J . Phys. Chem. 1989, 93, 7269-7275 TABLE VI: Comparison of Core Representations'
BE Zn(OH2)2+ BE Zn(OH)+ PA Zn(OH)+ PA (OH)-
P&D all electronb
H&W ECP, P&D basis setc
112.4 46 1 81.7 44 1
119.5 460 90.2 441.9
"All results in kilocalories per mole. bFrom ref 8. CECP from H&W and valence basis set from ref 8. energy and proton affinities were reproduced (see Table VI). This eliminates the ECP's as the source of error. The results obtained for the large complexes (Table V) indicate that water and hydroxide ion bind to (NH3)3Zn2+by 43 and 284 kcal/mol, respectively (see Table V, footnote a for the definition of binding energies). These results do not include electron correlation, but the results on the smaller complexes suggest that the increase in binding due to electron correlation is only 2-3%. Zero-point-energy corrections (ZPE) are also of the same magnitude but opposite direction. The proton affinity of the hydroxide complex is calculated to be 167 kcal/mol. Since the proton affinity is also equal to the difference in binding of hydroxide and water subtracted from the proton affinity of the hydroxide ion, the correlation correction in the latter will have an effect on the correlation correction of the proton affintity of the complexed hydroxide ion. Assuming a 2.5% increase in the binding energies due to the correlation correction and an 8 kcal/mol decrease in the hydroxide ion proton affinity, the net correlation correction for the proton affinity of the complexed hydroxide is a decrease of 14 kcal/mol. ZPE corrections would also decrease the proton affinity, but the correction would be less than the correction for the hydroxide proton affinity (8 kcal/mol) since the ZPE corrections for the binding of hydroxide and water are likely to be the same sign but subtracted from the hydroxide correction. We therefore believe that the estimates found in Table V of the binding energies of these large complexes are indeed good estimates for
7269
these properties and are not likely to need future modification. However, the proton affinity may be as much as 14-22 kcaljmol too large.
Conclusions (1) The H & W and SB&K ECP's and basis sets have been shown to be sufficient for obtaining reliable bond energy results for zinc complexes when double {contractions are used. (2) The effect of electron correlation on reaction energies for Zn and Cu is small on clased-shell reactions (typically the Hartree-Fock level is only 2% too low) while it is very si&icant on reactions involving open-shell species (typically the Hartree-Fock level is 50% too low). (3) The effects of the contraction of the basis sets reveal that minimal basis sets should give reasonable geometries but poor reaction energetics for closed-shell systems. The most important consideration in the choice of basis set is that there should be a flexible representation of the 4s orbitals (but not necessarily more than a minimal representation of the 4p and 3d orbitals). d polarization functions on oxygen have a significant largely predictable effect on the bond angle around the oxygen but not on bond lengths or reaction energetics. (4) Binding energies of water and hydroxide ions were calculated for mono- and tetracoordinate complexes. Binding energies were very dependent on coordination number. Water was found to bind to [ZII(NH,)~]~+ by 43 kcal/mol (about half of the previously calculated result), and hydroxide binds by 284 kcal/mol. These results have application to zinc enzyme systems such as carbonic anydrase. (5) Proton affinities were also calculated. For the [Zn(NH3)3(OH)]-complexes a value of 167 kcal/mol was calculated with an estimated lower limit of 145 kcal/mol.
Acknowledgment. We thank the ONR, N00014-86-K-0557, and the NIH, GM 26462, for financial support. Registry No. ZnH+, 41336-21-4; ZnOH', 22569-48-8; Zn(OH2)2+, 23444-32-8; Zn(NH3)2+, 72155-88-5; (NH3),Zn2+, 103057-99-4; (NH,),Zn(OH)+, 72147-20-7; (NH3),Zn(OH2)2+,721 55-90-9.
