ANALYTICAL CHEMISTRY, VOL. 50, NO. 1, JANUARY 1978
10 buffer used in the reported sulfate method is identical to t h a t used for total water hardness analysis, excepting the omission of MgEDTA (10).
163
(7) J. R. Munger, R . W. Nippler, and R. S. Ingols, Anal. Chem., 22, 1455 (1950). (8) K. Isagai, J . Chem. SOC. Jpn., Pure Chern. Sect., 75, 613 (1954). (9) W. G.Hunt, Jr., J . Am. Water Works Assoc., 535 (1953). (10) "Standard Methods for the Examination of Water and Wastewater", Michael J. Taras, Ed., American Public Heatth Association, Washington, D.C., 1971, p 181.
LITERATURE CITED (1) R. T. Sheen, H. L. Kahier, and E. M. Ross, Ind. Eng Chern.. Anal. E d , 7, 262 (1935). (2) R. J. Bertolacini and J. E. Barney, Anal. Chem., 29, 281 (1957). (3) M. E. Gales, Jr.. W.H. Kaylor, and J . E. Longbottom, Ana/yst(London), 93. 97 11968). (4) R. E. Humphrey and S. W.Sharp, Anal. Chem., 48, 222 (1976) (5) A. Lazrus, K. C. Hill, and J. P. Lodge, Jr., Technicon Symposium, 2nd, New York, London, 1965, 291-3 (pub. 1966). (6) A. Lazrus, E. Lorange, and J. P. Lodge, Jr., Adv. Chem., 73, 164 (1968).
RECEIVED for review July 25, 1977. Accepted October 17, 1977. Financial support from the U.S.Department of the Interior, Office of Water Resources Research (C-6307) and from the Environmental Protection Agency (R803727-01-1) is gratefully acknowledged.
Cyclic Voltammetric Studies of Ionic Strength and Nitrate Ion Dependence of Copper(I1) Reduction in Acidic Aqueous Nitrate and Perchlorate Solutions James L. Anderson'* and Irving Shain Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706
creasing ionic strength in both nitrate (13,17)and perchlorate (13, 18) solutions. Qualitatively, this behavior is consistent with known double-layer trends in hoth nitrate (19,201 and perchlorate (21) solutions. However, the magnitude of the rate difference between the two electrolytes is difficult t o account for solely by simple Frumkin electrostatic effects. Specific homogeneous anion interactions must also be carefully considered, since ion-pairing and complexation of Cu(I1) are more evident for nitrate than for perchlorate anion in aqueous solution (4,8). The rate increase with increasing perchlorate ionic strength has been attributed to decreasing water activity, favoring loss of 5 1 H20 ligands in or prior to the rate-limiting step (18). The increased rate in 1 M KN03 relative to 5 M HC104 has been attributed to activation by nitrate ion ( 1 6 ) ,though p H effects which could also account for the acceleration ( I , 14) were neglected. Possible catalytic mechanisms involving nitrate or nitrogen-oxide oxidation of copper species are unlikely in view of several lines of evidence, to be discussed subsequently. Nitrate ligand bridging has been considered as an important factor in acceleration of homogeneous electron transfer reactions (22). Nitrate has also been reported as a bridging ligand in the electrochemical reduction of Cr(II1) ( 2 3 ) . Ligand-bridging (by carboxylate anions) has been reported to enhance the rate of Cu(I1) reduction (24). Since nitrate has been reported to be a better bridging-ligand than carbonate-an analogue of carboxylate-in homogeneous electron transfer (22),nitrate ligand-bridging must be considered as a possible factor in Cu(I1) reduction. A previous report has presented a reaction scheme for Cu(I1) reduction in acidic aqueous solution (13, 14). Evidence is presented here which supports and elaborates upon t h a t scheme. The proposed (C)ECE mechanism involves a first-order rate-limiting chemical step (deaquation in parallel with hydrolysis) interposed between two electron transfer steps, perturbed by a rapid chemical reaction preceding electron transfer. The preceding reaction was evidently slower in perchlorate than in nitrate solutions. The ECE behavior appears to be perturbed in perchlorate solutions by rapid disproportionation (DISP1 limit of the ECE mechanism) (14), consistent with theoretical expectations (25). Evidence from
The reduction at a mercury electrode of hexaaquo copper(I1) has been studied by cyclic voltammetry in aqueous perchlorate and nitrate solutions of varying ionic strength and in mixed perchlorate-nitrate solutions at unit ionic strength. Studies in single-electrolyte solutions gave no evidence of any significant electrolyte anion participation in the reduction reaction. The variation of the overall reaction rate with ionic strength could be reasonably correlated with simple electrostatic double-layer effects on a fast chemical reaction (attributed to deaquation of a copper(1) specie in an ECE-type mechanism) occurring near the electrode. The reduction rate showed a direct dependence on nitrate ion in the mixed electrolyte, which was not evident in nitrate-only solutions. The reaction rate was much faster in nitrate-only solutions than in mixed-electrolyte solutions with identical nitrate concentrations. The results are aHributed to double-layer rather than bulk participation of nitrate ion in copper reduction. The evidence suggests ligand-bridging by adsorbed nitrate ions.
Nitrate and perchlorate solutions have often been used for t h e study of various metal ions such as Cu(I1) on the assumption (1,2) that no complexation or ion-pairing occurred. Considerable experimental evidence for both nitrate (3-8) and perchlorate ions (8-12) has raised major questions about the validity of this assumption. This investigation was prompted by observation of a marked rate dependence on supporting electrolyte anion for copper(I1) reduction in acidic aqueous nitrate and perchlorate solutions (13, 14). This work seeks t o characterize the effects (e.g., double-layer effects, ligand-bridging, or ion pairing) responsible for the significant dependence of both chemical and electron-transfer kinetics on the anion of the supporting electrolyte. T h e reduction rate of Cu(I1) is faster in nitrate than in perchlorate solutions (13-16). The rate increases with in-
'
Present address, D e p a r t m e n t of Chemistry, U n i v e r s i t y , Fargo, N.D. 58102.
