Automatic Elucidation of Reaction Mechanisms in Stirred-Pool

7 Automatic Elucidation of Reaction Mechanisms in Stirred-Pool Controlled-Potential Chronocoulometry

Downloaded by EAST CAROLINA UNIV on November 5, 2016 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0052.ch007

LOUIS MEITES and GEORGE A. SHIA Department of Chemistry, Clarkson College of Technology, Potsdam, NY 13676

During a symposium that deals with techniques for processing chemical data, it is appropriate to inquire why such techniques are important, and what effects their adoption may eventually have on the chemist's work and thought. They are important for several different reasons. They can facilitate calculations and interpretations that may involve many steps and, with numerical data, tedious graphical or other analysis. By doing so they can save much of the chemist's time and energy. At the same time they can yield more reliable results because they substitute the dumb patience and objectivity of a machine for the human frailty and occasional unconscious prejudice of the chemist. This makes it possible to find corre lations or interpretations that the chemist might miss, and to achieve greater depth and certainty in the final result. They can influence the design of experiments in several ways: by making it possible to find a data-acquisition schedule that s t r e s s e s the regions o f g r e a t e s t importance t o the d e s i r e d r e s u l t and enables the experimenter t o ignore others o f l e s s e r importance, by making i t p o s s i b l e t o o b t a i n the d e s i r e d r e s u l t from a simple experiment and thus o b v i a t i n g the n e c e s s i t y o f performing a more complicated one t h a t would y i e l d the same information i n a form more e a s i l y amenable t o o l d e r techniques o f data a n a l y s i s , and even by employing the data so e f f i c i e n t l y t h a t one experiment can be made t o y i e l d c e r t a i n t y as g r e a t as c o u l d have been obtained from three o r f o u r with the a i d o f the o l d e r techniques. Examples o f a l l o f these are already i n the l i t e r a t u r e , and new ones continue t o appear. I t i s a l r e a d y evident t h a t the growing adoption o f these techniques i s s u b s t a n t i a l l y easing the tedium o f experimentation and i n t e r p r e t a t i o n while improving the accuracy and r e l i a b i l i t y o f the values deduced from the data. As i t r e l i e v e s chemists o f unnecessary burdens, i t w i l l have longer-range e f f e c t s on chemical education, which now o f

127 Kowalski; Chemometrics: Theory and Application ACS Symposium Series; American Chemical Society: Washington, DC, 1977.


