Harry B. Mark, Jr. and Ronald A. Greinkel The Un~vers~ty of M ~ c h ~ g a n Ann Arbor, 48104
I
Determination of Carbonyl Mixtures by a Differential Reaction Rate Method A kinetic experiment for the analytical course
This article describes a laboratory experiment for the determination of carhonyl compound mixtures of 3-pentanone and anisaldehyde which illustrates the principles and applications of differential reaction rates to the simultaneous in situ analysis of closely related species. Unknown mixtures in the range 5-95% of either component have been determined with standard deviation of less than 3.3% using a simple recording conductance bridge which requires no elaborate or expensive instrumentation. The experiment which requires the determination of the reaction rate constants of the pure components with the hydroxylamine hydrochloride reagent in two different solvent systems and the determination of an unknown mixture was performed in one 3-hr laboratory period. Principles of Differential Reaction Rate Method
I n recent years, several different differential reaction rate methods for the simultaneous in situ analysis of closely related mixtures have been devised (1-4). Interest in this kinetic approach to analysis arises from the fact that in a practical analysis it is often necesary to determine mixtures of closely related species, such as isomers and homologs. Kinetic based techniques often have advantages over the usual equilibrium or thermodynamic techniques. Equilibrium differentiations or distinctions obtainable for the reaction of such closely related compounds are usually very small and not sufficiently separated to resolve the individual concentrations of the mixture. Thus, actual separation prior to the analysis reaction is usually employed. However, this a ~ ~ r o a is c ha t best laborious and time consuming. and in certain cases, such as the determination of the primary to secolldar~h ~ d r o x groups ~l in the
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' Present address: Research Development ~ Union Carbide Corporation, Parma, Ohio.
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polymer polypropyleneglycol (5),separation is impossible. I n contrast, the kinetic differentiations or distinctions obtained when such compounds are reacted competitively with a common reagent are often quite large and permit simnltancous analysis (6, 7). (Detailed discussions of the principles, applications, and limitations of differential reaction rate methods can be found in references (6) and (7).) The different differential reaction rate methods (1-4) are based on essentially the same principles (6, 7) although each is preferred for certain relative concentra tions of the mixture, relative rate constants of reactants, and/or reaction conditions (7). Thus, one example method is sufficient to illustrate the kinetic approach to the simultaneous in situ analysis of mixtures. The simplest method has been chose* here as an experiment for analytical courses. However, it is recommended that the theory and principles of all methods be discussed in conjunction with this experiment (1-4, 6, 7). For the irreversible bimolecular reactions of a binary mixture, A and B, with a common reagent, R, forming a common product, C, of the type A+R-%C B+R-%C
where kA and ks are the second order reaction rate constants for the reaction of A and B, respectively. The rate of disappearance of R or the rate of appearance of C is given by (3, '7)
+ kslBllRl
dB1 d[C1 -dt = dt = k ~ [ A l l R l
(1 1
where the brackets denote the concentrations of each, species of any time, t, during the reaction, ~f the reaction is run under pseudo firsborder conditions with respect of ~ to~the reagent, t ~ R (i.e., ~ the ~ initial t concentration , the two analyzed species is a t least 30 times greater than
Volume 46, Number 7 2, December 1969
1 869
the concentration of the reagent so that concentration of the reactants, A and B, do not change to any appreciable extent during the course of the reaction) then eqn. (1) can be written as
where k* is a composite rate constant for the mixture which is equal to K*
=
+
k ~ [ A l o ke[Bla
(3
and [Ale and [BIoare the initial concentrations of the reacting species. Thus, by determining the rate of change of the concentration of R or C with respect to time, -d[R]/dt, or d[C]/dt, respectively one obtains a composite pseudo first-order rate constant, K*, which contains the initial concentrations of the unknown mixture plus the second-order rate constants 1 c ~and ke To calculate the two unknown concentrations, two nonparallel simultaneous equations in the form of eqn. (3) are necessary. These can be obtained by altering the reaction conditions such as temperature, pH, catalysts, reagents, viscosity, and reaction media (7, 8). Two equations for the composite rate constant are obtained K*,
=
+ k~,[Blo
k~,[Alo
+
K*. = k~,[Alo ks,LBlo
(4) (5)
The numerical subscripts signify two different reaction media or other different conditions. Initial concentrations of [Ale and [BIo can be found directly from the solutions of the above equations provided that k~~ X lcm Z 1 ~ X~ ke,.' 2 As K* is a composite pseudo first-order rate constant for the mixture, it is easily determined by integration of eqn. (1) under the conditions when t = 0, [R] = [R]o and [C] = 0,to give the exponential form of a first-order rate expression (7) [Rl = [Cl, - [Cl = [ R l ~ e - ~ * $
(6)
By putting eqn. (6) in a logarithmic form, the expression InlR] = In([Cl,
- [CI) =
-K*t
+ InIRIo
(7)