Chemical Waves and Light-Induced Spatial Bifurcation in the HgCI2-KI System in Gel Media Ishwar Das,*vt Anal Pushkama, and Namita Rani Agrawal Department of Chemistry, University of Gorakhpur, Gorakhpur-273009, India (Received: December 1 , 1988; In Final Form: May 1 , 1989)
New results are reported on the one-dimensional propagation of a single red/yellow band (ring) of mercuric iodide in gel media in complete darkness. The influence of light on wave propagation has been studied by illuminating the species with light of various wavelengths. A liquid filter containing 12/CC14was used to get monochromatic light (A = 405 nm). A single red band bifurcates into several revert spaced bands when illuminated with natural light having wavelength X < 600 nm. The influence of electrolyte concentrations and temperature on the kinetics of yellow and red wave propagation has been studied that satisfy the relation d2 = kt, where d is the extent of propagation from the initial junction and k and t are the rate constant and time, respectively. The energy of activation for yellow wave propagation is found to be 9.2 kcal/mol. The dependence of bandwidth on time as well as on electrolyte concentrations obeys the relation A d = mt where AMJand m are the width of the yellow band and the slope, respectively. Changes in potential and [H'] during the propagation of the advancing front have been monitored. Results lead to the conclusion that the phenomena involve the transition from one state to another.
Introduction Interdiffusion of one electrolyte into another electrolyte may lead to a rhythmic depoSition,l which is commonly known as the Liesegang phenomena.2 It was noted that a concentration graPresent address: Reader, Academic Staff College, Gorakhpur University, Gorakhpur, India (up to March 1990).
0022-3654/89/2093-7269$01.50/0
dient was necessary for such a type of pattern formation. Experimental evidences are also available for pattern formation in initially homogeneous solutions of electrolytes, in the absence of (1) Hedges, E.S. Liesegang Rings and Other Periodic Structures; Chapman and Hall: London, 1932. (2) Stern, K. H.A Bibliography of Liesegang Rings, 2nd ed.; U S . Government Printing Office: Washington, DC, 1967.
0 1989 American Chemical Society
Das et a!.
7270 The Journal of Physical Chemistry, Vol. 93, No. 20, 1989
90.
8.0
i o 60 80
loo
1K) li0 TIME (h) Figure!2. Location of the lower front of the precipitate from the junction as a function of time for yellow band propagation. Conditions: [HgCIz] = 0.01 M,containing 1 .S% agaragar gel (lower portion); [KI] = 0.075 (Al), 0.10 (A2), 0.15 (A3), 0.20 (A4), and 0.30 M (AS); temperature, 36.0 i 0.1 OC. OA
a
b
Figure 1. Precipitation of (a) yellow and (b) red mercuric iodide in gel media at 35.0 "C. Conditions: (a) [KI] = 0.2 M (upper portion) and [HgCI2] = 0.01 M,containing 1.5% agar-agar gel; (b) [HgCI2] = 0.1 M (upper portion) and [KI] = 0.002M,containing 1.5% agaragar gel.
concentration gradient^.^^ Several other types of chemical reactions far from equilibrium are known to produce interesting temporal and spatial structures such as multiple stationary states, oscillations of concentrations of chemical intermediates and products, and chemical waves?'' Nitzan et aI.* reported that light absorption may play an important role in the macroscopic structure development that was later supported by the experimental observations of Das et on light-induced periodic precipitation of PbCr04. The main feature of this communication is the development of chemical waves moving as a result of the diffusion of mercuric chloride into potassium iodide in a g a r a g a r gel and vice versa, in complete darkness. Instead of sets of parallel bands, a single thick band (red or yellow) appears at the junction and later leaves the junction and propagates downward parallel to the axis of the tube. The color of the band depends on the experimental condition. This paper also describes the kinetics of the propagation of single yellow or red band propagation downward at various electrolyte concentrations and temperatures. Potential and pH changes during propagation of waves have also been studied. Another salient feature of this system is the bifurcation of a single red band into several thin red color revert spaced bands on illumination with natural light.