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n e c e s s i t y devotes time t o the teaching and l e a r n i n g o f techniques o f data a n a l y s i s t h a t might b e t t e r be spent on such t h i n g s as the design o f experiments and the i n t e r p r e t a t i o n o f r e s u l t s . In the course o f making these p o t e n t i a l i t i e s manifest, some b a s t i o n s o f i m p o s s i b i l i t y have a l r e a d y crumbled, as may be shown by s e v e r a l examples from t h e f i e l d o f potentiometry and p o t e n t i o metric t i t r a t i o n . I t has always been known t h a t analyses by d i r e c t potentiometry cannot be made as a c c u r a t e l y and p r e c i s e l y as analyses by p o t e n t i o m e t r i c t i t r a t i o n , but Brand and Rechnitz (1) and I s b e l l , Pecsok, Davies, and P u m e l l (2) have shown t h a t t h i s i s not so. I t has always been known t h a t a c e t i c a c i d (pK^ = 4.755) and p r o p i o n i c a c i d (pK^ = 4.876) have strengths too n e a r l y i d e n t i c a l t o permit i d e n t i f y i n g , much l e s s determining, both from the acid-base t i t r a t i o n curve f o r a mixture, but Ingman e t a l . (3) have shown that t h i s i s not so. I t has always been known t h a t a p o t e n t i o m e t r i c acid-base t i t r a t i o n cannot succeed i f there i s no p o i n t o f maximum slope on the t i t r a t i o n curve o r i f the c o n c e n t r a t i o n o f the reagent i s unknown, but Barry and Meites (4) and Barry, Campbell, and Meites (5) have shown t h a t these are not so. These are o n l y a few o f the many i n s t a n c e s i n which i t i s now apparent that f a m i l i a r experiments have always provided us with i n f o r m a t i o n t h a t we have not known how t o o b t a i n i n u s e f u l form. Probably there a r e very few chemists who would not r e a d i l y concede the e f f e c t i v e n e s s o f computerized procedures i n e v a l u a t i n g numerical parameters on the b a s i s o f numerical data. A p p l i c a t i o n s and examples l i k e the ones j u s t c i t e d are t h e r e f o r e comparatively easy t o understand and accept. However, there are many fewer chemists who are prepared t o accept the i d e a t h a t accurate and r e l i a b l e q u a l i t a t i v e d e c i s i o n s can be made by machines without human i n t e r v e n t i o n . In human terms i t i s o f course understandable why t h i s should be so. The chemist faced with having t o decide whether a compound c o n t a i n s , say, a phenyl group on the b a s i s o f i t s mass spectrum i s sure t o be aware, a t some l e v e l , o f the years o f t r a i n i n g and experience t h a t he b r i n g s to t h a t d e c i s i o n , and o f a l l the s u b t l e t i e s and p i t f a l l s t h a t i t may i n v o l v e . I t i s no easy t h i n g t o admit t h a t one's knowledge, understanding, and i n s i g h t cannot produce d e c i s i o n s s u p e r i o r t o those made by a mindless machine - o r , more p r o p e r l y , t h a t t h a t knowledge, understanding, and i n s i g h t can be reduced t o a s e t o f completely predetermined steps that w i l l produce as good a d e c i s i o n as the one t h a t c o u l d be made by a human b r a i n . Despite t h i s d i f f i c u l t y , i t i s c l e a r t h a t progress i n t h i s area o f f e r s prospects having overwhelming importance. Though the p o r t i o n o f chemical research t h a t deals with the e v a l u a t i o n o f numerical parameters can c e r t a i n l y be s i g n i f i c a n t and c h a l l e n g ing, the p o r t i o n that deals with q u a l i t a t i v e i n t e r p r e t a t i o n i s even more so. In experimental k i n e t i c s , f o r example, the r e a l problem i s u s u a l l y t o decide what the mechanism o f a r e a c t i o n i s . A f t e r t h i s has been s o l v e d , more o r l e s s severe experimental

Kowalski; Chemometrics: Theory and Application ACS Symposium Series; American Chemical Society: Washington, DC, 1977.


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d i f f i c u l t i e s may s t i l l have t o be overcome i n e v a l u a t i n g the r a t e and e q u i l i b r i u m constants a s s o c i a t e d with the r e a c t i o n , but o f t e n the values o f these w i l l be i m p l i c i t i n the data accumulated i n e l u c i d a t i n g the mechanism. What i s i n v o l v e d i n making such d e c i s i o n s ? There are two possibilities. One i s t h a t t h e system being s t u d i e d belongs t o one o f a l i m i t e d number o f c l a s s e s whose behaviors a r e a c c u r a t e l y known. The other i s t h a t i t does not, and i n s t e a d behaves i n some novel way t h a t no p r i o r i n t e r p r e t a t i o n w i l l s u f f i c e t o d e s c r i b e . In the f i r s t case the i n t e r p r e t a t i o n may be s a i d t o be r o u t i n e . Of course the d e c i s i o n s t h a t are i n v o l v e d i n a s s i g n i n g the system t o the proper c l a s s may be both s u b t l e and d i f f i c u l t . C a l l i n g them r o u t i n e merely means t h a t s i m i l a r d e c i s i o n s have been made before f o r other systems, t h a t the p r i n c i p l e s under l y i n g those d e c i s i o n s are known, and t h a t i t should t h e r e f o r e be p o s s i b l e t o e f f e c t them i n ways t h a t a computer can be p r o grammed t o execute. In the second case o n l y enough i s known t o make i t p o s s i b l e t o decide t h a t the system does not belong t o any known c l a s s . Beyond t h a t p o i n t d e c i s i o n and i n t e r p r e t a t i o n r e q u i r e imaginativeness and i n t u i t i o n , and these cannot be p r o grammed i n advance. Except i n s i t u a t i o n s so simple t h a t a l l the p o s s i b l e c l a s s e s are already known, every program designed t o make such i n t e r p r e t a t i o n s must provide f o r a c a l l f o r human i n t e r vention when a l l o f t h e known p o s s i b i l i t i e s have been t e s t e d and found t o be inadequate. The nature o f research i n any area would be profoundly changed by the a v a i l a b i l i t y o f a program t h a t would e f f e c t r o u t i n e i n t e r p r e t a t i o n and t h a t would c a l l f o r human h e l p when t h i s d i d not s u f f i c e . Chemists working i n t h a t area would be r e l i e v e d o f the n e c e s s i t y o f undertaking such i n t e r p r e t a t i o n themselves - o f r e t r a c i n g on each problem the thoughts they had had w h i l e s o l v i n g the one before i t . In l o s i n g t h i s burden they would g a i n the o p p o r t u n i t y t o spend more o f t h e i r time i n breaking new ground, i n improving t h e e x c e l l e n c e o f t h e i r experimental procedures and measurements, and i n s e l e c t i n g the systems t h a t would best repay study. I n v e s t i g a t i o n s t h a t turned out t o be r o u t i n e would be g r e a t l y f a c i l i t a t e d , and those t h a t d i d not could r e c e i v e the b e n e f i t o f the human imagination thus l i b e r a t e d . T h i s i s the r a t i o n a l e o f a program o f research t h a t began s e v e r a l years ago a t Clarkson C o l l e g e o f Technology. Near i t s s t a r t we i d e n t i f i e d the v a r i o u s kinds o f c l a s s i f i c a t i o n s t h a t might a r i s e (6), and these a r e l i s t e d i n Table 1. Table 1.

