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Numerical evaluation of complex stability constants from polarographic data for quasi-reversible processes
Arrtrlylictr Clrirnkr Ac’lrr. 74 ( 1975) I47- IS3 ci:l Elscvicr Scientific Publishing Company. Amstcrdom
NUMERICAL EVALUATION FROM POLAROGRAPHTC
147 - Printed
in The Ncthcrluntls
OF COMPLEX STABILITY DATA FOR QUASI-REVERSIBLE
CONSTANTS PROCESSES
an improved technique for the dctcrminution of comIn a previous paper’. plcx stability constants from polarogrrrphic data based on the method of DcFord and Hume2 was dcscribcd. This method was used to dcterminc stability constants of cudmium(I1) and lead( II) complexes with 2-, 3-, and 4-hydroxybutyratcs”. whcrc the cathodic reduction of cndmium( II) and Icad( II) is polarogruphically reversible. In the present work. essentially the same technique has been applied for detcrmining the stability constants of coppcr( II)-butyratc complexes; in this system the cathodic reduction of coppcr( II) is modcratcly quasi-revcrsiblc, The nleasuring system has been improved by utilizing operational amplifiers. EXPERIMENTAL
Polarograms were recorded by means of ;I controlled-potential polurographic instrument with operational amplifiers. Its potentiostut is similar in principle to circuit analysis was mudc by that described by Kelley et trl. 4.5. for which ;I detailed In order to reduce the iR drop through the solution Bczman and McKinncy”. between the working and the refercncc electrode. a three-clcctrodc technique was employed. The circuit diagram is shown in Fig. I. The polarographic cquiprncnt consists of ;I power supply (Hewlett Packard. model HP 60155C) and potcntiostatic circuit for the control of the potential in the proximity of the working clectrodc. This potential can be varied in discrete steps by means of ;I I kSZ (ten turn) precision potentiometer. The other part of the instrument is the current-measuring circuit. The current (which oscillates owing to the growth of the mercury drop) was passed through a low-pass filter (LPF) and a relay to the analoguc memory. The relay was actuated by a drop-life timer (Radiometer. model DLT I) just bcforc the end of the drop life. Both the potential and the current were monitored by a digital voltmeter. (DVM) (Hewlett Packard. model HP 3480 A) with a resolution of 0. I mV. The potential measurements were reproducible within 0.3 mV and the current measurements within less than I’,!<; (the ccl1 included). The polarographic cell has been described previously’.
13.GRABARIe.
148 +
M. TKALCEC.
1. PILJAC,
1. FILIPOVI~,
VL. SIMEON
-
REAR
Fig.
I. The politropr;Ipllic
;tpp;lrilttls
diagritm.
All the chemicals used were of analytical-reagent grade. Copper( II) pcrchlorate was prepared from copper(I1) oxide and perchloric acid. Sodium perchlorate. solutions of which were used us supporting electrolyte, wus rccrystullized three times. The measurements were made with buffer solutions having constant concentrations of butyric acid (HBut. 0.01 mole dm-“) and copper(I1) (0.4 mole dmm3) and a constnrlt ionic strength (2 mole dmm3. adjusted with NaCIO,): the tcmpcrature was maintained at (298.2+0.2)OK. Total ligund concentration was varied up to ~‘a. I mole dmm3. The capillary constant (/,I:’ t”). measured in open circuit in a O.l-mole drnB3 KCI solution for u mercury column height of 30 cm, was 1.79 mg* s- 1, The drop time was kept at 3.4 s by means of the drop-lift timer.
According to DcFord and calculated from the cxpcrimcntally I;;==
j _-Z(~l-~,)+ln “XPIRT
r;, = I + c p,, [ L]” ,!
Humc z the cumulative obtainable function
stability
co,nstants
/I,, are
.
