PROBLEMS CONCERNING THE ELECTROCHEMICAL THEORY OF DISSOLVING METALS IN ACIDS

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• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00039R000100100081-1
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 35
• Document Creation Date: January 4, 2017
• Sequence Number: 81
• Publication Date: February 16, 1951
• Content Type: REPORT

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50X1-HUM
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~CT~OCH~CAL T ~t ~ ORY OF UIS~OLVINU
Title PROI~L~ CONCL'R~~INa T~ ~
ACxDS by Yep V. lrurdin ~USSn)
METALS IN
Vnl XVIII ~ No 3, M~?rch 198 ~I~~~eeiari I
Source: Obeh�h 2 ~
mon Per ~ o ~ 69T2 I
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HF H~lAI
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Ff,~~ ~ 1 ~ ~ h a d
~U ~ ~l ~ ~ 4r~ ~Q
Yr~ ~ ' f~

~~~~~~t~ ~I}~~x~~i~l y9 ~ Y�~~~'~''!
l ~ i
~ ~
d~;c P ~
i�~~~rtk typl~; ~
' 'M1 ,j `
'r ~
r ~
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50X1-HUM
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PftOALEM9 gN~~UN`i'E~.~ IH THE ~,k;C'rR~CMF~IIC Tli .
GaVLPNINt1 T~iE DISSAL'~TION 0~' ML: 9 IN hCIDB IV
Yap V. Durdin
i,ab of Inorganic Chen
Leningrad State Univ
~ indioate that the speed of dissolution of metals
At present many works
he a eed id not markedly influenced by the dii'fueion o
(assuming that t F
in laws which govern the speed of the electrode
reagents) may be studied acccrd g i
~rooees of hydrogen liberation and the anodic
processes, i.e., the cathodic f
~e of metal ions into the solution (1-9). We find
process with the esca~
s sup oeition in experiments of Wagner and Traud
direct verification of thi Tp
n of the seed of dissoll:~tion of zinc amalgams and
. (2) on the determinatio
e on these amalgams, and also in the work of
the hydrogen overvoltag
kin on the speed of dissolution of lead and the
Kolotyrkin and A� N. From
drogen overyoltage an lead
hY
e of this supposition rests to a considerable degree
The theoretical bass
evich and N. Frumkin (7) and also upon the con-
upon the work of B. a� L
lesions obtained in our previous re~~orts (9)�
c
zed that these laws hold not only for the case of
We should emphaei
hick is studied in our works} but also for the
metals dt~ssolving in acids (w
'r~ corrosion since this type of laws corresponds to
general theory of metal
. ,
- and Khor diagrams (oathode-anode control)
. ~ _ ~ the special case of the Evans
r..
~ (10~ 11}~
f1 I R ~ ' i'. 1
~ - P 1'j~p ' ~ ' ~
y 4'.
` ~
~"f~ `
ii'.
1 k;x~l" d ~ ~ ~
)n riirgt' ~L' 3Y' ~x'
~ : i`J:

X11. a ~
Y
E
~,t
..f
0
s
.,r ~ Ap ~P4~f fi ~ 4+ ~ f~fi ~ t ~
n.+~ i,
9y F
k X11 ~"r ~ Nf ~ ~~f~5f ~ ~
1 ~r~~J, y ~~3~'6{i1~,oTr. 1~7 ~~p~. t~~~ , ~ .t'~'~ ~S YK' I ,i a 4~'Y f ~ ~ ~ ~ ~j
i
of 1'y~
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E
f ~I~~ ~
~O~~IO~H
t
j
In A. A. Ak~mQv~s Y~ecQntly publ,iahad monA~raph ~~`i'haary and MEthado
o#` lnv~otig+~~ing ~a~a~len in ~~etal.s" (1~ tl~ie ty~~~ laws in metal oor-
rasian is also considmrad as a real poaslbi],ity~
Thiia special intero~t is at,tac~hed to tho laws ~Qverning tha speed in
tho cathodic prACess ~i' h~raro~;en llberatiAn ar;d tho arl~lic process rel6aalrtg
metal ions into tho eol~~tion~
o'
In principle, ~rjN cart ~er~r~relly salve this E=,rot~lpm by �imultar~epuely
solving the equations describing t~~e speed o!' t~;e catha.iic and anodic proc-
oaeQe and by deriving ~r~e cor~~ieo~~or~ding ~~#~oral equ~~tian~ An attem~tt to
derive such an equation was made by A. I. Shulttin, by a m�thod involving
grew di!'fict~lties as is a~~parc~nt from hiA works `these dii'ftculti�e arise
~ partially fz~om t~~e complexity of the exfression obtE?ined, az~d also i'r~m t1~e
der~et~der~ce of this equation upon n?~antitic?s not easily determined In
addition, t~~e ~~er~4r+~1 Ar~?1At~inn will na~?~ra11~,y depend upon the corr~,ctness
o~ both individ~~al equations descr~:bin~; the spuds in the cathodic and anodic
rocesses and ~~~~on which equation should be used to express thet~dpeed~o! the
P ,
anoc'ic rrocess
Taking these facts into consi.der~ti.o~~, one should represent more con-
~a
rretely the problem of how much eetch oi' these processes influences the
t;
lcinetics of dissolution of metals
concrete presentation of this problem should treat quantitatively
the laws governing the dissolution of met~ls~
At first glance the laws governing the speed in cathodic and anodic
a~ ~ 1
rocesses in some cases can be treat in a substantially simplified manner ~
P ~
because the kinetic �~aeight degree of
influence) of the cathodic process
m so sharply predominate aver the kinetic weight of the anodic process
~4Y
that one may neglect the influence of the latter Actually, one could quite
naturally assume that the kinetic weightrg of the cathodic w.nd anodic processes
H
~t ~ yin s.;~ ~
S~ i ~ ~t. Qy1 r
f t 3~~rt.~ ~ ,t
~ ,
~ ~ ~ ~ ~ ~r r ~ y
t i y ~
~ ~
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-t _ ,
~ a
CDN
' r
~~~a
} j
:
to the amount of pol~&rl~atiQn i~n ooch
should carrespond, ~tY~ouph roughly! -0
Mareaver tho avsrvoltage eorre?~pc~nc'in~ t~o the catlludio
of thaae praceeeoe~ ,
rli .h while sna~ic (chet~?ical) palaz~~2ation is rQlativaly
-rocoss is gE~nerall.y , ;
weak f nr most metals. ~'l~ua ~ ~'cl ~ mar incl ides libez~a ~iQn and dlachargc of
A Cu h iar~s ernong el~ctrodA ~racessQS which begin immediatoly
Zn, Cd, any Phi ~ B
ai'tar attuinan~;nt a~' aquiliUr~.um potontialo (more i~recidply, for very low
~?o~.riiri~ation}.
`1'hua oc?o ,naturally asaurndo shat 1n trio dioaol talon of many metals the
f; ari~.ation m ~A A~' tl~e order of t~undreths di' a volt ar~d tk~o cathodic,
anodic p l aY
tenths of a volts i.e. cat,~~odie pol~4ri~ation may tea ton time�s ~;reatcr than
anodic pc~lari~.ation. At i'irot F;la~iee, with this ratio between th�se ~ti~nt-
~:tics we should rightly can5ld?~r that the cathr~llc process practically
r~~nea the kinet~.cs o!' the system, This should simplify considerably
date
meet of the laws determining; the sjaeed oi' dis~ol~~tion of metals
the tract
Unfortun~tQly, such evxl~?~tiona of thn uin~tic wpig;ht of these processes
are urel intuitive and therefore might 1 sad to incorrect conclusions.
p Y
In th~.s work, we attempt, using the methnd which we developed pre-
vir~usly for evaluating the kinetic weight of ~ocesses, to present more con-
' he en@ral icture of the possible relations between the kinetic
cretely t 6 p
`F
weights of the cathodic and anodic processes and at the name time to clarify
it
3`~
the significance to be attached to the relations between the values o
y cathodic and anodic polarization.
