7/25/2019 Nicholson 1965

1/5

m i n i m u m i n t h e T C

v s .

concentration

isotherm (21)-correctly describes th e

da ta obtained. However , i t seems un-

likely that so many compounds would

show maxima or minima in nitrogen but

none of them would do

so

in Ar or CO,,

while they do give positive and negative

responses in these gases.

One possible al ternative explanation

is that a concentration gradient is

established in the cell as a result of

thermal diffusion between the cell wall

and the hotter fi lament. This could

result in a t ransfer cf thermal energy

across the gradient, th e so-called Dufo ur

effect

7). If

so, it should be possible

to el iminate this effect by increasing

the tu1 bulence in the cell. Preliminary

investigation with such a cell indicates

t ha t t h is is

so.

T he lack of W peaks and th e low cost

of CO, suggest that it would be a better

carrier gas than nit iogen for preparative

work (and possibly even some analytical

work). Some workers hav e reported

collecting samples in CO, by freezing i t

to dry ice

(9).

Also, the wide variation

in response values (posit ive and

negative) might be useful for quali tat ive

analysis of pure compounds. Fur ther

work w ith CO z and oth er carrier gases of

low T C is p lanned.

A CK NO W LE DG M E NT

The authors thank Floyd Fredr icks

for obtaining some of th e data .

LITERATURE CITED

(1) Bennett,

L. A . ,

Vines, R. G., J .

( 2 )

Bohemen. J.. Purnell, J. H., J . A p p l .

Chem.

P h y s .

23

1587 (1955).

, .

. .

Chem. 8 , 433 (1958).

(3 ) Dal Piogare,

S.,

Juvet,

R. S. ,

Jr . ,

Gas Liquid Chrom atography, p. 192,

Interscience,

N e w

York, 1962;(

(4 ) Dreisbach, R ., compiler, Physical

Prop erties of Chemical Com pounds,

3 Vols., American Chemical Society,

Washington,

D .

C., 1955, 1959, 1961.

(5) Hansen, R.

S.,

Frost ,

R.

R., Murphy,

J. A., J .

Phys.

Chem. 68, 2028 (1964).

( 6 ) Harvey, D., Norgan, G. O., in

Vapor Phase Chromatography-Lon-

don, 1956, p. 74,

D .

H . Desty, ed.

Academic Press, New York, 1957

( 7 ) Hirschfelder, J.

O.,

Curtiss, C. F.,

Bird, R. B., Molecular Theory of

Gases and Liquids, p. 522, Wiley,

N ew

York, 1954.

(8) Hoffmann,

E.

G., ANAL. CHE f.34

1216 (1962).

(9) Hornstein, I., Croae, P.,

Ibid. 37

170 (1965).

(10) Jamieson, C. R., J .

Chromatog. 3

464. 494 11960): 4 . 420 11060): 8.

~~ , , -,

i i i ( i 9 6 2 ) : i S , i 6 0 ( i 964) .

(11) Keppler, J. G., Dijkstra, G., Schols,

J. A., i n Tapour Phase Chroma-

tography-London, 1956, p. 222, D .

H. Desty, ed., Academic Press, New

York, 1957.

( 1 2 )

Keulemans, A . I . M., KFantes, A,,

Rijnders, G. W .

A.,

Anal. Chim. Acta

16 29 (1957).

(1 3) Littlewood, A. B., Gas Chroma-

togra phy, pp. 329-33, ilcademic

Press, hew York, 1962.

(14) Madison,

J.

J.,

AXAL. CHEY.

30

1859 (1958).

(15) hIessner, A . E., Rosie, D. &I.,

Argabright, P. A . , Ibid. 31 230 (1959).

(16) Panson, A. G., Adams, L. lI. .

Gas Chromatog. 2 , 164 (1964).

117) Pauschma nn. H..

2

Anal. Chem.

,

203. 16 11964).

(18) Purcell,

J.