$} LI
(2)
This Cunction is usuully determined by recording the pdlurogruphic wuves of u series of solutions with a constant metal concentration and ionic strength but a variable total lignnd concentration: in al.1 cases, c’~.~~Pc’~~. so that [L]sc*~_. The values of I.?!. and I:, arc obtained from the polarographic curves either graphically or numerically. The corresponding data for simple aquo ions. I!?~ and f;, are either measured directly. from the polurogram of the solution containing no l&and (but otherwise identical to those described above). or by extrapolating the functions I?, us. [L] and 12 OS, [L]
STABILITY
CONSTANTS
FROM
I’OLAROGRAPHIC
DATA
149
to [L] =O. In the case of a partly rcversiblc electrode process. the magnitude of KY, as well as & can be estimated by a numerical method proposed by Momoki and Ogawa’. The procedures outlined above can bc. at least in principle. applied to quasi-reversible clcctrode processes provided that lhc rcvcrsiblc half-wave potentials are determined. According to Matsuda er u/.~-‘~‘, it is possible to determine the reversible E;, value from the polurographic wave of a quasi-reversible process by part drawing the tangent to the log i/(i,, - i) cs. E curve in its lower. positive enough where the clectrodc process is still diffusion-controlled. A similar approach was employed in the present work but the polurographic waves of quasi-rcvcrsiblc clectrode processes were processed numerically rather than graphicnlly. In the previous work’. tllc E., and i,, values were computed simultaneously. by using the Gauss-Newton least-squares treatment us proposed by Vouk ~1 crl. I I. in order to avoid any subjective smoothing of the polnrogntphic data. Howcvcr. when applied to the polurographic waves of quasi-reversible processes, this method gave slightly different vulucs for E., and i,, than would be cxpcctcd on the grounds of graphical estimates. This is exemplified by the dutn shown in Fig.. 2 where the logarithmic forms of the pblarograms of 0.4 mmole drnbJ coppcr(l1) in pcrchloric acid solutions ( 1 and 10 mmole dm-‘) of constant ionic strength (2 molt dm-“) arc The dntn points wcrc calculated first by evaluating i,, numerically and then . plotted.
+J 2
1
0
-1
Fig. 2. The intlucncc ol’ ~hc mctlrod or computing curve. Coppcr( II). 0.4 mmotc dm- ‘: I=Z(NuCtO.,). I-ICtOJ. (0) With numcricul I,,: (0) with glXptlic~lt
i,, upon the logilrittimic tbrm of 111~ potarogr;lphic (I) 0.01 mote dm-’ I-ICIO.,: (2) 0.001 mole dtn--’ I,,.
150
B. GRABARI~‘.
M. TKALCEC.
I. PILJAC.
I. FILIPOVI~,
VL.
SIMEON
graphically (circles and dots in Fig. 2. respectively). For low values of log i/( ill - i). the data points arc satisfactorily fitted by the lint of theoretical slope. whereas at higher values the data begin to deviate more and more both from the line and among themselves. The deviation from the theoretical line is easily understood if the quasi-reversibility of the electrode process is kept in mind. The discrepancies among circles and dots can be. at least partly. explained by the non-orthogonality of the numerical method used: in the method proposed by Vouk et al.‘]. the errors in any one parameter to be refined may cause considerable errors in the other (this can bc verified by inspecting the correlation matrix). especially if the model applied (in this case a perfectly reversible electrode reaction) is not completely physically adequate. Besides, the information on i,, contained in the first ten or so points of a polarographic curve (E s E+) can hardly be very abundant. Therefore it stems more correct to use a graphical estimate of id for the regression analysis of tl!c polarographic wave. Needless to say. in such an analysis only that part of the wave is taken into account which is still diffusion-controlled. RESULTS
AND
DISCUSSION
The linearized polarogrums of coppcr( II) in the presence of 1 or 10 mmole drnm3 perchloric acid or 10 mmolc drnmJ butyric acid as well ~1s in pure supporting electrolyte(2 mole dm-” NnC104) arc shown in Fig. 3. It cun be observed that with increasing acidity. the polarogrsiphic waves tend to be less reversible. The same was observed by Kolthoff and Okinaka ” for copper( IJ) reduction in perchlorate medium of lower ionic strength (0.1 mole dmS3). and by Hnwkridge and Bauer13 who investigated the kinetics of copper reduction in lithium nitrate medium by AC. polarography. Both groups explain the decreasing irreversibility by assuming the 2-
log
1
2
3
4
I Id
-i l-
Fig. 3. Lincurizcd pohrograms of coppcr( 0.4 mmolc dm-” CU(CIO~)~; I=2(NuCIOJ). HCIO,: (4) 0.01 molt dm-’ hutyric acid.
