REACTION RATES FOR THE PRACTICAL CHEMIST' JOHN 0. EDWARDS Brown University, Providence, Rhode Island
S o m years ago at a luncheon, Professor Peter Debye said, "Kineticists are like lobsters, they travel backwards." After a minute to let this sink in, he explained that a man who studies rate processes must he a chemist first and a kineticist second, for good kinetics depends on good chemistry. The truth is this thought has become more and more apparent in the intervening time. However, there is a corollary to this which is worth consideration. In modern chemistrv. " , kinetics and the mechanisms of reactions are of ever-increasing importance. Thus the corollary is: "A man doing chemistry today must have a
w n r k i n ~k n n w l d o e nf mte nrornaaes
"
., interested in kinetics. ~ 1 the~chemist ~ .in industrial research occasionally is handed the problem of a reaction that is economically feasible except that i t goes too slowly. Although it is somewhat more difficult to see why chemists in an analytical laboratory or small chemical plant should know the fundamentals of kinetics and rate processes, it can be shown that this information is just as important for them as for the others. All reactions proceed a t some velocity; sooner or later, every chemist encounters a measurable one. The reactions which go a t a measurable rate are often just as troublesome as those too fast or too slow. Even the most practical chemist must be aware of the possible troubles in working with such reactions. The primary emphasis of this discussion is that rate processes must he considered when a chemical analysis is being carried out. APPLICATIONS IN ANALYTICAL CHEMISTRY
All chemists depend upon analytical chemistry. For this reason, a primary example will he chosen from the reactions involved in a standard volumetric method. I n general, a reaction suitable for titrimetric analysis must be one which is essentially complete immediately, wit,h no side reactions. I t is not uncommon. however. 1 Presented at the Eighteenth Summer Conference of the NEACT, Durham, New Hampshire, August 20, 1956. The author gratefully acknowledges the support of the Office of Ordnance Research of the U. S. Army.
VOLUME 34, NO. 1, JANUARY, 1957
to find reartions with exact stoichiometries nhich proceed too slowly, or reactions which go rapidly enough hut have competing side reactions. Consideration of the rate processes involved might bring forth ways to make such reactions suitable for use in analysis. The reaction for the permanganimetric analysis of hydrogen peroxide (1) does not have any of the above faults, as normally carried out. Although it involves relatively large integers, the stoichiometry is without com~licationin acid solution:
+
-
2MnO.c . . 5H107 . - 4. 6 ~ +2Mnt+
+ 502 + 8&0
The reaction is not simple, however, and the first time added is decolorized so slowly that he is tempted to assume that no peroxide is present. After a minute or so, the purple perrnanganate color does fade away. When a second bit of permanganate is added, its color also persists but not as long. Succeeding additions of permanganate are decolorized more and more rapidly until finally he can add the reagent in a continuous stream with instantaneous loss of color. At the end point one extra drop of permanganate gives a definite, lasting, pale pink coloration to the solution. The peculiarity of this reaction is that it is catalyzed by one of its o w products, the manganous ion, (&In++). The direct reaction between permanganate ion and peroxide is very slow, but the over-all reaction becomes rapid in the presence of the catalyst. If a n analytical chemist were to add a small amount of a manganous salt, the slow initial reaction would be avoided. Then he would have a rapid and stoichiometric analytical reaction. The dramatic behavior of permanganate in the peroxide titration leaves little doubt in the mind of the chemist who carries it out about the complexity of the reaction and the complexity of the ratedetermining steps. Moreover, there are other troubles to be found in this analysis for peroxide. They are even more subtle than the above behavior. What about the analysis of mixtures of hydrogen peroxide and Caro's acid? The latter is peroxymonosulfuric acid with the formula:
Both peroxides oxidize iodide ion at nearly the same velocity so that one generally titrates the total iodine formed by both of the oxidation reactions:
This total iodine can be determined by thiosulfate titration and the total peroxide calculated accordingly. Analytical references ($1, report that permanganate will not oxidize such bound peroxides as the peroxysulfates. The amount of hydrogen peroxide alone in the mixture can thus be determined by titrating the original mixture with permanganate. The amount of Caro's acid is represented by the difference in the two results. How about mixtures of hydrogen peroxide and peroxyborate ion?