E., E

(19) Purnell, H., .Gas Chromatography,

Chromatog.

D.

286, Wilev. New York, 1962.

Xtre, L. S. ,

.

Gas

3

69 (1965).

( 2 6 )

Rothman,

A . J., Bromlep, L. A , ,

Ind. Ena. Chem. 47. 899 11955).

(21) Schmiuch,

L. J.,

Dinerstein; R.

A, ,

(22) Sm ith,

B .

I ., Bowden,

W .

W.

(23) SDencer.

H.

M. . Am. Chem.

SOC

ANAL.

CHEM.

32 343 (1960).

Ibid. 36 82 (1964).

(24) Stuve,~K. ,n Gas Chromatography-

1958,

p.

178, I). H. Desty, ed.,

Aca-

demic Press, X e w Ynrk. l Q 5

(25) lerzele, AI., J .

(1964).

Talanta 10

937 (1963).

(26) Williams,

A. F.,

Murray,

W.

.,

RECEIVED or review April 7, 1965.

Accepted July 22, 1965. Pre-ented at

the Pittsburgh Conference

o n

Analytical

Chemistry and Applied Spectroscopy,

March 3, 1965.

Theory and Applica tion

of

Cyclic Voltammetry

f m Measurement of Electrode Reaction Kinetics

RICHARD

S.

NICHOLSON

Chemistry Department, Michigan State University, East Lansing,

Mich.

b

The theory of cyclic voltammetry

has been extended to include electron

transfer reactions which are described

by the electrochernical absolute rate

equat ion . Results of theoreti cal calcu-

lations made it possible to use cyclic

voltammetry to measure standard rate

constants fo r electr on trans fer. Thus,

a

system which appears reversible

at one frequency may b e made to

exhibit kinetic behavior at higher

frequencies, as indi cated b y increased

separation of cathodic and anodic

pe ak potentials. The standard rat e

constant for electron transfer is de-

termined from this peak potential

separation and frequency. The

method provides an extremely rapid

and simple way to evaluate electrode

kinetics. The reduction of cadmium

i s

used as an illustration.

U R I N G

RECENT years a number of

D methods have been developed

fo r t he measu remen t

of

electrode reac-

t ion kinetics. I n one sense, some of

these determine electrode reversibil i ty

indi rect ly by measur ing the apparent

standard rate constant for elect ron

transfer from only cathodic (or anodic)

polarization. In a few cases both

cathodic and anodic polarization give

consistent results ( I S ) . M an y of the

relaxation techniques developed for fast

reactions have the disadvantage tha t

smal l ampl i tude per turbat ions are used,

and consequently differences or changes

in mechanisms are not easily detected.

A

method which overcomes this dis-

advantage an d a t the same t ime gives

a

direct e stim ate of reversibility is

cyclic triangular wave voltammetry.

Thu s, the presence of homogeneous

reactions in the mechanism is readily

detec ted, and in terpre tation of results

usually is simple. l direct estimate of

electrode reversibility is provided, be-

cause the potentials

at

which oxidation

and reduction occur are observed

directly. For example, at low fre-

quencies i t may be possible with a given

system t ha t electrochemical equil ibrium

always is maintained a t the elect rode

surface. Under these condit ions the

sepa ration of catho dic an d anodic peak

potentials is about 6 0 / n mv. , and t he

reaction is reversible.

Clearly for this case no kinetic in-

formation about the electron transfer

reaction can be obtain ed. However, if

frequency is increased sufficiently, a

point may be reached at which the

kinetics of ele ctron transfe r become

competi t ive with the rate of potential

change. Under these condit ions

it

m a y

be possible to stud y the kinetics of the

electrode reaction, and the separation of

peak potentials should be a measure

of t he stan dard r ate c onsta nt for elec-

tron transfer. Thu s, a t least in princi-

ple, one can est imate s tandard rate

constants simply by observing cyclic

polarograms on the oscilloscope, and

then increasing the triangular wave

freque ncy until the separation of peak

potentials becomes greater than 60/n

mv. The s t andard r a t e cons t an t t hen

should be a calculable function of fre-

quency at this peak po tential separation.