II) in pcrchloratc mcdicl with (I) pH 6: (2) 0.001 molt dm-”
varying HCIO,:
xid conccntrution. (3) 0.01 molt dm-”
STABILITY
CONSTANTS
FROM
POLAROGRAPHIC
DATA
151
formation of Cu(OH)(H,O)z species at higher pH values. A partial or complete dissociation of this spccics is believed to be faster than is the case with Cu(H20)iC species. The E,. and i,, values for copper(l1) reduction in various media evaluated by alternative methods are presented in Table I. As explained in the preceding section. those E, values computed with graphically estimated i,, values were considered as more reliable. Any of the E, values quoted (except those measured in the presence of butyric acid) could bc. in principle. selected as a final one. Howcvcr. the polarogrum perchloric acid is characterized by the recorded in the presence of I mmole dm-” values were acccptcd as most positive E, value and the highest i,, value. These most reliable. because the prescncc of u higher concentration of acid influences the kinetics of electrode reaction. The finally adopted values arc El = (42.5+0.1) mV and c, = (4.70 10.04) /tA. TABLE
I
HALF-WAVE POTENTIALS MEDIA AT 29X. IS’ K ( ~‘~,,=0.4 Acid __
mrnolc
AND
cImw3. I=2 molt drns3 __~___-._-____--.-_-.------s
trtltlrcl _____._
DlFFUSlON
____.
t8 Estimate
r1”“‘.
OF
29.6-eO.I 31.0f0.1 30.6-eO.l slope.
I
-__-------
COPPER(I1)
_..___ ___-.-__ (rrlv)
E’f.
~__.-_~---________-_-..-
dm -J dm-” dmeJ
ol’ the Ncrnst
(NaCIO,))
(rt1VJ’
30.2 _e 0.
HCIO+ I mmolc HC104. IO mmolc IO mmolc HBut. _.___--~--
CURRENTS
(IIIV) ___.. ---_-
41.61f:O.I 42.5 * 0. I 40.5 f 0. I 39.3 _+o. I
-----
42 43 41 40
IN
DIFFERENT
-_.__-.--__.--_.---.-. iy.
(/IA)
_.._.-_.---_-_-
3.92 _e 0.0 I 4.59 + 0.06 3.7 I * 0.04 4.01 _e 0.06 --_----_-._-_-.-.-----.-.
i;‘;.( prl ) _..-...-_. -___
4.20 4.70 4.58 4.4x
2.3 R-f/X.
The values of ,!?,,. and 1; obtained by polarographing a series of solutions containing it constant concentration of copper(I1) and a varying amount (0.03< with the computed cl,/mmole dmS3 < I) of ligand. are shown in Fig. 4, together of butyric acid estimates of the Nernst slope (s ~2.3 RTQF). The concentration in order to prevent the formation of hydroxo was maintained at 10 inmolc dm-‘. of butyric complexes. According to FilipoviC and Piljac 14. higher concentrations acid shollld be avoided. because. the presence of a higher amount would make Ei more positive through its influence on the viscosity of the solution and on the activity cocflicicnts of the spccics present. When the Lcdzn extrapolation was used. it was found that four successive ML,,complexcsare formed in the copper(butyrate system, and their approximate stability constants were estimated. These values wcrc then relined as described previously’. The computed relined values are quoted in Table II. together with the respective YS’X,confidence intervals. The same system has been examined by spectrophotometric alid potentiometric methods under identical experimental conditions’ s*16 and the values obtained (also quoted in Table II) ilre in very good agreement with thosedetermined in thd present work. Therefore, it can be concluded that correct values of complex stability constants can be obtained by polarography. even when the electrode reaction is not perfectly reversible. provided that adcquatc experimental and computation techniques are applied.