1. Concernin the Coefficients: J� � and in The S stem
(d - r~~1 Y
' I ~
de and Anode Prar.esses.
of Catho
~l~ ~ rocesa" ~
In the works entitled 'Concerning the Kinetic u~eight of a P ,
}
three coefficients that oharacterize the kinetic weight of a
we introduced
the coefficient J�~ governing the disturbance of equilibrium
r process: namely,
ocess the coefficient governing th� decrease in the process
in the pr ,
and the coefficient Ogoverning the influence of the parameters in
9~8@d
the equation for the procesa~ speed.
-3-
COH~IDEN1
l ~ e "
~~e N > r ~ i t
r f ~tii T+~I~
t FL
~ ~a 1' ~ ~ ~ ~ ~
+ ~ ~
1 1
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4
_ -

1
i
~O
NFIDEH7
Ill
n c+rder t~ olarif~r the meaning of theca Qao~'f'icienta in a giv@n system,
I
~ Qnditiar~all that t~lo ep�ed of tha cathodic procooo of
we at f1r~t aacQ~ t c Y
t ar,d tho spaad c~~' tt~t.e anadfc proceeo ro~.aaaing met~1 ions
~lydra~en libor~ ion
the ec~l~~ti.~n are prapQrti~~1a1 to t~~e ;anlsrixatian cerr~es~anndin~ to
into
t,r~oae ~~rocesses
~ we ha o to ohAw grapliiGallY
Adcpting at first this vory aimplo aAaum(tf n~ p
~e whole ,icturo of kinetic weight in the cat~~odic and anodic
how com~ale~tely t~ ~
~~o~~{saes chan~;ee wk,cn wo shift to mnrro rr~alietic assumptions ccncorning
p
th� 1'unatio ~ rflatione betwe�n e;?~ed ana ~~~l~ari~atio~l~
We adopt, ccnee~~ gently:
k
k
~ a c~
In these ec~uatiorls is a E~otential identical for both electrode
rocessos for a stationery ststo, relative to ar~y st,~,cla~'d elcctrode, for
p
exam le a normal hydrogen electrodes but taken with the reverse sign '
p ~
die overvc?lte:ge for the cathodic process of hydrogen libera-
Q ~k is t
t
tiara ~ is the equilibrium potential rorresponding to this prorese
under the given conditions; ~A is the corresponding equilibrium pot-
~ . ns ie the polgrization corresponding to th� anodic a
emb~al for metal i o ; ,L1
t
rocess releasing metal ions into the soh~tion. W`e assume=
fi p
~:.j ~
~n~ ~ ` ~A
Q ~ ~k
~k
a the resulting speed of the cor-
yk and ~A ~ here as later depot
T/ is the difference between the speed of the
responding processes; i~e.~ ~
direct reaction discharg~.ng hydrogen ions and the ionization speed, and
is the difference between the speed of release of metals ions into the
t
i
- 4 ~
FD
I BHT
+
T 1 K ~f r gfil~~,;;.~ 1
J I ~ ff 1
t 9 ~a1}+x , ~
4 ' r R
r~., r' ~
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, _ -
C H ~ al
0 ~ID~H I
1
9
x:
1
j,
e~lutian anti !.hQ s~~eod of their diooherge~ Wo r~xraider bath a~aoede measured
by thc~ corresE~onding val.uoe r,f current denall~y or b~ tha numb~?r af' gram-
equivaento o~ hydrag~ri (in ~hF ca~.A cat y ) or metal (in the oaao off' ~/A )
relAaaad ar diaoalvcd r ~~r unit time peer unit Cen,'~ triCal y ~rx~i'aco of the
mAtal~ (Wo also conelder the crirrar~t dor~sity mc~aaurad relative to unit
geamotrical a~trfa~ye of the metal dideolved)~ Uridor t~ie;~e cnnclitione, 'car
1~~1e dta~ioa,ary state w� havo the equality _
: ?/A
Figure l (kig~rres a~;perrded) o~~owe ~;ra~+t~ically ep�edo ~Jk and v ,
vere~te ~ , aecc?rdin~, to equations (la) r~r1c (lti) ~ ~'he ~jn~nt a des-
criboc? Gt~A ~tc.~t,ionary state, This paint is enttivalent to the unicaue speed
V � Vk � V~ ~?nd tlra ~~nigt~a potential ~ ~ This d~a~rc~m correer~onde to
~van'a ~lia~rs,m fir oathod~c~-anodic ~~or,tral~ A4 tho same titrid we easily s�e
+,liat in the system of the; c8thodSc and anodic. procossr~~ tl~e potential
ple~ys the {art of s regulotting ~,arameter, wh ~ ch w~~ deno~ ti~ in the general
case by Z; therei'ore, from the etandpoi~t of the ;1rinciple:~ developed in `
our work entitled "Concerning tree Kinetic Weight of a ~'rocess", ~F ~tt~is
dj pgram is a parts cular case of the speed dia~;r~un -that is, a regulating
~~ararr~eter. Making use of this, we mar easily clnrii'y the meaning of the
i
coeff~.cients � and ~j f~?r the given system of Rrocesses~
1
r
i
Recalling this, acr,~~rding to the definition given in our second report
entitled "Concerning tt~e Kinetic Weight of a Process" we set the coefficients f
a ! ;
a'
tt� An1,~1 t~~ rec~~.cti~cl~,
� ~ c 0
_ LiZA ~ zee
} A (2a)
J� = 4Z � d Z� (zb)
6 AB
r
1n the expressions (2), ~ Z ~ is a conditional measure of the dis- i
y> ~
t~.trbance of equilibrium corresponding to the processes A or B. QZ� ie equal ~
s
� ~ w
N~ D~NTlA
I
~
a
1 1
I ~ M
1 ~.x g
~t ~ i ~ ' ~+I Ii ~ ~ Y ~ ~ 1 ~ ~ ~
( f 7 ~
y F~ 7 1j.', i
l t EE//_ 't 1
I ~ " ~ '
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-
~~~I~~
~0~~~~
iatian of t~la regulating paranetbr (Z) wti~c~~ io note�~ary ire ardsr
to tl~e v r
e uili-
tA drive the given proGOSS trora a given at~~iot~ery stets to a stets of a
brium when all romaining ~~axa?n�t~rs in its spaod aquatlon amain eAnatarit~
~ Gc~tlditional mAaatrre of tt~e disturbance of oquilibrium of the syetemr
is a
A~' A b r
n tt~s ivsn system c~~' proceos~e 2 � ~ ; t~?orsfore ~ZK ~ Q Kf
i g
~,E~ ar.dr~~' to
~ ~ A ~ K A ~
A A AK
Therefore according to equation (2a), t~lo coefficient of equilibrium
distu~~baa~`~e oi' tt~� rat~~od~e ~-rococs is equal to:
~ ~ .
and the coet'ficir:nt a3' ea~~ilibrium disturba~~tre in the anodic ~:arocesA J~ is
eq?ia1 to
a a
e~
stem of cathodic and anodic processes, the quantity ~
thus, in thn sy
e took as a mQasure of c~ouilibrit~m disturbance of the system is equal
whjch w
~ c
e between the equilibrium potentials ~ and ~k
to the different A
Whili~ the coefficient of equilibrium dist~~rbance of each of these processes
I"
' is a ual to that frartian of this quantity ~?ich is due to poliarization in
q
the correspon~~ing proce9s~ The meaning of the coefficients for the
~
iven s stgm of ~1rocpsges cR.n be clarified in the following manner: '
g Y
r= If we assume that in firgure 1 the straight line Vk occupies its same
osition while the straight line V coincides with the normal NA, then the
P ~ A I
mate is determined by the point V ~ In this case, the co-
stationary k max
~,r' ~ efficient of equilibrium disturbance of the annodic process is equal to zero,
~~y
-6-
a~
N
l~~~DE
C4
, ~ ~ ,'I"' , ~ ~
~ , ~ ~ 3s? ' ~
i t' ~ ~
r `-i;~
~
r
~j�
~ ~
' ~
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PY pp

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-

i
4
1
CO~~ID
~HYIAI
~V
e
ff~.
T;
Y
d?
