J. Phys. Chem. 1984, 88, 5 132-5 134
5132
= 84 cal/mol. On the other hand, 2.303RTA was found to be about 1130 ~ a l / m o l . ' Accordingly, ~ the ratio of the second term to the first term in the bracket of eq 29 amounts to about 1/ 13 (-8%). The present analysis cannot be applied to this particular example, since both conformational change and aggregation occur in solution. However, the result on the relative contribution evaluated above is still useful information. Discussion In the first place, the relation to the previous studyL6will be considered. In the present study, the meaning of the area A defined by eq 23, in the case of phase separation is explicitly given by eq 29. It is likely that the second term in the bracket can be neglected as compared to the first term in ordinary cases. The meaning of the area A in the case of phase separation was also considered in the previous study for a particular case in a highly approximate manner,16according to the result the effect of phase separation was suggested to be practically negligible. Consequently, consistent results are obtained in the two studies on the effect of phase separation. However, the analysis of the effect of phase separation in the previous study should be replaced with the present results, since it was not general and highly approximate. An important consequence of the present result is obvious if the effect of phase separation contributes significantly. Such a situation is supposed to be encountered in the titration of the @ structure of poly(~-lysine).'~The previous interpretation has provided inconsistent and puzzling concl~sion.'~ A reasonable
interpretation of the obtained data can be provided by the present result (eq 29), according to which a possibility is suggested that the area A underestimates the stability App(0)/x. However, a full discussion of the subject requires details of the complex situations inherent to the system such as the coexistence of the a-helix and the @ structure, the aggregation in the solution phase, and the irreversible conversion from the @ structure to the mixture of random coil and the a-helix. Therefore, the subject will be discussed in a separate report together with the applicability of eq 14 to the @ aggregates. Note Added in Proof. Some remarks are given about the applicability of eq 14, which plays an important role in the present analysis. Based on a reasoning similar to that given in the text for a two-component phase, the following relation is obtained for a three-component phase (polymer alkali water):
+
dp;
= 2.303RT[-abx dpH
+
+ abx(nwb/nw)d log n; + abx(nwb/nw) d log ab]
Equation 14 holds for a three-component phase when the last two terms can be neglected as compared with the first one in brackets. Therefore, eq 14 is expected to hold for gels in general. On the other hand, eq 14 scarcely holds in the case of crystalline precipitates, since titration occurs on the surface and hence is not readily related to bulk properties. However, in a particular case of uncharged precipitates (ab = 0), which is often the case, eq 14 is valid because dp,b = 0.
A New Iodate Driven Nonperiodic Oscillatory Reaction in a Continuously Stirred Tank Reactor R. P. Rastogi,* Ishwar Das, and Abhai Raj Singh Chemistry Department, Gorakhpur University, Gorakhpur, India (Received: November 28, 1983; In Final Form: May 31, 1984)
Oscillations have been observed in the iodate-arsenite reaction system in a CSTR. The visual oscillations are accompanied by oscillations in the redox potential and [I-]. Oscillations are inhibited by C103-, C1-, and NaHCO,. Oscillations depend on the [IO,-], [arsenite], and ko, the reciprocal of the residence time. There is an upper limit and a lower limit to [IO,-] as well as [H,AsO,], in between which oscillations are observed. Bistability has also been investigated. It is found that oscillations occur in a narrow range of flow rate around ko = 0.0175 m i d which is close to the region when the system can switch from the monostable state to a state of bistability. Oscillations do not occur for situations when 0.0175 > ko > 0.07 min-'.