North Dakota State
0003-2700/78/0350-0163$01 .OO/O
GZ
1977 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 50, NO. 1, JANUARY 1978
164 I5
.5
1"
1
2
I_-
3 fi
Figure 1. Cyclic voltammograms for 0.50 mM Cu(I1) in nitrate and perchlorate solutions of varying ionic strength. Scan rate, 50 V/s; average electrode area, 0.030 cm2; data uncorrected for minor electrode-area and viscosity variations. (a) Nitrate solutions: (A) 2.50 M NaN0, 0.0994 M HNO,, (6) 0.895 M NaNO, 0.108 M HNO,, (C) 0.500 M NaN0, 4- 0.0994 M HNO,, (D) 0.0994 M HNO,. (b) Perchlorate solutions: (A) 2.50 M NaCIO, 0.100 M HC104, (6) 0.900 M NaC10, 0.100 M HCIO,, (C) 0.500 M NaC104 0.100 M HC104, (D) 0.100 M HC104
+
+
+
+
oxidative studies a t rotating copper electrodes qualitatively supports the ECE interpretation given here (26). Cyclic voltammetry studies were carried out at p H 1 in this investigation t o minimize the importance of hydrolysis and to ensure that reaction 1 was the principal rate-limiting step: slow
C U ( H , O ) ~ -e ~ ~ + Cu(H,O),-,.,'
+ pH,O
(1)
Here, likely values are n 5 2 and 2 5 p 5 4,based on likely Cu(1) coordination numbers. Ionic strength studies were carried out in solutions containing either nitrate or perchlorate ion as the sole anion, t o investigate nonspecific supporting electrolyte/activity and double-layer effects (primarily ionic-strength dependent) on t h e rate-limiting reaction steps. Nitrate-dependence studies were carried out a t unit ionic strength in mixed nitrate-perchlorate solutions to probe specific chemical (concentration-dependent) effects. Correlation of t h e results from the two types of experiments yielded evidence of a chemical dependence on nitrate anion, which was not readily apparent from ionic strength studies alone. T h e results demonstrate the utility of cyclic voltammetry as a probe of electrode reaction mechanisms. EXPERIMENTAL Cells, chemicals, and instrumentation were as described previously (13,24). Data were acquired and manipulated by means of a Raytheon 706 minicomputer described previously. All experiments were carried out at 25 f 1 "C. Experimental conditions are outlined in the legend of Figure 1. RESULTS I o n i c S t r e n g t h Dependence of Copper(I1) Reduction in P e r c h l o r a t e a n d N i t r a t e Media. Typical cyclic voltammetric curves a t constant scan rate and varying ionic strength are illustrated in Figures l a and l b for nitrate and perchlorate solutions, respectively. Substantial differences are evident between t h e kinetic behaviors in the two electrolytes. T h e overall reaction is clearly slower in perchlorate solutions than in nitrate solutions. The key parameter for kinetic analysis is the reduction peak current function X = i p / ( C * A ) , where i, is the reduction peak current (A), C* the bulk concentration of the species under study (M), and u the scan rate (V/s). The normalized parameter x/xd is also useful, where Xd is the limiting reduction peak current function expected when the reaction rate is controlled solely by diffusion. Experimentally, Xd for
1
1
4
5
I
~t-J
(v1/2se;"2!
Figure 2. Ionic strength dependence of the inverse reduction peak current function C ' f i l i , with square root of scan rate (0.50 mM Cu(II), C10,- electrolyte, pH 1). Current corrected for spherical diffusion with amalgam formation. Supporting electrolyte: (A) ( 0 )0.100 M HCIO,, (B) (0)0.500 M NaCIO, + 0.100 M HCI04, (C) (+) 0.900 M NaCIO, + 0.100 M HCIO,, (D) (0)2.50 M NaCIO, + 0.100 M HC10,
a given experiment was found from the intercept a t zero scan rate of a plot of l / X vs. x h , as described previously (13,14). Values of Xd for perchlorate solutions were taken as t h e average value for nitrate solutions (0.0625 A M-' s'/' V-'/') since limiting values were not attained at the slowest scan rates used in perchlorate solutions. Other useful diagnostic parameters are the reduction half-peak potential Epp; the separation between reduction peak and half-peak potentials [ E , - E,,21; the separation between reduction and oxidation peak potentials IE,; and the ratio of oxidation to reduction peak currents i,,/i,,, obtained after correction for charging current and I / & decay of reduction current during the oxidation step. Notable diagnostic features for the ionic strength studies in perchlorate and nitrate solutions are discussed briefly below and in greater detail elsewhere (13). Perchlorate Solutions. Peak current function plots of 1/X = C*dL/ip vs. v5 (Figure 2 ) indicate relatively little variation in apparent rate constants for ionic strengths between 0.1 and 2.6 in perchlorate media. The slopes a t low scan rate indicate a slight increase of overall reaction rate with increasing ionic strength. Limiting values of l / X converge toward a common limit at low scan rates, but increase with increasing ionic strength a t high scan rates. The variation a t high scan rates is greater than expected for simple viscosity effects (27). PEAK CURRENT RATIOipa/ipc. The ratio declines smoothly from near 2 a t low scan rates toward a value of 1 at high scan rates for ionic strengths p 5 1. The trend reverses between scan rates of 0.05 and 1 V / s a t ionic strength 2.6. However, a simple CE mechanism cannot explain the observed decline in peak current ratio. The marked slope of the plot a t scan rates less than 