Kinds o f C l a s s i f i c a t i o n s 1. Binary Ά. Simple B. M u l t i p l e 2. L i n e a r 3. Branched



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I t i s always supposed t h a t data are a v a i l a b l e showing how the value o f some dependent v a r i a b l e changes as t h a t o f some i n d e pendent one i s a l t e r e d , and t h a t the problem i s t o account f o r the data by s e l e c t i n g the appropriate one o f a f i n i t e s e t o f hypotheses, each o f which can be expressed by one o r more equat i o n s r e l a t i n g the dependent and independent v a r i a b l e s and i n v o l v i n g numerical parameters as w e l l . A simple b i n a r y c l a s s i f i c a t i o n i s one t h a t r e q u i r e s o n l y a s i n g l e "yes-no" d e c i s i o n . A compound may o r may not c o n t a i n a p a r t i c u l a r k i n d o r group o f atoms; i t may o r may not have a p a r t i c u l a r k i n d o f b i o l o g i c a l a c t i v i t y ; i f subjected t o p o l a r o graphic examination i t may o r may not be r e v e r s i b l y reduced. Much o f the research t o date on p a t t e r n r e c o g n i t i o n i n chemistry has d e a l t w i t h such questions. I t may o r may not be p o s s i b l e t o express one o r both o f the a l t e r n a t i v e s by an equation r e l a t i n g the independent and dependent v a r i a b l e s : our work has concent r a t e d on cases i n which t h i s i s p o s s i b l e , while p a t t e r n recogn i t i o n has concentrated on those i n which i t i s not. A l l such questions share the property t h a t the two a l t e r n a t i v e s being considered are both exhaustive and mutually e x c l u s i v e : i f e i t h e r can be r e j e c t e d the other must be r i g h t . F o r the kinds o f data considered here, there may be two d i f f e r e n t p o s s i b l e equations o f which the data must conform t o one, o r there may be o n l y one equation and the question may be whether the data conform t o t h a t equation o r not. In e i t h e r event i t i s r e l a t i v e l y simple t o express the r e l i a b i l i t y o f the c l a s s i f i c a t i o n i n the c l a s s i c a l s t a t i s t i c a l f a s h i o n : t h a t i s , by s t a t i n g the l e v e l o f confidence a t which i t can be upheld. M u l t i p l e b i n a r y c l a s s i f i c a t i o n s are those t h a t r e q u i r e two or more independent "yes-no" d e c i s i o n s . A not very complicated one i s shown i n F i g . 1. T h i s arose i n p o t e n t i o m e t r i c t i t r a t i o n s o f sodium o r potassium l a u r a t e with h y d r o c h l o r i c a c i d (7). Depending on the c o n c e n t r a t i o n s o f l a u r a t e and hydrogen ions i n these two s o l u t i o n s , and a l s o on the c o n c e n t r a t i o n o f any a l k a l i metal s a l t (such as sodium or potassium c h l o r i d e ) t h a t was added, any o f three d i f f e r e n t and independent phases might have separated d u r i n g some p o r t i o n o f the t i t r a t i o n . M i c e l l e s o f l a u r a t e i o n might o r might not have been present i n the i n i t i a l s o l u t i o n , and both an " a c i d soap" and the f r e e f a t t y a c i d might o r might not have p r e c i p i t a t e d . E i g h t d i f f e r e n t kinds o f t i t r a t i o n curves can r e s u l t , although not a l l can be obtained with l a u r a t e and sodium o r potassium ions i n aqueous s o l u t i o n s a t 25°. A program was c o n s t r u c t e d t o e f f e c t t h i s t r i p l e b i n a r y c l a s s i f i c a t i o n , beginning with e x a c t l y the same i n f o r m a t i o n - the compositions o f the r e a c t i n g s o l u t i o n s and the coordinates o f the p o i n t s on the experimental t i t r a t i o n curve - t h a t would be a v a i l a b l e t o a human chemist. When i t was a p p l i e d t o about 30 experimental curves secured under widely v a r y i n g c o n d i t i o n s , i t s e r r o r r a t e was approximately 5%. Two s k i l l e d chemists u s i n g the same information managed, with some d i f f i c u l t y , t o achieve an e r r o r r a t e o f about 35%.