is obtained. Thus, a plot of either ln[R] or ln([C], [C]) (or any parameter proportional to these concentrations) versus time will yield a straight line with a' slope of -K*. The Experimenl The reaction rate of a carbonyl mixture (or pure componeht) as a, function of time is followed continuously by means of a simple direct recording oonductsoee a p p a r a t ~ s . ~ The complete circuit diagram of the instrument, is shown in Figure 1. Basically, the conductance cell, R, serves as the input impedance to the operational amplifier A . The measured output voltage of the operational amplifier is linearly proportional to the conductance of the solution in the cell, as a , , ~ = e,.(Rl/R,) (10). As R. and
Figwe 2. (A) Typicol conductance versus time c L n e for lhe reaction of corbonyl compounds with hydrorylom'ne hydrochIor.de. (81 A plot of tho doto ol IAl os loa-IConouctonce It = - 1 - Cond~ctoncei t = 111 versus . time. The dope is equal to the pseudo firrt-arder rote constont k' of the reaction. ei. are fixed during an experiment, eout = l/R1. (The value of R2may he varied, however, to provide a.suitable sensitivity range of conductance readings.) The input signal, cis is an ao signal of about 0.350 V provided by the powerstat and two filament t,ransformers which are employed simply to attenuate the 115 ac line voltage source. The output, voltage of the operational amplifier which is an ac signal, is rectified to a dc signal by means of t,he diode and t,he simple filter; capacitance C. I n order to obtain a zero base line on the recorder ( a Sargent Model SR recorder was employed in this experiment), s n adjustable bias voltage circuit, composed of the battery B and R8 and Rc is inserted in the output circuit as a bucking voltage. Circular platinum eleetrodes,~mployed in the conductance cell, have an area of 5 cma. The distance hetgveen the two parallel electrodes is 0.75 om. (However, any type or configuration of platinum conductivity electrodes could be employed.) A water-jacketed cell, 150 ml in capacity, is connected to a circulating water bath maintained a t 25.0 =tO.l°C. Stock solutions of hydroxylamine hydrochloride (0.12 g reagent grade hyM )are drdxyla,mine hydrochloride per liter of solution, 2 X prepared using two solvent mixtures (i) 78% MeOH, 22% HZO and (ii) 42% MeOH and 58% H,O ( % b y volume) and placed in the water bath for one hour or more prior to analysis. Seventyfive ml of the 78% MeOH-22% H 2 0reagent and the conductance electrodes are placed into the cell which is equipped with a magnetic stirring motor and a teflon coated magnetic stirring bar. The recorder is started. When a. constant baseline is obtained
2 As the reaction is pseudefirstdrder, with respect to R, only a medium or other cdndition changes which results in a variation of the ratio of rate constants of the two reactions can give the non-redundant equations where the concentrations, [Alo and [B]. are proportional to K* (7, 8). Changing t or [Rlo only leads to two redundant equations (8). As the reaction of carbonyl compound with hydroxylamine hydrochloride results in a net increase in conductsnce which is proportional to the rate of reaction ( g ) , this experimental method of following the course of the reaction was chosen because of the simplicity of the instrumentation. The general ~reaotionis given by
Bawllne Ad,
Figure 1.
870
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Circuit diogrom of the direct recording sonductonce bridge.
lournol of Chemical Educofion
The electrodes were platinized prior to use by placing the electrodes in 100 ml water solution containing 3 g HIPtC1e. 6H20 and 0.03 g PhlO(CHzCOO). and applying the secondary voltage from a 6.3 V filament transformer. The current was passed until s. grey black coating formed. The electrodes were rinsed with distilled water. Prior to plstinieation the electrodes were cleaned in conc HNOa.
(usually aft,er 2 3 min), a sample of pure 3-pentanone is injected into the cell using a one-milliliter hydrodermic syringe. (It is necessary that the needle point be immersed int,o the solution to which disturbs the baseline.) The second-order avoid b~~hhling rate const,ant k*, is calculated from the conductance curve obtained (see Fig. 2A for an example of rate mrve) by plotting the log of t,he conductance change, 1ogIConduotanee ( t = m ) Conductance (t = t)], as a fnnction of time. This plot yields a. pseudo firsborder rate constant k'~, which is the slope of this resulting line (see Fig. ZB) in the manner described above. As this pseudo first-order rate constant is equal to
k'~,
=
k*,[AIo
(8)
the value of k~ is easily calculated as [A]. = 0.126M for 3pentanone. The same procedure is carried out using a one milliliter sample of pure anisaldehyde ([Blo = 0.110M) and ksl is calculated. The values of k ~ and , knl are terms of eqn. (4). scarried out again using the second reaction The same procedure i medium (42% MeOH and 58% K O ) , and k ~ .and kal are calculated. The analysis of the unknown mixture is carried out in the same manner. A 1-ml ssmple of the unknown mixture of 3-pentanone and snisddehyde is injected into the two solvent mixtures and the two resulting condoct,ance curves recorded. The pseudo firstorder rate const,ant,s I. - - - - ,. (5) HANNA,J. G., AND SIGGIA,S., J. Polymer Sci., 56, 297 (1962). (6) MARK,H. B., JR., PAPA, L. J., A N D REILLEY,C. N., in "Advances in Analytical ChemistIy and Instrumentation," V d . 2, (Edilor: REILLEY, C. N.), Interscience Publishers (division of John Wiley & Sons, Inc.), New York, 1963. (7) MARK,H. B., JR.,RECHNITZ, G. A., A N D GREINKE,R. A. "Kinetics in Analytical Chemistry," Interscience Publishers (division of John Wiley & Sons, Inc.) New York, \
106% .7"W.
m- 0
r. -0" ,n a m l a Mealum L%O-HC* *Im)
Figure 3. Second-order rate constanb for 3-pentanone, A, and anisaldehyde, 8, reacting with hydroxylomine hydrochloride a. a function of reoclion medium.
(8) GREINKE,R. A,, A N D MARK,H. B., JR., Anal. Chem., 38, 340 (1966). (9) J. H.. MRK. H. B. JR.. A N D , , PAPA. L. J.. PATTERSON. RE;LLEY, C. N., Anal. h e m . , 35, 1889(1963). (10) REILLEY,C. N., J . CHISM.EDUC.,39, A853 (1962).
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