' while that of the cat~h�dio pra�eeo is equal to unity 'i'he cathodic prc,ceoe
ie etas is the proceed determin~.ng the kineti~~o of trle oyetem, and the
in t~h
kinotia wei ht of tl~e anodic r~roceeo ie equal to ~,ro~ rho speed carroepefi3dl~g
g
to this stationary dtato is ~+qual to thA maximum speed Vk maxi which the
3
cathnde rrocaae cex~ have for the given otraight lino Vk and the givQrfi dif-
ial In X11 cases wherQ the straight ling V~ deviates
f~~~enco n1 patent A
tx,o otatianary state i'or tt,e Demo straight
from th� normal NA and J~ ~ 0,
line V will co~~res~�~ond to o ~11aed lase then V~~i for oxam~~le~ as the
k
epecd corroep~nding to paint a in 3'ig~~re 1. We can rAfi~~iu~x~ tii?Ib decrc~~~
in tht~ cathodic ~arocees' speed com~~arod with tk?~ cl~oc~d Vk max an a result
o#' t~~e su~~erposition of t~~e infl~efijco ri' tt~Q nt~odic pfic~cese~ `1`~~e~~efore, as
of this infjluefi~c� w� cafi~ take the co�1'~'acient of reduction in tn�
a mQtGeure
cathodic process' d~,~�d equal to
' l k~~ ~pi.~x a ~r~,aX
We cafi~ write a similAr ex, ress~on for the coet'f~cipnt of reduc;tiori in
the a.nc~c~ic process' speed i
f
� / v (~~e)
a~
A/K Amax
is the s ~E ~d corresponding to the ata~Eiofi~aty state for J� � 0
Here V~~ P K
}
i ~ e ~ s t~ttes) cort~esronds to the ,~traigk~t line Vk colfi~c~din~ with
which
the normal N, and to the same straight line V corresponding to state des-
k. A
~ cri ~~d ~t~ ti?~ ~~irt ~
5ince
Va ~ (P,31~8,b)
k max d
s
we have
~ ~ (5a)
� .J�1....~
!KA A ~ � APo '
` and similarly
9:'
A/K a k
.7.
A~
11
~N
ID
CONS
.
~ ~ ~ ~ I
~ ,y YI ~,J ;J .E ,
~ F~t~ ~eJ "w.`F1 P~ 'r'1'~ r ~
~ ~ h
I,~r i j ~ ~ ~ ~
i
t
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C
ON
~IDFH
TIC
t
i.
Tile clit'#'Qr~Erjt#al c~oQ#'ficiant characterising the in~luenco of the proooae
~ar~unetere adopted by ue as a third cl~Aract~riotio Qf the kinetio weight ~
a~' a ~~rc~c~ASa, wao Gonaid~=rod at length i.n thQ work entitled 'Concerning the
i;
. y~inAtic Weight Qr a ~ r~Qcaee , [l~~ ar~d ~eQd in a latter work entitled
'~Tc~e ~~'t~ol,lcrn or t,l~is l~l~ctro-Cl~~mical Machaniom~', (9), ~'heretore~ we simply
' mf~ntian th~~t th# s coc#'!'#cierat ie equal to the dit'~erential quotiont o#' t~~o
inc~~tia af' tt~~? correscaonc~ir~g pr~ceee
/
ss~~~~~ ~ ~ s ~
~ A~ p
~
w;a~~re ~A and are t~,e clil't'er~e;;tl al coet'i'icicnts a!' in~luer~ce o1' tl~e para-
meters, rea ~ ~cet~ vely, of the ~~rocesses A ar;d B; i and iB are the dii'f'ert~ntl al
A
4nertias ~f theHe prnceeeee corresponding to the given stat,iortary state
Y' and VA are t1'~e absol;.ite vt~luea of the ~~artiel derv vativea of the seeds
A
ni' the r~rocesses A and B wit~~ reg~eet to the general regulating parameter Z
for t~;e same stationary state; whereupon i / Z ~ ar~~l 1 - ~
a A Q o,
In the case under consideration Z � ~ ; they@f'c?re because of the
linear relation between the speeds Vk and VA and phi ~ , as is immediotely
apparent ~'rnm ~'i a� rA 1 c ~ u ~ ~ ;
E, .Y' n
k ~A
e~ (p�349,a)
k
~
from wh#,rh we get
~ a
' ~k A k k (7a) and
e
~i o
~~o~P1Q~A) ='J^
k 7 ~
~A ( 7
t
s~
-8-
C
QNF
ID
~H
T
V F
t M3 ~
i. } n ~ b
~ ~
t'r'~,:v~~~~'k~4.~~" ~ �
~ ,~r~
i
' I

1
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~ -
C
_ off
~Ia
EH
TIA
t
r
Accc~rdin~ to exr~reaeians and (7 ao t�vet
~1~6
~k ~ ~ Jk and ~A ~ ~ aK F J' (a )
A/k ~A A
Ae was shown in our socvr,d ropart on tha kinetir; wai~ht Af' a pracdaa 111 pp.
1.~~9-1~80~, this equality of all thrao coQ.~'i'ie~,onts holds in all cases in
which t,~~o ar?oede of both prr~~oeeea are linear 1'unctione tha r�guluting
parameter� Me~reovcr~ according to thQ same r~~jAxt (p. 1~6?)~ if thQ apocde
pf Loth prace~eeo Are linF~Ar functions of t~~o rct;ulating parameter, th�n
the c!~t od c~~arr~~ol~andin~~ to th~~ stationary state can ~e c_~~,1 rQased by ~i ~,c?,~ation
oint,~lr~r to ~hm~e iaw, in w~~ich tale va1,~~e ~L~, adopted ~?y ~~e ae a m�aeure
o~' ~~quil~brium dist~~rbonce in ttia system, ra~?laces t~~e dii'!'erer~c~t of poter~tiale,
wkiile the r~~olctanco of the conc'uctors ie re~~laeed ~jy the incrt~ ae iA and
!IZ'
iB� '~~~en in t1~~~ !_;eraerr~l cage we have V � In thQ case undrr cc~n-
iA ? iA
sic~era~ion, P?~A is rc~~~al as in Ohm~e Law to thy! differencR in patcntiala
1 1
� - the inertias i and i are equal tb i ~ anc! i
A k A B A kA B KB
Wherefore in the given ca;-~e we have
~ ~
v � 'i -tu z) = C~`~ ~k ~kA k~~~~A~"k~) � (p, ~5o a
A k ACA ~
Assuming linger de~~endency of the s~?eeds of the cathodic ar~d anodic processes
ur~on the polarizations corresponding to these processes, d. B, Akimov derived
a ger~erel equation for current strength in a local ce11� The expression
which we obtained is essentially similar to the particu~.ar expression obtained
by B. Akimov for the case of cathodic-anodico ontral~ (See ~12~, p.81~)
a dZ^Q
We should also note that the equation V � ~ may be retained even in
E lA B
nonlinear functions V (Z) and V (Z) if one understands the inertias f and
A B ' A
i to be the ~~average ~.nertias of the processes for the ete.tionary state,
$
as discussed by us in the aforementioned second report on the kinetic y~ight
-9-
a~
FIQ
Tip
s:
,~,i` 4' ,
~1
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l

i
C N~IDEN~IA~
0
f
o#' a >>z~oceas (p~l~??)~ We a~~oulc~ re>rne?tl~,er, ~,~~wevez~, that in ttle~e oaseo
ln~:rti+~ le ~~~io#.derably snare cam~lcx f'?~r~~tlon tti~n in th@ ease
1in~E~r try~utetieno V (Z) ar,d V a,id ollmj-c z~esiatr~ce in Gc,uductQrs~ For
A ~
1#r~~ar da~p~ndenoe n#' the ve~.ocitiea V and VH upon Z, oACh of the processes
corr~~~~orrd try a N~~hc'i~ic value inertia 1 which ie determnnad by the
elope a~' tho carreol-~onding straight line I~ut in the caao Q1' tho nonlinear
Functions V (G) an~I V tk,p v~~.~l~ ~~f' the "average #~rertias of the ~}raceea
A ~
#'nr t,f~e r~~1v�n tit~ttia~rlary state" wil# tae deti~rmic~~~d oat ~~art].y by the t~chavior
n$' the c~~rvQ V(G) a2' th~o ,trcaccoo, t,irt, alao day tt~e behaviAr af' tk~~; curve
v(Z} 01' ~i~ie socorid ~~roceos~
Ega~~i~~t ohaw t,i,r~~ fit' the cj~~iede nr th� eat~~f~c~ie ar~d anodic prc~eesses
were nroparti,~n�~ to th~� polnri~r~tic~n~+ cor~r~~eponc~ing to ~t~ese I~r�cr~oseo,
tt~o kinetic we~~ht a3' LI~r~ cathn~ic ar~oc~~c ~~roces7e9 would act~>>rso~.ves only in the de;~endence of the speeds of
this work ~
the cathodic ar~d anodic processes upon a limiting change of potential, that
i
is, the equations of the polarization curves corresponding to these processes.