Unfortunately, there is no a priori way

VOL.

37,

NO. 1 1 , OCTOBER 1965 0

1351

7/25/2019 Nicholson 1965

2/5

0.4

n

0

I

120 60 0

60

-120

(E - E h mv.

Figure 1 . Cyclic polarograms showing

effect of charge transfer coefficient, a

iC

=

0 . 5 ; CY =

0.7

...... C

=

0 . 5 ; a = 0.3

to mak e thi s correlation because effects

of con centr ation polarization can be

treated only by mathematical analysis

of the mass tran spo rt processes. Such

an analysis is not available for the

present case, and consequently applica-

tions of these ideas using cyclic voltam-

metry have been limited to simple

s ta tements tha t a given sys tem appears

to be reversible or irreversible

( 7 ,

IO).

I n the st ud y of electrode reaction

mechanisms, it often is useful to be able

to obtain experimentally a rapid esti-

ma te of electron transfer rate s. Be-

cause this appeared to be possible with

cyclic vol tamme try in the w ay jus t

described, we have attempted

a

theo-

retical treatment

of

the problem which

includes the effects of c once ntratio n

polarization. Our primary objective

was to determine if cyclic voltammetry

could be used to provide rapid and

reasonably accurate determinations of

s tandard ra te constants for e lectron

transfer. Thu s, the theoretical correla-

tions between peak potentials, standard

rate con stant , and rat e of potential

scan have been emphasized, although

other correlations are possible.

A

seri-

ous limitation of this approach would

result if peak potential separations

depended also on the charge transfer

coefficient, C Y . This would require an

independent measure of C Y and m ake the

meth od of little use in ter ms of t he

stated objectives. However, through

proper selection of conditions, peak

potential separations become nearly

independent of

a .

Becauqe there is neither theoretical

nor experimental ad van tage to consider-

ing more tha n one cycle of th e applied

triangular wave, theoretical calcula-

tions havt been limited to this case.

ConsideratioIL also has been restricted

to the case of an situ generation of the

reduced form

of

the couple under in-

vestigation. This actually has two

advantages. First, it reduces by one

th e number of indep endent variables in

th e theoretical calculations. Second, it

has the experimental advantage

of

not

requiring preparation

of

amalgams of

known concentration for the study of

reductions at mercu ry electrodes.

The method described can be applied

to systems in which homogeneous

chemical reactions precede or follow

electron transfer provided such reac-

tions are either rapid or slow compared

to the s tandard ra te constant for e lec-

tron transfer. The cases in which

these conditions are not met are easily

detected from the form of th e experi-

mental current-voltage curves 11) .

Th e redu ction of ca dmiu m is used as

an i l lustra t ion of the method developed

here. Application to other systems is

in progress and will be reported else-

where.

THEORY

We assume the following mechanism:

O + n e * R I

There k , and ka are heterogeneous ra t e

constants of t he electron transfer, and

are assumed to be f unctions of potential

as expressed through the electrochem-

ical absolute rat e equation. The time

depend ence of electrod e pote ntial is th e

form of an isosceles triang le. Syste m I

is assumed to be initially in equilibrium,

Both and R are to be soluble either

in the electrode or solution phase.

T o account for concentration polariza-

tion, diffusion to a plane electrode is

assumed to be th e only source of m ass

transport . Mathematical formulat ion

of this problem follows

kf

kb

aco

v o

_ -

a t - D O T a x

t 2 O , x = O

Undefined terms have their usual

significance 11).

With the e lectrochemical absolute

rate equat ion, Equat ion 6 can be t rans-

fo rm ed to

There

E

is the electrode potential; E o

is the s tandard potent ia l ;

k ,

is the

s tanda rd ra te cons tan t

at

E

= E O

LY

is the transfer coefficient; an d the

remaining terms have their usual

significance.