B.GRABARle.
M. TI&LcEC.
1. PILJAC,
1. FILIPOVI~.
VL. SIMEON
0.5
I 11/mol dm-’ Fig, 4. The dcpcndcncc TABLE
IIIOIC
CONSTANTS dmwJ
OF
reduction
on butyratc
concentration.
-.-.--.----_1 SIC
1 &Z./e 1 s/II: 1 ele I
COPPER
BUTYRATE
COMPLEXES
AT 298.15”K
(NiICIO,)“) ~~J/tlr~J~/JYl/dl~~ --_____.-.-__.-_
Ml~fIffJll
” c”=
poluropraphic
II
STABILITY (I=’
of E, and id for coppcr(ll)
NIIJII.
Grccph.
I .x3 CO.03 2.54_eo.o9 t.93+-0.12 ,.ln_eo. I3
1.X5 2.53 2.94 2.x2
.._.._-.--------_-
~‘fJl~Jl~i~JlJJ~~J’~“”
S~J~~~lr,J/‘hfJt~~JJl~Ir~”
NIIJII.
NMJVI.
__._. __.-.-___
lnolc rJm_” . .I*(‘= 1 : ctfth thcfsipn.
...-.---. -
-.--
’
-----------.--1.85+o.ol 2.49 f 0.0 I
95::, conklcncc
intcrvuls
I.89 * 0.02 2.76 + 0.08
iIrC
qilotcd.
SUMMARY
Stability constants. of copper butyrute complexes were determined by polarography. Numerical treatment of polarographic data for quasi-reversible electrode’processes was developed and yielded good estimates of reversible E, values. An improved three-electrode polarographic apparatus was constructed based on operational amplifiers.
STABILITY
CONSTANTS
FROM
POLAROGRAPHIC
DAT’A
153
REFERENCES 1 2 3 4 5 6 7 8 9 IO II I2 13 14 15 16
I. Piljac, B. Gruburic and I. FilipoviC. J. Elccrrotrr~ctl. Clron.. 42 ( 1973) 433. D. D. DcFord nnd D. N. Humc. J. AI~IL’P.Clrcrr~. Sot.. 73 ( 1951) 5321: S. Nushi. 1. Piljxc. B. GrubarE and I. Filipoviti. Crnctr. Clrcrrr. Acvcr. 45 (1973) 453. M. T. Kcllcy. D. J. Fisher and I-I. C. Jones. Arrtrl. Clrern.. 3 I (1959) 1475. M. T. Kcllcy. D. J. Fisher and H. C. Jones. Arrtrl. Clrcr~t.. 32 ( I9hO) 1262. R. Bczmcn and P. S. McKinncy. Aria/. Clrc~~~.,41 ( 1069) I5hO. K. Momoki nnd H. Ogawn. A~rctl. Chon.. 43 (1071) 166-L l-i. Mntsuda. %. E/cklroc*lter?r.. 61 (1957) 4X7: 62 ( 19%) 977. I-I. Mntsudtt rend Y. Aynbc. Z. B/~~I~o~/IL~Iu., 63 (1959) I 164. H. M:Ltsudit. Y. Ayilbc and K. hdxhi. %. E/ck/rr~c’lrc~~,,..67 (1963) 593. V. B. Vouk. P. K. Kurmalkar nnd 0. A. Wcbcr. prlr. k’rr~.. 27 (1955) 9. I. M. KoltholTand Y. Okinakn. J. AUIL’I*.Cltcrn. Sot.. K I ( 1959) 2296. F. M. Hnwkridgc and I-I. I-l. BnLlcr, Awl. Chw.. 44 (1972) 364. I. Filipovic itnd I. Piljnc. Crotr/. C’lrcrn. Acttr. 36 ( 1964) IX I. 13. Grctbariti. B. Mnycr. I. Piljac and I. FilipoviL J. fr~oq/. N&. Clrcrrr.. in press. B. GrubariL B. Mnycr. I. Piljac and I. Filipovi& submitted for publication to E/cc*rrochirr~.