1 V/s reflects sphericity effects on amalgam formation (28). HALF-PEAK POTENTIAL, EPi2. After correction for liquid junction potentials (13),the low scan rate limiting value of E,,? a t ionic strength 2.6 [ + 5 2 mV (SCE)] is 16 mV more positive than the value found at other ionic strengths. This deviation exceeds probable experimental uncertainty of ca. 1 mV. SEPARATION BETWEENREDUCTION PEAK AND HALF-PEAK POTENTIAL, E, The plateau value of E , - E,,' at high scan rates increases slightly and is achieved a t increasing values of scan rates as ionic strength increases. The increase of ca. 20 mV in the plateau value, between ionic strengths 1.0 and 2.6, primarily reflects the positive shift of E,!', simultaneous with the apparent overall reaction acceleration a t the higher ionic strength. Interestingly, a similar increase in the limiting plateau of E , - EpI2was observed near p H 3 in pH-dependence studies
ANALYTICAL CHEMISTRY, VOL. 50, NO. 1, JANUARY 1978
165
Table I. Kinetic Parameters for ECE or DISPl Kinetics of 0.50 mM Cu(I1) Reduction in Nitrate Supporting Electrolyte of Varying Ionic Strength Supporting electrolyte 0.0994 M HNO, 0.500 M NaNO, + 0.0994 M HNO, 0.895 M NaNO, + 0.108 M HNO, 2.50 M NaNO, + 0.0994 M HNO,
~ E C /(a E n 1”
d e
f g h
24 i 4 6 5 + 10 1 2 0 i 30 1 5 0 + 20 1 7 0 i 20
K21ECEb 12i 2 32i 5 6 0 i 15 7 5 i 10 8 5 z 10
kDISPl / ( a n ) c
37 f 107 i 196 i 250 r 290 t
5 13 21 10’ 40
K21DISPlb
18k 3
54i 7 9 8 i 11 1202 5 140i 20
Obtained from use of working curve ( 3 0 ) assuming a simple ECE mechanism with no disproportionation; a and n are Obtained assuming that K22 is functionally equivalent to tlhe irreversible k of parameters of the first charge transfer. Nadjo and Saveant ( 3 0 )(shown previously ( 1 4 ) t o be a reasonable approximation in the analysis of pH-dependent kinetics). The value of a n for the first charge transfer is taken t o be 0.5. Obtained by the same method as ( a ) but assuming a DISPl mechanism. Assuming X, = i,/(C* vG)(diffusion) = 0.0637 A M-’ V-”z sl’*. e Assuming X d = 0.0637. f Assuming Xd = 0.0612. Assuming Xd = 0.0573 (smaller than Xd at lower ionic strength due t o increased solution viscosity and, hence, decreased diffusion coefficient). Assuming Xd = 0.0563. Note ca. 15% variation in kinetic constant for 2% variation in x,. a t unit ionic strength (14). In t h e p H studies, E, - E p I 2 increased as the apparent rate of the pH-dependent reaction increased. Both the positive shift of E,,* and the decrease of the high-scan-rate limit of X/Xd at high ionic strength could be indicative of a chemical step-either weak perchlorate ion-pairing or deaquation of copper species-prior to electron transfer. The ionic strength dependence of these two diagnostic parameters, together with the parallel between ionic-strength and pH-dependent behavior of E, - E p l Scan be rationalized by assuming a (C)ECE mechanism with the intermediate chemical step as the primary rate limiting step, dominating kinetic behavior a t low scan rate. The reaction rate of this step-attributed to deaquation and hydrolysis of Cu(I1) (14)-accelerates with increasing ionic strength. The initial chemical step appears to be much faster than the intermediate rate-determining step, becoming kinetically important only a t high scan rate under conditions where the intermediate step is accelerated (e.g., increasing ionic strength or pH), or where the initial step is decelerated (e.g., increasing ionic strength). While ion-pairing would tend to slow the reaction, medium effects such as changing outer Helmholtz double-layer (&) potential or decreasing water activity could speed up the reaction. Double-layer parameters for perchlorate media do not favor acceleration, and are thus apparently subordinate to bulk effects. T h e overall increase of reaction rate with increasing ionic strength (perchlorate concentration) argues against significant reaction inhibition by perchlorate ion. Weak ion-pair formation could account for a slight slowdown of the preceding reaction, b u t this effect is subordinate to acceleration of another process-probably Cu(I1) deaquation--which causes a slight rate increase with increasing ionic strength. Available evidence indicates much weaker aqueous ion pairing of Cu(I1) with C104- than with NO3- (4, 8, 9). Raman spectra of saturated Cu(C10J2 solutions show no evidence of ion pairing (4), although UV spectra suggest interaction at ionic strengths of 2 or greater (8, 9). A decrease in water activity with increasing ionic strength could accelerate the overall reaction by shifting a deaquation equilibrium toward the deaquated, electroactive species, consistent with data of Malyszko e t al. (18) on the wateractivity dependence of Cu(I1) reduction at high ionic strength. Nitrate Solutions. Behavior of diagnostic parameters in nitrate solutions was much less complex than in perchlorate solutions. T h e scan rate dependence of the parameters primarily reflected t h e increase of the rates of the coupled chemical reaction&) with increasing ionic strength or nitrate concentration. SEPARATION OF REDUCTION P E A K AND HALF-PEAK POTENTIALS. Plots of E, - E,,* vs. log u exhibit plateau values of E, - Ep/2a t high scan-rate for low ionic strength, but not
