FARE tl
CHAPTER x * Principles of foUngr^
28
Polarography introduced by Jaroslav Hayrovsicy in
the early twenties is based on the characteristics of the
ourrent-voltage curves obtained when unstirred solutions
of electro oaddixabla or oleetro reducible substances oro
electrolysed in • coll in which ono of to® electrodes
is a dropping aoreury electrode.
then an electrolyte is subjected to electrolysis in a
call in which ona of the olootrodos is a dropping oars try
alactrod® and a saeond non-polarizable electrode, it is
plausible from the resulting currant-voltage curves or
polarograma to dotanaina both tha nature and eoaeantration
of tha reducible or 03& disable substance or substances
present.
The height of the curve is called the Halting current.
This Halting our rent obtained with the dropping electrode
is caused fcy a state of concentration polarisation which
results from the depletion of the concentration of the
electrolysed substance at the alactrode surface by the
electrode reaction (oxidation or
urrent
approaches tha Halting plateau whan tha reducible or
oa&dlxable substance is redused or ojd. diced as aeon aa it
roaches tha elactroda surface and its eoneentratlon at the
eleetrode surface remains constant at a value that ia
negligibly smell compared to that in the body of the solution*
Under these conditions^ the eurrent resulting from tha
electrode reaction Is independent, within certain Units
of the appHed e*a*f« and is governed solely by the rate
of supply of the reducible or oxldlsabl* Ion to the electrode
surfsee from the surrounding solution*
In general two forces are operating when ions are
supplied to the depleted region at tha electrode surface*
(1) a diffusive force proportional to the concentration
gradient at the electrode surface end (2) an eleetrieal force
proportional to the potential difference between the electrode
surface end the solution* The Halting currant can,therefore,
be regarded as the sub of diffusion currant end the algration
current*
The current through an electrolyte solution is carried
by all the ions present irrespective of whether they take
pert in the electrode reactions or not* The fraction of tbo
total current carried by an ion dapanda neatly upon its
relative concentration and to a lessor degree on its charge
or in other words on the transference number of the ion*
If a salt whose ions do not take pert in the electrode
reaction is added in excess to a solution of relatively snail
concentration of the reducible or o 3d disable ionsv the current
through the solution is that transferred practically by tha
large excess of the added ions* Under these conditions the
eleetrieal foreea on the ions talcing part in tha electrode
reaction are practically eliminated and the Halting current
becoaes singularly e diffusion currant*
30
Xn the cage of reducible or
ojcL disable
uncharged
sibstance* diffusion usually plays tbe main rale ia gewenaiag
the Halting e arrant bees use tnehargsd sibstaneas are net
sibjested to eleotrioai migration.
The indifferent salt whith
is added for stgipresalag the algratien component is sailed
the • exporting electrolyte, base eleitfelytet beet grated
electrolyte or earrier electrolyte*.
Few salts have the
ee^laa&ag ability tee.
Sene netals yield wares only ia eertaln
supporting electrolytes.
These salts also give a snail residual
currant at d.n»e. which is a sun of eeadeaaer current endthe
faradie current due to reducible Impurities present ia the
solution* The aagdtude ef the condenser currant ia air-free
eolations dth a normal eapillery and drop tine ia a few tenths
ef e dare empore. Xn aeeurate diffusion currant neaamaeiita
it ia aaeantial to detardaa tha reddml eurreat ia tha
partieuXar supporting olaetrolyto used.
The diffusion currant ia dependent on a amber of
factors iaeiuding tha diffusion oooffioiont ef the depolerieiag
a ib stance and its aonaantretion ia tha body of tha solution,
tha aiaabar of Faradays consuned ia oaa nels of the olootrodo
reaction and tha araa of the electrode.
Polarogrm>hie measure*
aente are neatly ussd to dstsrdae ths ooaecatratioa ef the
ioa or the asleoules in question but they are also voluble
ia stadias of diffusion oooffioients sad of the produsts of
the electrode reaction.
31
An important oatheaatioal relationship pertaining
to the diffusion current is shown in the Illtovic equationi
ta
- 607 n C
DV* ,V3 tV«
ld
•
avaraga diffusion currant, ui (1Q~* tap)
a
»
nuober of Faradays par as la involved ia the
electrode reaetian
C
•
concentration of tha electro active arterial*
nllliaoles/lltre
D
-
diffusion coefficient of tha eleetro active
arterial* an2/sec
a
•
rata of flow of aaroury through tha eapillary9
Og/Sac
t
»
tiaa between successive drops of aaretary9 See.