The potent ia l in Equat ion 7 f o r t h e

first scan (reduc tion) of th e trian gular

wave takes the form

(8)

=

E ,

- ut

and for th e second scan (oxidation)

E

=

E , + u t - 2uX

9)

Here, E , is the initial equilibrium poten-

tial, v is dE/d t , and X is the period of

the triangular wave.

If

Equa t ions 7 , 8, a n d

9

are combined

th e result is

aco

ax

o

k , ( C o * / C ~ * ) - " [ S x ( t ) ] - *

x

CO,

=

0 -

( C O * / ~ R * ) ~ A ( ~ ) ~ R ,) (10)

Th e func t ion Sx t) is defined as

t < X

(11)

2ax

t >

( t ) =

where

a =

nFv/RT

12)

Equa t ion

10

is t he final form of bound-

ary condit ion

6 .

By application of Laplace transf orm

methods the above boundary value

problem can be converted to the follow-

ing dimensionless linear integral equa-

tion w ith v ariabl e coefficients

X(Y) [?(CO*/cR*)sd( / )

=

4

T o m a k e E q u a t i on

13

dimensionless the

following substitutions and changes

of

variable were made:

Y

=

(Do/DR)"' (14)

y =

at

(15)

16)

4 = y 4 s / l / * a D o

(17)

x(y) = Do

aco

,/Co*l/?rao,

For

large values

of

$ (large k ,

or

small v Equa t ion 13 becomes independ-

e n t

of

4

and CY and reduces

to

t h e

1352

ANALYTICAL CHEMISTRY

7/25/2019 Nicholson 1965

3/5

(E

- E,,h, rnv

Figure 2. Cyclic pol arograms showing

effect

of

charge transfer parameter, +

$ =

7 .0 ; CY = 0.5

. $ = 0.25; CY =

0.5

..

6

80

100-

6 ,

3 120-

140-

160-

corresponding equation for reversible

(Nernstian) electron transfer

11).

Likewise, as

$

approaches zero, Equa-

tion

13

approaches the case for tota l ly

irreversible electron transfer

(11).

T h e

int erm edi ate case, which is of int erest

here, is described completely by Equa-

tion 13.

Solution of Integral Equation.

E q u a t i o n

13

cannot be so lved an-

a ly t i ca lly . Al though a so lu t ion in

th e form of an infini te series can be

obtained, series solut ions for more

th an one-half cycle becom e hopeless ly

com pl ica ted . Th e on ly p rac t i ca l ap-

proach , the re fore , which fo r the

presen t case can be app l ied wi thou t

loss of ge nera lity, is numeric al evalu a-

tion. We hav e used

a

method described

previously (1

) .

Several othe r methods

also are poss ible , and apparent ly the

method used by DeTtries and VanDalen

(6) involves less computational time

for comparable acculacy ( 5 ) .

Solutions of E quat ion

13

were inde-

pendent of values of r (C , * /CR*) pro-

vided r ( Co*/CE*) was greater than e6 5.

This corresponds to the experimental

f a c t t h a t

if

R is absmt ini t ia l ly and the

voltage scan is begun a t potentials

anodic of th e pcllarographic wave,

current-voltage curves are independent

of the exact initial potential selected,

All calculations have been performed

using

r (Co*/CR*)

=

e65.

With this s implif iaat ion i t

was

possi-

ble to calculate numerically current-

voltage curves. These curves depended

on three vaiiables,

p

y, and

A. It

has

been shown previously that

h

affects

only the anodic wave, and that there

the effect on anodic peak potentials is

qui te small

( 1 1 ) .

This is particularly

the case when switching potentials close

to the cathodic peak are avoided

[ Ex- El ,Jn> 90 mv.].