for high ionic strength. This behavim is consistent with either ECE behavior or quasi-reversibility of the electron transfer, influenced in either case by the double-layer potential. PEAK POTEKTIAL SEPARATION. Comparison of experimental LE, values a t scan rates of 50 V / s with the value of LE, predicted by data of Nicholson (29) for various quasi-reversible electron transfer rate constants k9kLyields the following estimates for the apparent overall standard heterogeneous electron transfer rate constant hsh (cm/s) as a function of ionic strength: 0.02 0.01 c m / s (ionic strength 0.1);0.04 f 0.01 (0.6); 0.04 f 0.01 (1.0); 0.06 =k 0.01 (2.6). PEAK CURREKT RATIO. Interesting reversals are exhibited in scan-rate and ionic-strength trendls of this parameter. The biphasic variation (midpoint a t ca. 5 V/s) of i,,/i,, with increasing scan rate a t ionic strength 0.1 may be indicative of mixed kinetic control of the rea.ction. This behavior is qualitatively similar to the behavior in perchlorate solutions a t ionic strength 2.6. The marked variation a t scan rate less than 1 V / s reflects sphericity effects on amalgam formation (28). EXTRACTION OF KINETICPARAMETERS FOR NITRATESoLUTIONS. Kinetic parameters obtained assuming an ECE mechanism-either uncomplicated or accompanied by a first-order rapid disproportionation step (DISP1 mechanism)-were extracted for the reaction depicted in Equation 1 by comparing the normalized reduction peak current function X/Xd-Le., the ratio of kinetic current to the limiting diffusion current-as a function of scan rate (Figure 3), with the working curve of Nadjo and Saveant (30) by a previously discussed method (13,14). The main variation of x/xd occurs at sufficiently low scan rates that qua,si-reversibility of electron transfer should not substantially affect the kinetic parameters obtained. The limiting diffusion peak current function for each ionic strength was obtained from the reciprocal of the intercept of a plot of C* v%/i, vs. v’K The kinetic factors obtained from the data of Figure 3 are tabulated in. Table I. Discussion of the data will be temporarily deferred. It is important to note, however, that the rate increase with increasing ionic strength is significantly less than expected if ;a chemical reaction with nitrate were an important step. Thus, a 26-fold increase in nitrate concentration yields only a seven-fold increase in the apparent rate constant, hECE. The results suggest either that any reactions with nitrate are peripheral to the main reaction sequence, or that bulk effects may be less important than double-layer effects. Catalytic mechanisms involving nitrate or nitrogen-oxide oxidation of copper species are unlikely in view of several pieces of evidence. The reduction reaction accelerates with increasing p H throughout the acid range (13, 14), opposite to the trend expected for likely nitrogen-oxide-catalyzed
*
166
ANALYTICAL CHEMISTRY, VOL. 50, NO. 1, JANUARY 1978
10 iI
L
I IO
1
3
1
1
10 0 v (V/SeC)
Figure 3. Variation of normalized reduction peak current function X/Xd with logarithm of scan rate for 0.50 mM Cu(I1) solutions in nitratesupporting electrolyte of varying ionic strength. Points represent experimental data. Curves represent theory for an ECE mechanism. X = ( i J C + f i ) (experimental, A M-’ V-”‘ s’”); Xd (diffusion-controlled) is taken to be the intercept at zero scan rate of a plot l / X v s . log v ; current corrected for spherical diffusion with amalgam formation. Solution and kECE/(an)(s-’) [ kECE= K2,111,ff; a n = electron transfer coefficient and number of electrons for first electron-transfer step] are as follows: (A) 0.0994 M HNO,, X, = 0.0637; 24 (-) and 37 (--), assuming DISP1 kinetics. (B)0.500 M NaN0, 4- 0.0994 M HNO,, X, = 0.0637; 65. (C) 0.895 M NaN0, 0.108 M HNO,, X, = 0.0612; 120. (D) 2.50 M NaN0, i- 0.0994 M HNO,, X, = 0.0573 [Xd diminished partially due to increased solution viscosity]; 170
l/sec
,
10 0
Figure 5. Variation of separation of reduction peak and half-peak potentials with logarithm of scan rate for 0.50 mM Cu(I1) in mixed perchlorate-nitrate supporting electrolyte at unit ionic strength (pH 1). Nitrate concentration (M) for (A) 0, (B) 0.0994; (C) 0.299; (D) 0.500; (E) 0 700; (F) 1.00
+
I
1
I
01
IO Y(
-
zor 00
0 ICC
- 0 100 E(V/SCEl
-0200
-C300
I
10 0
1
v/secI
Figure 6. Variation of normalized reduction peak current function with logarithm of scan rate for 0.50 mM Cu(I1) in mixed perchiorate-nitrate supporting electroiyte of unit ionic strength at pH 1. Points, experimental; lines, theory for DISPl limit of ECE mechanism. Nitrate concentration (M) and kDlsPl/(an)(s-’) are given as follows, respectively: (A) (0): 0, 2.8 f 0.6. (B) (X): 0.0994, 3.2 f 0.3. (C) (0): 0.299, 12 f 3. (D) (+): 0.500, 30 dZ 4. (E) (0): 0.700, 59 dZ 5. (F)(A) [Two theoretical curves are shown for F: unbroken line for DISPl limit; dotted line for simple ECE limit]: 1.00, 200 dZ 20 (-) [kinetic parameter obtained assuming DISPl] and 120 f 30 (--)[kinetic parameter obtained assuming ECE]
