Iterative computational method for the rapid analysis of iron and plutonium by controlled potential...

J.RADIOANAL.NUCL.CHEM.,LETTERS 126 /I/ 1-16 /1988/

ITERATIVE COMPUTATIONAL METHOD FOR THE RAPID ANALYSIS OF IRON AND PLUTONIUM BY CONTROLLED POTENTIAL

COULOMETRY AND SOME INTERESTING OBSERVATIONS ON THE COULOGRAM OF THE Pu(III)/Pu(IV) COUPLE

R.C. Sharma, P.K. Kalsi, L.R. Sawant, S. Vaidyanathan, R.H. Iyer

Department of Atomic Energy, Nuclear Materials Accounting Cell,

BARC, Trombay, Bombay - 400 085, India

Received 15 September 1987 Accepted 29 September 1987

An iterative computational method for the determination of metal ions in aqueous solutions which form reversible couples such as Fe<II)/Fe(III), Pu(III)/Pu(IV) etc. by controlled potential coulometry has been developed. The method involves carrying out the electrolysis to about 95-97% and calculating the total amount present in the sample by an iterative computational method. The method utilizes the direct application of the Nernst equation. The important criterion to be met is that the coulogram of the couple should strictly obey the Nernst equation. The validity of the method has been checked by analyzing about 50 samples of a standard iron solution. Results of analysis of mixtures of Pu and Fe by the iterative technique show that the interference of Fe can almost entirely be eliminated. However, analysis of Pu samples by this procedure gives results about 2-3% lower than the expected value. A careful examination of the experimental coulograms of Pu in IM HCIO 4 indicates a slight deviation from the theoretical coulogram, where as those of Fe match exactly.

Elsevier Sequoia S. A., Lausanne Akadg~niai KigdS, Budapest

SHARMA et al.: ANALYSIS OF IRON AND PLUTONIUM

INTRODUCTION

Coulometry is a well-known and widely used method in

inuclear materials accounting for the accurate determination

of U and Pu. However�9 there are certain minor disadvan-

tages like high background current, interference from ions

having formal potential values /E O / close to the ion of

interest and analysis time on the higher side for routine

application. In order to shorten the time of a determi-

nation, several calculational and extrapolation techniques

have been proposed for locating the end point of the

electrolysis without actually carrying it to completion I'2

However, these computational methods assume a constant

formal potential E O /Ref. 3/ for the reversible couple,

which is not found to be always valid. In the method des-

cribed in this paper, the exact value of E o' is computed

by an iterative technique and this value of E O' is used

to compute the total amount of the read-out for the

complete electrolysis of the sample.

THEORY

The Nernst equation is

E = E ' + (RT/nF)in([Ox3/ERed3) o

from which we get

([Ox3/ERed]) = exp[(E-E O )/K3

Ill

121

where E is the redox potential, E o is the formal potential,

K is the (RT/nF) which�9 for a one-electron reaction at

25 ~ equals to 0.025692 V. [Ox3 is the fraction in the

oxidized state and [Red3 in the reduced state. Substituting


[Red] = (1-[Ox]) in Eq. /2/ and solving for [Ox] and ERed]

we obtain:

' F EOx] = [exp[(E-E O )/K3]/[!+expE(E-Eo )/K]] /3/

ERed] = I-EexpE(E-Eo')/K]]/[I+exp[(E-Eo')/K] ] /4/

By substituting the redox potential after reduction, S red'

for E in Eq. /3/ and the redox potential after oxidation,

Sox, for E in Eq. /4/, the sum of [Ox] and [Red] is equal

to the fraction of the total metal ions which was not

electrolyzed for a given Sre d and Sox pair. Subtraction

of the fraction not electrolyzed from unity is the factoJ

f, i.e., the fraction electrolyzed which simplifies to

exp[(Sox-Eo')/K] exp[Sred-Eo')/K] f = - /5/

l+exD[(S -E ')/K] ox o

l+exo[(S _-E ')IK] - re~ o

Eq. /5/ permits the calculation of metal ion content for

any set of oxidation and reduction potentials.

In this method, the solution potential is initially

brought to approximately (E o' -O.i V). Read out is set to

O.OO and the redox potential E 1 measured exactly. The

oxidation is carried out to a potential of ~E ' and the o

read out (R.O) 1 and solution redox potential E 2 are noted.