Experimental Section Materials. Mercuric chloride, potassium iodide (AR; S. (3) Flicker, M.; Ross,J. J . Chem. Phys. 1974,60, 3458. (4) Feinn, D.; Ortoleva, P.;Scalf, W.; Schmidt, S.;Wolff, M. J. Chem. Phys. 1978, 69, 27. (5) Mtiller, S. C.: Kai, S.;Ross,J. J . Phys. Chem. 1982, 86, 4078. (6) Eyring, E., Ed. Periodicities in Chemistry and Biology; Advanas in Theoretical Chemistry; Academic Press: New York, 1978. ( 7 ) Physical Chemistry of Oscillating Phenomena; Faraday Symposia of the Chemical Society No. 9; Royal Society of Chemistry: London, 1974. (8) Nitzan, A.; Ortoleva, P.; Ross. J. J . Chem. Phys. 1974, 60. 3134. (9) Das, I.; Lall, R. S.; Pushkarna, A. J. Phys. Chem. 1987, 91, 747. (IO) Das, 1.; Pushkarna, A.; Lall, R. S . J. Cryst. Growth 1987,82, 361. ( 1 1 ) Das. I.; Lall, R. S.; Pushkarna, A. J. Cryst. Growth 1987.84, 231. (12) Das, 1.: Pushkarna. A. J. Non-Equilib. Thermodyn. 1988, 13, 209.
20
Merck), and a g a r a g a r (Difco) were used without further puri fication. Procedure. Propagation of the Yellow Band. Mercuric chloride solution of known concentration was prepared in doubly distilled water, containing 1.5% agaragar at 85-90 "C. The solution was homogenized and heated with a magnetic stirrer with hot plate. The hot solution (10 mL) was then poured into a clean and presteamed Corning tube (i.d. 11.7 mm) and cooled at room temperature to solidify. An equal volume of the aqueous solution of potassium iodide of relatively higher concentration was filled in the upper portion of the tube containing solidified gel, and the tube was sealed. In order to check the reproducibility of the pattem, three tubes were simultaneously prepared. Experiments were performed in an air thermostat that could be maintained accurately to rt0.l "C. As soon as the potassium iodide solution is poured on the solidified agar-agar gel containing mercuric chloride, initially an orange precipitate in the form of a ring is formed at the junction, which later converts into a yellow ring, leaves the junction, and propagates downward. This result is shown in Figure la. Propagation of the Red Band. When the position of the electrolytes in the lower and upper portions of the tube are exchanged, a red band is formed instead of a yellow band at the junction. After some time, it leaves the junction and propagates downward. Potassium iodide solution (0.002M) containing 1.5% agaragar gel was kept in the lower portion and aqueous mercuric chloride solution (0.1 M) in the upper portion of the tube. Experiments were performed in complete darkness. Result is shown in Figure lb. Characterization of Yellow and Red Products. Yellow and red products obtained from the tubes shown in Figure 1 have been characterized qualitatively. The yellow product is soluble in aqueous KI, which, on treatment with AgN03, yields a yellow precipitate of Ag2Hg14, according to the following reactions: K2Hg14+ 2AgN03
-
Ag2Hg14(yellow)
+ 2KN03
Further, the yellow product is soluble in ether. These two results confirm that the yellow species is Hg12 (see ref 13). The red product has also been confirmed to be HgI2 as it is also soluble in KI and gives a yellow precipitate of AglHg14 on (13) John, A. D., Ed. Longe's Hundbook of Chemlsrry, 11th 4.; McGraw-Hill: New York, 1979.
Chemical Waves and Spatial Bifurcation in HgC12-KI
,
8.0
The Journal of Physical Chemistry, Vol. 93. No. 20, 1989 7271
A3 A2
7.0
AI
6.0
Ob
20
io
60
so
loo
120 120
TIME(h1
Figure 3. Location of the lower front of the prcciptate from the junction as a function of time for red band propagation. Conditions: [KI] = 0.002 M,containing 1.5% agaragar gel (lower portion); [ HgCI2]= 0.05 (Al), 0.10 (A2), and 0.20 M (A3); temperature, 24.0 f 0.1 "C. 8.0*
7.0
a
b
Precipitation pattern of mercuric iodide in gel media: (a) in complete darkness and (b) when illuminated with natural light. Conditions: [HgCI2]= 0.1 M (upper portion); [KI] = 0.002 M,containing 1.5% agar-agar gel (lower portion); temperature 35.0 f 0.1 "C. Figure 5.