An apparent value of an of 0.38 could be extracted from the slope of the plots of E,/? vs. log L‘ (slope = 3 0 / ( a n ) mV/decade u ) for various nitrate concentrations, consistent + with the range of values from other experiments described + here and elsewhere (13, 14). SEPARATION OF REDUCTION PEAKAND HALF-PEAK Po+ TENTIALS. The behavior of the parameter E , - E,,Q (Figure + 5 ) is especially interesting. The values of E , - E P j zlevel off at a constant plateau of ca. 120 mV at high scan rates for lower oxidation reactions. T h e reduction peak current functions nitrate concentrations, b u t a t the highest nitrate concenin nitrate and perchlorate solutions converge toward a common trations do not reach a plateau. Such a transition is consistent limit at low scan rates as pH increases. The limiting reduction with increasing reversibility of a quasi-reversible electronpeak current function a t low scan rates in nitrate solutions transfer or of a reaction occurring within the double-layer, and is essentially invariant with p H and ionic strength. Thus some is similar to that observed in the ionic strength study in nitrate property of nitrate ion other than its oxidizing power must solutions. account for rate differences between nitrate and perchlorate PEAK CURRENTRATIO. At low nitrate concentrations, the solutions. peak ratio declines from a maximum value of ca. 2.0 or greater Nitrate Ion Dependence at pH 1 and Unit Ionic Strength. at low scan rates to a minimum value of ca. 1.4 a t high scan As a final check on the relative contributions of double-layer rates. The trend reverses a t high nitrate concentrations, so (ionic strength) effects and specific nitrate ion chemical that the peak ratio rises from a minimum of ca. 1.3 a t low scan (concentration) effects, a series of experiments was carried rates to a maximum of ca. 1.7 at high scan rates. The out at p H 1 by varying nitrate ion concentration a t a constant maximum ratio diminishes slightly with increasing nitrate ionic strength of unity maintained by addition of perchlorate concentration. Such behavior may be indicative of mixed ion. Typical cyclic voltammetric current-potential curves for t h e reduction of 0.50 mM Cu(I1) are illustrated in Figure 4 kinetics, such as found in the (C)ECE mechanism suggested earlier. for various mixtures of perchlorate and nitrate supporting EXTRACTION OF MIXED-ELECTROLYTE KINETIC PAFXWB. electrolyte. Plots of the kinetic parameters extracted by the method of T h e variation of diagnostic parameters with scan rate and Nadjo and Saveant (30) are illustrated in Figure 6. The very nitrate concentration can be summarized as follows. HALF-PEAK POTENTIAL AND PEAK POTENTIAL SEPARATION. small difference between the plots for the solution containing no nitrate and the solution containing 0.1 M nitrate is more T h e parameters and SP exhibit parallel trends with consistent with a double-layer effect than with a bulk chemical increasing nitrate concentration. T h e largest change occurs effect. The data a t most concentrations exhibit closer adbetween 0.1 and 0.3 M nitrate concentration, and the curves herence to the DISPl limit than the simple ECE kinetic limit, becomes more closely spaced with increasing nitrate conas was found for pure perchlorate supporting electrolyte (14). centration. Figure 4. Cyclic voltammograms for 0.50 mM Cu(I1) in mixed perchlorate-nitrate supporting electrolyte of unit ionic strength. Scan rate, 50 VIS. (A) 0.895 M NaNO, 0.108 M HNO,; (B) 0.700 M NaN0, 0.200 M NaCIO, 0.105 M HCIO,. (C) 0.500 M NaN0, 0.400 M NaC10, 0.105 M HCIO4. (D) 0.200 M NaNO, 0.0994 M HNO, 0.700 M NaCIO,. (E) 0.0994 M HNO, 0.900 M NaCIO,. (F) 0.900 M NaC10, 0.100 M HCIO,
+ +
+
+
+
ANALYTICAL CHEMISTRY, VOL. 50, NO. 1, JANUARY 1978
167
Table 11. Kinetic Parameters for Reduction of 0.50 mM Copper(I1) in Mixed Perchlorate and Nitrate Supporting Electrolyte of Unit Ionic Strength at pH 1 kECE/(QnIb, 5.’
M
2.0 i 0.6 2.2 i 0.4 8 i 3 18t 6 38 * 8 120 i 30
0
0.100 0.299 0.500
0.700 1.00 a
(NO;)
+ (C10;)
K 2 1 ~ ~S-’ ~‘,
=
1.00 M.
See footnote
1.0
i
k D I S P l l ( “ n ) d , s-’
2.8 3.2 12i 30 i 59 i 200 i
0.3
1.1 f 0.2
4 i 9 i l9i 60i a
2 3 4 15
of Table I.
The average kinetic parameters obtained for each solution are presented in Table 11. T h e kinetics for a given concentration of nitrate ion are faster in solutions containing nitrate as the only anion than in perchlorate-only solutions at the same ionic strength, or in mixed-electrolyte solutions maintained a t unit (Le., higher) ionic strength by addition of perchlorate ions, as may be seen by comparison of the data of Tables I and 11. The relative invariance of t h e activity coefficient of Cu(I1) in aqueous C U ( N O ~solutions )~ (31) in the ionic strength range studied here tends to rule out major bulk activity effects as a source of the observed kinetic variations. I t is concluded that ionic strength or bulk activity effects alone cannot account for the increase in chemical kinetic rate with increasing nitrate concentration. In nitrate or perchlorate solutions containing only a single type of anion, the rate increases with ionic strength but acceleration is less than expected if bulk anion participation in the reaction were required. By contrast, the acceleration with increasing nitrate concentration in the mixed electrolyte is very marked. The increase in kinetic parameters on changing from pure perchlorate to pure nitrate supporting electrolyte, shown in Table 11, is nearly a factor of 10 too great to be accounted for by a simple Frumkin lCp effect, based on double-layer data t o be discussed subsequently. A 10-fold increase in nitrate concentration yields a 60-fold increase in kDISP1.