MEITES AND SHiA

7.

131

Controlled-Potential Chronocoulometry

A MULTIPLE BINARY CLASSIFICATION

P o t e n t i o m e t r i c t i t r a t i o n o f an a l k a l i - m e t a l

l a u r a t e ML w i t h HC1


Were m i c e l l e s o f l a u r a t e p r e s e n t i n i t i a l l y ?

D i d t h e " a c i d s o a p " MHL p r e c i p i t a t e d u r i n g t h e t i t r a t i o n ? 2

D i d t h e f r e e f a t t y a c i d HL p r e c i p i t a t e ?

1

2

3

5

6

7

8

Figure 1. Triple binary classification of the potentiometric titration curve obtained in a titration of laurate ion with a strong acid. The purpose of the classification is to reveal which, if any, separate phases were present at any stage of the titration.

L i n e a r c l a s s i f i c a t i o n s may be d e f i n e d as those i n which the equations t h a t correspond t o the s u c c e s s i v e hypotheses can be arranged a p r i o r i i n a l o g i c a l order t h a t i s a l s o the order o f i n c r e a s i n g complexity o f t h e equations. Figure 2 shows the simplest example i n the l i t e r a t u r e (6). In some cases the number o f p o s s i b l e hypotheses may be very l a r g e , but i n o t h e r s , i n c l u d i n g t h i s one, i t may be very s m a l l . The l i t e r a t u r e contains no example o f any t e t r a f u n c t i o n a l base whose d i s s o c i a t i o n cons t a n t s a r e a l l so c l o s e together t h a t successive steps could not be p e r c e i v e d on v i s u a l i n s p e c t i o n o f t h e t i t r a t i o n curve, and t h e r e f o r e i t was decided t h a t no hypothesis beyond the t e t r a f u n c t i o n a l one would be allowed. Together with the f a c t t h a t the s u c c e s s i v e d e c i s i o n s were based on an estimated standard d e v i a t i o n o f measurement, t h i s d e c i s i o n made i t p o s s i b l e t o c l o s e the loop and ensure t h e eventual acceptance o f one o f the p e r m i s s i b l e hypotheses. Programs t h a t e f f e c t l i n e a r c l a s s i f i c a t i o n s are e a s i e r t o design than those f o r m u l t i p l e b i n a r y c l a s s i f i c a t i o n s , and a r e


CHEMOMETRICS:

132


A LINEAR CLASSIFICATION

E v a l u a t i o n o f t h e f u n c t i o n a l i t y o f a monomeric base from p o t e n t l o m e t r l c acid-base t i t r a t i o n

data

Is t h e base m o n o f u n c t l o n a l ?


