edited by RALPHK. BIRDWHISTELL University of West Florida Pensacola.FL 32504
textbook Forum Some Provocative Opinions on the Terminology of Chemical Kinetics -
John C. Reeve The Technical University of Denmark, 2800 Lyngby, Denmark Definitions and Introduction
Unless otherwise indicated the reactions considered will he relativelv s i m ~ l and e homoeenons. involvine a seanence .. of steps unierconditions where only one step is ratc:detcrmining r~rovidinpa hottlc-neck effuct~.'Simultane~ius (paralikljreacti~~s, autocatalytic processes, chain reactions, reactions approaching equilibrium, etc., are not included. When effectivelyconstant intermediate concentrations have been achieved, the rate of the reaction may be expressed in the form:
-
rate = k [ ~ l ' [ ~ l ~ [ ~ l ~ . . .
(1)
Here . IAl. IB1. ., . ., IC1. . .. etc.., are the concentrations ofthe snecies r resent,^ and k is the rate constant (or rate coefiiciek ( I ) ) . The anantities a,. b.. c.. etc... are constant^.^ Eachmavbe zero. a small integer, or a fraction that can be expressed in terms ofsmall integers (e.g., 112,113,312,etc.). In thegeneral case the following definition may be used: a = [a log (ratell a log [A]]~,[B~,[c~,... Partial reaction orders (a, b, c, etc., sometimes called reaction orders, or better, kinetic orders) refer to particular species. In most works there is a quantity defined as a + b + c +... called the overall reaction order, and very often referred to simply as the order of the reaction. Most texts remind the reader that kinetic orders (reaction orders) are experimental quantities and also that students must be ca;eful not toconfuse reaction order with the fundamental mechanistic quantity, molecularity rthe number of molecules involved a reactive encounter in an individual step). I n an attempt to be very clear and complete even some very excellent texts confuse the student in this area. Indeed, they often perpetuate the misunderstanding of 50 years, thus necessitating the above reminder. Almost unnoticed, a n increase in the status of
overall reaction order begins. Statements such as those below are common. "The dissociation of hydrogen iodide is a second-orderreaction." "The reaction between nitric oxide and oxygen is a third order reaction." "The following are examples of second-order reactions." These statements unquestionably associate the reaction order with the reaction itself; the value is meant as an overall reaction order of some sort. It gives the reader the false impression that it has real significance (cf. molecularity) for the reaction, rather than for one or more experiments. Some authors avoid the term reaction order and use kinetic order. However, referring to the kinetic order of a reaction is a small but first step in the wrong direction; these small steps are unnecessary and always seem to multiply. Also, the above statements, which seem informative, are so incomplete that standing alone they are of questionable value. Even worse, they directly mislead students about the status of overall reaction order, and they are totally unnecessary Difficulties with and examples of this misleading terminology follow. Arguments and Examples Overall reaction order is defined in most physical chemistry texts and is thus well-known. It must be defined and included because it is often used to test students. However, i t is time to expose it as misleading academic nonsense. The same is true for order of reaction when used in much the same sense. A striking example is found in one of the very best texts of general physical chemistry in its discussion of the hydrolysis of sucrose:
' Rate deterrniningstepis oflen abbreviated rds.
For reaction rates described by eq 1 , one authoritative encyclopedic work ( 1 ) specifically states that only stoichiometrically involved reactants and products should be included in the concentration product term outside the rate constant. All other influences (e.g.,catalytic) should be included within the rate constant. As seen below some works do not follow this restriction. When more than one step simultaneously exerts a boffle-neck effect,these quantities will change between limiting values if the influences of the steps change in relative importance. If a product species is produced in an equilibrium that precedes the "rate-determining step",a negative order will result. Such equilibriacan give rise to fractionaland multiple orders, depending on the relative values of the stoichiometric coefficients of reactants and intermediates produced in the equilibrium.
728
Journal of Chemical Education
(sucrose)
(glucose) (fructose)
It is stated that although the reaction is pseudo-firstorder with respect to sucrose, it has been found to be about sixth-order with respect to the water used as the solvent and first-order with respect to H30t. It is then stated that the reaction thus has an order of eight. If the situation is analyzed f i r t h e students' point of view. the difficulties created for the serious student are not mrpksing. Two natural and intelligent questions that can arise are: What does the number imdv . . and for what can it be used?