2.0Y 1.0
:O
20
Lo
60
so
loo
120
140
TIME (h 1
Figure 4. Location of the lower front of the yellow precipitate from the junction as a function of time at various temperatures: 24.0 f 0.1 (Al), 30.0 f 0.1 (A2), and 36.0 0.1 "C (A3). Conditions: [HgCI2]= 0.01 M,containing 1.5% agar-agar gel (lower portion), and [KI] = 0.2 M.
treatment with AgN03. The red spacies is insoluble in ether. The red species reversibly changes to yellow on heating at 127 OC.I4 Kinetics of Propagation of the Yellowand Red Bands. As soon as one of the electrolytes A or B (A = KI; B = HgCIJ is poured on the solidified gel containing another electrolyte (B or A) of relatively low concentration, precipitation starts. The kinetics of the propagation of the bands (yellow or red) has been studied by measuring the location of the band from the initial junction as a function of time, using a cathetometer. Results are plotted in Figures 2 and 3. The maximum uncertainty in the measurement was found to be fo.002 cm. All these experiments were performed in complete darkness. The kinetics of yellow band propagation has been studied at various temperatures, viz, 24.0.30.0, and 36.0 "C,and results are shown in Figure 4. Influence of Light on Band Propagation. The influence of light on the band characteristics has been studied by precipitating yellow and red species in gel media in complete darkness as well as in the presence of natural light. It was observed that light does not influence the characteristics of the yellow band. However, a remarkable effect is observed in the case of the red band (Figure (14) Liptrot, G. F. Mudern Inorgcmlc Chemlsrry; Ball and Hyman: London, 1981.
Figure 6. Precipitation pattern of mercuric iodide in gel when illuminated light of different wavelengths. Tubes 1-6 (from left to right) were illuminated with white (natural), violet, blue, green, yellow, and red light, respectively. Conditions: [HgCI2]= 0.1 M (upper portion); [ K I ] = with
0.002 M (lower portion), containing 1.5% 35.0 i 0.1 "C.
agar-agar gel; temperature
5). Experiments were also performed in the presence of light of various wavelengths. To study the influence of light during the precipitation of the red band, 18 tubes were taken for three sets of experiments. In each set containing six tubes, four were wrapped with differentcolored transparent papers (blue, green, yellow, and red) and exposed to natural light. The fifth tube was
7272 The Journal of Physical Chemistry. Vol. 93, No. 20, 1989
Das et al.
n A
Figure 7. Experimental setup of a liquid filter to obtain monochromatic light (A = 405 nm).