Careful evaluation of data is required to assess relative contributions of double-layer and nitrate-concentration contributions in the mixed electrolyte. However, the marked variation of rate with nitrate concentration in the mixed electrolyte, in contrast with the relatively minor dependence on nitrate in the nitrate-only solution, strongly suggests a double-layer kinetic effect involving competitive adsorption of perchlorate and nitrate ions.
DISCUSSION Mechanistic Considerations. Double-Layer E f f e c t s on Rapid Homogeneous Reactions. Two simple mechanisms other than modification of reactant activity may account for increasing rates of homogeneous chemical reactions with increasing ionic strength: (a) chemical interactions with a component of the supporting electrolyte, resulting in a more reactive product (e.g., ion-pairing with nitrate to yield a more reactive nitrate complex or ion-pair, although ion-pairing quite often results in less reactive species); or (b) double-layer effects. Ion pairs or complexes of copper(I1) with nitrate ion in aqueous solution have been reported on the basis of numerous techniques ( 3 - 6 , 8 , 3 2 ) . Raman studies ( 3 , 4 )provide the strongest evidence for Cu(I1) interaction with NO3-. Reported equilibrium constants, based on ESR and thermochemical measurements, are 0.40 f 0.02 for the outersphere ion-pairing constant of Cu(I1) plus NO3- and 0.15 0.06 for t h e inner-sphere (complexation) constant ( 5 ) . Nitrate (19, 20, 33-35) and perchlorate (33, 36-38) adsorption data a t mercury electrodes indicate stronger adsorption of nitrate than perchlorate when the supporting
*
i
0.6
f
0.3
KZIDISPlC,
s-l
1.4 z 0.3 1.6 i 0.2 6f 2 15i 2
3 4 5 20
30i 3 1 o o i 10
See footnote b of Table I.
See footnote c of Table I.
Table 111. Outer Helmholtz Plane Potential L. 2 a in Perchlorate and Nitrate Media of Varying Ionic Strength Perchlorateb i
>,mVd
cen- E = + 3 0 mV
..
0.109 0.543 0.931 1.86
-22 -23 -25 -29
NitrateC
0 -8
-6 -6
L’ *, mVd
E=-337 mV
Concer 1
-32 -36 -35 -31
-27 -22 -20 -18
..
0.100
-17
0.600 1.00
-29 -32 -45
2.00
-27 -30 -39 -42
Values interpolated and extrapolated from original data. All potentials corrected t o SCE. HC10, data (21 ). Calculated adsorbed charges which include assumed constant adsorbed charge contribution (- 3 pC/cm2)due to a “salt exclusion layer” ( 2 1 )are denoted “SEL”. Calculated charges assuming no salt exclusion layer charge are denoted “NS”. “,NO, data ( 3 7 ) . + calculated from electrode charge and adsorbed charge according to diffuse-double-layer theory ( 5 3 ) . a
electrolyte concentration is greater than 0.1 M. Perchlorate Solutions. The data of Parsons and Payne (21) presented in Table I11 under the heading SEL (“salt exclusion layer”) show that the outer Helmholtz plane potential 1C2 at mercury electrodes in perchloric acid solutions is typically negative (except in a narrow potential range a t low ionic strength) and relatively independent of ionic strength in the potential range of interest to this study (+O.l5 to -0.35 V (SCE)), especially near the formal potential of the couple Cu(II)/Cu(O)(Hg). Parallel but somewhat conflicting data have been presented by Wroblowa et al. for sodium perchlorate solutions (37). The Parsons and Payne experimental data appear to be more reliable and consistent with other experimental evidence (39, 40), e.g., relative constancy of lCq with varying ionic strength. The actual G 2 values reported by Parsons and Payne (21) are biased by an arbitrary assumption of a -3 yC/cm2 adsorbed charge contribution due to a “salt-exclusion layer”. For comparison, values are also presented in Table I11 under the heading N S for the $2 values expected if the assumed “salt-exclusion layer” charge is not included. Other evidence supports the concept of a water layer inaccessible to nonspecifically adsorbed ions in perchlorate solutions (38). NS perchlorate data are presented to conform to assumptions for nitrate literature data (12,191. Results obtained here appear more consistent with NS than SEL data for perchlorate solutions. Nitrate Solutions. Variation of the ionic strength is expected to have a greater effect in nitrate than in perchlorate media, since the outer Helmholtz potential (19, 20) for nitrate media is substantially more negative and more dependent on ionic strength than observed for perchlorate media in the electrode potential region employed here, as illustrated in Table 111. Literature data are in good agreement for nitrate adsorption (19,20). The increasingly negative value of & a t
166
ANALYTICAL CHEMISTRY, VOL. 50, NO. 1, JANUARY 1978
fusion coefficient D = 7.2 X lo4 cm s-' ( I ) and backward rate constant h b 108-109 s-l for Cu(1) reactions, comparable to ligand exchange rates for Cu(I1) species (56-58). Since 99% of the potential drop in the diffuse double-layer occurs within a distance of 1 4 / v c A for a univalent electrolyte (53) of concentration c b , the reaction rate will be significantly influenced by the double-layer in all solutions investigated here. Spatial averaging of experimental rate constants across the reaction layer can be broken into two contributions:
-
Table IV. Predicted Double-Layer Acceleration of Homogeneous Chemical Reactions
Assumed
Reaction layer thickness
