1 1. B. Weisfeld U. S. Rubber Company Wayne,
New Jersey
A thermoanolyfical kinetic experiment
The Catalyzed Reaction of Phenyl Isocyanate with Butanol
T h e rate at which heat. is absorbed or evolved during a chemical process can give a rapid and convenient est,imate of reaction kinetics. Various calorimetric methods have been described in the Merature ( I ) , demanding, for the most part, elaborate and expensive apparatus and a complicated interpretation of thermal data. Recent methods applied most successfully and precisely t,oward t,his end have been differential enthalpic aualysis (DEA) and differential t,hermal analysis (DTA). Both t,hese techniques employ a differenhl thermocouple immersed in reactive and incrt materials of approximately equivalent, heat capacity, and t,emperat,ure differences during reaction are sensed by a recording device. In DEA, descrihed by Eyraud (3), temperat.ure differences between the active and reference substances are maintained at zero by supplying heat to either during a react,ion. The amount of heat input is recorded. In DTA (3) the t.emperature difference between materials is recorded directly as the environmental temperature is changing. A smooth closed curve results, the area beneath proportional to the heat of react,ion. This latter technique has proved of great,er value in the consideration of reaction kinetics. Thns, Kissinger has developed the relationship between t,he "shape index" of a differential thermogram and t,he order of reaction in solid state react,ions (4),and Borchardt and Daniels have derived rate constants and activation energies from single curves through t,he application of DTA t,o reactions in solution (5). These methods are, however, limited to specific types of reactions not often encountered in the common organic laboratory; and the equipment required, though relatively simple in the Borchardt and Daniels experiment,, may not be immediately available or indeed warranted by the nature of the experiment. Thermal analysis (TA) is the natural precursor of the forementioned methods. I t relies solely on the rate and extent of development of an exotherm upon rapid mixing of reactants and hence requires only the most rudimentary apparatus. The equipment used in the present experiment is that found in any conventional laboratory: a small Dewar flask, a thermometer calibrated in O.l°C units, a magnetic stirrer, and a stop-watch. The Theory of Thermal Analysis
The observed rate of temperature change in an exot,hermic reaction, under approximately adiabatic conContribution No. 196 from the Research Center of the United States Rubber Company, Wayne, New Jeney.
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ditions, may he related to the rate of change of react,ant roncmtration by the expression,
where AH is the heat of reaction aud cis the calorimeter constant. The initial rat,e of temp~raturechange is similarly related to the initial conceutratioo change:
Integrating (1) : AT
=
- A W / C ~ , " (dn/dl)nt = - A H / c ( n )
(3)
and dir-idmg ( 2 ) by ( 3 ) :
or, (dn/al). = ( d T / d l ) ~ . ( n ) / A T
(4)
This states that the init,ial reaction rate is directly proportional to the init,ial temperature rate and inversely proport,ional to t,he t,otal temperature rise. The reaction rate is also proport,ional to the rate constant, thus (6): (&/dl).
= k(n)"
(5)
where k is the rate constant at the temperature of reaction initiation, x is the order of reaction, and n is the init.ial concentrat.ion of reactant,. Substituting in equation (4).
and for a first order reaction,
Thus, for a first order (or "pseudo-unimolecular") reaction, the initial slope of a temperature-t,ime curve divided by the total temperature rise is simply equal to the rate constant for reaction. This assumes that the heat of solution (or dilution) of the last introduced reactant is negligible compared to the heat of reaction. A typical temperature-time curve is illustrat,ed in Figure 1. To determine t,he initial slope, a smooth curve is fitted to the raw "stop-watch" data and graphically differentiated, extrapolating to the zero intercept. It may be expedient, however, to feed raw data into a programmed computer, thus obviating a great. part of human error.