unwrapped to pass light of all wavelengths (white) while the last tube was wrapped with black paper so as no light could pass through it. All the tubes were kept in an air thermostat maintained at 35.0 f 0.1 OC. The banded structures obtained at various wavelengths are shown in Figure 6. Precipitation of the Red Band by Monochromatic Light (A = 405 nm). The influence of a monochromatic light on the precipitation of the red band has been studied. To produce monochromatic light (A = 405 nm), a liquid filter containing I2 in C C 4 was used. The experimental set up shown in Figure 7 consists of a Corning tube containing the liquid filter in which another tube of lower diameter containing the reactants was placed. The whole assembly was then put in an air thermostat maintained at a constant temperature. The pattern obtained by illuminating the sample with a monochromatic light of wavelength 405 nm is shown in Figure 6 (tube 2 from left). Potential Changes during Precipitation of Yellow and Red Products. Experiments were performed in a cylindrical Corning tube of diameter 22.0 mm. For precipitation of the yellow species, mercuric chloride (0.01 M) containing 1.5% agar-agar was taken in the lower portion of the tube. A bright platinum electrode and a calomel electrode were immersed in it when the gel was not completely solidified. The experimental setup (Figure 8) was kept in an air thermostat maintained a t 35.0 OC. A thin orange ring appears at the junction immediately after the pouring of aqueous potassium iodide (0.2 M), which later changes to the yellow ring with continuously increasing width moving downward. The progress of the reaction was followed by recording the potential as a function of time with a digital multimeter (HIL, India). As soon as the lower front of the ring (band) approaches the tips of the electrodes, the potential shoots up and finally attains a steady-state value. The results are shown in Figure 9a. A simildr procedure was adopted for the study of potential changes during the precipitation of the red species except with a slight change in the experimental conditions. In this case, potassium iodide (0.01 M) containing 1.5% agar-agar gel was taken in the lower portion of the tube and 0.2 M mercuric chloride (aqueous) solution as a diffusing electrolyte was put in the upper portion of the tube. Potential changes as a function of time were recorded, and the results are shown in Figure 9b. p H Changes during Precipitation: The variation of [H+] during the precipitation of the yellow and red species has also been studied with the same experimental setup as shown in Figure 8 except
Figure 8. Experimental setup for measurement of potential (or pH) changes during wave propagation: PI = Pt electrode; P2 = calomel electrode; A = aqueous solution of diffusing electrolyte; B = another electrolyte containing 1.5% agar-agar gel; M = multimeter or pH meter.
ob
20
4i
60
eb xx,
TIME (h )
eoy
120
' I
1
5.51
0
'
20
'
40
'
60
'
80
'
'
100 I 2 0
TIME (h)
I
Figure 9. Plot of potential change (or pH) during the propagation of yellow [curves a and d] and red [curves b and c] mercuric iodide in gel media. Conditions: (a, d) [HgC12] = 0.01 M and [KI] = 0.2 M (upper portion); (b, c) [KI] = 0.01 M and [HgCI,] = 0.2 M (upper portion); temperature, 35.0 f 0.1 OC.
that a pH glass electrode was dipped in place of platinum and calomel electrodes. pH was measured with the help of a "Toshniwal" pH meter. The results are plotted in Figure 9c, d. Results and Discussion Experiments show that the red or yellow precipitate of mercuric iodide precipitates when mercuric chloride reacts with potassium iodide in the agar-agar media under different experimental conditions. The color of the precipitate was yellow when KI (0.2 M) diffused into a less concentrated solution of HgClz (0.01 M) containing 1.5% agar-agar gel in complete darkness and propagated downward (Figure la), whereas a red precipitate was formed when the foregoing systems were inverted. Mercuric chloride (0.01 M) diffused into a less concentrated solution of potassium iodide (0.002 M) containing 1.5% agar-agar gel, and the red precipitate
Chemical Waves and Spatial Bifurcation in HgC12-KI
.Di
The Journal of Physical Chemistry, Vol. 93, No. 20, 1989 7273
6oi 50
/
TIME ( h l
Figure 12. Plot of d2 versus time
(t)
for the values plotted in Figure 4.
1.4.
A4
A5
Figure 10. Plot of d2 versus time (1) for the values plotted in Figure 2.
d"'
0
* P 0 20 4 0 60 80 100 120
TIME (hl Figure 13. Plot of the yellow band width (Aw) as a function of time (t) at various iodide ion concentrations. Conditions: [HgClJ = 0.01 M, containing 1.5% agar-agar gel (lower portion); [KI] = 0.075 (Al), 0.01 (A2), 0.15 (A3), 0.02 (A4), and 0.30 M (AS).
Figure 11. Plot of
d2
loo
80 120 140 TIME(h) versus time ( t ) for the values plotted in Figure 3.