k b , S-l
@,A
lo8
27 8.5 2.7
109
10'0
Approximate acceleration factor, ( K Z~),,,el/(Kz o o p-4'1 p-q=2 1.3
1.8 2.4
1.9 4.0 6.5
a given electrode potential as nitrate concentration increases, tends to cause a corresponding increase of the apparent electrochemical rate constant and chemical rate constants for rapid coupled reactions of positive species. In addition to double-layer considerations, previously discussed evidence for weak ion-pairing and complexation of Cu(I1) by nitrate ions requires consideration of the possible chemical role of nitrate in any reaction step. Specific adsorption of electroinactive ions may also affect the reaction rate more strongly than predicted by the simple Frumkin correction, because of electrostatic effects on the electrical potential (41-43) at the reaction site, or the activity coefficients(s) of transition-state species (44). Other phenomena such as ligand-bridging (45-49) or anion-induced adsorption (50-52) may also be important. Consider the reaction type:
AP+ +
k'
Bq-
f, A B ( P - Q ) +
( 2)
i,"
with equilibrium constant K = kfO/kbo in an electrically neutral environment. A composite, pseudo-first-order expression for excess B can be obtained for this reaction occurring within the electrical double-layer, at potential $, assuming exponential Frumkin concentration terms:
(3) Here, K,ff is the apparent effective equilibrium constant and leffthe sum of the apparent effective rate constants kfe, tkbefr for an ECE or DISPl chemical step; kfo and kbo are the rate constants and [B], the concentration of specie B in a neutral environment (+ = 0); and the exponential term,
(4) expresses concentration and apparent rate modification in the double-layer relative to a neutral environment. Strong-field dissociation effects on complex AB ( 5 4 ) are neglected here. Under these conditions, the equilibrium constant K is unaffected by the double-layer potential. Approximate reaction layer thicknesses 1 = (55) estimated for reaction 1 range from 8-27 A assuming a dif-
vm
(5) where dl signifies reaction within the double-layer, and o signifies reaction outside the double-layer. .4pproximate numerical evaluation of double-layer enhancement of Peffleffis presented in Table IV for reaction 2, assuming kb >> kf, in a univalent, 1 M electrolyte solution with +2 = -30 mV. Accelerations (K21)accel obtained relative to a field-free reaction (K21),range from 30 to 550% depending on the magnitude of kb. Although independent estimates are unavailable for kb of &(I) species reactions, double-layer effects are expected to be important. The factor p q (which determines the magnitude of acceleration factor io) has a value of 2 for simple deaquation or hydrolysis reactions of Cu(I1); a value of 1 for ion-pairing of Cu(I1) with a univalent anion such as nitrate, or for simple deaquation or hydrolysis of Cu(1); and a value of 0 for ionpairing of Cu(1) with a univalent anion. Double-layer effects will be operative for sufficiently fast reactions whenever the value of p - q is nonzero. For any two ionic strengths a and b, the ratio f[=A?l(a)/@l(b)] will be proportional to exp(-(p - 4 ) F [ $ 2 ( a )- $2(b)I/(RT)J. As seen in Equation 3, the rate parameter P e f f l e fwill f be proportional to the square of nitrate concentration if nitrate ion-pairing is a fast, required reaction preceding the ratelimiting step. The proportionality can rise to the third power if complexation with nitrate is a kinetically limiting required step. If complexation occurs parallel to another reaction, the exponent will depend on the relative kinetic importance of the products of each reaction and, hence, may vary from zero to three. Kinetic parameters for reactions involving Cu(1) may still depend on Cu(II), because of double-layer or homogeneous ion-pairing effects on Cu(I1) concentration and reactions. I t should in principle be possible to use the ratios to make inferences about the kinetic significance of reactions of Cu(I1) or of Cu(1). Ionic Strength Results. Table V lists the ratios of the kinetic parameter Pl obtained at different ionic strengths in nitrate-only electrolyte referred to the value obtained a t ionic strength 0.1, and the ratios of double-layer rate-enhancement factors expected for charges p - q of 2 and 1,also -
Table V. Ionic Strength Dependence of the Kinetic Factor K21 for Reduction of 0.50 mM Cu(I1) in Nitrate Supporting Electrolyte at pH 1 Double-layer Supporting Normalized kinetic factor Specifically acceleration factord electrolyte adsorbed nitrate concn, M RECE' RDISmb chargec, pC/cmz f ( Z = 1) f(Z= 2 ) 1.0 1.0 -14 1.0 1.0 0.0994 0.599
1.00 2.60
2.7 5.0
6.2
3.0 5.4 6.7
- 18 - 22
1.8
1.6
- 32
3.0
REcq is the ratio of the kinetic factor K 2 1 ~ atc ~a given ionic strength to its value at ionic strength
2.5 3.2
8.8 0.0994.
R,,,p,
is the ratio of the kinetic factor K 2 1 ~ = nat a given ionic strength to its value at ionic strength 0.0994. Obtained directly or interpolated and extrapolated from data of Tilak and Devanathan (37), at the formal reduction potential of Cu(II), + 27 mV (SCE). The double-layer acceleration factor is the ratio of the term exp{-ZF$,/(RT)} at a given ionic strength to the value at ionic strength 0.0994. Given for electrode potential + 27 mV (SCE).