All calcula-

t ions reported here are based o n

a

value

of (Ex - = 141/n m v. Thus ,

-

-

I I I

calculated current-voltage curves could

be interpreted on the basis of only two

variables,

\L

a n d

a.

Results of Calculations.

W h e n

becomes sufficiently large

( k ,

large,

or v sm a l l ) , cur ren t -vo l tage curves

calculated from Equation 13 are inde-

penden t of the kinet ic param eters

$

a n d

CY. For this case results are identical

to ones obtained previously where the

electron transfer was assumed to be

S erns t i an

11).

Thi s limit occurs when

$ > 7, which is in good agreemen t with

calculations of Ma tsuda and Ayabe (8).

W h e n $

0.5

th e converse holds.

The second effect involves

a

slight

displacement

of

the waves along the

potential axis. Fo r example, as

Y

decreases, the cathodic peak is displaced

cathodical ly. At leas t for the data used

to construct Figure I , th e effect is slight.

Lloreover, as the cathodic peak shifts

cathodically with decreases of CY t h e

anodic peak also shifts cathodically.

Ther efor e, in ter ms of differences of p eak

potentials, AEP, changes in

CY

t e n d t o

cancel. Th us, value s of

AEp

for the

present case are nearly independent of

cy in the range 0.3 < CY lode1 SK2-V operational amplifier

(G.

A. Philbrick Researches, Inc.

Boston, Mass . ) . To improve rise-time

and increase current capabilities,

a

Philbrick Model

K2-BJ

booster

amplifier was used in series with the

potent io s ta t . T he bandwidth of the

potent ios ta t was adjus ted for the solu-

tion used to provide optimum rise-

t ime and s tabi l i ty .

To

do th i s the

ideas of Booman and Holbrook were

used

I , 2 ) . A

good qualit y commercial

potent ios ta t (e .g. , Wenking Potent io-

s ta t , Br inkm ann Ins t rum ents , Wes t -

bury ,

3 Y.)

presumably could be used

in place of th e poten tios tat just de-

scribed.

Two different signal generators were

used, and both proved adequ ate . One

was constructed from operat ional ampli-

fiers and has been described previously

1 0 ) .

The o the r was an Exac t Mode l

255 funct ion generator (Exac t Elec-

tronics, Inc. , Hillsboro, Ore.) which

proved useful and v ersatile.

The d etector was

a

Tektronix Model

536 oscilloscope provided with

a

Po-

laroid camera a t tachment (Tektronix

T y p e

C-12).

The vert ical input

was

always

a

T y p e

D

plug-in preamplifier.

This could be operated in the differen-

tial mode and p ermitted use of a floating

load resistor in the po tentiostatic circuit

10).

To measure scan ra tes for the

function generator constructed from

operational amplifiers,

a

T y p e

T

plug-in

preamplifier was used for the horizontal

inp ut of th e oscilloscope. W ith the

Exact funct ion generator, scan ra tes

could be dialed directly with an

ac-

curacy of

=t2

and this proved to be

a

considerable advantage over th e othe r

signal generator.

To

measure peak

potential separations

a

T y p e

H

plug-in

preamplifier was used for t he horizo ntal

inp ut of t he oscilloscope. T he hori-

zontal axis then was driven by the cell

potential, and peak potential separations

could be measured with a n accuracy of

a b o u t 1 2 m v.

Th e cell assembly has been described

previously

10) .

Materials. S olu t ions were p repa red

f r o m c a d m i u m s u l f a t e ( B a k e r

A. R.)

and anhydro us sod ium su lfa te (Baker

A . R. ).

Th e concen t ra t ions were : cad-

mium sulfate, ea.

2 x 10-4M1;

sodium

sulfate,

1.0 X ,

The exact cadmium

concentra t ion was not determined.

Xeasurements were made in

a

cons tan t

t em pera tu re room a t am bien t t em pera-

tures of

23

t o

25 C.

RESULTS A ND DISCUS SION

Both one-cycle and multi-cycle

(steady state) experiments were run

and as would be expected the differ-

ences between A E p for the two methods

were of t he order of ex perim ental erro r.