0
40
60
propagated downward (Figure 1b). The reactions may be written as 2KI (cl) HgCI2 (c2) 2KCI
+
HgClz (cl)
--
+ 2KI (c2)
+ Hg12 (yellow)
2KC1 + HgIZ (red)
where cI (aqueous) and c2 (in gel media) represent the concentrations of the electrolytes (cl > c2). The yellow and red species have been characterized as Hg12 by chemical methods. Precipitation starts immediately after pouring the aqueous solution containing one of the electrolytes on the solidified gel containing another electrolyte. The extent of propagation, d (distance between initial junction and lower front of the precipitate), versus time, t , for both yellow and red precipitates have been plotted in Figures 2-4. Experiments have been carried out by varying the initial electrolyte concentrations and temperature. The data plotted in Figures 2-4 are best fitted by the relation d2 = kt as evident by the plots of d2 versus t (Figures 10-12). Values of slope k and correlation coefficient obtained by the method of
TABLE I: Electrolyte Concentration, Color, Bandwidth (Aw ), Ionic Product ua = [Hg*+][I-]*,Slope (k),and Correlation Coefficient (R) for Straight Lines Plotted in Figures 10 and 11 color of u X [HgC~zIl [KIII propagating Awl M M band cm lo4 M3 k/cm2/h R 0.010 0.0751 yellow 1.180 7.5 0.2493 0.999 0.1ool yellow 1.160 10.0 0.3059 0.999 0.1501 yellow 1.140 15.0 0.3793 0.999 0.2001 yellow 1.100 20.0 0.4532 0.999 0.3004 yellow 1.020 30.0 0.5562 0.998 0.0501 0.002 red 2.480 1.0 0.3363 0.999 0.1001 0.002 red 2.405 2.0 0.4382 0.999 0.2001 0.002 red 2.330 4.0 0.5062 0.999 "Concentrations in u = [Hg2+][I-]2 refer to the unmixed solutions. Solutions of higher concentrations marked by (1) are put above the gel and diffuse downward. TABLE II: Dependence of Rate Constant (Slope, k ) on Temperature for Yellow Propagating Band with [HgC12Y = 0.010 M and [KI] = 0.20 M tempIoC k/cm2/h R 24.0 0.1435 0.999 30.0 0.2032 0.999 36.0 0.2994 0.999 "Solution contains 1.5% agar-agar gel.
1214 The Journal of Physical Chemistry, Vol. 93, No. 20, 1989
Das et al.
TABLE 111: Dependence of Slope on [I-] for Yellow Propagating Band Obtained from the Straight Lines Obeying the Equation A w 2 = mt
correln [HgCI,]"/M 0.010
[KI]//M 0.075 0.100
0.150 0.200 0.300
slope (m2)/cm2/h 0.0188 0.0178 0.0172 0.0153 0.0132
coeff (R)
0.999 0.997 0.997 0.997 1.000
1.1
3 D z
1 \ \
l
"Solution contains 1.5% agar-agar gel. Solutions of higher concentrations marked by (1) are put above the gel and diffuse downward. [I-] M Figure 15. Plot of the yellow bandwidth as a function of diffusing electrolyte concentration at a particular time (viz., 72 h).
3.01
b
n
1.4
20
40
60 ab loo 120 140 TIME (h)
Figure 14. Plot of the red band width (Aw) as a function of time ( t ) at various mercuric chloride concentrations. Conditions: [KI] = 0.002 M, containing 1.5% agar-agar gel (lower portion); [HgC12] = 0.05 (Al), 0.10 (A2),and 0.20 M (A3).