Ac*lcc.
NUMERICAL EVALUATION FROM POLAROGRAPHTC
147 - Printed
in The Ncthcrluntls
OF COMPLEX STABILITY DATA FOR QUASI-REVERSIBLE
CONSTANTS PROCESSES
an improved technique for the dctcrminution of comIn a previous paper’. plcx stability constants from polarogrrrphic data based on the method of DcFord and Hume2 was dcscribcd. This method was used to dcterminc stability constants of cudmium(I1) and lead( II) complexes with 2-, 3-, and 4-hydroxybutyratcs”. whcrc the cathodic reduction of cndmium( II) and Icad( II) is polarogruphically reversible. In the present work. essentially the same technique has been applied for detcrmining the stability constants of coppcr( II)-butyratc complexes; in this system the cathodic reduction of coppcr( II) is modcratcly quasi-revcrsiblc, The nleasuring system has been improved by utilizing operational amplifiers. EXPERIMENTAL
Polarograms were recorded by means of ;I controlled-potential polurographic instrument with operational amplifiers. Its potentiostut is similar in principle to circuit analysis was mudc by that described by Kelley et trl. 4.5. for which ;I detailed In order to reduce the iR drop through the solution Bczman and McKinncy”. between the working and the refercncc electrode. a three-clcctrodc technique was employed. The circuit diagram is shown in Fig. I. The polarographic cquiprncnt consists of ;I power supply (Hewlett Packard. model HP 60155C) and potcntiostatic circuit for the control of the potential in the proximity of the working clectrodc. This potential can be varied in discrete steps by means of ;I I kSZ (ten turn) precision potentiometer. The other part of the instrument is the current-measuring circuit. The current (which oscillates owing to the growth of the mercury drop) was passed through a low-pass filter (LPF) and a relay to the analoguc memory. The relay was actuated by a drop-life timer (Radiometer. model DLT I) just bcforc the end of the drop life. Both the potential and the current were monitored by a digital voltmeter. (DVM) (Hewlett Packard. model HP 3480 A) with a resolution of 0. I mV. The potential measurements were reproducible within 0.3 mV and the current measurements within less than I’,!<; (the ccl1 included). The polarographic cell has been described previously’.
13.GRABARIe.
148 +
M. TKALCEC.
1. PILJAC,
1. FILIPOVI~,
VL. SIMEON
-
REAR
Fig.
I. The politropr;Ipllic
;tpp;lrilttls
diagritm.
All the chemicals used were of analytical-reagent grade. Copper( II) pcrchlorate was prepared from copper(I1) oxide and perchloric acid. Sodium perchlorate. solutions of which were used us supporting electrolyte, wus rccrystullized three times. The measurements were made with buffer solutions having constant concentrations of butyric acid (HBut. 0.01 mole dm-“) and copper(I1) (0.4 mole dmm3) and a constnrlt ionic strength (2 mole dmm3. adjusted with NaCIO,): the tcmpcrature was maintained at (298.2+0.2)OK. Total ligund concentration was varied up to ~‘a. I mole dmm3. The capillary constant (/,I:’ t”). measured in open circuit in a O.l-mole drnB3 KCI solution for u mercury column height of 30 cm, was 1.79 mg* s- 1, The drop time was kept at 3.4 s by means of the drop-lift timer.
According to DcFord and calculated from the cxpcrimcntally I;;==
j _-Z(~l-~,)+ln “XPIRT
r;, = I + c p,, [ L]” ,!
Humc z the cumulative obtainable function
stability
co,nstants
/I,, are
.