However even in ti?is cage we do not have equations whose correctnees can be
k
f
nsidered full proven; the Aq~~ation for the anodic process speed is more
co Y
. indefinite. Therefore, keeping in mind that the aim of this work is only
,n,,
it
to make more concrete the general picttare of the passible relations among
F" ~ the kinetic weights of the cathodic and anodic processes and their dependence
u on the polarizations corresponding to these process�s, we proceed in the
P
following manner
-ll-
f 11A!
DAN
0
C
~f~ ~ , a
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j
e
- ~ ~~~~NTia~
a
ravese aped is taken to be the
ThA beslc equation tar the cat,hadio p
ex~~reaeion~ (g) ~
~ ~ e ~ o~K b
v~ p ~
}
~~~~TF~,,sp~v.
wllera
' I,Q coy -vas l lent to ~~e the mars complete
~~r~z~oovor, in ~o ~~c~ cases it wi~.l
e1�; resdion: 10
M~
v 'G~ - ~ ~ a
Qrree ~onda esgQt1t~a~ly to Tafel~s oq~catian
~~he firm of t~?e~e equations c p
or that it reflecto quite well the de~Andence
ar~d consequently we may cc~nsid
~ dro en
geed ~~pon overvolta~.e for moat cases of by ~
of the cathodic ~~roc~ss eous~tian
s d gyring electrolysis. ~eeumin~, that this
liber~?tion at cathode cnctal we
~n l~~,nrcL~nn at thcc s;~rt'ace of a di~~olving
also holds for hydrogc taro of
tcmc~tion. ~i~a~ion !10) r~rrrr~nonds to the ry
make the previht.19 Ass ~ 6 describes
rear in , In thin oc~~latio , p
~1p1 surd disc ~ ~ , rX ~d~ ie
ions end ~ ~ k
hereof hydrogen ~
the screed of direct disc ~ ~ before
roc�gs df hydrogen ionization. Ae was sho
the s} red of the reverse ~
ro~r,equal tc~ 0.0~ - 0.1 V (depcnding upon
by Fob. c mar, for values of A ~ ~P~
term of eg1.iation (10) may be disregarded,
the acc racy of calculation), the last
becomes pq,~al,ion (9
whereupon eq~~ation X10) }
resaions, we will corisi~er the velocity V ~
fr In these and furt~h~r exp
its stipt.~lated above in equations (1)�
measured in the un
a nation for the anodic process speed is
The problem of selecting an Q sad
era/ authors ~2 ~ 3 ~ ~.t ~ E>> 9 J have aurmi ~
considerably more difficult Sev
to the theory of delayed discharge could
' that an equation, corresponding .
' s rocess. rn this case, we might write:
be used for the speed of thi p Q~ 11
~ ( )
~ x p
A
12 .
fY3 �,t
+'~~~q i ~t~7;~ ~ a ~ r
~ ~ 4 ,i ,r,
y'~'Ik 1~ ~ d'r
~
~ +
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s--~, _ . .
_w

i
Al
NTI
DE
K~I
0
C
~a
R T RT
r Fot ~ n Foci
If
wo aaeu~m~ t'urthar~ by ana~,o~y with the oathadic proGeea of hydrogen
f
liheratior , that a ~ = a j ~ ~~L ar~d take thA valenco of tt~o metal ~ e
ions n ~ Z ,then we haves
4E`
a~a....~.~-rF~~b.
L
a
With increiee of ariQd�p lariZitiAn, the seGOnd term in equation (11) -
must become small ira oomparie~n with t~~e f'iret; then this equation is simp-
a ~,,a ?dA~ Nn ~at,ian l10~ ~
trsr~xl~ Az
(12
v~ ~ rip ~
It is easily seen treat for tt~e corx~ition CC ~ ~ h this eimplii'ication
may b� adopted, depending on the desired acc~iracy of calculation, fo?~ values
of ~ ~A of tl~e order off' 0.02-0~0~ V.
~'he employment of the theory of delayed discharg� for the ~?~^dic N~-w
~~~d in dissolving metals was based, to a considera~ile d�gree, on the works
of V. A. Roy~der, V. A. Yuza, Ye. ~'oluyan [15-], and also on those of
V. A. Yuza ar~d L. D, Kopyl ~16 J, in which Lhasa a~lthors showed that the
datra obtained from oscillo~ra,~h studies rf
the polarization oi' metallic
elwctrodes from iron, zinc, nickel and copper could be reconciled with the
7
j
d'
eq,.~ationa stemming from the theory of delayed discharge. At the same time,
however, as these authors show, this correspondence with the theory of
a
delayed discharge is obtained only with the oscillograph method oi' invests- s
gating ;:olarization. Ii' the usual methods are used, however, ot~ner dependences
x, r
are obtained. Thus, V. A. Royter and V. A. Yuza found that ttie spud of
the abodi~~~process in dissolving iron could be best exr~ressed by an equation
corresponding in form to Langmuir~s isothermal curve;
~ 13
A A
~7
t
,
-13-
H ~EM~ia~
~o
.,~f
r i ' i aA,t ~ i
~ ~
(z:
i
~ }
ti
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.
0
i
o~
c
ore cane tents, while Ot naturel~y
In a uat~ion (1~) Ot tnd
q
~.~e rom the D1 in Fah~ner~ a eQuation~ In tho Dame
is ~f a dif fercnt v~ _ f_
that Shokl~e data on tho anodio polarisation of nickol -
i wcark, it ie shown
r
tho equations
k' CAn be O~thY'@0sed by
~ (l~~ )
A
x
E ra aASUm~d that these devlatlAnn rrom logarithmic dependence
Tk~e~o auth4
r
Qe of the electrode surface when loaded by currac~t~ f
are determined by Chang
y ~ 9 on the
c~~axi�~es de~a�nd upon the current deg sit and cona~e uently,
Theoe
Alvin met~l� t~je Ql~eed corresponding to the eta- .
val,~e Af ~ ~ ~ In dies g ~
hick ie cetat1list?~}d certain time interva~j aftQr the test
tiAnary regime, w
therefore in this case, it ie rnore correct
begins, is uoually investigated] ,
"~izatian C.:: ,cc NwYiMin~~ ~'~r t~!`~e ano~ir nrAneee in s
usual method 'rhe introduction of a coefficient
metal electrodes by tl1e
~ face cl~an~~es (ae~ xae done, fnr example, in the works
which allows for the e.ir
~ i'aile in ate p~arpneo, since we do not know the
of A. I ~ ~hul tin ['l~�~~ ~
de ~endenc~ of this cneffl c_~ent upon c1irrer~t de11sity~
l;
e it is ex~~~~dlf~nt to consider x'rc~m the start thosd relation-
Nevertholes ,
f.
obtained An the bgele of equation (11), since in the first
ships which are
s as f'or example, in the dissol~~tion of amalgams),
a p~.ace in some case ( ~
m
~ t?e olari~ation curves caused by surface changes may not
distortions _f p
the second ?dace the laws obtained in this case are i
possibly occ.tr, in
sentative and the basic characteristics of these laws can be
quite repre
t e endent only upon whether the anodic proceee~s speed is in
shown to bed p
on a m not be equal to b ~ The
agreement with equation (12), whereup aY
r.