WhsPO
Tha torso
aad t^ ora dapandant ea tha oharaotor aad
also of tha capillary^ tha tarns ay C9 aad O1^2 art deter*
alaad hy tha propartlas of tha solute aad aolrtioa»
sonatinas tha faetors pertaining to any oaa alaetrode
process uadar a fined sot of aj&ariaaatai conditions ara
cortined ia a single factor l9 sailed tha diffusion a tar ant
o on stent given as
X
«
$07 aD*^2
*
1 1 1..
32
The diffusion our rent is dependent on aunber of footers
including the diff usion coeffioiexit of the depolarising stiN»
stance and its ooneentretlon in the body of the oolhilsioa*
atadber of faradaya eonsuaod in oae mole of the electrode
reootiea9 the area of the electrode and the transfer
coefficient.
The zlkovio equation is valid wily if the ware
obtained is solely due to diff usion of ions fron the body
of the solution to the eleetrode surfaae» This equation
fails if the wave obtained is partly or wholly controlled
by the Kinetics of the reaetioa9 the preaaaae of oatalytieally
active s distances in solution or the adsorption or either
the oaddised or reduced ion or greips on the surface of
aeroury drop*
So the validity of this equation is daoidod
by considering Whether the poleregraphlc wave obtained, is
diffusion controlled or not*
To deeldo this tho following
factors are const fered*
(1) id is proportional to
%V^» igm the other
factors in tho Xlicevll equation art oonstant*
The drop
tine *t* dapends iq>on the heights of narcury coltm* K«net9
if tha wave is diffusion controlled K *• i^ / yli^* This
is tho frequently used aethod of asoertaiaing whether tha
height of the wave la diffusion controlled or not* If *K»
is net oonstant within the Halts of experimental error
33
•W a aid* range of the aereury heights it My he concluded
that the a trreot mat be either partly or wholly governed
by the rate of
mm
process ether then the diffuses of
natal ions*
(2) *B*f is the diffusion eeeffleient in the Xlhavlc
equation is given by the Nernst equation as
idieref
R
*
the gas eonstait in volt-coulonba per degree
f
)vf»
»
absolute temperature
the equivalent conductivity at infinite dilegion
2
a
the ehirge of the ion
P
•
the niMber of oouleabs per Parsday
the conductivity ef the solution varies rapidly with
testerat tre eaitsing ohanges in D and henee in value id*
Noraally D and id values Inerease by 2 and 3 per cent
respectively per degree rise in teaperetmre*
High devi­
ations fro* these values are seamen tests for kinetic ami
catalytic currents*
(3) When ether footers in ths Ilkovi'c aquation rsnala
constant ths diffusion current id is dlroetiy proportional
34
to the concentration of the reducible or oxidisable st*~
stances* Hence a graph plotted between the diff uaien current
end eoneentretlon of the e&steaee should give e straight
line if the were is diffusion controlled* Shi s fores the
quantitative aspect of pelaregrqphy*
Conpl* action of s estel ion dsereeses the diffusion
current if the ligsnd is bigger in sise to the water noiseules
it replaces and shifts the half-wave potential generally to
the acre eathedie value* These too variables induced by
increasing concentration of ligand allow the deteradnetion
of coordination nusber, siss9 and stability oonstsnts of
complexes in solution or servo to oluaidsto tho idnetiea of
the rate dotarnining step depsnding upon the type of the
electrode reactions*
Pelerographie analysis is oerrisd out with an
enperinsntsl set up that tnsurss Arep fernatien uadi abutted
by vibration or stirring* This hoops convection in a solution
at aittiata* However, a oonvaation or streasing of solution
results from the oleatrodo reaction itself and is therefore
very reproducible* This phenomenon exists in s thin layer
around the mercury drop* Since much more notarial is brought
to tho electrode by convection then by diff uaioaf the o tar onto
become very ouch larger than pure diffusion current a. They
are easily recognisable alnoa they are not maintained over
35
ft large voltage apan bat diminish mare dr leas abruptly
to the manlier value of the diffusion currents, giving
rift* to sharp or rounded aaadae on th* pelaregraphle
curves# Hftada* are observed most frequently «t the
beginning and oocasionelly la the middle of the straight
portion of « Uniting ourrent.
A aeadmua aajr be found
during ft reduction or oaddition of ionised or non-lonised,
organic or inorganic substances* the aaadnft my be aeUte
or rounded dreading on the nature and eoneeatrfttioa of
the material radueed bid also on the concentration of the
indifferent electrolyte and the real stance of the circuit.
In general the maadms become smeller the ledger the drop tine
of the electrode, increases with an increasing concentration
of the electromotive netoriel, tm kinds of naadna may ha
ebsexved and these art naadna of the first kind end asjiaa
of the second kind*
Maxine of both kinds arc obstacle to quantitative
polarographlc analyses.