Yes Is i t d i f u n c t i o n a l ? Yes Is I t t r i f u n c t i o n a l ? Yes Is i t t e t r a f u n c t i o n a l ?

Yes P r i n t t h e c o n c l u s i o n and

Revise the estimated value

the corresponding values

of the standard e r r o r o f

o f c ^ and t h e K j

measurement

L Figure 2. Linear classification of the potentiometric titration curve obtained in a titration of a weak base with a strong acid. It is assumed that no phase separation occurs during the titration. The purpose of the classification is to reveal the number of protons consumed by each ion or molecule of the base during the titration.

l i k e l y t o be a t l e a s t as r e l i a b l e , i f not more so. The one represented by P i g . 2 was t e s t e d with a great many s y n t h e t i c and experimental data f o r bases l i k e a c e t a t e , s u c c i n a t e , and c i t r a t e , and c o u l d not be made t o f a i l when i t was provided with an honest estimate o f t h e standard e r r o r o f measurement. I f i t was given an estimate t h a t was much too l a r g e , i t wielded Occam's Razor with r u t h l e s s s k i l l , e x a c t l y as a human chemist would, a c c e p t i n g the simplest hypothesis t h a t c o u l d not be disproved. Occasionally, when i t was given an estimate t h a t was n e a r l y a f u l l order o f magnitude too s m a l l , i t d i d conclude t h a t c i t r a t e i o n was


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Controlled-Potential

133

Chronocoulometry

t e t r a f u n c t i o n a l ; human chemists a r e o f t e n s i m i l a r l y m i s l e d by data that a r e l e s s p r e c i s e than they are thought t o be. Very much the most complicated k i n d o f c l a s s i f i c a t i o n i s the branched c l a s s i f i c a t i o n , i n which t h e r e j e c t i o n o f one hypothesis must be followed by a t e s t o f another one, and i n which there i s no l o g i c a l l y necessary order i n which the t e s t s must be arranged. T h i s paper d e s c r i b e s the s t r u c t u r e o f the f i r s t program designed to e f f e c t a branched c l a s s i f i c a t i o n .


