The effect of cell resistance on acute polarographic maxima

JOURNAL

THE

OF ELECTROAN_XLYTICAL

EFFECT ACUTE

OF

RESISTANCE

=POLAROGRAP%tIC

I. %I. KOLTHOFF. School of Chemistry.

CELL

CHEMISTRY

of Afinmsota,

(Received

ON

MAXIMA

J_ C_ III-XRSHXLL

University

209

AND

S.L.

Xinmapolis

May znd,

GU-PTA I$, Mime.

(U.S.A

.)

1961)

INTRODUCTION In systematic studies of the effect of various factors upon the height of acute polarographic masima in solutions of high specific resistance, it was noted that the height of such masima varied with the dimensions of the electrolysis cell and especially with changes in the separation between the dropping mercury electrode (D.&l.E.) and the mercury pool reference electrode. It was obsen-ed that the effect of increasing the separation betxveen the D.M.E. and the mercury pool electrode was qualitatively equivalent to the introduction of an e-sternal resknce into the circuit. In a private communication Prof. H. .,A. L_~TISEK suggested that the resistance of a polarographic cell consisting of a D.M.E. and a mercury pool reference electrode be considered to be composed of an internal resistance located in the immediate licinity of the growing drop, designated as Ri. and a constant external resistance designated as N,. The internal residing in the liquid separating the electrodes, the life of each mercury drop reaching a minimum as the of internal resistance with the growth of a mercuv drop has been calculated by ILKOVIC~_ This author idealized the system by considering the electrodes to be concentric spheres of radii 7 and 7’ separated from one another by a space filled with an electrolyte of specific resistance Q_ The resistance, Ri, is given by the following expression :

resistance varies during drop falls. The variation

BRDICK.~‘, who made an extensive study of the effect of estemal resistance on the height of acute maxima eshibited by weakly acidic mercurous nitrate solutions, pointed out that the effect of Y’ in eqn. I may be neglected when it is greater than IO Y. Neither ILKOVIE~ nor BRDTCK-42 in their treatments take into account that a fraction of the cell resistance, Rcell. act s as an estemal resistance, R,. Therefore, eqn. 2 should describe both components of the cell resistance: Reel,

=

Rr+R,

=

“+R=

(2)

+=

where Ri is the “true” internal resistance and equal to Q/+ZY. Eqn. z predicts that the component which acts as internal resistance in a polarographic circuit depends only on the specific resistance of the solution and the characteristics of the capillary, J_

Eleclroaxal.

Cherrz.,

3 (1~62)

209416

I. M. KOLTHOFF,J.

210

C. MAR%iALL,

S. L. GUPTA

and not on conditions of cell geometry_ Therefore, any change in total cell resistance arising from changes in cell diameter or electrode separation must be due to changes in the estemal component, Re, of the total cell resistance. According to BRJXCK-4B, the x-zuiation of Ri with time (t) during the growth of a drop is given by espression (3) : Qt Rr

=

-113 =

3+‘d 47

&-'I3

(3)

113

(

+7

)

where nz is the mass, in mglsec, of mercury flowing and a the density of mercury in mg/cma. This relation is only valid if no polarization occurs. Combination of eqns. z and 3 yields the simplified expression r R CCL1=

Ri+R,

=

kt-lf=+RC

(4)

drop should According to eqn. 1 a plot of R cell US_t-113 during the life of a mercuv >Gid a straight line with a slope of k and intercept R,. Introducing into eqn. 4 the values of 22, and kt-l/3, with t equal to the drop time, yields the minimum cell resistance. The xvork presented in this paper is concerned with an esperimental determination of the value of k in eqn. 3 and with the validity- of the form of eqn. 4. EXPERIbIENT=V.

Mercurous nitrate was prepared according to the directions of BLAXCH-~RD~. The final product, a pure white crystalline compound, was stored o\rer anhydrone. Potassinrn chloride, analytical reagent grade, was twice recrystallized from conductivity Grater and fused at SooO. Mercury \vas triply distilled. Nickel perchlorate, copper perchlorate, sodium perchlorate, and potassium nitrate were of C.P. quality and used without further purification. Air useb to saturate solutions for the study of osygen masima was pre-treated by passing it through an acidified solution of potassium permanganate and then through water.