Of course, it is wrong to answer such questions by simply stating that the quantity is so defined, and leaving it a t that. Such numbers are just misleading remnants of old ideas and easily produce specious statements. The statements conceal the detailed and useful information on which they are based. The number, once calculated, has no use unless enough detail remains to reverse the ridiculous summation. I t can mislead the reader into thinking that it provides a reasonable basis for classifylug reactions (indeed, an approach followed in many works). This is also readily confused with something like molecularity. A better name might be false molecularity, but i t will hopefully soon be eradicated. The summation of the meaningful individual orders becomes all the more absurd if the text has no reminder that all the orders must be determined under exactly the same conditions of ~olutioncomposition, e t c , to be cnrnpatible. Otherwise, the various orders might refer to conditions with different rate determining step6 or even entirely different mechanisms. Thus, kinrticorders d e t e m n e d by the Ostwald Isolation Method would hc inaoorooriate. This is the method most familiar to s t u d e n t i ' ~ o k ~ a t i b i l iist ~ considered below in connection with the direct exoerimental determination of the sum of a number of selected partial kinetic orders. Further. there is a conflict between the definition of overall reaction order and the cautionary statement that reaction orders are determined exoerimentally. Kinetic orders are determined onlv to obtain clues regardlng the various steps in the overall chemlcal process. Calculat~ne(or even considerine~auantltiessuch asoverall reaction or& misleads the stu%eht The cornplicatingand superfluous term canonly be introduced with thc usual simpli~ngexrlusionofall but simple consecutive reactions. There is no sound reason for reaction orders or kinetic orders to indicate anything other than values determined experimentally. Complications only arise due to the false tradition of inventing new numbers by addition, as discussed above. There is no fundamental kinetic basis for the clasification of multistep reactions. As stated in the introduction. many texts (including the one reIuctantly criticized above) indicate catalyst wncentration terms withthe [A], [Bl, etc., ofeq 1,instead ofwithin the rate constant. Thus, for the decomposition of hydrogen peroxide withiodide catalyst, the rate is given as aproduct: k[H~021[I-I. If the wncentration terms outside the rate constant are not rieorouslv restricted. the conceot of overall reaction order be&mes even more difficult to justify. The order must be aualified with a statement: For all combinations of influences examined, the score is two. c hen add aualifvine notes when necessarv: For moderatelv low aciditfes4;he score must be changed to three, a s thereattion has been found (2)to also have a kinetic order of about one with respect to H80t. Another example of poor terminology (from a kinetics text) is provided by the reaction described by eq 3. I- + ocl-
+ o r + CI-
(3)
The rate law is stated a s rate = k[OClI[n[OHT
(4)
"1 intermediate acidities a two-term rate law is involved (3, and the definition order no lonaer osed. .- o -f overall - ~. . - - can -~ ~. . "- be ~- ---Tnese are me formsg ven lor !he rate in ref 3. Th s lerm IS ~ s e loo d freey . When poss ole, panlal kmetic orders should be given, the qualification pseudo becoming superfluous 'Detailed considerations are found in ref I. ~
' ' ~
in aqueoussolution. It has also been said to have a reaction order ofone(by the traditional addition processr. This bare statement of ovcrall order (without the detailed result on which it is based) is by comparison strikingly incomplete andconfusing. i'urthennore, norulesareplvcn lirnitincrhr choice of species i n r a t e expressions, a n d since [OH-I[H+l=K, in aqueous solutions, the rate law may also be written,5 rate = k[OCI-I[rI[Htl or rate = k,[HOCII[I7
(5)