$} LI
(2)
This Cunction is usuully determined by recording the pdlurogruphic wuves of u series of solutions with a constant metal concentration and ionic strength but a variable total lignnd concentration: in al.1 cases, c’~.~~Pc’~~. so that [L]sc*~_. The values of I.?!. and I:, arc obtained from the polarographic curves either graphically or numerically. The corresponding data for simple aquo ions. I!?~ and f;, are either measured directly. from the polurogram of the solution containing no l&and (but otherwise identical to those described above). or by extrapolating the functions I?, us. [L] and 12 OS, [L]
STABILITY
CONSTANTS
FROM
I’OLAROGRAPHIC
DATA
149
to [L] =O. In the case of a partly rcversiblc electrode process. the magnitude of KY, as well as & can be estimated by a numerical method proposed by Momoki and Ogawa’. The procedures outlined above can bc. at least in principle. applied to quasi-reversible clcctrode processes provided that lhc rcvcrsiblc half-wave potentials are determined. According to Matsuda er u/.~-‘~‘, it is possible to determine the reversible E;, value from the polurographic wave of a quasi-reversible process by part drawing the tangent to the log i/(i,, - i) cs. E curve in its lower. positive enough where the clectrodc process is still diffusion-controlled. A similar approach was employed in the present work but the polurographic waves of quasi-rcvcrsiblc clectrode processes were processed numerically rather than graphicnlly. In the previous work’. tllc E., and i,, values were computed simultaneously. by using the Gauss-Newton least-squares treatment us proposed by Vouk ~1 crl. I I. in order to avoid any subjective smoothing of the polnrogntphic data. Howcvcr. when applied to the polurographic waves of quasi-reversible processes, this method gave slightly different vulucs for E., and i,, than would be cxpcctcd on the grounds of graphical estimates. This is exemplified by the dutn shown in Fig.. 2 where the logarithmic forms of the pblarograms of 0.4 mmole drnbJ coppcr(l1) in pcrchloric acid solutions ( 1 and 10 mmole dm-‘) of constant ionic strength (2 molt dm-“) arc The dntn points wcrc calculated first by evaluating i,, numerically and then . plotted.
+J 2
1
0
-1
Fig. 2. The intlucncc ol’ ~hc mctlrod or computing curve. Coppcr( II). 0.4 mmotc dm- ‘: I=Z(NuCtO.,). I-ICtOJ. (0) With numcricul I,,: (0) with glXptlic~lt
i,, upon the logilrittimic tbrm of 111~ potarogr;lphic (I) 0.01 mote dm-’ I-ICIO.,: (2) 0.001 mole dtn--’ I,,.
150
B. GRABARI~‘.
M. TKALCEC.
I. PILJAC.
I. FILIPOVI~,
VL.
SIMEON
graphically (circles and dots in Fig. 2. respectively). For low values of log i/( ill - i). the data points arc satisfactorily fitted by the lint of theoretical slope. whereas at higher values the data begin to deviate more and more both from the line and among themselves. The deviation from the theoretical line is easily understood if the quasi-reversibility of the electrode process is kept in mind. The discrepancies among circles and dots can be. at least partly. explained by the non-orthogonality of the numerical method used: in the method proposed by Vouk et al.‘]. the errors in any one parameter to be refined may cause considerable errors in the other (this can bc verified by inspecting the correlation matrix). especially if the model applied (in this case a perfectly reversible electrode reaction) is not completely physically adequate. Besides, the information on i,, contained in the first ten or so points of a polarographic curve (E s E+) can hardly be very abundant. Therefore it stems more correct to use a graphical estimate of id for the regression analysis of tl!c polarographic wave. Needless to say. in such an analysis only that part of the wave is taken into account which is still diffusion-controlled. RESULTS
AND
DISCUSSION
The linearized polarogrums of coppcr( II) in the presence of 1 or 10 mmole drnm3 perchloric acid or 10 mmolc drnmJ butyric acid as well ~1s in pure supporting electrolyte(2 mole dm-” NnC104) arc shown in Fig. 3. It cun be observed that with increasing acidity. the polarogrsiphic waves tend to be less reversible. The same was observed by Kolthoff and Okinaka ” for copper( IJ) reduction in perchlorate medium of lower ionic strength (0.1 mole dmS3). and by Hnwkridge and Bauer13 who investigated the kinetics of copper reduction in lithium nitrate medium by AC. polarography. Both groups explain the decreasing irreversibility by assuming the 2-
log
1
2
3
4
I Id
-i l-
Fig. 3. Lincurizcd pohrograms of coppcr( 0.4 mmolc dm-” CU(CIO~)~; I=2(NuCIOJ). HCIO,: (4) 0.01 molt dm-’ hutyric acid.