The Experimenk Iron (Ill) Acetylacetonate Catalysis in the Reaction of Phenyl lsocyonote and n-Butanol
Aromat,ic isocyanates react rapidly with alcohols t.o form, predominantly, urethaues: Ar-NCO + R 4 H Ar-NHCOO-R
-
The reaction of diisocyauates with diols and polyols to give po1yurct.hanes has created an ent,ire new indust,ry (elast.omers, foams, coatings, etc.). Fortunat,cly, t,he react,iou above is not simple, but many side react.ions do occur t,o varying extents, creating materials of wide property range. Therefore, catalyst,^ are employed t,o promote certain reactions in polymerizing media and hence minimize ot,hers. Iron (111) acctylacet,onat,c is one such ratalyst, specific to the urethane reaction (71, a r ~ dhas found wide use. However, rat,alytir panlmet,ers have not heen described and, for that mat,t,er,are rare for almost all known urethane catalyst,^. I n a mechanist,ic discussion a t these laboratories, it was postulated t,hat the iron complex might accommodate more than one isocyanate group in a transition st,at,eint,ermediate, and t,his study was undert,aken witah t,hat feature in mind. We also desired to set up a method for t,he determination of catalytic parameters for uret,hane catalysts in general. Iron (111) acet~ylacet~onate was prepared hy mixing an ammoniated solut.ion of 1.3-pent,anedione with an equivalent amount (one-third molar ratio) of iron (111) sulfate hydrate. The red precipit,at,e was filtered and recrystallized twice from henzene and petroleum ether, mp 187-188O. Quanthies of the catalyst were dissolved in dried, dist,illed n-hutanol. Exact.ly 100.0 ml of the hutanol-cat,alystsolut,ion !yere placed in a small Devar flask fitted with a magnet,ic stirrer, vented stopper, t,hermometer calibrated in 0.1 units, and a small calihrat,ed rapid delivery addition funnel. A hypodermir syringe may he used in place of the latter. The init,ial t.emperat,ure of t,he solution in the Dewar was adjust,ed to 2 4 . P n.ith t,he aid of a cold h g e r and, a t t,his temperature, b e b e e n 1.0 and 3.0 ml of freshly distilled phenyl isocyanate were added rapidly. Temperature was recorded every 15 seconds thereafter up to four minutes, then leveling temperatures were recorded a t one minut,e interrals up to 10 minutes.
All reactions inr~est~igatedwere essentially complete well &hin that 10-minute period. Typical smoothed temperature-time curves are shovn in Figure 1. The data were analyzed via a Burroughs E-101 comput,er. In this manner, as many as 30 experiments were run (and 30 rat,e eoustant,s calculated) in a single day. Catalytic coefficients may he calculated from t,he Br9nsted relationship (8): k = ko + k,[CatlZ (8) where li is the rate constant for reaction, ko the uncat,alyzed rate constant., 16, the catalyst coeffirient, [Cat] the catalyst concentration, and z the order of catalysis. In logarithmic form: log ( k - k.) = lag k,
60
120
180
240
300
360
420
t (recondd
Figure 1. Typical temperature-time curves for the reaction or ~he",l irocyanofe with n-butonol.
(9)
Figure 2 shows the results, plotted as indicated hy equation (9). The slope is the order of catalysis and t,he intercept t,he logarit,hm of the catalyst coefficient. The catalytic equatioi~ -log ( k - ko) = 0 0305 - 0.7739 log [Cat] R = 0.933 S. = 0.072
where R is the correlation coefficient. and S, the standard error, shows a slope term close enough to uuity to rule out the possihility of mukiple occlusion of isocyanate in the t,ransition state. The catalytic coefficient, li, = 0.932 l/mole-see, is useful for future romparison of other cat,alysts. This method is, of course, subject to low precision of measurement which can he minimized hy t,he rapid accumulation of replicate data aud statistical analysis. In addition, it is best suited for reactions with half lives of no less than 30 seconds and no more t,han three minut,es, to ohviate, respectively, temperat,m.e measurement lag and heat losses. AT should be less than 10°C, the al-erage temperature lying fairly close to ambient for this latter reasor>. As mentioned before, heats of solution and dilution should he neeligihle comuared to
u
2.02.7 0
+ I log [Cat]
2.8
2.9
3.0
-log
3.1
3.2
3.3
3.4
3.5
[Cat]
Rgure 2. Bronated plo* for FeICH&OCHCOCH& cotdysis of ~ h y e n l isocyanate andn-butmol: least quarearlope -; unitrlope,
- - - - -.
Volume 38, Number 2, February 1967
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Acknowledgment
The author wishes to thank Dr. Hans Borchardt of the General E1ect.n~Company for his helpful discussions. Literature Cited ( I ) See WEISSBERGER, A,, editor, "Technique of Organic Chemistry," Val. 1; "Physical Methods, Part 1," 3rd ed., Interscience Publishers, Inc., New York, 1959, p. 634 and references therein.
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( 2 ) EYRAUD, C., Compl. rend., 238, 1511-12 (1954). (3) BORCHARDT, H. J., J. CIIEM.EUUC,,33, 103-7 (1956). (4) KISSINGER, H. E., Anal. Chen~.,29, 1702--6 (1957). (5) BORCHAEDT, H. J., IND DANIELS,F.,J . Am. Chem. Sac., 79, 4 1 4 (1957). S., "Textbook of Physical Chemistry," 2nd ed., (6) GLASSTONE, D. Van Nostrand Co., Inc., New York, 1951, p. 1067. (7) Rubber Abstracts, 1934-2446 (May, 1958). (8) GLASSTONE, S., op. d l . , p. 1136.