Introduction The thermodynamic theory of instability developed by Glansdorff and Prigogine serves as a useful guide for the search for new systems in which dynamic instability such as multiple steady states, temporal oscillations, and spatiotemporal oscillations can be There is the possibility that a reaction system may become destabilized provided it is maintained at a significant distance from equilibrium and has an autocatalytic or autoinhibitory reaction subset. In the iodate-arsenite system, the following reactions occurs which autocatalytically produces I-: 3H3AsOl
+ IO
-E r
I1 I --r
I50mV
I
L
0
25
50 75 TIME ( S E C O N D S )
100
125
Figure 3. Oscillations in redox potential as a function of ko ( [ H ~ A S O ~ ] ~ = 0.1539 M, [KIO,Io= 0.1 168 M): (I) ko = 0.0175 min-', flow rates, QHIAsO3 = 0.5 mL/min, Q,IO, = 0.2 mL/min; (11) kD= 0.035 min-I, flow rates, QH,Aso, = 1.0 mL/min, QKIO, = 0.4 mL/min; (111) ko = 0.07 min-I, flow rates, Q H 3 A s 0 3 = 2 mL/min, QKIO, = 0.8 mL/min; (IV) ko = 0.14 min", flow rates, QHIAs03= 4 mL/min, QKro, = 1.6 mL/min. The volume of the reactor was 40.0 mL; sensitivity, 50 mV/cm; chart speed, 5 s/cm.
Figure 1. Experimental setup of the continuously stirred tank reactor: G , reactant tank; C, control valves; E,, silver-silver iodide electrode or platinum electrode; Ez calomel electrode; R, recorder; SP, suction pump; T, reactor; M magnetic stirrer.
>
E
-c
J 4:
2 Y
z o x
Y
n
b
-1
5
w
I
7
I
0
0
20
40
60
I
80
100
120
TIME ( S E C O N D S )
H p e 2. (a) Redox potential changes as function of time (with platinum electrode). (b) Changes of [I-] as a function of time (with silver-silver iodide electrode). The flow rate of potassium iodate (0.1168 M) was 0.35 mL/min; the flow rate of sodium arsenite (0.1539 M) was 1.0 mL/min; the volume of the reactor was 40.0 mL; ko = 0.0337 min-l; sensitivity, 50 mV/cm; chart speed, 5 s/cm. A indicates the instant at which KIO3 solution was fed to the reactor to while B indicates the instant at which the flow of KI03 was stopped. solutions were prepared in a sulfate-bisulfate buffer of pH 1.5. The arsenous acid and iodate solutions were fed to the CSTR (40.0 mL volume) at definite flow rates from glucose bottles through polyethylene tubings as shown in Figure 1. The level of the solution in the CSTR was kept constant by a continuous outflow of solution using a suction pump, The solution in the CSTR was stirred with a magnetic stirrer at =800 rpm. Visual oscillation i were immediately observed. Since in color (yellow =colorless) in blank experiments the temperature rise in the oscillating reaction system was found to be insignificant (0.1 "C), experiments with a CSTR were performed at room temperature. [I-] was monitored by the Ag/AgI electrode coupled to a calomel electrode with an electronic recorder Model No. 83 11 (Encardio-Rite, India). The course of the reaction was also followed by noting the potential change of the platinum electrode with reference to calomel electrode by using the above recorder. Oscillations both in [I-] and redox potential were observed (Figure 2 ) . Dependence of Temporal Oscillations on Different Ions. So that the mechanism of the oscillatory reaction could be understood, the influence of ClO;, C1-, Clod-, and NaHC03 on the oscillations was studied. Dependence of Temporal Oscillations on the Flow Rate. The occurrence of oscillations depends on the magnitude of ko. Os-
25
50
73 TIME (SECONDS)
I00
,
125
Figure 4. Dependence of oscillations in redox potential on [H3AsO3]0at fixed iodate concentration (0.1 168 M) and KO (0.035 min-l). The flow rates were as follows: sodium arsenite, 1.0 mL/min; potassium iodate, 0.4 mL/min. the volume of the reactor was 40.0 mL: (I) [H3As03]o= 0.6156 M; (11) [ H ~ A s O=~ 0.3078 ]~ M; (111) [ H ~ A s O=~ 0.1539 ]~ M; (IV) [H3AsO3lo= 0.0769 M. Sensitivity, 50 mV/cm; chart speed, 5 s/cm. cillations were found to occur when the value of k, was between 0.0175 and 0.07 m i d . Oscillations did not occur with k, = 0.14 min-' (Figure 3). Further, when ko was kept equal to 0.035 min-', the [arsenite] was also fixed, and only the iodate concentration was varied, oscillations were found to occur in the range 0.1068-0.1268 M. For [IO
