fourier analysis of chemical oscillations

oxidation reaction and bromination reactions coupledwith the autocatalytic Irornatic n of HBIO~. Theautocatalytic step would remain intact so long ascercus and bromate are in the mixture. The organicsubstrate in Belousov-Zhabot inskii reagent merelyaffects the rate of redox reactien and the brornina-tion reaction. Since most of the organic compoundswhich showed oscillations have a reactive methylenegroup or a ~-keto group, it was thought for quitesometime that such a group would be necessaryfor oscillation. It should be noted that ~-keto gi oupsimply facilitates brominatic n.

It follows horn the above arguments that a binarymixture of organic substrates one component ofwhich undergoes br ominatir.n reacticn and theother undergoes oxidation should also exhibit oscil-lations under suitable circumstances. Tartaric acidand mandelic acid do not undergo br ominationwhereas acetone can undergo brominati: n readily!".Tartaric acid and mandelic!" acid are oxidized easily.It has been reported that acetone can also be oxidiz-ed by ceriuml" but perhaps the rates of oxidatic nof tartaric and mandelic are faster and hence acombination of acetone and tartaric acid and acetoneand mandelic acid should exhibit oscillations. Sincethe expectation is experimentally satisfied, it followsthat more organic substrates can be found whichmay have desired rates of oxidation and brorninatic nto yield r scillations.

Thanks are due to the UGC, New Delhi, for finan-cial support.

References

1. CHANCE, B., PYE, A. K., GHOSH, A. K. & HESS, B.,Biological and biochemical oscillators (Academic Press,New York), 1973.

2. NICOLlS, G. & PORTNOW, J., Chern. Rev., (1973), 365.3. NOYES, R M. & FIELD, R. J., Ann. Rev. Phys. Chem.,

25 (1974), 95.4. RASTOGI, R P. & YADAVA, K. D. 5., Indian]. Chem.,

12 (1974), 687; 12 (1974), 974; 12 (1974), 1280; 13(1975), 352; .f. phys. Chem., in press.

5. DEMAS, J. N. & DIEMENTE, D., J. chern. Edn, 50 (1973),357.

6. KOROS, E., LADANYI, L., FRIEDRICH, V., NAGY, Zs. &KIS, A., Reaction kin. cat. Lett., 1 (1974), 455.

7. KOROS, E., BURGER, ;\1., FRIEDRICH, V., LADANYI, L.,NAGY, Zs. & ORBADI, M., Faraday symposium onphysical chemistry of oscillatory phenomena, 1975.

8. BUSSE, H. G., Biological and biochemical oscillators(Academic Pres" New York), 1973, 04.

9. PRASAD, K., VERMA, G. P. 5., PRASAD, A. & DHAR,V. B., Indian .T. Chem., 14A (1976), 786.

10. NOYES, R M., FIELD, R. J. & KORos, ENDRE, J. Am.chem, Soc., 94 (1972), 1394.

11. FIELD, R. J., KOROS, ENDRE & NOYES, R. M., J. Am.chem. Soc., 94 (1972), 8649.

12. JING-JER Jwo & NOYES, R M., J. Am. chem. Soc., 97(1975), 5422.

13. NOYES, R. M. & JING-JER JWO, J. Am. chem. Soc., 97(1975), 5431.

14. EDELSON, D., FIELD, R. J. & NOYES, R. M., Tntn. J.Chem. Kin., 7 (1975), 417.

15. YADAV, K. D. S., Ph.D. thesis, Gorakhpur University,1974.

16. DANIELS, F., WILLIAMS, J. W., BENDER, P., ALBERTY,R. A., CORNWELL, C. D. & HARRIMAN, J. E., Experi-mental physical chemistry (McGraw-Hill, New York),1970, 153.

17. KRISHNA, B. & TEWARI, K. C., J. chem, Soc., (1961),593, 3097.

18. STEWART, R, Oxidation mechanism (W. A. Benzamin,New York), 1964, 81.

NOTES

Fourier Analysis of Chemical Oscillations

PRASHANT RASTOC.I & ASHWINI KUMAR

Chemistry Depart ment, Gorakhpur UniversityGorakhpur 273001

Recei!'ed 1 September 1976; accepted 20 October 1976

Fourier analysis of oscillatory traces of e.m.f. versustime in Belousov-Zhabotinskii reaction having differentorganic substrates has been done. The number ofsignificant harmonics have been ascertained.

SIGNIFICANT work on the mechanism of oscil-lations in Belousov-Zhabotinskii reacticn has

been reported recently-A Characteristics d oscil-lations have also been intensively studieds+, Sincetypical oscillatory waves are obtained dependingon the nature of reactants which are net pericdicsine and cosine waves, it was thought of interestto perform Fourier analysis of the waves with theobject of estimating the number of harmonics andcharacterization of escillations,

Temporal oscillations in reactien systems (1)to (5) were experimentally studied.

Malonic acid + KBrOa+ Mn2++H~S04 (1)Malonic acid + KBIOa + CeH + H2S04 (2)Malic acid + KBrOa + Mn2+ + HZS04 ••• (3)Citric acid + KBrOa + Mn2+ + H2S04 ••• (4)Acetyl acetone + KBrOa + Mn2++H~S04 ... (5)The reaction was performed in a cell as was done

by previous workers+ In all these svstems theconcentration of the organic substrate- used wasO'032M, those of KBrOa, Mn2+ (or Ce4+, in system-2)and H2S04 were O·OHM, O·008M 1·5M respectively.The oscillations in e.m.f. denoting [CeHjCeS+] or[Mn3+jMn2+] were recorded by a potentiometricrecorder (Encardiorite Electronics Pvt. Ltd, Luck-now) at 32°. The potentiometric traces are re-poducible and characteristic of the system. Theseare represented in Fig. 1.

