimental

apparatus,

and

for his continued interest during the course of this investigation. The work was supported, in part, by predoctoral fellowships from the U-SPublic Health Service, Division of General Medical Sciences (PJL) and from North

American

Aviation,

Inc_

(JHC)

_

SUMMARY The applied

theoretical

to the

study

relationships of catalytic

Ti(III)-hyclroxylamine tion

for the reactions

reaction_

The

double were

kinetic

potential-step

verified

parameters

by

chronocoulometry

an investigation

obtained

in this

of the

investiga-

are;

where ported

k 398=434&1-r

l/mole

E, = 17_2 + I_1

Ircal/mole

kiss is the rate values

of k=Bare

cons-taut

set

at 2~~ and E,

is the Arrhemus

energy.

in ezcellentagreementwiththevaluereported

previously-reportedvaluefortheArrheniusenergy

Previously-reherebutthe

appearstobeinexplicably

inerror-

REFERENCES L -4 BLA?EIE ~fjD J_ I
+ 3 6 7 8 g IO II 12

13 14 15

COl~eCZiOw CZSC~L Chem. CO7m?ZUn.. I8 (1953) 326. AND T. BERZINS, J_ _-lm. Ckem. Soc_, 76 (1954) 53rg_ P_ DAVIS. M_ G_ Evi~xs AND W. C. E_ HIGGINSON, J_ CJresm_ Sot., (1951) 2563_ 0. FISCHER, O_ DRACICA AND E. FISCHEROVA. Collection Czec7i_ C7zem. Comnzu~z.. 26 (1~61) 1505. J_ H. CHRISTIE XND G_ LATTER. Amzl. Chem., 36 (1964) 2037~ G. LXUE_S. pnvate communicationH. B. HER~LLP; AND A. J_ BARD. LXTL~Z_Cfienz.. 36 (1961) 510. J_ H_ CHRISTIE. J_ EZe~dronnal. Chem.. 13 (1967) 7g_ XV. C. BRAY, M. E. SIU~SON _SND A. A. IMACKENZIE, J_ ,4tn. Chem_-Sor;., 41 (19x9) 1363. J_ H. CHRISTIE, G_ LXUER AND R_ A_ OSTERYOUNG, J_ Etectrcanal_ Chem.. 7 (x964) 60~ G_ LAKER. H. SCHLEIN AND R. A. OSTERYOUNG, Atzal. Chem_, 35 (1963) I7Sg. I?_ J_ LINGA~T. AND J. H. CHRISTIE, J_ Electyoanal. Chew.. IO (x965) 284. J_ KOUTECKP. Collectim Czech. Chem. Comnrtrn.. 18 (1953) 311J_ M. S-~VE~T AXD E. VIAh-EILO, EZed~ochim_ Acta. IO (1965) go=j_ G. L_~UER AND R_ A. OSTERYOUNG, Ayzat. Chem.. in press.

J_ Elactroanal.

Chem.,

I3 (1967)

227-235