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Chemical Instrumentation Edited by GALEN W. EWING, Seton Hall University, So. Orange, N. J. 0 7 0 7 9
T h e s e ariicles are intended to serve the readers O ~ T K I SJOURNAL by calling aUention to new deuelopments in the theory, design, or availability of chemical laboralorg instrumentation, or by presenting useful insights a n d ezplana/ions o j topics that are o j practical importance to those who use, or leach /he use oj, modern inslrumentation and instrumental techniques. The editor invites correspondence from prospective conlributors.
LX. Step Perturbation Relaxation Techniques Z. A. Schelly, Deporfmenf of Chemisfry, The Universify of Georgia, Athens. Georaia 30607. - . , nnd " -E. M. Eyring, Department of Chemistry, University of Utah, Salt Loke City, Ufoh 84 1 12 Introduction Chemicd relaxat.ion spectroscopy was introduced b y h1. Eigen and cowo~.kers in the 1950's for studying the rates and mechnnisms of fast, reactions in s o h tions (1, 3). The term "isst reaction" is of course relative, h u t in general usage i t means a reaction that is fast compared to the Qrne required for mixing and observabion by conventional methods. Thus, a reaction with a. half-time of a second or less wo~tld he fast according t o our criterion, if t,he reaction is conducted a t ordinarv temoeratures and eoncentrations. he" restriction "ordinary" is necesswy since reactions that are fast a t room t,emperat,nre may become accossible t o conventional techniques if the temperature is lowered, or a fast, secondorder reaction may take place slowly if the concentrations are small enough. With increasing rates of reactions, effective, rapid mixing becomes impracticable even if carefully designed high flow velociby jet,s are used. The basic idea of relaxation speot,roscopy is t o circumvent mixing b y starting with a. premixed equilihriom system. Perturbation of the eqoilibrium b y varying a parameter (such as temperature, pressure, or electric field intensity) causes n. shift t o new eqrdibrium concentrstions. Measurement of t,he rate of this shift permits the kinetics and eventually the mechanism of t,he reaction t o be determined. Aside from therelavation methods many other techniques have been developed for measuring rapid reaction rates. On this general subject. the reader may refer t o some excellent treatises (.9-6).
Principles of Chemical Relaxation T o begin with, let us consider the single
Dr. Zoltan A. Schelly rereived his n.Sc. n pliysic:il r11emist1.s-in Viennn Technical Unirorsity. Austria in 1967. Ire spent a ienr ns n postdortorll fellow a t the Cniiersity of \Iriseonsin (Nilmnukee) workng on mass spectrometric measurements ,f diffusion and isotope errhnnge reaction 'ntes in solids. Subsequently, he spent w~ years with Dr. E. 11. &ring at the
step reaction
with t,he forward and reverse rate constants kt and k,, respectively. The activities of the species xt equilibrium are fixed, and their relation is expressed b y the thermodynamic eqrdlibrim~constant K. T h e equilibrium ronsbant is a fonetion of external as well as internal parameters such as temper~t.ureT, pressure P, elect.rio field intensity E, total concent,rsi tion CT,ionic strength p, et,c. Suppose t,hst. one or more of these parameters is suddenly changed. The pert,orhation momentarily will result in a deviation of the activities from those required by the new conditions. The deviation, however, will tend t o vanish. The ~ y s t , e m will ndjrmt itself and will approach its stable e q ~ d i h r i n m in a mannor described b y the rstc equntions. As long as t,hese deviat,ions from the new eqttilihriom are small, a linearioation of the rnle equations with respect, tn the t,ime dependent concentration variable is possihle. This moms, that. tho rate of disrrppearanoe of thc difference between the actual and equilibriwn eoncerrtrntions is proportionnl t o i.his difference itself. The reciprocal of the proportionslit,y fact,or k has the dimension of bime and is cdled the relaxation time 7 . At the inst,ant of a perturbation the concent,ration Ci of any of the reacting species i will-differ from the find equilibrium value Ci b y Xi, i.e., Ci = Ci Xi. If Xi ozpe~.imenli s the irl;/unlii,n i.tll.vr (I