Nevertheless , data reported here are

for one-cycle experiments to conform to

theoretical calculations. Fo r all experi-

ments an initial potential of

-0.370

volt

us.

S.C.E.was used, and the ampli-

tud e of t he triangular wave always was

300 mv.

Results for reduction of 2

X 10-4M

cadmium in

1.022

sodium sulfate are

summarized in Table 11. To conver t

experimentally determined values of

Table

II

Determination with Cyclic

Voltammetry of k, for Reduction of

Cadmium

AEP

v , x

n,

ke,

volt/sec. mv. 5 cm./sec.

48.0

94

0.70 0 . 2 5

60.0 98

0.61 0.25

90.0 108

0.48 0.24

120, o 115 0.41 0.23

a Determined from Figure

3;

see

b 2 X 10-4M

cadmium sulfate,

1.OM

Equation

17.

sodium sulfate.

to

k,,

the

diffusion coefficients

of

Okinaka

12)

were used.

A

value of

IL

equal to

0.25

also

was

used. Although

no effort was made to determine a

accurately, the value of 0.25 was esti-

mated by comparing with theory the

symm etry and shape of cathodic and

anodic waves for cadmium. Th e calcu-

lated value of

k ,

is fairly insensitive to

variations of

a

s already mentioned.

The values of k , in Table

I1

agree

reason ably &-ellwith some oth er workers

14).

The disagreement with others

(12,

14)

is no t entirely explained. Th e

appar ent ra te constant does change some

with different supporting electrolytes.

Fo r exam ple, we find

k ,

equal to about

0.6 cm./sec. in 2 M perchloric acid.

The value in sulfuric acid is slightly

higher. In addi t ion, e lectrodes are sub-

ject to an aging effect noted b y D elahay

( 3 , 4 ) .

We also observe this decrease of

apparent ra te constants with t ime, but

the effect in our solutions is no t as g reat

as

Delah ay found (about

a

facto r of tw o

change in

k ,

for the first

20

minutes

quiescence).

Th e upper limit of rate constan ts tha t

can be determined by the above method

appears to be s e t by

a

combination

of

factors . F irs t , in the measurement

of peak potential separations, uncom-

pensated ohmic potential losses are

a

serious source of error. Thus, for the

rapid scan ra tes required to s tudy fas t

electrode reactions, peak c urre nts be-

come fairly large and even relatively

small solution resistances can introduce

serious error. Moreover, the effects of

uncompensated iR drop qual i ta t ively

are very similar to kinetic effects

(9).

This is amply i l lus tra ted by Figure

3

where the dashed cu rve is

a

plo t of da ta

calculated previously for the effect of

iR losses on cyclic voltammetry 9).

Th e definition of th e horizontal axis ($)

of Figure

3

for this case should b e

(9)

:

=

l / ( n F / R T ) n F AX

( T ~ D O ) ~ C ~ * R ,18)

Th us, the variation of peak po tential

separation w ith scan rate is quite similar

for th e two cases.

The effect of ohmic potential losses

can be minimized in three mays. Firs t ,

1354

e

ANALYTICAL CHEMISTRY

7/25/2019 Nicholson 1965

5/5

relatively conce nt-rated electroly tes of

high conductivity can be used to reduce

the tota l cell resistance. Second, with

a

three-electrode potentiostat place-

me nt of th e Lugg-in capillary probe in

close proximity with the working elec-

trode serves to compensate for

a

ma-

jor ity of th e tota l cell resistance [see

Iiooman and Holbrook for the exact

relat, ionship

(2)1.

Thir d, re la t ively low

concentra t ions of dectroact ive materia l

can be used to keep tota l cel l currents

small. Thi s latte r approach is limited,

however, by charging curren t . Thu s , a t

high scan ra tes charging current may

become an appreciab le fraction of t he

total cell cuirent, especially when

lo^

concentrations of electroactive mat'erial

are used.