~k' ritr value of'a, can be considered independent
last equation, for an arb arY
of the theory of delved discharge
k~
- ~ -
at
11
H
D~
~I
M
C
~ ~ .
t.y. `~:r
1
~ 1
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~IDEM11~
~cpr~eseions e'er th� Coe~ficiente ~ in the ~e ar~th~nie
Type a~ Pnlerisation Ourvao Qf tho Cathode dnd Anode Proooeeee
9~nco tt~a valuoe 0 ~ and a ~ dro connof~t~~d ~y the rolatione
~ A
~t
' we can ~~y ?nakin~ ~tk,e propea autaatitutlAne' 3n tk~a Aquati~~ns for the epeodo
of the cathodic and anodic Croce�ees c~w~ye ex~~reee both Af' these epeede~~ae
1'~~no t~ one of Q ~ or a ; whereupon on� of the ~
~ ~A
lattor will a'ct ae tie r~~ulatir~~ par~inleter in the ~ive~~ system of �quatione~
However, in tl~e soar~h for exprecalAns fnr th� ,~art~al derivatives v~,'
onr~ ?~~j such a euhetit~~tion is e~~r�erfluoue, since we can rind these
r.
v~~1ua8 u~~'r~~' ~l~' k'.~~ t;s ~~'nr~~,~ ~i ~�.1 n~~ pn?~Ai,i ntll4 ~1~1 sncl f ~.1) recoectivelY
xith res~cct to D ~ and ~ ~ , w. ere the q~ Eantj ty undar t~iese
k
circumstartcc~s must tie cor~sidE~red a constant, and and ~ are
A
e~uel to the absrlutF varies of the cnrres~~or~c~in~; ~~erltial c~er~.vativcs ~ Let
ue assume from the be~~.nriin~ that in en~~ation X11) d~ = !l~ 6 , w~tr.re
x
n � 2, ~'or the sake of ronvonience we introduce the de.~i~~atj.ortat
~
;g p ~ ~ ~
f P, 353C~?)
I 'r""~
9
~ ~Ations (10) ur.d (11) may then be written in the forms
V � ~(hl - h) and (158)
K 2
lY
A 2
Y.
Hence V' ~ ~~x ~ (lba)
k b
{
~q
V ' ~ ~r~, ~ --E-~ rye , (lib )
A b
<
x
The rlltlo of these der~.vatives in ec~~aation ~6~ Zs equal tos
.F ~ h I ~ ' 1 ~ 2
~lA ~I rn ~ h1i

1 ,
- -
r.~,;.;
r
V
~N ~
~~s~
~ ~
J ~}4w7y! y f ~ ~ -
~ f�
~ r. ~ b ttA ~ r ~ ~ _ tip,
b r;x L9 ~ ~
`1 i~ r ,
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1 .
I
C N
Oda ~
~ ENTI !
~'ar thQ stationary ot~a~e, V and V ara ~q~lal so that acaardin~ to squetiona
k
~151t) aid ~1~), we have
at~d true on the baeie sr?uitiane ~1?) and (6) we c~Utairi
> A
~,r..__.
We do not gave tiA write t~~a corre9~ondir~g exi.reseion far '~a, since we have
t~~e relatiariship ~~A � 1 -
In equation (19), ie com~~lotely det~,rmir~ed the val�e;~ of anodic
and cathodic pal~rization~
Figure 3 sh4we t~~6 curves carres~aol~dr~g to this oquation, which exr~reae
,~.~~w ~1+n +..1 ~�nr. . 0 nanri~ n hhrl
tote de~~�ndence of tk~e c~�e~fic:le,~ta j~k ~n Mid., Yf,4
cathodic ~~olurizatian~ In this ~'iglare, the dame quantitie� ae in Figure 2
used for the cnnrd~.nate axes; ~ � is taken eq?~al to 0~5 V for con-
. are
venionce, '
~y comparing the curves shown in ~'igureg 2 and we see that for
exponential det~ertdency �f the 9p~Ed9 0~' the CAthod~C and anodic proC8sr~6~
~~pon polarization, we hav� an entirely different type of curve ~ )
than for a linear det~endence.
S:
1 Actually in Figure 3 and ~~igure 2, we have ~A � 0 a~Ed � 1 in the '
4,',
E'
li.m~.ting case 6~A 0~ ~q = ~ ~ a,r,d we have I k � 0 and /A � 1 in the case
o I
F y.
~ n ,J�~ ~ ~ But for finite values oi' cathodic and ~tnadic poleri- {
~k
' nation, the curves in ~~igure 3 give bn entirely different picture thsn the
in ~'i re 2. The most representative concl~~sion to be obtained
straight lines gu ~
from the curves in ~'i~~ure 3 3~~ that 1n the given case the coefficients ai'
influence in the parameters in both processes acquire a certain constant
value t ; Z ~ and l~3 ,which we will call charactEri~tic~
~A
~a
a
L
- 16 ~
~a
~ ~~I ENT
~ ~~,~r ~ w ,
,y
~ d rt r R TS 1 a i~a` ~
,~.i,,+, t ~ ~''r ~
1
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i
1 .
COMA D N ~
I~
This oharacterie~io value is aaquixad by both co6t'i'iciQnto iroal tho
momQnt that the cath~dio and tnodio polarization a~hi6v�a ae~'tY~ e
value
i.'
From Figure 3, we eek that we can consider that the oodfi'iaiente
aoquire the characteristic value approximately even far oathadio polarization
~ O~OS V and anodic y`' 0025 V and accurate/ for G~athodic o ariza
_ / , y p 1 Lion
~0~1 V and anadio 0.0 V e s ~
5 ~ Qn i easily convinced tk~at these va~uee
k
of anodio and cathodic polari~,atiar~ are ~~recisely thQSe values for which
t
we may diare~ard the second terms namely, h2 and m in the oe~~~ations of '
2
speeds VA and Vk ar1d derivs~ti~ es V A and Vk j ~+er,ce, ttjoee values of
cathodic and anodic polar nation i'or w~,ich the awed of the reverse pro-
cesses (that is, the ~~rocese of hydrogen ioni~r.ation and the ~:+rocese of
dis-
charainR m~t,nl ic;;y; �~c;,,,,~ duil~ c;~ently ernall in comc~arieon with the sp�~~da
oi' the correepc~~~din~; direct f~~roc�eaes,
According to tkhis, we have a right to expect thr.~tk fnr existence of
the characteristic values of the coeff9c~ents ~ , it is suTi'icient that P
the speeds �i' the cathodic and anodic process con~'orm to equations (9) and
(12)~
Actt~a],ly, the derivatives Vk and V ' in the given case are equal
A ~
~t� Q
~k b
(2,~a)
~ ~~A
" ~ ' ~ Xp ~
(2db)
�t /
It is important t~tat the derivatives in thQ liven case be proportional
tr, the apFeda; that is, we writes
~ k~ ~21a)
f
,y
r
A
and since for the stationary state , then we have
~ A
-17-
~D
I
t', '.4 1 Y,: k
~ ~G~ `l~v k i
F ~ 1
1. y
t ~ ~ ~ ~ ~ ,t~
d~' ~ r ~'~a"Rl+ ' a'` ~:4 ~ ~
t ~ ~
~ ~ ~1 it ~ ~ ~ ~ ~
f ~ t' �
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_
i
~
~EI
C
y Thie constancy a~' the retie elf' th~a ~'Qriva#~ivca, obviously, ie tine ~~eaaon
4 ~'c~r she exiatenaQ o1' charaoterietio val~l~o i'or the coOffioients ~y '
c
oul~etituting tho oxrreasian whioh xe ot~toined for ttse ratio Q~` dQr~.vativea
inta equation (6), we hover
In the a . acial caee wk~ere =r= ~ we haves
p ~
, ~/2 ~
4n tho ~asie of the abAVa, wo mako the i'ollowing conclusions:
cl~aracterietic values ~fc~r the coorfic~ents ~ will bo ~~reo�nt when the epeQde
o#' the cathodic and anodic processes can be �~~;~rese�d by cq~~atione (9) and
(1~
The characteristic value of the coe~'ficients ie determined, according
to equation~(2a), by the retie of al and b. If al � b, then tho character-
istic values of these coet'ficients wre equals ~l~ ; is al ~ b,
1
!