II) in pcrchloratc mcdicl with (I) pH 6: (2) 0.001 molt dm-”
varying HCIO,:
xid conccntrution. (3) 0.01 molt dm-”
STABILITY
CONSTANTS
FROM
POLAROGRAPHIC
DATA
151
formation of Cu(OH)(H,O)z species at higher pH values. A partial or complete dissociation of this spccics is believed to be faster than is the case with Cu(H20)iC species. The E,. and i,, values for copper(l1) reduction in various media evaluated by alternative methods are presented in Table I. As explained in the preceding section. those E, values computed with graphically estimated i,, values were considered as more reliable. Any of the E, values quoted (except those measured in the presence of butyric acid) could bc. in principle. selected as a final one. Howcvcr. the polarogrum perchloric acid is characterized by the recorded in the presence of I mmole dm-” values were acccptcd as most positive E, value and the highest i,, value. These most reliable. because the prescncc of u higher concentration of acid influences the kinetics of electrode reaction. The finally adopted values arc El = (42.5+0.1) mV and c, = (4.70 10.04) /tA. TABLE
I
HALF-WAVE POTENTIALS MEDIA AT 29X. IS’ K ( ~‘~,,=0.4 Acid __
mrnolc
AND
cImw3. I=2 molt drns3 __~___-._-____--.-_-.------s
trtltlrcl _____._
DlFFUSlON
____.
t8 Estimate
r1”“‘.
OF
29.6-eO.I 31.0f0.1 30.6-eO.l slope.
I
-__-------
COPPER(I1)
_..___ ___-.-__ (rrlv)
E’f.
~__.-_~---________-_-..-
dm -J dm-” dmeJ
ol’ the Ncrnst
(NaCIO,))
(rt1VJ’
30.2 _e 0.
HCIO+ I mmolc HC104. IO mmolc IO mmolc HBut. _.___--~--
CURRENTS
(IIIV) ___.. ---_-
41.61f:O.I 42.5 * 0. I 40.5 f 0. I 39.3 _+o. I
-----
42 43 41 40
IN
DIFFERENT
-_.__-.--__.--_.---.-. iy.
(/IA)
_.._.-_.---_-_-
3.92 _e 0.0 I 4.59 + 0.06 3.7 I * 0.04 4.01 _e 0.06 --_----_-._-_-.-.-----.-.
i;‘;.( prl ) _..-...-_. -___
4.20 4.70 4.58 4.4x
2.3 R-f/X.
The values of ,!?,,. and 1; obtained by polarographing a series of solutions containing it constant concentration of copper(I1) and a varying amount (0.03< with the computed cl,/mmole dmS3 < I) of ligand. are shown in Fig. 4, together of butyric acid estimates of the Nernst slope (s ~2.3 RTQF). The concentration in order to prevent the formation of hydroxo was maintained at 10 inmolc dm-‘. of butyric complexes. According to FilipoviC and Piljac 14. higher concentrations acid shollld be avoided. because. the presence of a higher amount would make Ei more positive through its influence on the viscosity of the solution and on the activity cocflicicnts of the spccics present. When the Lcdzn extrapolation was used. it was found that four successive ML,,complexcsare formed in the copper(butyrate system, and their approximate stability constants were estimated. These values wcrc then relined as described previously’. The computed relined values are quoted in Table II. together with the respective YS’X,confidence intervals. The same system has been examined by spectrophotometric alid potentiometric methods under identical experimental conditions’ s*16 and the values obtained (also quoted in Table II) ilre in very good agreement with thosedetermined in thd present work. Therefore, it can be concluded that correct values of complex stability constants can be obtained by polarography. even when the electrode reaction is not perfectly reversible. provided that adcquatc experimental and computation techniques are applied.