For th e cadmium sys tem inves t igated

here

a

concentration of

2

t o 5 X

10-4Jl

appeared to be opt imum for low cel l

currents without excessive charging

current contribut ions . hIas imu m peak

cur ren ts n-ere of the ord er

of 0.2-0.3

m a.

Total solution resistance (ea.

20

ohms)

measured by peak potent ia l shif ts on

moLing the Luggin probe more than

10 radii from the working electrode

agreed with values calculated from the

conduc tivity of th e solution

2).

B y

careful placement of the Luggin probe

the uncompensated resistance was esti-

m a ted to be

3

to ohm s

2) ,

s o t h a t

maximum ohmic potential losses were

of t he o rde r of

1

m v.

The upper l imit

of

ra te cons tan t s

measurable with cycl ic vol tammetry

therefore depends on several factors.

The most im portan t of these is proba bly

conduc tivity of th e solution und er

investigation . W ith electrolytes of rea-

sonably high conduct ivi ty, i t should be

possible to measure rate constants as

large as

1

to

5

cm./sec.

LITERATURE CITED

(1)

Booman,

G. L.,

Holbrook,

W.

B.,

( 2 ) Zbid.

35, 1793 (1963).

13) Delahav,

P.,

Trachtenberg,

I., J . Am.

ANAL.C H E M .

7, 795 (1963).

Chem.

S i . '80 094 (1958).-

(4 ) Delahay,

P., J . Chim. Pkys .

54,

369 (1957

.

(5) DeVries,

W .

T.,

Free University,

Amsterdom. The Xetherlands. orivate

communication, 1965.

Electroanal.

Chem. 8 366 (1964).

Zbid.

5 , 17 (1963).

chem.

59. 494 11955).

(6) DeVries,

W. .,

VanDalen,

E., J .

(7 ) Galus, Z., Lee,

H. Y.,

Adams, R. N.,

(8)

hlatsuda, H., Ayabe,

Y.,

2 Elektro-

(9) Nicholbon,

R .

S. ,

ANAL.CHEM.37

(10 ) Nicholson, R .

S.,

Shain,

I., Ibid.

667 (1965).

p.

190.

(11)

Zbid.

36 06 (1964).

( 12 )

Okinaka,

Y., Talanta

11,

203 (1964).

(13 ) Selis.

S. >I.. J . Phus. Chem.

68.

~

2538 (1964).

(14) Tanaka,

X.

amamushi, R.,

Electro-

RECEIVED

or

review June 28, 1965.

Accepted August

3,

1965. Presented in

part at the Division of Analytical Chem-

istry, 150th XTeeting ACS, Atlantic City,

N . J.,

September 1965. Work supported

in part by the United States Army Re-

search Office-Durham under Con tract

No .

DA-31-12PARO-LL308. Other sup-

port was received

from

the National Sci-

ence Foundation under Grant

KO.

GP-

3830.

chem.

-4cta 9,96 3 (1964).

Pola r o g

ra

phy o f Lead(II) i n A q u e o u s H yd r o f u or ic

Acid 1 to 12M) with

a

D r o p p i n g - M e r c u r y

Electrodle of Tef lon

HELEN P. RAAEN

Analytical Chemistry Division, Oak Ridge Nation al Laboratory, Oak Ridge, Tenn.

b

The polarographic behavior of

Pb+2 -0 .03 to 0.8rnM) in aqueous

HF

1.00 to 12.00M) was studied with

a D.M.E. of Teflon. The po lar og rap h-

ically usable potent ial span for

12.00M

HF i s

about

+0.4

to

-1.0

volt

vs.

S.C.E.; for

.OOM

HF, the limit extends

to about - .2 volts. With in this span

only one polarographic wave for Pbt2

exists; it is for the polarographically

reversible 2-electron-change reduction

Pb+* -+ PbO.