~ then ~ ~fA ; if al > then ~f~ ~ j)~ to the special caee ~
1 ~ ~
k` where al � ~ b, then the roei'fi.cient of inflti~ence in the c~tt~odic process
r~arametere is twice as large as that nf' the anode It' the equality ;
t is defined so that b � ;~k'~-~~ and where n � 2, then the twice greater
n
!v,
value f nr the coet'ficient of influence in the cathode ~rncess ~ s prarameters
,
is the result of a twice greater charge of the mete/ iohe~ F'or n � 3, we
would have ~ , = ~ b and correspondinglys ~ And =
3 ~ k ~ ~A
;.Q1 ~~rther, w� tibgerve t~~et ii' the speeds of the cathodic and anodic pro-
Ces58d Con~'orm to equations (9) anti (12 then th~a ~,eneraa. tiype of curves
- )should correspond to the type of curves Shown in Figure 3,
since the correctness of these eq~.~ations as we have seen is determined by
r
the existence of horizontal sections in these curves; moreover, the end
points of these curves must al~�ays satisfy these conditions:
4
fore ~ C ~i~ i; 7~ = l ~ ~ (P,356a)
~a ~ ~k ~A
w
k /
-18-
co
~ ! t t-~, ~r~' ~ s
ti
kl j~ r~:~~~~~~l ~~i, la y~I}y{_ E7,
'!Sil N~~~J~,, ~`Y'V: r,,~s ~6~ ~
'
~ .1 aJf~lh(~~' ~1 i
t ~a,e ~ ~ A �a~ ~ ~ ~ ~ 1
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I
1
N
E
r
ee Ae ~a roe,ed F,~~al~ion 1,~
l~, The 9 eed of tha Anodio Prooe
- - ai' tale cathn~ic preceee id ex~~reeeed by
We now aeeuiae that the speed
d the a sod or thQ anodic process ~y @quation The
er~uatian (9) ~ P
'�4 ~ ~ r ie ex reee~-d by equation (ZOay~
derivative ~~k in this case ae farms 1y P
in this oaae ie equal to
The dorivativ@ Af VA
wre=n
A ~
a ~l�rivation similar to that diecumead in the preceding
from wl ~ ich, by
~
cases, we haves
y ,
~ nd
In the s;~r~cial cave =:=1, we have
(26)
j n ~ ~ ,
l
`u vetl oo:~rd�"3ndir.~ to these equations will ~e Considered later
t, r ~
that ex reesion (26) ie quite similar to the ex~`~ression for
tie note A
wk~ich we o?~1,ained in one o!' the preceding reports fir
the coef tic iei~t ~~k t
t in the systems cathodic prooeee - electroco~lduotivity
this coefficien
difference is that in erntation (26) we have the anodic
process; the only
the ohms c potential drop in the mir.rocell
polarization instead o
F f the Anodic ~'rocess as reseed uation 1
The S eed o
seams that the speed of the anodic process ig ex~~ressed by
We now a
cation (9)~
equation (13) and th� cathodic speed, as before, by eq
~
Then the derivative 7/A ie equal to:
v, _ ~ 4 ~ ~
~ ~
ordin to ec~ ~ations (13) and (21a) we have, accordin~lys
Acc ~ r1
rV I '
~-~~~A)
~ ~

r
~l~ue for a stationary state Vk � VA we haves
and
i
_.~_,___Y_r__..r.. ~ (P, 356, c )
a Q ~ ~ ~A
C ~A
- -19 .
~ � ~ a
~
.1 ~iy: F~" ~ ,
ti'
r
~ ~
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t

f
~F D
EN11~
l
,
~ making tl~~a proper eubetitut~ion in equation (2? we ubtaiY~
fA
Hence
v ' ;v' ~ C~..~ a~ b
k ~ .~~Y
~ (2~)
i
{
{ip
f /
ar~d
~ i~ d ~
~ (2~)
a
1
7i f
t
1 F
~n oiler to draw tli~+ actual c~~rve k(D ~ A) oocree~~onding to cc~uation
F
(29) we moat kr~f~w nc~t only the coefficient b~ but also the coef~'icient a
he val?ae cif this eooff~eient can ~~e 'f'ound by an exY~erimental determination
T
i of the anodic polari~i~ation curve, but we a~~oulcl think th~~t tl~le val~~e of
i
~ may ch~ge substantially in the c~?an~;eo~~er fro~i ens conGr~te case to
F
s another,
j
?n thi4 wc,x~k, wr, cur7 limit ourselves in uriy congirleration of the curve ~
9
i
~i
) to same ~rbritr~:rily asq~gn~tl but plausible values of Ot
!
~{'or t~~is u -ass we mfr consi~cr that t~~e polar~~7,ation curves Va
s A
cnrrFSponrlin~ to ec~~aation (13) must be of ~e saturation curve type, with
e
~ 6t ~ ~E3~ U$ ~q~l~lll~ t~i~t tlrlia li'mif,ing, v~1uc
t>~e limiting value ~ ~ A
of ~ is of tt;e order 0.2 V. This ig of the dame offer off' magnitude
~ A
~ ants/ curves for er~odic pol~r~ zAtivn ohtaf ned b3~ V. Royter
as tl~e erg Brim .
ar~d V. Yu~.a for technical iron
r mV and b � ~0 mV in e~ua~tion (2y), we obtain the
getting a 200
curve C ) ehewn ag curve I in Figure I~ ~ or graphic illustration of
k( ~ A
~1
the effect of changing 0~ upon this curves characterigtirF, the curve
~i
)for ~ � I~00 mV. (curve II) ig alyo s1~?own in this figures
Ic ~A
}
F
8
- 20
ca~~~o~~
d
;
~ :i ~
i
~ ~
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_
W
~ D hl
C
}1 6. The Coei'ticient of Roduation in ttie Gattiod~.o Prooaoe 9 geed
Y.,
Far t~revity we ~il~ 1lmiit aursalvea to the doriv~ Sian QP are e~~~reesian
far tree coet'tioient of raductiar~ in tl~e cat~aAdia ~arc~eaae speed, w~~~ich ie
~ ~ ant far ttl@
mgr o inter~e�tin~ and de~ini to t~ian tho Gorz ea ~ o~ clingy co~~ i is i
i
anodic prooesa ~ ~~~r tx~e cathodic p~ ocQt~n e~?eed we shah: take e~uatiAn (9
ire which ~?e r~ ~l~ce the quantity ~ with its ~~quivr~l~r~ti - A ~~a);
~k
t
then we haven Q~A
y~
y
r ~
~~rY ~l
~ ?,~nx (31) s,:
nr tl;;;; ht~ai;, ~~?~~l~~+i pxE-rer~sion nor tllt~ co�f~'~cient pt` reduction
I ar?d ec~uatior~s (0) and (31) we have:
of procee~ er>~ od (ia) 3
~
k/~
the coe3tic~ent of reduction in the cathodic '
According to equation (,32 ,
x, E~rocess sic ed is com~~lgtely determir~c-d by tl~e amnunt of anodic polarization
ar~d the value of the coei'ficient b in the cqu~tion ~'or the ca~l~ndic process
speedy
Nate; '+t~e if~80 note that, in the general cage, wrkpr thEre 3s not Only
ct ( ~ I
~0
a m8rker~ 8m~~unt of anode polari~.ation, gut al;~o an ohmir, ~a tential drop,
I
the ro�ffi.cient of reduction in the cathodic procesa s~.?Eed may be expressed
r~., ~ ~ ~ f 6
k/~~-
wh~rb ~ i~ the ohmic potential drop in the mir~rocell~ When e � 0
we obtain equation (32); with ~ �A � Q,we shah. obtb.lr~ a s~m3lar expression
,Ir ~'or the systems cathodic process-Electroeonductivity)~
.