On carrying out the above two separate analyses, one obtains identical results. Surprisingly, the amount of hydrogen peroxide found by permanganate titration corresponds exactly to the total amount of peroxide shown by the oxidation of iodide. One could draw the incorrect conclusion that no peroxyborate ions were present. The peculiar thing about the peroxyborate ion, which is not true about the peroxysulfate ion, is that wliile it is fairly stable thermodynamically, it still can hydrolyze rapidly to hydrogen peroxide. The equilibrium concentrations lie predominantly to the right as demonstrated by a variety of physical measurements (PI). The reaction of water with the peroxyborate ion to form borate ion and hydrogen peroxide is so fast that the equilibrium point cannot he determined by a chemical method. The hydrogen peroxide which reacts with permanganate ion in the analysis of the mixture is replenished rapidly by hydrolysis of peroxyborate ion until the latter is exhausted. The main point for consideration is, then, that whenever a chemical procedure i s applied to a compound or a substituent group, it should be done only after the chemist has asked himself whether the various equilibria involved are achieved slowly or rapidly. In retrospect, the point is fairly obvious, but hindsight always is better equipped than foresight. The facts of the matter are that the need for such consideration has been recognized only recently.
constitute a clear explanation of why so much is known about chromium(III), cobalt(III), and platinum(1V) complexions, yet why there is so little information available about vanadium(III), manganese(III), or zinc(I1) complexes. The former three ions are readily identified because the replacement of groups in the coordination sphere is slow. For example, the simple exchange reaction
has a "half-Life" of about forty hours at 25'C. (6). Taube calls such ions "inert." In the ions of the second set of metals, groups attached to the metal are hydrolyzed so rapidly that chemical methods cannot he applied successfully to analyze for the ions. I t is no exaggeration to say that the constitutions of few easily replaceable (or "labile" as Taube calls them) complexes are well known. One can easily get the impression from inorganic chemistry books that the constitutions of coordination compounds are well known and easily established. Unfortunately, this is not usually true. The examples found in textbooks are almost invariably coordination compounds of the "inert" classification. This is reflected in what is taught, and it is an exceptional student indeed who when told that silver nitrate will discriminate between chlorine atoms in the compounds [Co(NHs)rC1]C12and [Cr(OH2)5CI]C12 will ask himself if it is really justifiable to apply this test to [Fe(H,0)5C11CI.. -->
The chloride ions in the coordination spheres of the inert cobalt and chromium complexes are replaced by water molecules so very slowly that only two equivalents of silver chloride are precipitated when silver nitrate is added. On the other hand, the iron-chlorine bond in the last complex is broken rapidly sn thet three equivalents of precipitate can be formed, two equivalents corresponding to ions outside the coordination sphere and the third corresponding to the labile chloride ion in the coordination sphere. The problem of "inert" versus "labile" behavior also can be considered with respect to peroxyauions and oxysnions (6). As noted before, peroxy groups on the borate ion are labile while those on sulfate ion are inert. It is not a coincidence that those peroxyanions that are well established fall in the "inert" class. The others are too fugitive to be identified by a chemical method. There is one more example which should be mentioned. The two ions, phosphate and arsenate, are remarkably similar in both chemical and physical properties. However, the rates of replacement of atoms attached to the central arsenic in arsenate are rapid. Similar replacement of the atoms in phosphate is slow. Pyrophosphate and many higher polyphosphates are well known and are found t o be relatively inert towards hydrolysis. I n contrast to this, polymers of arsenic acid and arsenates are rare. It is impossible to maintain them in aqueous solution (7) as the result of rapid hydrolysis reactions such as:
COORDINATION COMPOUNDS
One has only to read the review of Henry Taube (4) on rates of replacement in coordination compounds to see how crucial a factor this is. The rates involved
The rapid rate of replacement in arsenates is also reflected by the fact that neither organic esters of arsenic acid nor stable peroxyarseuates exist. JOURNAL OF CHEMICAL EDUCATION
the series A second point for consideration is that cata2ysts often can be found to speed u p slov reactims. There are many important reactions which are accelerated by trace impurities. Peroxide reactions especially are susceptible to catalysis. The catalytic influence of copper ion on peroxydisulfate reactions is well established (8, 9). Both hydrogen peroxide (10) and peroxymonosulfuric acid (9) are decomposed rapidly by adventitious metal ions; for example Ball (9) has found that as little as a billionth of a mole per liter of cobaltous ion will cause Caro's acid to decompose at a measurable rate. By no means should it he inferred that trace metals influence only rates of analytically important reactions and of decomposition reactions. Preparation reactions which normally proceed at a negligible velocity often can be accelerated by judicious addition of a catalyst in trace amounts. The production of tartaric acid by oxidntioil of fumuric or mil& acids Ly chlorate ion is immensurably slow ( I ! ) . 0 1 1 addition of a small amount of osmium tetroxide, however, the rate becomes measurable. Thus one can use an inexpensive oxidizing agent t o produce either racemic or meso tartaric acid. Although the transition elements and their compounds are often the best catalysts, other types of materials are known to affect reaction rates. I n some reactions, trace amounts of water have an astonishing effect. The presence of a trace of chloride ion in an aluminum container to be used for containing concentrated hydrogen peroxide can be disastrous. The chloride ion can, under some conditions, induce a violent decomposition of hydrogen peroxide. To avoid certain decompositions or side reactions, it may be desirable to slow down the rate. Trace inhibitors, which might be called "negative catalysts," are useful. These often act by removing the active catalyst from the reaction. A small amount of the powerful sequestering agent, ethylenediaminetetraacetic acid will often tie up metal ions so that they are no longer effective ( 9 ) as catalysts. The inhibitors of free-radical chains such as the substituted phenols are well known and widely used.