B.GRABARle.
M. TI&LcEC.
1. PILJAC,
1. FILIPOVI~.
VL. SIMEON
0.5
I 11/mol dm-’ Fig, 4. The dcpcndcncc TABLE
IIIOIC
CONSTANTS dmwJ
OF
reduction
on butyratc
concentration.
-.-.--.----_1 SIC
1 &Z./e 1 s/II: 1 ele I
COPPER
BUTYRATE
COMPLEXES
AT 298.15”K
(NiICIO,)“) ~~J/tlr~J~/JYl/dl~~ --_____.-.-__.-_
Ml~fIffJll
” c”=
poluropraphic
II
STABILITY (I=’
of E, and id for coppcr(ll)
NIIJII.
Grccph.
I .x3 CO.03 2.54_eo.o9 t.93+-0.12 ,.ln_eo. I3
1.X5 2.53 2.94 2.x2
.._.._-.--------_-
~‘fJl~Jl~i~JlJJ~~J’~“”
S~J~~~lr,J/‘hfJt~~JJl~Ir~”
NIIJII.
NMJVI.
__._. __.-.-___
lnolc rJm_” . .I*(‘= 1 : ctfth thcfsipn.
...-.---. -
-.--
’
-----------.--1.85+o.ol 2.49 f 0.0 I
95::, conklcncc
intcrvuls
I.89 * 0.02 2.76 + 0.08
iIrC
qilotcd.
SUMMARY
Stability constants. of copper butyrute complexes were determined by polarography. Numerical treatment of polarographic data for quasi-reversible electrode’processes was developed and yielded good estimates of reversible E, values. An improved three-electrode polarographic apparatus was constructed based on operational amplifiers.
STABILITY
CONSTANTS
FROM
POLAROGRAPHIC
DAT’A
153
REFERENCES 1 2 3 4 5 6 7 8 9 IO II I2 13 14 15 16
I. Piljac, B. Gruburic and I. FilipoviC. J. Elccrrotrr~ctl. Clron.. 42 ( 1973) 433. D. D. DcFord nnd D. N. Humc. J. AI~IL’P.Clrcrr~. Sot.. 73 ( 1951) 5321: S. Nushi. 1. Piljxc. B. GrubarE and I. Filipoviti. Crnctr. Clrcrrr. Acvcr. 45 (1973) 453. M. T. Kcllcy. D. J. Fisher and I-I. C. Jones. Arrtrl. Clrern.. 3 I (1959) 1475. M. T. Kcllcy. D. J. Fisher and H. C. Jones. Arrtrl. Clrcr~t.. 32 ( I9hO) 1262. R. Bczmcn and P. S. McKinncy. Aria/. Clrc~~~.,41 ( 1069) I5hO. K. Momoki nnd H. Ogawn. A~rctl. Chon.. 43 (1071) 166-L l-i. Mntsuda. %. E/cklroc*lter?r.. 61 (1957) 4X7: 62 ( 19%) 977. I-I. Mntsudtt rend Y. Aynbc. Z. B/~~I~o~/IL~Iu., 63 (1959) I 164. H. M:Ltsudit. Y. Ayilbc and K. hdxhi. %. E/ck/rr~c’lrc~~,,..67 (1963) 593. V. B. Vouk. P. K. Kurmalkar nnd 0. A. Wcbcr. prlr. k’rr~.. 27 (1955) 9. I. M. KoltholTand Y. Okinakn. J. AUIL’I*.Cltcrn. Sot.. K I ( 1959) 2296. F. M. Hnwkridgc and I-I. I-l. BnLlcr, Awl. Chw.. 44 (1972) 364. I. Filipovic itnd I. Piljnc. Crotr/. C’lrcrn. Acttr. 36 ( 1964) IX I. 13. Grctbariti. B. Mnycr. I. Piljac and I. FilipoviL J. fr~oq/. N&. Clrcrrr.. in press. B. GrubariL B. Mnycr. I. Piljac and I. Filipovi& submitted for publication to E/cc*rrochirr~.
Ac*lcc.