least-squares analysis have been reported in Tables I and 11. It is found that the slope increases with the concentration of the diffusing electrolyte as well as with temperature. The energy of activation for the precipitation of yellow Hg12 is found to be 9.2 kcal/mol from the slope of straight line obtained by plotting log k versus 1 / T . The width of the band Aw depends on time as well as on the concentration of the entering reagent. The width of the yellow band varies nonlinearly with time as shown in Figure 13. The plot of Aw2 versus time yields a fairly good straight line as evidenced by the correlation coefficient values recorded in Table I11 and obeys the relation A d = mt where m is the slope. In contrast to this observation, the width of the red band varies linearly with time (Figure 14) and satisfies the relation Aw = mt + c. We observe that the width of the yellow band decreases with an increase in the concentration of the entering reagent. The widths of the yellow band at any particular time (viz., 72 h) taken from Figure 2 for various [I-] have been plotted in Figure 15, and it was found that the equation Aw = -m[I-] + c was obeyed. However, no remarkable change in the width of the red band could be observed when [ H g z + ] was changed. Another interesting feature of this system is that it is photosensitive. Propagation of a single red band is observed in complete darkness whereas in the presence of natural light it bifurcates into a number of bands (revert spaced) separated from each other in the same region of the precipitate zone.I5 The result is shown in Figure 5 . The sharpness and bifurcation of the bands depend on the wavelength or energy of light used. It was observed that the sharpness of the red band decreases by increasing the wavelength (15) Kai,
S.;Muller, S. C.; Ross, J. J . Phys. Chem. 1983, 87, 806.
n Figure 16. (a) Plot of separation of bands versus the number of separations between two successive bands vertically downward. (b) Band location x, versus band number n. Conditions: [KI] = 0.002 M,containing 1.5% agar-agar gel (lower portion); [HgCI2]= 0.1 M.
(or decreasing the energy) of natural light falling on it. Bifuraction phenomenon could not be observed when the tube was illuminated with red light (Figure 6, tube 6 from left to right). However, the illumination with light of yellow and other colors having higher energy (or low wavelengths) causes bifurcation. Experiment with monochromatic light (A = 405 nm) with a liquid filter (12/CC14) was also carried out that yields a pattern of sharp red-colored bands (Figure 6, tube 2 from left to right). Bands show revert spacing, that is, the spacing between two bands decreases with distance (Figure 16a). The plot of band location versus band number yields a straight line (Figure 16b). In complete darkness, the yellow or red single band is formed at the junction immediately after pouritlg one of the electrolytes that after a certain time interval leaves the junction and moves downward, leaving behind soluble K,HgI,. As soon as the precipitate of Hg12 (yellow or red) reaches the tip of the electrode, a sharp transition in the pH or potential versus time curve was observed (Figure 9). The yellow and red species show, respectively, an increase and a decrease in pH (or potential) with time (Figure 9). The curves AB, CD, A'B', C'D', PQ, RS, and P'Q, R'S' in Figure 9 denote the stable branches while the curves denoted by BC, B'C', QR, and Q R ' represent the unstable branches. The potential or p H in the regions AB and PQ represents steady-state I due to HgCl2. Similarly, the potential or pH in the region C D or R S (Figure 9) represents another steady-state I1 due to K2Hg14 which is formed due to solubility of Hg12 in KI, according to the following reaction: HgI, + 2KI K2Hg14 (colorless)
-
J . Phys. Chem. 1989, 93, 7275-7280 A similar explanation may be given for curves A'B' C'D', P'Q, and R'S' obtained for the precipitation of the red species. The regions A'B' and P'Q' represent one stable state due to KI in agar-agar gel, and the regions C'D' and R'S' represent another stable state due to K2Hg14. A detailed theoretical understanding of the results awaits further study.
Acknowledgment. We are grateful to Prof. R. P. Rastogi,
1215
Vice-chancellor, BHU, for his help and inspiration, Prof. S. Giri, Head of the Chemistry Department, for providing laboratory facilities, and Dr.P. S.Pandey, Director, Academic Staff College, University of Gorakhpur, for encouragement. Thanks are due to CSIR, New Delhi, for financial support to Dr. Anal Pushkarna. We are thankful to Sudha Chand for rendering help at various stages in the experimental work. Registry No. Hg12, 7774-29-0.