-21-
DE~ ~
D~1
�~1 dJ~ ,f
fa~i ~
4 ~ a,~ dad l~
a ti ` � ~y 4`' ~ ~
h 4 ~
~ P#(~f ~~Ni. # 7 ~ ,
dt
. ( Y~ .t}~r ~ ~e
i

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~1
t
i
N
aE
F~
N

r
? ~ later retation pf t~?e Rooulte
tae have obtained in ordor to
Let uo try row to aeo the aquati
t~~e kinetic woi~ht of the catt~odic procoee
eval~.~at~ the cio~rea to which 6
Bence Qf tY~o anodic praaese ire t~ra syst?wm.
io redur~ed bccaueo of the pre
an the Qgaation for thQ cathodic
1~ ~ury~o ee, it ie convenient t4 rrly
For th Y on t,ecomae invalid
to find tc what dc~rea tt4ie e~uat
p roceee a Y~ecd ar?d tr~r
reseed ~sinetio wQi~ht of ttio ~adic procose.
because of the Inc
doocrik?� th� �l=coed of t~~� cath~+dic
uatioa (30) It~� r~ to
We will use cq t
~~rc~cdse.
t, f,lari~~~?~ion equals taro, we have the
In thcaco cease wttr~re anodi P
s
Cbi'1~1~~~irane~ Jt }1`, J`i/Ih~~ (p.3~d~p~
~f t /
~
m a written in the f ~+rm s
ver in tliie case, e~r~atior~ C34) aY
Moreo ,
,I ` J 4
k /J l~ J
n -ens is dptermirir~~; the kinetics, and y
1n this case, the ceth~dic rr c
~ d in the system of c~,thr,dic and
is a valid e~;pregsion of ape
er~>>.ation (31) ~
anodic nrocPssea~
k
r ti ~ we have the inequalities:
When AI ' / ~ a ~ ,~c~ ~ (~~35~~b)
�T~ > ~ ~ i ,
~ ~i ~'~~rk ~ l
~7~ Ja Ik ~
e, erally a1~eakin~, no longer dpterm~.nea
~~Y1p cathodic prr.,cess in this cage, ~
r dc,es not
m~ because of
this, enuation (31)
Ij` t i
the kinetira of the ayste ~
~5} ~
cathodic e~r?d anodic processE�a~ ~nuation
eterm~.ne the speed of the system of
d valid since the regulntin~
y' remains correct, but is not complEtely ~
(3~ )
r~
j is rocees speed, the Teault off' which is a
varies the anod p
pe~rameter ~ ~ A e e ua1~f on pr
ametNrs in th a f
of the coeffj.cient of influence in the per
reduction
t~ecames ~ 1. For
ed' that ie, the iner_!uality ~,c
oathodie process ape ~
-22-
0 0~
~
y. r,,
q ~J44 R i
A';; ~P~ ~ ~
r~,~ '
~ "~~r~ ~;~,x~`~~ r. t~ a .
~ fi~ ` :
~ ~,r. ~ ~
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iw
' ~D
ENT
Ill
�
the tlature nr t~}e d�~reQ a~ ~ni'lu~nGO 0~' t~~Q anodic ~rocQSe, wo find it
env-Qnient~ not tQ oxaminc tha value ~ itaol~, but ratkler the vt~lue 1� r
c ~:t ~k
ar the value (1 )+1A0~ iaet quar,ti~~ cl~areeterizee the reduction
~k
tr,e value Q1' k, ~x(-reseed in ~~ei~cer~ta, wk,iGh ie deterrlined try tht
in#"l~~enao of the ana~lic prc+ceae (wa recall, also, treat l~k �
w
~i~el.doe z~k c~ucing the val~~o ~i' tha caafficient ,the 1nf'luenca of
a ~k
h thQ en~+c~c ~roGlese ie also ~~~flectdd irr tkic fact tkrat the o ~~ood cor-
f
'E i
p responding to the ~tat~.Anc~ry state t~ecomea le�e t,?nn t~~e speed vkm~x~ ~
1
oaffloient f � ctraracterix.oe tkGe ~?mount o!' this reduction
Thee ~~~A
i<
rf e~tieed v , wkliokr c~lao we find cor?vr~nicnt t~ ex~~~esc in ~�ercer~te, thus a
k
tcj be 100~f` 0 ~ irtareover, at t 9 ~0, tare coef#'icienti
t,aki~r~; tkre value ~ p
~~~A j
~1� na~enrl on valises
cathc~ic ~c~1~ri~~,ation or, er~rl~ec~uet~tly, uE~on the r~?~ia ~~k f~~ end the
tl~~e solid ~ ortior~ off' curvy, ~
nu~ntity P ~'hf sine ;~rir~rl~lr- holds ~'rr ~
i`.
~ 3 s3nre for ~ r ~ 0,1~ V, tale ~ern~s X71 and h2 in equat~.on (19) drop I
~ ~ Ic I
out. lt~ tla~y r~~latiorts~~ip, we have tiie es~~?r~tial difi'erence of the curves
'
1-5 from the stras.~t~t line 6, whose slope will vary with D ~ � ~ 'this
clGt~rarterigtic of ~Ghe curvNS 1-~ ~.s dt~e to the fpct that the continuous
rN .
sections ni' these curves corres~~ond to the same initiel equation 3'or the
cathcx~ic prc~ceag st~ced (9) ~tnd, Conswgtaently, to the proportionality o ~
4~ ~
the q,,en,titi.es V and V ,for w?rich as wes shown shove t}tie cocfficienta
k k
1,ecome independent of the value of ~ ~ corresponding to the given process
.
mhos, we can conclude thet whenever equation {9) holds fhr the cat~iodic
process speedy the reduction of the cdei'ficient ref influence in the cathodic
process parameters is determined by the amount of anodic polarizat nn

`y F,
� - Y~ r
~ y~^_
'
'
,fir t'v ~t i'f.. y)n
r i i 4ItM ~ 1S.
i n d f ~ ~ ~
~ Y 1I r WA
! ~ ' ~ h
~~~r ~ ~'n
,.firr {,,ntt' influ�r~ra in t,kGC~ ~ ~ara1?~eters
~rfim tie stendpa
ai;d even more sc~ 3'rnm tl~e ,~tandpaint of tk,A cnef't'i c~ ants of speed reduction
M' i t,inn pvcr. fcr convik~~rabl�. e~~l~~ii14 E�~ul~rl~~.~tic~r,, tl~a kit;;~tic ~rei~rt
In acid ,
~ ,att~odfc ~�rncebs ae we havt~ seen, m~? be ~:~rednrnir~Ant, in the system
F= of t~,e r
I
Thus in the realization o!' curves 1-2, we can ex~~~~ct for s~tff'icient anodic
po? arizgtion an a;~pNr~~nt, rc t~:rn ~o tl,~, re~ularitfes carrersponding to very
i,ion p'urt,hor in tt~e rE~aliZa;tion of
small val~1ee c~i' anodir polarize ~ ~
f;
curve 3 the coe~t'icient ~~ntil the condition ~ ~ k~ 0~0~-0.01 V is
~k
~l observed, w~~ich ronclition is prar.tically always fulfilled in metals dis-
we natural/
solvin in ar,ida~ At the same time, on tote i-,asi.s hf tl~e atudy~ Y
must ascribe to the anodic process a very substgntial influence upon the
kinetics of dissolving metals The kinetic weight of tt~e anodic process ,
f,.
s considprabl greater and its relationship with the kinetic weight of
i Y
E:
the cathodic process is much more complex than might have been exp�cted
from assuming linear polarization curves fc~r both prncesses or from the
ratio of polarization D ~ and D Y or the coefficients of enuilibrium
k A
nce J' and J�~ From this standpoints we must acknowledge that more
disturbs k A
r detailed studies of anodic polarization curves ~ and also measurements of
the otentials of dissolving metals are very important for the theory
P
S' ; ~ .i
.
. 30 .