The integrator is again reset to O.00 and the oxidation

carried out at a potential (E ~ +O.1 V). The solution

redox potential E 3 and (R.O) 2 are noted exactly. All these

potentials are refered to SCE. In order to calculate E f

O ' these 3 sets of values are substituted in Eq. /5/, we then

get Eqs /6/ and /7/

F f expE(E2-E o )IK] exp[(EI-E o )IK] fl = - /6/

I+exp[(E2-Eo')/K3 l+exp[(Ei-Eo')/K]

3


exp[(E3-Eo')/K] expE(E2-Eo')/K3 f2 = - 171

l+expE(E3-Eo')/K3 l+expE(E~-E ')/K3 �9 Z O

fl - fraction electrolyzed between potentials E 1 and E 2

f2 - fraction electrolyzed between potentials E 2 and E 3

fl = (R.O) 1 x C f2 =( R'O)2 x C, where C is a

constant.

Dividing Eq. /6/ by /7/ and equating it to zero,

(R.O) 1

exp[(E2-Eo')/K3

l+expE(E2-Eo')]K3

exp[(E3-Eo')/K3

l+expE(E3-Eo')/k~

expE(Ei-Eo')/K3

i%exp[(Ei-Eo')/K3

exp[(E2-Eo')/K3

I+expE(E2-E~')/K3

= o I s ~

The value of E o' can be calculated by an iterative tech- I

nique. Substituting the value of E o in the following

Eq. /9/, we get F, the fraction electrolyzed.

exp[(E3-Eo')/K3

F ~ l+expE(E3_Eo,)/K3

expE(Ei-Eo')/K3

l+expE(EI-Eo')/K3 191

Read out for complete electrolysis (R.O) 3 is calculated

as: (R.O) 3 = L(R.O) 1 + (R.O)23/F /iO/

EXPERIMENTAL

Apparatus and instrumentation

The cell composed of a Pt working electrode, Pt count-

er electrode and a saturated calomel reference electrode.

An indigenously fabricated CPC-352 coulometer and 4 1/2

and 5 1/2 digit multimeters were used for all voltage

measurements.


Sample material

A.R. grade ferric sulphate and spec. pure standard iron

wire were dissolved in IM perchloric acid from which ali-

quots were prepared /each aliquot ~4 mg of iron/. Pure plu-

tonium nitrate solution was evaporated to dryness and then

taken up in IM HCIO 4,

PROCEDURE

The expected E O for Fe(II)/Fe(III) in IM HCIO 4 is

+0.47 V vs. SCE and +O.71 V for Pu(III)/Pu(IV).

Step I.

Step 2.

Step 3.

Step 4.

Transfer the aliquot of the sample Fe(III) or

Pu(IV) quantitatively to the cell.

Reduce Fe(III) to Fe(II) by applying a potential

of +0.3 V till the solution potential drops to

about +0.37 V, i.e., (Eo'-O.l V). Note down the

exact solution potential E 1 and reset the cur-

rent integrator to O.O0. /The corresponding value

of El, i.e., (Eo'-O.l V) where Pu is used is

about +O.61 V./

Oxidize the sample at an applied potential of

+0.52 V till the solution potential reaches about

+0.47 V /i.e., Eo'/. Note down the exact solution

potential E2, i.e., /~Eo'/ and read out RO I.

/The corresponding value of E2, i.e., /%Eo' /

when Pu is used is about +O.71 V./

Reset the integrator to O.00. Oxidize the sample

at an applied potential of +0.65 V till the

solution potential reaches about +0.57 V, i.e.,

/E o' +O.I V/. Note down the exact solution po-

tential E 3 and read out RO 2. /The corresponding

value of E3, i.e., /E O' +O.i V/ when Pu is used,

is about +O.81 V./

SHARMA et at.: ANALYSIS OF IRON AND PLUTONIUM

J..IRead E1, E2~E3, R01& R02 J w

0.5 J [. Catcutate RI=L.H.S. of Eq.(2 ) J

t [., CaL~o.t~ R2-L...S. of,Eq.(2) 1

!

J Calculate F as per Eq.(a)J I JTota[ R03=(R01+ RO2)/F J {

J Write F & Tota[R03 J

No

/es

Fig. I. Flow chart for the calculation of the fraction analyzed and total read-out using iterative method

CALCULATION

Step i. Using the values El, E2, E 3, RO 1 and RO 2 and sub- l stituting in Eq. /8/ the exact value of E o is

calculated by the iterative method indicated in

the flow chart /Fig. i/.

Step 2. Substituting the calculated value of E O, in Eq.

/9/ we get, F, the total fraction electrolyzed.