Any periodic function j(t) of time t can berepresented in general by Fourier series of thefollowing type

f(t)= Ao=A1sin wt+A2sin 2wt+Aasin 3wt+ '" .+B1 cos wt+B2 cos 2wt+Bs cos 3wt+ ....

where Ao, AI> A2,···· and B1, B2, Bs,···· areconstants. w denotes the frequency. The numberof sine and cosine terms in the series depends onthe number of harmonics present in the system.The constant terms in the above equation can beevaluated by standard method described in theliterature".

In case of system (3), a square wave is obtainedawl evaluation of constants is easy. For system(1), we observe that it is a combination of squarewave and saw-tooth waves. In the case of (2), (4)and (5) the decay curves are parabolic curves. Theequation for these cruves was fitted by the methodof least squares and the Fourier constants evaluated.The results are recorded in Table 1 where y denotesthe e.m.f. of the redox couple [CeHjCe3+] or[Mn3+jMn2+].

It should be noted that in the reaction wherecerium ion is a reactant, noise in oscillations is

339

INDIAN J. CHEM., VOL. 15A, APRIL 1977

I---l

40 See

T In n n n n n n n rIl0f mV

•.........•• TRACE 340Sec:

"lmv~TRACE 4-

Fig.

~40 See

1 - E.m.f. versus time traces (1-5) for(1-5) (see text) respectively

the systems

TRACE 5

observed which is probably associated with theinstrument. Experiments have shown that thefrequency in the above cases depends on the concen-tration of H2S04, KBrOa• Ce4+ or Mn2+ and theorganic substrate an.d temperatur~3-5: In sOJI.lecases it depends on time, The periodic curves III

Fig. 1 can be regarded as made up of simple harmoniccurves of definite amplitudes, phases and periods.The wavelengths of the components are in theratios ")..:")../2:"),,/3: •.••. , so that their frequenciesare in the ratio w: 2w: 3w: .

I t should be noted that the number of harmonicscan be ascertained by Fourier analysis providedthere is not anharmonicity. Very often relaxationoscillations are observed in Belousov-Zhabotinskiireagent and the task would become difficult.

One may expect a relation between the numberof harmonics and the number of redox couples.Detailed mechanistic examination is necessary toestablish such a relationship.

Thanks are due to the CSIR for supporting theinvestigation and for the award of a senior researchfellowship. Authors are thankful to Prof. R. P.Rastogi and Dr Kehar Singh for helpful discussions.References

1. FIELD, R. J., KOROS, E. & NOYES, R. M., J. Am. chem,Soc., 94 (1972), 8649; 95 (1972), 1394.

2. NOYES, R. M. & JWO. J. J., J. Am. chem, Soc., 79 (1975),5422.

340

TABLE 1 - FOURIER ANALYSIS OF THE SYSTEMS (1) to (5)

Reac-tion

system*

Fourier series Number ofsignificantharmonics

Frequen-cies

present

w, 2w, 3w(1)

(4)

y = 4·8 + 1-16 sin wt -5,6sin 2wt+3·7 sin 3 wt 4·2cas wt + 0'5 c-is 2 wt-1·04 CDS 3 tot + .

V = 6,09-2·1 sin wt -5·5 sin· 2 wt .

+ 0·2 sin 3 wt + 0·7 sin4 wt .+ 6·14 cos wt -0·5 cos2 wt + 0'2 cos 3 wt - 0'3cos 4 wt+ 1·0 cos 5 wt +: .

y = 6'5-8·3 sin wt -2·76 sin2 uit-1·65 sin 5 wi-1·2 sin 7 tut .

V = 6·5 + 7·6 sin wi + 3·8· sin 2 wi

+ 2·5 sin 3 wi + 1·9 sin4 tut+1·5 sin 5 wt ..... :+ 7·0 cos wt + + 1·76cos 2 wi+ 0·78 cos 3 wt + 0·44cos 4 wi+ 0·3 cos 5 wt + .

V = 5·7 + 2·4 sin wt + 0·14· sin 2 wi

-1·8 sin 3 wt-- 0·6 sin 4 wi + 1· 5 sin5 wi+ 3·7 sin 6 wi + .-0·5 cos wi -9·1) cos2 wi- 2·6 cos 3 wi + 2 5 cos4 uit + 4·3 ens5 wi .

5 w, 2w, 3w,4w, 5w

3

(2) 4 w, 2w, 4w,5w

(3) 4 w, 3w, 5w,7w

5 w, 2w, 3w,4w, 5w

(5)

*See text.

3. RASTOGI, R. P., YADAVA, K. D. S. & PRASAD, K., IndianJ. Chem., 12 (1974), 974.

4. RASTOGI, R. P. & ASHWINI KUMAR, J. phys. Chem., 80(1976), 2548.

5. RASTOGI, R. P. & YADAVA, K. D. S., Indian J. cie«,12 (1974), 687.

6. KHANNA, R. D. & BEDI, R. S., A text book of sound(Atma Ram, Delhi), 1969.

Studies on Thermo-osmosis of NaCI & KcS04Solutions

P. C. SHUKLA

Department of Chemistry, St Andrew's Postgraduate CollegeGorakhpur

Received 9 January 1976; revised 16 A ugust 1976;accepted 2 September 1976

Hydrodynamic permeability and thermo-osmoticpermeability of different solutions of sodium chlorideand potassium sulphate have been measured throughpyrex membranes impregnated with copper ferrocya-nide. It has been found that hydrodynamic permeabi-lity remains the same for differ:ent solutions of thesame electrolyte but thermo-osmotic permeabilitychanges significantly. It decreases with increasingconcentration of the electrolyte.