Abracadabra! Acwrding to the rules we now have the choice of calline this reaction first-order. sewnd-order. third-order, o r a n y of these three ord&sprefixed by oseudo6-, if the influence of water a s a catalvst is recoe&zed. ~ t c a nalso be called fourth order, if thiinfluence i f water is included. Overall reaction order is again exposed a s worthless. Ex~erimentallvSummed Individual Kinetic orders7 There is a quantity easily wnfused with overall reaction order that is experimental and of considerable value. Also, consideration of the background is instructive rather than nonproductive and confusing. Unfortunately, the quantity is usually not even mentioned in general physical chemistry texts. An example of the confusion that can arise, even among professionals, regarding order, overall order, partial orders, and experimentally summed partial orders, is provided by various reports (from about 1968) and a more recent discussion with references (4) concerning the kinetic behaviour for the oxidation of sulfite by pemmdisulfate. If all reactants are either in &at excess or stoichiometric proportions, a s described by the reaction equation, the relative concentrations are constant during the reaction. For example, it can be easily shown ( I ) that, if the concentrations of C, etc., in eq 1are large and constant, while A and B are taken in stoichiometric proportions, the rate can be wn'tten: k1[AIntb or kdBIa+b, where kl and K, have a simple relation. Although the investigation gives no immediate information about the individual values of a and b, the result can have considerable value. If one of the values is known or can be determined, or if a well-based assumption of its value can be made, the sewnd value can be calculated. Also, the values of a and b are fully compatible, having been determined (as a sum) in the same (though changing) environment. Additionally, this value may be compared with the sum(s) of the individual values of a and b found by other methods. Special names for experimental quantities (a + b), etc., are not necessary and might exaggerate their status. Since examples of such important determinations are rare in textbooks, I include a few appropriate examples with references. 1. At an early date (1895) the method was used by Noyes (5) to
investigate the oxidation of Sn2' by Fe3+in aqueous
aohltinn ......
2. A smple rase from nrganlc chemical wartrons id provided by fhr rrsultr ofSmith and 1.cvenson fi for thr alknlme lU.05 40 hvdrolvsu uf cthvl neetnte 0.05 M and aomr other esters in as% al&hd at various temperatures. 3. A somewhat more complicated case is provided by the investigation of the oxidation of CN- by MnO; in aqueous alkaline solutions (7), when the conditions were such that the stoicbiometrywas described by:
~~
The concentration of OH- was large enough to be treated as a constant, and the initial concentration of permanganate was twice that ofcyanide.The results indicated that the sum afthe Volume 68 Number 9
September 1991
729
Variation in Concentration of Mo(CN)% with Time during Oxidation by ~ 2 0 8 time (h)
0
26
75
45
98
142
239
kinetic orders for cyanide and permanganate was two under the given conditions. 4. This example will be given in more detail. Although it is not found in reference works, it provides a useful example for students: it concerned oxidation of octacvanomolvbdate(N) bv oeroxvdibdfate in aoueous solution (8). The reaction can b i . written:
.
rate = k1[~2~;-]"= ~ , [ M o ( c N )I"~
(8)
t h e n n = 2 a n d k2 = 0.56 L(mo1.h)-'. T h a t is, t h e s u m of the partial orders for S20&a n d Mo(CN)& is 2; the r a t e equation is second-order. However, t h e individual orders a r e not indicated.
Summary T h e usually defined quantity overall reaction order is a pseudomolecularity, which is misleading a n d baseless. Regretably, it i s often used in a t t e m p t s t o classifyreactions. However, t e x t b w k s d o not give examples of a similar, b u t directly determined, experimental quantity t h a t is importa n t a n d well-based. Literature Cited 1. Map"son, D.in CompmhensiueChemleolKiwlics;Bamford, C. H.:Tipper, C. F. H.;
Eds.; Elsevier: NY, 1969:VoI.l.Chapter5.
In o n e s e t of results a solution initially containing 10.00 mmoVL of SzO& a n d 20.00 mmoVL of Mo(CN)Q- w a s k e p t at 20 OC. T h e concentration of molybdenum(N) complex w a s determined at various intervals. (See t h e table.) W h e n t h e r a t e is expressed as follows:
2. Wilson, I. R. in Ref. 1,1972, Val. 6, pp 406407. 3. Wilson, I. R. in Ref 1,1972, Vol. 6, p 402. 4. Wilson, I. R. in R e f 1,1972, Vol. 6, p 350. 5. Noyes, A. A. 2i1. Physik. Chem iL&rigJIssJ, 16.54. 6. Smith, H. A ; Leuenson,H. S. J. Am. Chem. Soc 1989.61,1172. 7. Roes. S.: Van derLinden. R. Con. J.Chem. 1960.38.2237.
. .
. .
8. Tmell. E. Dissertation.Lund Uniueraitv. Sweden. 1937.-36.
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