They can be eliaiaated by Idas
addition of small quantity of mead mum suppressor to the
solution.
Shis aid stance la adaerbad on to the surface of
c dropping electrode end then retards or prevents motion of
the solution past the drop surfsee* Host popular mead nun
suppressors are some of the surface active reagents like
gelatin, agar, organic dyes and friten X-1QQ.
They wist be
36
preaeat la aaaller concentration.
At higher concentration
they r«d«, Interpretation of polarograma 41111a alt tor
dial al old ng the lifting current #1 the adtosteaee itself,
fhe effectiveness of a suppressor tan toe expressed as the
nasi nun dilation ex* tha mini sura nseassary lor soap let#
stpprasslan of a glvan aaxlnua.
Polarogrephic analyses eon too used directly for tha
determination of say suhataneo solid* liqtd.d* or gaseous*
organic or Inorganic* loola or nolasular that oan too rsdtsad
or ojddlsod at dropping mercury electrode.
One of tha aost
inportant advantages of polarography Is tha dateraiaaftion
of too or aora sUtstaasos toy ototalalag a single a tarantpotential curve.
Another important technique Is tha anparo-
natarla titration which involves polarographla asaairaaonts*
Zn addition to analytical uses, polarography la one of tha
aost fruitful techniques of rassarsh la physisal* inorganic
and organic ahanlstry. This technique is ^reading mam
widely la stf>si diary fields Mho toioshe*atry» pharaaaautical
ahanlstry* anvironnental ahanlstry and others.
Zt la toeing
used to study diverse topics as hydrolysis* aolifcility,
copies fornatlon* adsorption* the stolehlonetry and kinetics
of elradeal roaotlona* tho noehanlaaa of olootroda raaotlon
and of ehanleal roaotlona aesaqpanylag than* standard and
fernal potentials, nsleculatr dimensions* the affects of
struct is* on reactivity, sad many otters of intorost sod
Importance.
Electrode reactions at cUawe. can be broad2y divided
Into reversible end irreversible processes* Reversible
reactions are so rapid that thenaodynaadc equilibrium Is
very nearly attained at every Instant dirlng the life of a
drop at any potential* On the other hand Irreversible
reactions are so slow that they proceed only a fraction of
tho way towards equilibrium during the life of each drop*
For these reactions It Is the rate of the electron transfer
process and the aanner in which this la influenced by the
electrode potential that governs the relationship between
tho currant Mid potential* Between these two electrode
reactions there is an Interasdlate class of reactions that
are feat enough to approach the eqt&llbritm during tho drop
life but net quite ao fast that they appear to rente It
within the experlaentai error of the aeaauraaenta* This
type of electrode reactions ere known as quasi-revert* bio
reactions* She values of standard rata constant. 8L of
■* a
these three types of reactions are given as follows!
38
1*
Reversible processes where
K8 » 2 x 10“* on See'
2.
Irreversible process
Ks < 10“* on Sec*4
%
Quasi-raver sible process
\*2x 10“2 to
Vf* on S
the theory of reversible processes was well-e st ablished
in the early stages of the development of the field.
R«r«r.hl. .1—trod. r—mam «t d-m...
Consider a reduction rotation occurring at tbo
dropping mercury electrode which mey bo represented ne
0
♦ no^=±ft
...
(1)
that the oxidised species Is brought to the electrode
sirfaee it can be redtsed at a proper potential,
The trans­
fer of the species Is due to the three nodes of transfer
vis., Migration, convection and diffusion.
Diffusion
baaones the nolo node of transfer, convection and aigrafcien
being avoided,
the current depends upon die kinetics of
the electrochemical reaction and on the rate of ness trans­
fer to the electrode surface.
When this reaction is rapid
and chemical equilibrium is attained at the electrode, the
process becomes reversible, and Merest equation can be
applied.
Then the potential of the electrode is given as
as
E * E? •
Jn
3
(2)
^tare ^ is the standard potential, a° and *g ara tha
aetivlties of tha species at tha electrode sirfaoa
correlating E, E^2f tha helf««ave potential* 1, tha current
at potential E and id tha diffusion currant*
Heyroraky and
I Urnvie derived the equation as
h/z
& - j§ 3a
• **
(3)
and
*•• (4)
... (9)
whara
£daa * appSiad petantial of tha dropping aarcurjr alaatroda
*
E^2 • half-wave potential of tha d«pelaxi ser
1
« aaan currant at tha appliedpotential
id
« tha diffusion currant
a
- amber of eleatronainvolved la tha preeass
F
* Faraday
40
The Above equation indicates that
log i/id *1 Til dheuld give
a
a
plot of
straight Mm with slope
equal to 0«0591/a telts which is the met common criteria
for the thermodynamic reversibility* The intercept on the
freuds gives the helf-wevc potentisl9 E^g.