TABLE 1

Analysis of pure ferric sulphate solution by iterative method

S.No. Fe, mg g-1 S.No. Fe, mg g-1

i. 28.325 16. 28.416

2. 28.336 17. 28.325

3. 28.451 18. 28.450

4. 28.428 19. 28.380

5. 28.394 20. 28.370

6. 28.268 21. 28.367

7. 28.325 22. 28.386

8. 28.360 23. 28.300

9. 28.405 24. 28.420

iO. 28.348 25. 28.390

ii. 28.256 26. 28.304

12. 28.336 29. 28.350

13. 28.371 28. 28.267

14. 28.427 29. 28.256

15. 28.291 30. 28.279

N = 30 -i = 28.362 mg g

RSD = +0.2% Expected X = 28.366 mg g-I by conventional

coulometric method.

Step 3. The total read out of RO 3 which corresponds to

the entire sample is calculated using Eq. /I0/.

RESULTS ANDDISCUSSION

The results of analysis of 30 samples of pure iron solu-

tion by the iterative method and compared with the con-

ventional coulometric method are given in Table i. Table


TABLE 2

Analysis of spec. pure iron standard solution by iterative method

-i S.No. Fe, mg g

l,

2.

3.

4.

5.

6.

7

8

9

lO

ll

12

13.

14.

7.313

7.322

7.312

7.310

7.338

7.346

7.340

7.348

7.321

7.329

7.313

7.331

7.333

7.319

N = 14 -i

= 7.3268 mg g RSD = +O.18%

-i Expected X = 7.3259 mg g

2 shows the results of 14 determinations of a spec. pure

standard solution of iron by iterative method. The re-

sults given in Tables 1 and 2 show that the iterative

method is as precise and as accurate as the conventional

coulometric method.

The iterative technique differs from the conventional

controlled potential coulometric technique in that, only

l


95-97%.of the electrolysis is carried out in the former

while in the latter, electrolysis is allowed to proceed

to completion. Thus the time saved in the measurement is

about 70% without any loss of precision and accuracy.

The fraction electrolyzed is calculated by an iterative

procedure using the HP-IOOO computer available in NU~C.

Error due to background current is reduced because the

span of electrolysis is narrowed to /E o' ~0.i V/ as

compared to /E o' ~O.2 V/ in the conventional method,

where E o' is the formal potential of the reversible

couple. The reduced span of electrolysis practically

eliminates interference from impurities having a formal I potential E ~ which is approximately 0.2 V higher or

lower than that of the ion being analyzed. The important

criterion to be met is that the couloqram of the couple

should strictly obey the Nernst equation since the method

utilizes the direct application of the Nernst equation.

The formal potentials of the Fe(II)/Fe(III) and

Pu(III)/Pu(IV) couples are +0.47 V and +O.71 V vs. SCE,

respectively, in IM HCIO 4. In conventional coulometry,

iron is expected to interfere with the estimation of

plutonium. In the present method since the electrolysis

is carried out over a narrow span /E o' ~0.I V/, no in-

terference from iron is expected. This has been verified

in a few preliminary runs. However, the amount of Pu in

the sample was fDund to be about 2-3% lower than the ex-

pected value /Table 3/. This can be explained with the help

of Fig. 2. The total number of coulombs obtained as per

the theoretical coulogram in the span of E' +O.i V are o --

from point A to B. The actual /experimental/ coulogram

is slightly deviating in the region of 0.5-0.65 V. The

total coulombs obtained as per the experimental coulo-

gram in the same span of E o" ~ O.i V are from point A'

to B, showing that the coulombs from point A to A' are

S H A R M A e t a l . : A N A L Y S I S O F I R O N A N D P L U T O N I U M

m

0

0

O -f-t

-~I

C~

, , - q

1 , 4 0 ,-

N 4 ~ O

O I> I1)

,-~

0

4J flJ

~J

~, -,~

~ 4J H

,tJ 0

,--t r~

0

4-1

O U

0

r-i

OO r~ O

I I I

kD r-'4 CO O4 O m ~ O ~ O

O4 O4 O4

OO 03 ~D O ~ O

Cq O4 O4

r--[ 04 0"3

10


1.0 . , 8

]_ "6

o.5 . . . . I c f I

I I i 1

I I -Exper i rnento[ cou log ram ~ ' / T heore t i ca l

u jA'_ .... ~// c o u l o g r a m 0 r -~ - 7 -~--"----~'; I I

O 4 �9 E o ' - 0 . 1 Eo ' E o ' * O , 1 0.9

Potential w . r . t SCE

Fig. 2. Comparison of theoretical and experimental coulogram

lost. It is because of this unaccounted loss of coulombs

from point A to A' that the results of Pu are low. To

study the deviation observed, several coulograms of Pu

samples both during oxidation and reduction steps were

plotted and critically examined. All the coulograms be-

haved in the same ways but the magnitude of the deviation

varied slightly from sample to sample. The reason for

this deviation may probably be due to the compiexing

of Pu(IV) or may be dependent on the sample amount etc.