The

w-ater

used

for the

preparation

of all solutions

was

of conducti\
grade.

measurements were made at room temperature, 35 + IO. The measurement of electrode separation was carried out with a cathetometer. The reported values for rmined under conditions as identical as the rate of ftow of mercury, wz. were dete possible to those used in the determination of R-t cun-es. The polarographic cell used in most of the work consisted of a glass tube 2 cm in diameter sealed at the bottom and provided with a “cap” drilled to accommodate the D.M.E. A mercury pool on the bottom of the cell served as a reference electrode in most cases. Electrical contact with the pool electrode was brought about through a platin&n wire sealed in the bottom of the cell. Except in esperiments with osygen maxima, solutions were made osygen-free by purging with Linde nitrogen which had -1_A slow stream of nitrogen was been treated according to the directions of MEITES directed over the surface of the solution while an esperirnent was in progress. Cell geometry was changed by surrounding the D.M.E. by a narrow tube of the desired inside diameter which estended into the mercury pool at the bottom of the cell. Occasionally, wider cells of a conventional t_ype were used. All

J_ EZectuoanal.

Chem..

3 (1961)

zag--216

211

CELL RESISTAXCE Resistance

measurements

were

made

with

a

Leeds

and

Northrup

Wheatstone

Bridge, Model No. SSIZO, in conjunction with a signal generator operated at 0.5 V and IOOO cl-cles. An oscilloscope (Tektronic, type 502) with a masimum sensitivity of ZOO pV/cm served as a detector. The variation of resistance of the polarographic cell with time was esamined by settin g the bridge resistance displayed by the cell during the life of a mercuT drop. moment

the

stopwatch. the range

drop

fell and

the

moment

bridge

balance

This was repeated at re,@ar increments of resistance exhibited by the cell during

Resistance-time

measurements

were

usually

in the range of cell resistances The elapsed time between the occurred

was

timed

with

a

of bridge resistance throughout the growth of the mercury drop.

made

using

capillaries

of

normal

diameter (obtained from E. H. Sargent and Co., estemal diameter about 6 mm); these are denoted as blunt capillaries. In order to study the effect of the size of the diameter of the capillaq-, capillaries were prepared by drawing out wide bore (original inside diameter of I mm) capillary tubing to a very sharp point. Dropping electrodes so prepared had an estemal diameter at the tip of 0.5 mm or less, and are denoted as sharp capillaries. All polarograms were run with a Leeds and Northrup Electrochemograph. type E, without damping. The currents plotted in current -potential lines refer to maximum current at the moment the drop falls. The inverse of the slope of lines so plotted was taken to be the minimum The Specific resistances taken from with a cell apparatus_

cell resistance. of I- 10-r and

the data of JONES of the \irashbum

I- 10-e

M

potassium chloride solutions were All other values were measured AND BRADSHAW~.. t)pe and the above described resistance-measuring

RESULTS AND DISCUSSION The

effect

of electrode

separation

on

current

-potential

lines

in the

electrolysis

of

I- 10-3 111 mercurous nitrate in nitric acid is illustrated in Fig. I. In order to obtain large changes in cell resistance with changes in electrode separation a g mm tube, estending into the mercury pool, was placed around the D.RI.E. The esperiments shown in Fig. I were repeated by keeping the electrode separation at about Z+cm (corresponding to line I in Fig. r) and inserting ohmic resistance into the external circuit so as to obtain current -potential lines identical with lines 2-7 in

Fig. I. Current -potential lines in air-saturated solutions that were I. IO-" to 5-10-3 M in potassium chloride, in oxygen-free copper solutions that were 5- IO-~ M in copper perchlorate and I- 10-a M in potassium nitrate and in os)-gen-free nickel solutions that were I- 10-a i&1 in nickel perchlorate and I- 10-a M in sodium perchlorate were found to be affected in the same way by changes in electrode separation and external resistance as the current -potential lines shown in Fig. I. In all instances acute maskma were observed, but the current -potential lines were usually not as straight as those in Fig. I, indicating partial polarization before the maximum. As an esample determined in 0.1

of the validity M

potassium

of eqn. 3 the straight line plot of R&u vs. t-li3 chloride is presented in Fig. 2. In order to obtain a

relatively large cell resistance, a glass tube 12 mm in diameter the mercury pool was placed in the polarographic cell. Similar esperiments were carried out in I. IO-~ iW potassium J_ Ekctroaual.

and

extending

chloride;

5- 10-3

into M

Chzm.. 3 (1962) 109-=16

212

I. M.

KOLTHOFF,

J. C. JIARSEZALL,

S. L:

GUPT..4

mercurous nitrate that was I- IO-’ AZ in nitric acid and I- IO.? 111 mercurous nitrate tbat was 2-10-3 M in nitric acid. In all solutions the strai-ght line relation between t-113 and Rou was found to be obeyed. According to eqn. 4 the internal resistance, Ri, should depend only-on the characteristics of tha capillary and the specific resistaxe of the sol&ion in the cell, but-

80

0

0.2

0.4

0.6

0.8

E “5.