Clod- > HSOI-
> HsPOI
decrease from left to right (15). Rates of oxygen replacement (7) decrease in the reverse order:
It is common knowledge that perchlorate ion and nitrate ion in aqueous solution oxidize substances slowly in spite of their powerful potentials, whereas less powerful oxidizing agents such as selenious acid or nitrous acid perform quite rapidly. The next point is that the products isolated from a reaction mixture ore not necessarily the most stable ones. The magnificent accomplishments of the synthetic organic chemists of our day would not be possible if a reaction always led to the configuration or product of greatest stability. One can compare the reactions of cyclopentene to see how various strong oxidizing agents affect it. If peroxyacetic acid is used, the initial product is cyclopentene oxide which can be treated with water to give trans-1,2-cyclopentanediol:
Treatment of the olefin with hydrogen peroxide in the presence of light or osmium tetroxide gives cis-1,2-cyclopentanediol:
The use of selenium dioxide as the oxidant can form the interesting product cyclopentene-one-3:
When lead tetraacetate is employed, the oxidation produces, among other things, the compound cyclopenteneacetate-3, which can be hydrolyzed to give the alcohol:
RELATIONSHIP OF THERMODYNAMIC STABILITY
The third point for consideration is that kinetic stability (or inertness) may parallel thermodynanzic stability, but often it does not. The energy of the oxygenhydrogen bond is greater than that of the carbon-hydrogen bond (I$), yet the rates a t which hydrogen will exchange with deuterium are in marked contrast. The hydrogen on oxygen is so labile that direct measurement of the rate of exchange has not yet been accomplished; the hydrogens on carbon are, on the other hand, exchanged exceedingly slowly a t room temperature. Mention already has been made of the difference in the behavior of peroxymonosulfate ion, which is thermodynamically unstable but inert towards hydrolysis, and peroxymonoborate ion, which is thermodynamically stable yet is labile in aqueous solution. There is also little correlation between oxidation potentials and either the rates of oxidation or the rates of replacement. I n 1.0 M acid the oxidizing abilities of VOLUME 34, NO. 1, JANUARY, 1957
These specific reactions are by no means all the possibilities. The reagents chromic acid, permanganate ion, ozone, periodate ion, etc. make other products. Readers interested in the oxidation of olefins can refer to the review of Milas (14) to see what unusual things are possible. This variety of products that can be obtained by oxidizing cyclopentene does not reflect anything more about their thermodynamic stability than that all are possible. The direction taken by the reactions to lead to specific oxygenated products is a result of the fact that the individual reagents present different reactions paths of greatest rate to the olefin. One can certainly appreciate why organic chemists are so intrigued with reaction mechanisms when one realizes that the products of organic reactions usually ?re determined by a mechnism rather than by thermodynamic stability factors.