The Chemical Problem C o n t r o l l e d - p o t e n t i a l e l e c t r o l y s i s has been s t u d i e d i n t e n s i v e l y i n s e v e r a l l a b o r a t o r i e s s i n c e about 1955 with a view t o emp l o y i n g i t f o r the e l u c i d a t i o n o f the mechanisms o f e l e c t r o chemical processes and f o r t h e e v a l u a t i o n o f the r a t e and e q u i l i brium constants f o r the i n d i v i d u a l steps i n these processes. Roughly 25 d i f f e r e n t mechanisms have been imagined. A few were invented a_ p r i o r i o r s t u d i e d because they were known t o have consequences t h a t c o u l d be observed by other e l e c t r o c h e m i c a l techniques; most were devised i n order t o account f o r the phenomena observed i n studying r e a l systems, both organic and i n o r g a n i c ; a few were i n v e s t i g a t e d b r i e f l y so t h a t they c o u l d be r u l e d out as being unable t o e x p l a i n those phenomena. There a r e s e v e r a l thorough reviews (8-10) s t r e s s i n g d i a g n o s t i c c r i t e r i a and ways o f d i f f e r e n t i a t i n g among the v a r i o u s mechanisms, and only a very b r i e f summary w i l l be undertaken here. C o n t r o l l e d - p o t e n t i a l e l e c t r o l y s e s are performed i n c e l l s f i t t e d with three e l e c t r o d e s . One, t h e "working e l e c t r o d e , " i s the e l e c t r o d e a t which t h e h a l f - r e a c t i o n o f i n t e r e s t occurs. Often i t i s a l a r g e pool o f mercury, though platinum gauze and other m a t e r i a l s can a l s o be used. The s o l u t i o n surrounding the working e l e c t r o d e i s e f f i c i e n t l y s t i r r e d t o f a c i l i t a t e mass t r a n s f e r o f the r e a c t a n t from the bulk o f the s o l u t i o n t o the s u r f a c e e l e c t r o d e and t o maintain a constant value o f the mass-transfer c o e f f i c i e n t s_. An a p p l i e d p o t e n t i a l i s imposed across the working e l e c t r o d e and an " a u x i l i a r y e l e c t r o d e , " which i s u s u a l l y i s o l a t e d i n a separate compartment o f the c e l l and serves merely to permit the flow o f an e l e c t r i c c u r r e n t through t h e c e l l and working e l e c t r o d e . The z e r o - c u r r e n t p o t e n t i a l E j ^ o f the working e l e c t r o d e i s sensed by comparing i t w i t h the p o t e n t i a l o f a "reference e l e c t r o d e , " such as a s a t u r a t e d calomel o r s i l v e r s i l v e r c h l o r i d e e l e c t r o d e , through which c u r r e n t does not flow. A l t e r i n g the a p p l i e d p o t e n t i a l causes the. value o f Ew. . vary. By means o f a p o t e n t i o s t a t , the a p p l i e d p o t e n t i a l i s continuously adjusted t o as t o keep Ew.e. equal t o some predetermined value, which i s u s u a l l y so chosen t h a t ions o r molecules o f the r e a c t a n t A are reduced as r a p i d l y as they are brought t o the s u r f a c e o f the working e l e c t r o d e by convection and d i f f u s i o n . Of course o x i d a t i o n i s a l s o p o s s i b l e , but only r e d u c t i o n w i l l be a l l u d e d t o here. # e #

t

o

e


134

CHEMOMETRICS:


The simplest p o s s i b i l i t y i s t h a t A i s reduced to a s t a b l e product Ρ i n a s i n g l e step and without any s i d e r e a c t i o n o r other coupled chemical process. T h i s i s d e s c r i b e d by the equations (11) A + η e + Ρ

(1)

i = i°e-§_t

(2a)

2=

2»

(2b)

( i - e-£l)

where η i s the number o f faradays consumed i n reducing each mole of A, jL i s the c u r r e n t t h a t flows through the c e l l and working e l e c t r o d e It s (seconds) a f t e r the e l e c t r o l y s i s has begun, £ the q u a n t i t y o f e l e c t r i c i t y (coulombs o r faradays) t h a t has flowed up t o t h a t i n s t a n t , i ^ i s the i n i t i a l value o f i ^ , and gpa i s the t o t a l q u a n t i t y o f e l e c t r i c i t y t h a t w i l l flow i f the e l e c t r o l y s i s i s i n d e f i n i t e l y prolonged. The value o f in faradays i s given i n t h i s simple case by Faraday's law:


i s

2po = η N °

(3)

A

where N ° i s the number o f moles o f A present i n the i n i t i a l solution. D i f f e r e n t mechanisms y i e l d d i f f e r e n t r e s u l t s . I t i s possible f o r A t o undergo reductions along p a r a l l e l but independent paths to y i e l d d i f f e r e n t products} A

A + n^e = Ρ

;

A + n2£ = Q

(4)

Then the c u r r e n t w i l l decay e x p o n e n t i a l l y with time, as i t does i n the simple case, but the apparent value o f η d e f i n e d by the equation

2app. "

2.^ϋ°

(5)

Α

w i l l l i e between the values o f n j and n_2 and w i l l r e f l e c t the r e l a t i v e magnitudes o f the o v e r a l l r a t e constants f o r the two h a l f - r e a c t i o n s . There may be a "continuous f a r a d a i c background current" i f , r e d u c t i o n o f hydrogen i o n , water, or some other major c o n s t i t u e n t o f the s o l u t i o n , a t a r a t e t h a t i s constant and u n a f f e c t e d by the c o n c e n t r a t i o n o f A o r P. Then the c u r r e n t i s given by d

u

e

t

o

t

n

e

c

1=

Automatic Elucidation of Reaction Mechanisms in Stirred-Pool

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