~ ,
A
~~`~~t ~~R,f I~
fl ,'~~71 f~
l~ Y
I ~ ~ I
'
1C k
~ ,Iw; ~ ~ .~T x^ a~~, t ,~~y
f ~ f d, M,
~ e ti- l b t t

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PY pp

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w
e with aalutiano. In princ:i~}~le~ th� meaeuroment
of interaction of motel
' a vin metals may bo considered an ex~aerinuntal
Qi potential oi' d~ae 1 ~
~nothad for dFtermining trio magnitude and variat~ione of the regulating
of cstt~odie and anodic prnceaeee~ which thearetiaally
~aaraneter in tY?e system
ar tho inadequacy at thA formula tar the cathc+dia pro-
could oam~jeneeto t
e uac b the auper~poei tiara p!' the int'luenae
coca opood caused (i.e. road q y) Y
i
4 ~i' t~!@ anodic nr~?oeoe.
s
t
Conclueione
` t has be@n made in thiB work to evaluate to what ext@nt
An attemp ,
th� cathodic ~~roc��s in hydros@n lit~eration snd tki@ anodic process
~~as~n ~ metal ions irtt~ Oho sal~lt~~n ini~ur--nee on the kinetics of int@r-
r@1 ~
n between mE~ts?ls and acids. In this ~tut1~? we assumed that difi'usion
~ actin
4
d cendt~ct,jvity had no marked effect upon tt~e speed c~i" phis rE~aetion.
we em 71a ed the mett?nd for tl~e evalu~tirn cf kinetic
with this p~r~ose, ~ y
in tl~e a~~thar ~ s ~~r~vious works (1li) ~ It turned
wei~:hte which was developed
a
a t~lat th� rglatior~ship between th� kinetic weights of th~+ catt,r~dic
of
de ending upon what typ@s
and anodic processes could vary gw~ntitively~ p
j
y,
~f olsri2ation curves correspond to th@ss procegses~ According one
A
inaceuratp ideas by attempts to evaluate tf7@ relation
arrives at completely ,
wai ht of the cathodic proc@es e~~d that of the anodic
betty@en the kinetic ~
m assume for sim~~lification that linear polarization curv@s
process yhic
degcri.be thQae proc@sseg~
Thd relationel~ip between the kinetic weights of tl.e cathodic and
of be @valueted, in ~ez~er'al, from knowlgdg@ of the
anodic process@s Cann
amounts of cathodic and anodic polarisation.
@ of anod~.c rocesses on th@ kin@tics of dissolving m�tals
The influent p
e @ven for small values of anodic polarization of the
may become noticeabl

. t
. �31-
a
c
J ~ 1 t
, ~ ~ r~ F ,
,rr
~ :r b
' ~ '
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~,,.........-r�
� ~ at
0
ie indQ pendent o~ tYle amount of polari.-
ardor a~ 001 V or even lace, and ~
action ~or~eaponding t4 th@ cathodio praceae~ Thus, oaeoe where one ia~y
�rd uantitatively i,ni'l?~Qnce the anodic prQaoee in dieaalvifl~
oomplotely ~
metals are not considered likely. At thu same time, hawever~ there may
~ e an a ar�r~t return to regul ~ritiee carreepondin~
bQ edeeo w~+?.r~ one Abraerve pP
small valuoe o1' tnadic polarisation for sufficient inoreaee in
tc v�ry
anodic polarixation~
E Hiblio a
Z o. Ch. 160 llb (1932)
1. A. N. ~'rumkin~ . phy ~
u
2. Wainer and Traud, Z. ~,ektroch~ 4L?, 391 (1938).
k
Durdin Uch. Zap. L~nin~,r~?d Mate univ., No. ~0~ 3, (1939).
3. Ya. V. ,
N. ~'rumkir~ Works ~r tl~e .~~cortd C;onference on Corrosion of Metal',
A. ,
i
(1 !~0 .
AN t1SSR, 1, 5, ~ )
Pi, ~'rumkin ;Gh, n~tl~~';ii, 1[, 3, (19'1).
a. Kolot rkin artd A. ,
Y
4~,
~'hul~tin Zh, Fiz. Khimii, 15~ 3, 3, 9, 370 (191).
6, A. I ~ a ,
R V C. Levich artd A. N. Frumkin, Zh ~ ~'ix. Khimii, 15, 5, (19 1
�
ry1
? n Zh, ~'i7~ ~ Khimii, ~.K, 1-2 ~ 61 (19Id1~) �
8 ~ A, I ~ Shul ti ,
Zh. FiZ, Khimii, 1~ ~ 1-~, 69 C1~~~,
~ ~ E~b2 (151?
9 ~ Ya. V. Durdin, Zh4Kh 1? , 17 ,
r
vane end 4. P. Khor~ The Electrochemical Theos of Corrosion
f 10. U. R. ~1
5,
(Symr�) P� 1~~0, anriTr (1938).
t
11. d. A. Akimov, W~rke of Second Conference an Corrosion of Meta18~
~z
' 33, AN USSR (1910).
1"~,h,~. cwt MAt,hnd~ for Inveeti~atin~ the Corroaion~'rocees
12 . 4. 8. Akimov, T??~1,r. , a�~
in Metals, AN USSR (1945) �
M~ Fol~m~r Zh. Fis. Khimii 5~ 319 (1931~)~
l3~ ~
,z '
~t {
~K , k.
.32.
A
FI
N
C
si. ~ ,
~a.~
~'~t~, r.. ~ ~y~, ~ r y,
~
~ ~ zit
k Yi~,tl r ~ ~ ~ 1 t{
i N. ~ ~1~,
w i r ,
~ ~ ~
s y
! 1'.
t, i #~~Gy 'rF f' d 'e " r ~W~
iy.k 1~;, r ~~'P~~ra v z~
,,xc i-, 9~ ~ ,f~ ~ ~ 1
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/ ~ i
Zh~~4h ~b R~purt 1, 115, Report 2, 1~T5 (19~b)�
1!~ ~ Y~� Va D~~rd~n, ~ ~
ter V ~ Yutie~ and Xo ~ 9 � Poluye~, 2h � Fi.x ~ Khimi~i, l3,
605, (1939).
nd L� KQpY1, Zhu Fizz ~(hi~nii, 1~, 10~~ (19~�)
16� v. Y~xa ~
uxa Gh� fix. lihi~ia, b, 1252 (1935)�
17 � V � JI � Rai ter e?nd V ~ A ~ Y ~
9ubmit~ed January 13, 1g~7
,n
~ y
l~
(~'ie~~resfall~w)
~tl
3
1~.
1
ti
}
A
7
,P
I
r
k;
~ 1
'
i, i
. 33 - ,
i ~ t*a
} ,
h6.r
hE~~
l~~~ii~{[k ~
C
~
r ' i.
~ t ~t~ ~ 'Gird' f ~5~~~~~ ~
~t~~ f ~ a ~ ~ ~ _
`IPV rr Dt Y~.~ } 1_ ~ ~

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e
-~.-..y,:. ,
- ~ r
~ NK
A
~4
�
~ D ,
~ ~K*~K as
~ r - r- n O e
V ti
i
i n , ~ia ,
a ~ Al ~J ~,vaf as a~ A
L,.. K
r~o ~ ~y1 ~I~j ~ gyp ~rf
F ~ ~ ~p ~ )
0
as a
O A~ ai o,s o,r os '
d,~" a~. 0 D~~ D,~ ors R~' a~A
a~ 0.~ ai a ~~it
O. s' G,v o,i o~l D,1 ~ ~Q~K
F~~, 3 ~ r~r~
k
t
T
o r~
~:..~.~...w._..,~..~......_.._.,.
~
t
~ ~
J ~ ~ ,
~a ~ r V ~
s~
~U i ,
~ ~ V~
y'0 I
~ , ~ ~ ~
tiro ~ ~ - ~t
i VK
i
r:~~ 4 ~ ~~~~,t~~
a D' 1
.w. IU
I
0 ~ D.l o, x d,~ 0. y 4~J~ ~ ~H
ID
EH1'!A
l
~6
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tit ~ ,
Vdi9 ~ ~r ~ ~ ~
}71, y
i i7 S!
~AA p o

: 1. ~1~ ~ _ _
t ti ~ , 1
~r ~ ~ ,
~ i; ~ ~
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