The coulogram of pure Pu standard obtained from Radio-

chemistry Division, BARC showed the same deviation as 4

shown in Fig. 2. The couiogram plotted by Chitnis et al.

was replotted and examined. Again the same deviation was

observed as shown in Fig. 5. The coulogram plotted in

the report 5 was also studied~ The coulograms were super-

imposed by theoretical couiograms. The theoretical and

I]


0.3 "6

0

"U

~0.~ c ( ~ a~~logram L~Coutogra m i ,

02 0.4 0.6 0.8 1.0 Control potential

Fig. 3. Coulograms of plutonium and iron: A - theoretical coulogram; o - experimental coulogram

experimental coulograms of Fe matched well, whereas, the

coulograms of Pu showed deviation, as shown in Fig. 3.

In 1981 and 1983 a few coulograms of Pu were plotted by

us; they were reexamined and they also showed the same

deviation. All these results give enought evidence to

confirm that the Pu(IV)/Pu(III) coulogram deviates from

the theoretical one. But this deviation so far went un-

noticed because the coulombs obtained for the complete

electrolysis of Pu are the same in all cases, but when

the coulogram was scrutinized because of the reduced

span used, the deviation was noticed. The exact reason

for this deviation is not clearly understood at present.

It is possible that this deviation may be linked with

some complex formation and/or amount of Pu in the aliquot.

Since our main aim was to analyze Pu in the presence

of Fe, a few analyses were carried out to study the ef-

fect of Fe /Table 4/. The ratio of Pu:Fe was varied from

i:o to 15:1 by weight. The results showed increased positive

12

S H A R M A et al.: A N A L Y S I S O F I R O N A N D P L U T O N I U M

oel

r~

-;..4

,-w

0 .el

i>

0 LI

,-Q

~,C5 0

~ . l J 0

. , - I

,-I

r~

- , - I

0 4..I

tll

0

0 , - 0 - ,- I

r~

.el

O I

u

0 u

-,-I

O I b~

0 u

r ~o 0 ,-I

I I I I

0 oo Ma r

0 o~ 0 0

I ~ D c o

+ + +

I'~ ko i '~ O'h 0 ~ ~ ,~

o e J e e � 9 a l

d r-q

O -el

t~ ~4

�9

0 ,.~

0

4a

0

0 4~

D r

,.el

.ml

13


- - 0 . 4 12

E0.3 _ 9 E iO

._o >

~o.2. 6 8 t _

2

i

I 0 J I [ 0 90:10 80:20 70:30 60:40

Pu:Fe (Equivolent ratio)

Fig. 4. Theoretical estimates of errors: E o' of Pu = O.715 V vs SCE, E o' of Fe = 0.465 V vs SCE; Electrolysis span for iterative method: E o' +0.i V, electrolysis span for conventional method-- E ' +0.2 V o - -

bias with increase in the amount of Fe by conventional

coulometric method. On the other hand, even though a

slight negative bias of the order of 2-3% was observed

by the iterative method, it was found to be independent

of the amount of Fe. The observed negative bias is in-

herent in the coulogram itself. This very clearly in-

dicates that when the Pu:Fe weight ratio is 15:11 the

interference due to Fe is negligible in the determination

of Pu by the iterative computational method reported

here. This is further illustrated in Fig. 4 which shows

that the theoretical estimates of errors introduced in

the determination of Pu by the presence of Fe in the

aliquot.

14


!=,,

A 0.5 0,6 0.7 0.8

E Vs SCE n volts

Fig. 5. Coulogram of pure Pu: o - experimental curve; A - theoretical curve

When the ratio of Pu:Fe is 80:20 /equivalent ratio/,

the bias in the iterative method is +0.07%, whereas in

the conventional method the bias is +3%. This shows

that the conventional method gives an error of 40 times

higher than the iterative method.

0.24 0

~5 0

0.18 I !

0.12

0,01

0.01!

The authors are thankful to Mr. M.R. Ponkshe, Radio-

chemistry Division, BARC, for fabricating controlled

potential coulometer, CPC-352, which was used in the

work.

15


REFERENCES

i. M.K. Holland, J.R. Weiss et al., Anal. Chem., 50, II /1978/ 236.

2. F.B. Stephens, F. Jakob et al., Anal. Chem., 42 /1970/ 764.

3. F.A. Scott, R.M. Peekema, U.S. At. Energy Comm. Rep. HW-58491.

4. R.T. Chitnis, S.G. Talnikar, R.G. Bhogale, S.K. Patil, Anal. Chem., 50 /1970/ 53.

5. M.V. Ramaniah et al., India, At. Energy Commission, Rep. BARC, 464, 1970.

6. W.D. Shults, Talanta, i0 /1963/ 833.

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