Fig. I. Current-potential Ekctrode separation - . . K (srope] in ohms:

lines in solution r - 10-3 in cm ; 4-S 4.0 12.700 15.100

EXPERIMENTS

time

=

g-3 set;

m =

IX

0.812

0.1

111

m g/set;

I .2

I .a

iI1 I

in Hgz(NO1), 6.5 20,500

5-7 7.800

TABLE Drop

IO

PJOI and 7-3 2”.700

nl in HNO,.

2.0.10-3

8.6 27,100

10.5 ; 32.700.

I POTASSIUX

e =

77.8

CHLORIDE ohm

cm;

cell diameter

12 mm. (Rn)mrn

(ohms)

o-75 1.gr 3.90 6.53 ro.rg

f4-4-t

386 392 392 391 380 380

241 346 525 677 1168 1571

59

IS2

I”5

IO-3

179

=77

I52

151

491

500

403

398

161

185

338

187

492 992 1390

I85 I76 IS1

she-uld be independent of the ceu gkometry and the distance-between the electrodes. Results-in Table I &h&v that in a givgh solution-t& slope of the R vs. t--1/3 plots, &cl therefore_ .I& _jnteti%l’re$is$ari~e -at -a given _ti&& t remtied constant, witbin experi-

213

CELLRESISTANCE

mental error, ahhough then electrode separation was varied from o-75 to x4_++ cm. Also reported in Tablet I are -Values of the rninimum~cell resistance, (Reen)niin, when the drop falls and of the portion bf cell resistance which acts as-external resistance (Rc)cen_ The last column in Table I gives the minimum internal resistance. (Ri),i*, bemg equal to (Rce&in --(Rd,eu which is -independent of electrode separation. The experiments reported in Table I were repeated in four different solutions with specific resistance varying from 77-8 to IIgo ohm cm. In Lll instances (Rs)&xvas found to vary in proportion to the specific resistance of the solution and- tb be independent of the geometry of the cell and the separation of the electrodes. Furthermore, according to eqns. 3 and 4 the minimum internal resistance, using the ~same capillary, in solutions with different specific resistances should be in the same proportion as the specific resistances and independent of the height of the mercury column_ This was verified bv data obtained in I- 10-3 _M mercurous nitrate that was a- 10-3 M in nitric acid where the chop time was 4-0 set, BPZ,1.65.mg/sec and e = 1190 ohm cm; and 5.10-3 M mercurous nitrate which was I- IO-" _M in nitric acid where the drop time was

1730 Ill0 4100

1590 1750 :

5 1650 S. CT 1630

2

1610 1670 1

1510

2300

1530 I 0.5

06

1

I

I

0.7

0.6

0.9

I

I.0

p3

Fig. z. Rcell vs. t--1/3plot in 0.1 _MKCL. Slope = 350 ohms seclj3; intercept = 1390 ohms.

05

06

0.7

0.6

0.9

1.0

I.1

t-53

Fig. 3. -Effect of diameter of capillary on sloDe R,11---t-~13 Dlots h solution r *IO-” M in kgq(NOa) and ;.o-10;3 _&f-in NH03. I. blunt capkary. drop time = 4.00 sec. m = 1.65 mg/ set ; 2. sharp capilhry. drop time = 4-10 set; 212= 1~70 mg/sec:

9.3 set, wz, 0.713 mg/sec and e = 242 ohm cm: The ratio of the specific resistances of the two solutions, IIgo/z@, is 4.9 which is in good agreement with the ratio of the respective minimum internal resistances, which was found to be &zo/5gI _= i-8_ Eqn. 3 does not consider the effect of the shape and diameter of the glass wall of the dropping electrode. That the diameter of the face of the capilky h_as ax-reffect /_ EZectvoanaZ. Chem.,~3

(x962) 2og-216

I.