ANALYTICAL CHEMISTRY, VOL. 50, NO. 1, JANUARY 1978
169
Table VI. Hypothetical Estimated Adsorbed Anionic Charges and Outer Helmholtz Potentials for Mixtures of Perchlorate and Nitrate Supporting Electrolyte at Unit Ionic Strength (pH)
Hypothetical adsorbed charge (wC/cm’) - 41, c 10, b
-qI,NO, b -
SEL
NS
SEL
19 17 13
15 14 10
0
0
0.099 0.299
2 7
2 7
0.500
10
8
11
0.700 1.00
6
5
11 15
0
0
15 22
(NO3-)=,M 0
NS
22
,-91,tOtal
SEL
NS
19 19 20 21 21 22
15 16 17 19 20 22
-w,(~V)~ SEL NS 22 23 26 28 30
32
6 9 13 21 25 32
f(0,)“
SEL
NS
1.0 1.1
1.0
1.4 1.6 1.9 2.2
1.3 1.7 3.2 4.4 7.6
a (NO;) + (C10;) = 1.00 M. qI,anionsignifies hypothetical charge due t o an anion in the inner (adsorbed) Helmholtz layer. Assumed t o vary linearly with bulk anion concentration (perchlorate or nitrate, respectively) between zero and the value observed for a solution containing only the specified anion. SEL denotes values expected assuming a salt exclusion G 2 = 0.0514 sinh-’ layer contribution t o adsorbed charge (21 ). NS assumes n o salt exclusion layer charge contribution. { ( q M + q1)/(11.72 where qM (the charge on the electrode) and g~ (specifically absorbed anion charge) have units of pC/cmz, C, is the concentration of a 1 : l supporting electrolyte ( M ) and $, is the outer Helmholtz potential (V). Determined at the formal potential of Cu(I1) reduction [ + 2 7 mV (SCE)], where the electrode charge q M is approximately +14 f ( $ > )is the ratio of pC/cm2 in both nitrate and perchlorate supporting electrolytes at unit ionic strength (19, 20, 3 6 ) . the kinetic enhancement factor exu 1- 2FL;./(RT)l for each solution. to the factor for pure perchlorate solution.
a)},
referred to ionic strength 0.1. The data in Table V show that t h e increase of t h e apparent kinetic parameter K21 with increasing ionic strength a t no time greatly exceeds the increase predicted on t h e basis of simple double-layer effects for a reaction involving a specie with charge +2. The increase is somewhat greater than predicted for a reaction involving a specie with charge +l. Any effect of copper(I1) ion pairing with nitrate ion would appear to be minimal and if a t all operative, acting to diminish t h e reaction rate slightly only at t h e highest ionic strength. T h e limits of estimated accuracy of the kinetic parameter F?l(ca. 3 3 0 % at a given ionic strength), coupled with the possible errors in t h e Frumkin double-layer correction, prevented unequivocal determination of the charge of the species undergoing chemical reaction. However, no significant effect of complexation or ion-pairing of any copper(I1) with nitrate ions was detectable within the limits of experimental accuracy. On the basis of t h e ionic strength studies, it is concluded t h a t the effect of increasing nitrate supporting electrolyte concentration is virtually completely a double-layer effect, and t h a t within the limits of experimental accuracy, there is no evidence of any major effect of homogeneous ion pairing on t h e coupled chemical reaction. Mixed Electrolyte Results. Remarkably, the kinetics show a strong correlation with bulk nitrate concentration in the mixed electrolyte, although no such dependence was evident in pure nitrate media. This unusual behavior can be conveniently rationalized on the basis of double-layer phenomena. Double-layer data for mixed nitrate-perchlorate solutions are, unfortunately, unavailable. Hypothetical double-layer parameters for mixed electrolyte at constant ionic strength were, therefore, very crudely approximated at a given potential by assuming that the specifically adsorbed anionic charge is linearly dependent on the bulk concentration of each adsorbed specie (Henry’s law, assuming no interaction between like or unlike adsorbed ions). While this is a poor approximation and must be regarded with some skepticism, it allows qualitative testing of the plausibility of several possible mechanistic interpretations. T h e Henry’s law assumption precludes unequivocal differentiation between bulk and adsorbed nitrate participation. Any such differentiation must rest on other evidence. Near the formal potential of Cu(I1) reduction, the electrode charge is nearly identical in perchlorate and nitrate solutions (19,20,36),while the adsorbed charge changes with solution composition. The maximum adsorbed charge attributable to
each anion is approximated by assuming it to be the charge obtained for a solution of unit ionic strength containing only that anion. Approximations for both the adsorbed charges and $* potentials so obtained are presented in Table VI. After dividing the apparent homogeneous rate constant by the bulk nitrate concentration and normalizing to a single nitrate concentration (0.1 M), the normalized rate constant parameter (RSC in Table VII) was found to correlate reasonably well with Frumkin double-layer effects. The values of RNCwere approximately of the magnitude expected for double-layer effects on the rate of a very fast reaction occurring largely within the electrical double-layer region, and intermediate between values expected for a singly-charged ( f l or doubly-charged (f’) copper specie, if t h e double-layer parameters calculated assuming no salt exclusion layer (NS) are used. The acceleration is greater than expected for data assuming a salt exclusion layer (SEI,). The dependence on nitrate suggests that the nitrate reaction must precede the rate-limiting chemical step (Equation 1). The ionic strength study in perchlorate media suggested t h a t perchlorate does not inhibit the reaction, since the apparent rate increased slightly with perchlorate concentration. Consequently, a mechanism which can account for all the data must not depend on either homogeneous complexation of copper species with nitrate ion, or inhibition by perchlorate. Assuming no major errors in the magnitude of the $2 values used, the data can be qualitatively accounted for by either of two simple mechanisms involving specific adsorption of the supporting electrolyte anion, assuming approximate Henry’s law adsorption behavior in mixed electrolyte to account for linear dependence of rate on nitrate concentration. The first alternative (adsorption) mechanism assumes the inner Helmholtz plane (assumed to lie a t the centers of adsorbed anions) lies closer to the electrode for planar adsorbed nitrate ions than possible for spherical perchlorate ions, allowing greater interaction of the electroactive species with the electrode. This possibility would be particularly relevant for a reaction resulting in amalgam formation, where the product must be deposited in the electrode material. An alternative mechanism involving adsorbed nitrate species is ligand-bridging. Nitrate has been reported as a bridging ligand in Cr(II1) reduction