The

E l l 2

values de-

termined are

-0.:380

for

1.00M

HF)

fa -0.370 for 141.00M

HF)

0.003

volt vs. S.C.E.; the values are not

affec ted by change in Pb+2 concen-

tration. The wave is

of

excellent

form and is usable for both quali-

tati ve and qirantit citive purposes. The

relation of

j d ,

andl also of ( /dt )maz,

to Pb+2 concentrati on is linear; plots

of these variables pass through the

origin. With increase in

HF

concen-

tration from

1.00

to 12.00M, no

change occurs in the number of lead

waves, shape of the wave, polaro-

graphic reversibility of the reduction,

or

n ;

the

i d

deceas es slightly; and

the El/* becomes about 10 mv. more

positive.

HE

D R O P P I N G - N E R C U R Y

electrode

of

T

e f lon (DuP ont )

has

been described

8),

nd i ts operat ion in noncorroding

media was inves t igated

(9,

1 0 ) . A

review w as given

(8)

of th e polarogra phy

-done before th e D. 3I .E. of Teflon was

developed -of substances in liquid hy-

drofluoric acid and in aqueous acid

fluoride media.

The polarography of lead in acid

fluoride media has been s tudied to

a

l im ited e s ten t . Wes t , Dean , and Breda

( 2 1 ) obtained a well-defined wave for

lead in

0 . 5 X

Na 2F 2 [qic]-O.Ol gelatin

solutions of p H 1.1 to 2 . 75 tha t con-

tained considerable amo unt s of nitric

acid added to dissolve th e lead f luoride

precipitate; the solutions therefore con-

ta ined lead ni t ra te and s l ight ly dis -

sociated hydrofluoric acid. Th e polarog-

rap hy of lead, as

PbF2,

n l iquid hydro-

fluoric acid was invest iga ted briefly by

Clifford

(2).

Mesar ic and Hum e

( 7 )

used polarography to s tu dy lead f luoride

complexes and their solubi l i t ies ; the

solut ions they s tudied were 1mJf in

P b + * , u p t o

0.7M

in

F-,

and of 2M

ionic s t rength adjus ted by adding

KaC104. Wi th

a D.M.E. of

Teflon,

Headridge and associates s tudied the

polarographic behavior

of

the ions

of

a

num ber of e lements, including lead, in

0.1X NH4F-O. lM

HF

4 )

and polaro-

graphical ly determined molybdenum in

niobium-base alloys using

0 . 5 X

HF-

0.5M H2S04 as sup port ing medium 5) .

W i t h t h e D.M.E.of Te flon, the polaro-

graphic characterist ics of Pb + 2 in

aqueou s hydrofluoric acid solutions have

now been s tudied in some detai l . Th e

data given herein are the f i rs t polaro-

graph ic da ta repor ted fo r P b+2

in

aqueou s solutions of reasonably high

HF

concen t rat ion and t ha t con ta in no o the r

add ed constituents-e.g. , a salt to con-

tr ibute ionic s t rength or a maximum

suppressor.

EXPERIMENTAL

R e a g e n t s . S t a n d a r d

Solutions

of

P b + 2 n

Aqueous

HF.

A q u a n t i t y

of

l ead f luor ide , F bF z ,

B &

X purified

g r a d e ) c a l cu l a te d t o g i ve 1 m X

solu-

t i o n w a s a d d e d t o a n a q u e o u s s o lu t i o n

of HF (1.00, 4.00,

8.00,

o r 1 2 . 0 0 M ) .

Af te r m axim um d is so lu tion the so lu -

tion was filtered to remove undissolved

P bF 2. The P b+* concen t rat ion

of

the

filtered solution was determined by

a

separate analysis in which

HF

was

removed from tes t port ions by fuming

VOL.

37,

NO.

1 1 ,

OCTOBER

1 9 6 5

1355