Thermal Modulation Voltammetry Response of Reversible Redox Systems: Theory and Experiment J. L. Valdes and B. Miller* AT& T Bell Laboratories, Murray Hill, New Jersey 07974 (Received: November 28, 1988; In Final Form: February 14, 1989)
Thermal modulation voltammetry (TMV) at a rotating disk electrode (RDE) is a new technique developed for understanding electrochemical processes in the temperature domain. A theoretical analysis of this method and its experimental verification are conducted here for cases of reversible (Nernstian) electrode reactions. When both the oxidized and reduced forms of the electroactive species are present, the thermally modulated component of the current can exhibit a well-defined peak near the equilibrium electrode potential as the potential is scanned between the limiting current plateaus. The existence and magnitude of this characteristic peak are shown to be a sensitive function of the thermodynamic entropy change (ASo)of the electrode reaction and also to de end upon the thermal properties of the solution. TMV experiments on two separate redox systems, Fe(CN)6*/C and Fez+ 3+, confirm theoretical predictions. Results are shown to be consistent with steady-state measurements at different temperatures in a thermostated cell.
P
Introduction In recent the steady-state and frequency-dependent behavior of mass transport limited currents and open circuit potentials at a thermally modulated rotating disk electrode (RDE) has been examined. In these cases the electrochemical response was found to be determined by the prevailing surface temperature perturbation AT. To gain insight into electrode reactions through the thermal parameters, it is necessary to broaden the treatment to cover the response of currents over the entire electrode potential region of interest. In this work, we present a theoretical analysis and an experimental study of thermal modulation voltammetry (TMV) at a RDE for reversible (Nernstian) electrode reactions. In a TMV experiment, the electrode temperature is modulated at a given frequency while the electrode potential is scanned in the region of interest and the corresponding cell current modulation is extracted. The modulated current response will depend upon the temperature coefficients of the many variables which contribute to the electron-transfer process; they may be grouped as thermodynamic, kinetic, and mass transport. In a purely reversible system (reactions not limited by kinetics), we will show that the limiting current (mass transport) and standard electrode potential (thermodynamics) are two such quantities whose disparate thermal sensitivities govern the net response. In this work we develop the theoretical model necessary to describe the complete voltammetric response of a thermally modulated reversible reaction. This understanding allows obtaining thermodynamic reaction entropies from a TMV experiment. The theoretical predictions derived in this paper have been experimentally tested by conducting TMV measurements on the redox system, Fe(CN)63-/e, in either 1 M KCl or 0.4 M Sr(N03)2 electrolytes, under conditions approaching reversibility. Addi(1) Miller, B. J . Elecfrochem. SOC.1983, 130, 1639. (2) Valdes, J. L.; Miller, B. J . Phys. Chem. 1988, 92, 4483. (3) Valdes, J. L.; Miller, B. J . Electrochem. SOC.1988, 135, 2223.
tionally, steady-state current-voltage curves have been taken at two temperatures in a thermostated cell and their differences obtained to test the "zero thermal modulation frequency" analogue of the TMV experiment. TMV scans were also performed on the system has Fe2+/3+system in 1 M HClO,; although the slower electron transfer than that of Fe(CN)63-/4-, the reaction entropy of the reaction is comparable in magnitude, but opposite in sign, to that of Fe(CN)63-/4-, and thus provides an additional test of theory developed here.
Theory A purely reversible redox system of the general form Ox
+ ne- = Red
(1)
is described by the Nernst equation
U = UO
+ -1nRT
Gx
nF
Cscd
cd
where and Cox refer to the concentration of the reduced and oxidized species at the electrode surface, respectively, and UO is the standard electrode potential of the reaction. For a system with defined mass transport conditions, G
X
y = l + & '
i
(3)
'Lox
and (4)
where i is the current (positive for anodic and negative for cathodic), il,+ and il,oxare the absolute values of the anodic and cathodic limiting currents, respectively, and bulk species concentrations are denoted by a superscript b. At a RDE the anodic
0022-3654/89/2093-7275$01 .50/0 0 1989 American Chemical Society