Erenthough
this linear reXstlonship is usually taken as an ioportant
orlterian for estabMahing reversibility of the polarographie
process it should be used with great caution.
W*ry often
a linear plot is obtained for processes classified as
irrereral ble.
is non-integer.
However, in such a process the value of n
Sometimes the observed slope of such a
plot for a reversible wave nay differ from theoretical value
by 3-5 aV but nay difference is greater than this is a
proof for irreversibility*
The diffusion coefficients of
the osddised hQ and reduced species
are very nearly sane
in ntsfeer of eases. Therefore# it felloes from equation (3)
that the half-wave potential in the ease of reversible
processes is Identical with the standard potential of the
system.
The other footers which can be considered to decide the
roversibiMty of an electrode process are given belt*
Teats method requires the measurement of Ej^ end E^ i.e.
the potential! at ttoleh the current is equal to thrae-fourtha
and one-fourths of the dlffwion current.
At E^# we have
41
6*5349
V* ■ Va-2*^ **
la -1^
Ml
(6)
...
(7)
lag 3
•
Co)
leg ^
...
(9)
• •*
(IQ)
“ El/2 " a*Jaa >•* V3
end at
* ^1/2 **
ao that
E*^ — ^1/4 * *
.
*
0*0564
n
Hence for e reversible electrode reaction
m Ea/4 mm* *• equal to * 0.0564/n
7iie
half-wave potentiel of e reversible wave ie lade*
pendent of the concentration of the substance being reduced
or oiddixed*
in appreciable variation of
«dth
concentration is a proof of irreversibility of the reaction.
The reverse is not trusv however, for the half-vev-e potential
of nanjr irrararaible waves are alec independent of
concentration*
The neat conclusive pooni of ravarslbillty of a
reaction is secured whan poXerograms of solutions containing
the reduced fora of redox couple involved in the reaction
a.
It, UNIVERSITY
S.NTAPUR'S'S00*
42
are found to give medio waves whose half-wave potentials are
identical with the cathodic half*«cve potentials of the
oxidised fora*
This is the same thing as see taring «
ooqpeslte naira with no inflaation around the residual current
curve with a solution eontaining both the oxidised and the
reduced forms* It Is worth while to sake sure that the
eathedle and anodic *id‘ s obtained with equal oono antrations
of the reduced and oxidized species srs approximately equal*
Zn such s esse the point of inflection is the redox potential
of tha erst no*
In addition to thaaa common criteria of reversibility
there are several others that ara lass eftan used, partly
baoause spatial information must be obtained to permit their
application and the important one among thaaa ia tanparatura
coeffielant values*
The tMperature coefficients of s reversible wavs
depends on the nature of the eleotrode rotation* For a
reduction to e natal soluble in mercury dEjy2 / dfc is about
•0*7 mV/degree and for a homogeneous reduction &y2 / dt
may be either positive or nagativa but is rarely greeter
than * 1 nV/degree* The temperature coefficients of E^2
for an irreversible wave is almost always positive and ia
usually of the order of several mV/degree* larger temperature
eoafflelants of Ey2 thersfors constitute a fair evidanee
against tha rsvaraitoility of the wave*
Various aathods to studr rsvarsibl* and irrsrarsibla
•lootrods roaations at d»n,s. h«ra toon given in detail
in suBoaediag sections.
CO
*1
44
Books referred
Nab*,
l*
Hsyrovsicy, J, sod
J*» Principles of Polarographjr,
Acadeadc Proas* Now York* 1966*
2*
Xolthoff* X,N»* *Polarography* * Inter science Publishers
Inc,* New York* ¥01# X and XX* 1992*
3,
MeLtes* U* 'Polarographic Techniques* * Inter science
Publishers, Xne,* New York* 1965*
4,
Lingene, J,J,* *Elootro Analytical Chemistry' *
Interscience Publishers, Inc,* New York, 1933*
3,
Milner, G. W*c., 'The Principles «M§& Applications of
Polerogrcpkr* * Longmans* Green and Co, * New York* 1938.
6,
WOlssberger* A. and Bo salter, B»W,* * physical methods
of Chenistry* * klley-Interseienoe Polishers, New York*
¥0X# X* part XX* 1971,
7#
Crew* i), h» * *poXerography of natal eoaplexexes*,
Aoadeoie Press* New York* 1969,
8,
Longm&r* X.S.* ‘Advances in Polarogr^hy**
Symposium Public stions OLvisLon* Pmrgaman Preaa*
Oxford* Vol# X - XXX* I960,