FUTURE DEVELOPMENTS
I t is appropriate a t this point to make some mention of possibilities for the future. It does not take clairvoyance to see the following things coming for the practical chemist. The vast amount of interest in the fields of reaction rates and relative reactivities has made it possible to find and apply many correlation equations. These equations, of which the Bronsted (15) and Hammett (16) equations are famous examples, now enable the calculation of rates for many reactions. The Bronsted equation kn*
=
arKd
d e r e a and 0 are constants relates the rate (k,,) of an acid-catalyzed reaction to the ionization constant (K,,) of the same acid. The Hammett equation log k. - log kn = p o
where D is a ronstant characteristic of a substituent group on a benzene ring and p is a reaction constant relates the rate (kJ of a reaction for a molecule containing a substituted benzene to that (ka) for the molecule containing benzene itself. The nature of present progress in the development of these correlation equations is largely empirical. Although future directions are uncertain, there is little doubt concerning the outcome. Rate data will be applied in much the same fashion as equilibrium data are used now. To be sure, there always will be the problem of the presence of an unsuspected catalyst, but even this problem can be overcome. There is another outlook for the future which appeals even more than the prediction of reaction rates. This is the possibility of synthesizing reagents which can react rapidly with a particular substrate. Chemists are just now coming to the stage of being able to understand what the factors are in molecules which affect reaction rates. The influences of basicity, electrode potential, polarizability, ionic potential, etc., are being sorted out. Within the next few decades it will be possible to choose molecules for a specific task purely on the basis of a pa-
per calculation. The predicted rate calculated for a synthesis probably will match the experimental one within a factor of two. The possibilities will he limited only by the chemist's ability to dream up new compounds and then make them. Other new things will come along in the field of chemical kinetics. What they will be is hard to say, but students trained in these days must be ready to understand them. A chemist today certainly must have a working knowledge of rate processes; the practical chemist of tomorrow will make good use of them. LITERATURE CITED (1) HUCKABA, C. E., AND F. G. KEYES,J . Am. Chem. Soc., 70, I640 (1938); also references therein. (2) PRICE, T. S., "Per-acids and Their Salts," Longmans, Green & Co., London, 1912, p. 53. (3) (a) MENZEL,H., 2. p h y ~ 3 .Chem., 105, 402 (1923). (b) EDWARDS, J. O., J . Am. Chem. Soc., 75,6154 (1953). ic) KERN,D. M. H., J. Am. Chem. Soc., 77, 5458 (1955). (d) ANTIRAINEN, P. J., Soumen Kemistilehli, 28B, 159 (1955). (4) TAUBE,H., Chem. Revs., 50, 69 (1952). (5) HUNT,J. P., AND H. TAUBE, J. Chem. Phys., 19,602 (1951). (6) EDWARDS, J. O., J. CHEM.EDUC.,31,270 (1954). (7) THILO, E., AND I. PLAETSCKE, Z. anoTg. Chem., 260, 297, 31.5 119501. . (8) (a,) KING,C. V., AND 0 . F. STEINBACH, J . Am. Chem. Soe., 52, 4779 (1930). (b) ALLEN,T . L., J. Am. Chem. Sac., 73, 3589 (1951). ( 0 ) B.4w~.C. E. H., AND D. ManoEnISON, T ~ a n sFnraday . Soc. 51, 925 (1955). (9) BALL,D. L., Ph.D. thesis at Brown University (1956). (10) SCHZXB,W. C., C. N. SATTERFIELD, AND R. 1,. R'ENT-
.~~~ ~
WORTH,"Hydrogen Peroxide," Reinhold Publishing Corp., New York, 1955, Chap. 8, 111) M.. A N D H. A. TAYLOR. J . Am. Chem. SOC.. ,~ -, ZELIKOFF. , 7 2.
50x1 (ig5oj. (12) PAULING, L., "Nature of the Chemical Bond," Cornell University Press, Ithace, New Yark, 1940, p. 53. (13) LATIMER, W., "Oxidation Potentials," 2nd ed., PrenticeHall, Inc., New York, 1952. (14) MILAS,N., "The Chemistry of Petroleum Hydrocarbons," Vol. 2, edited by B. T. BROOKS, C. E. BOORD, S. S. KURTZ A N D L. SCHMERLING; Reinhold Publishing Corp., New York 1955, Chap. 16, p. 399. (15) BRBNSTED, J. N . , Chem. Reus. 5, 231 (1928). L. P., "Physioal Organic Chemistry," Mc(16) (a) HAMMETI., Craw-Hill Book Co., New York, 1940, Chap. 7. (b) JIFFE, H. H., Chem. Revs. 53, 191 (1953).
JOURNAL OF CHEMICAL EDUCAlION