31. KOLTHOFF,

J. C.

BIARSHALL,

S. L.

GUP-I-A

so

PI

,”

N”

::

J_ E+tvoanal.

a

Chem.,

3 (1962)

zag-2

16

CELLRESISTANCE

215

is illustrated in Fig. 3_ With capillaries of about the same characteristics and in the same solution the slope of the R-t-l/a line was found to be considerably less using a sharp capillary with an external diameter of 0.5 mm than with blunt capillaries with diameters of 6 mm_ EL-idently the value of k is affected by the external diameter of the tip of the capillary. Slopes of Rceu 2.5. 8-113 lines are reported in Table II in solutions with specific resistance varying from So to IZOO ohm cm using both blunt and sharp capillaries. The characteristics of-the capillaries measured under esperimental conditions are also given in this Table. Because of the shielding effect, the calcuIated slopes of then lines (eqn. 3) given in column S are considerably less than those found with blunt capillaries (column 7). Making an empirical correction by multiplying the k ~IVeqn. 3 by 312 the internal resistance at time t becomes: Rr = 31" kc-113=

The slopes of resistance-time curves calculated from eqn 5 were found to be. in satisfactory agreement with the e_sperimental slopes, as is evident from comparison of columns 7 and g of Table II. The shielding effect of the sharp capillary (last esperiment in Table II) is evidently so small that the esperimental slope is in satisfactory agreement with that calculated from ILKOVIC'S original equation (eqn. 3). The variation of the minimum cell resistance with changes in electrode separation was examined for all solutions studied. Plots of the minimum cell resistance zrs. electrode separation gave, in all cases, straight lines. The slopes of the plots, when normalized for differences in the specific resistance of the various solutions (i.e. d(Rceu)min/d electrode separation e), were found to be constant for a particular cell regardless of the specific resistance of the solution in the cell. This result indicates that (Qceu varies in a linear way with distance in electrode separation. This was verified in plots of (R,)celi ‘IS. separation. After the completion of this work a recent paper in Hungarian by DEVAY~ came to our attention. This author considered only (Ri)ceu and not (Rc)ceu and calculated from the dimensions of the capillary the correction to be applied to the k value in the ILKOVIC expression (eqn. 3) to account for the shielding effect of the glass walk of values of the capillary. Even though he did not consider (RJceu his calculated (Rceu)min agreed fairly well with the esperimental data. This agreement is accounted for by the small electrode separation throughout his work which minimized the effect of (Re) cellACKNOlVLEDGEhIEXT

This investigation was supported by a research grant from the National Science Foundation. We are indebted to Prof. LAITINEN for his comments when this work was

started.

In the absence of estemal resistance in the circuit the resistance of a polarographic cell, Rcell = Rg + R,, in which Rs acts as a true internal resistance in the immediate vicinity of the growing mercury drop and varies with time (t) according tomthe expression Rd = kt--1/s_ The component R, acts as external resistance, is independent of t J_ Eleclroanai.

Chew.,

3 (1962)

zag-216

216

I. &I. KOLlHOFF,

J. C. RIARSEMLL,

S. L.

GUPTA

and increases with increasing separation between the dropping electrode and- the reference electrode. The x%lue of k is smaller than-that caicnIated by ILKOSKC anddepends on the diamkter of the tip of the capillary_ With a capiLl& with an external diameter of the orifice of 0.5 mm the vaIue of k was in satisfactory agreement with that calculated by ILKOVIC. REFERENCES 1 D. ILKOVI~. CoZZect. CzechosZov_ Chem. Conzmuns., 8 (1936) 13. 2 R. BRDICKA. Collect. Czechoslov. Chem. Communs.. S (1936) +rg_ 3 A. A. BLXxCHXm, J. W. PFIELAE‘; AND A. R. DAVIS. Spzfhetic Inovgarric and Sons, Inc.. New York, 1936. p. 333_ 4 L. MEITES. PoCarograpAic Techniques. Interscience Publishers, Inc., New 5 G. JOKES ~-hn> B. C_ BRIDSMW, J_ Am. Chem. Sot.. 55 (1933) 1750. 6 J_ Dnr_ax-, ~Va~yar I-S-m. Fotyoirat. 66 (1960) 207. J_ Electvoanal.

CF.~~ntisfvy,

York,

Chem..

1955.

John

\iley

p. 34.

3 (Ig6a)

zag-216