Undergraduate kinetic experiments would appear to have three major aims: (1) to provide experience in ob- taining and processing kinetic data, (2) to give an idea of the scope and variety of experimental methods which can be used for rate measurements, and (3) to illustrate how kinetic results can provide information about the mecha- nism of a reaction. Frequently however published experi- ments do not achieve all these aims, (3) generally being the one which is neglected.

This report describes an experiment which appears to satisfy all three aims and which in the author's experience works extremely well, either as a formal class experiment or as a project type exercise of longer duration.

Essentially i t involves the measurement of the rate of a reaction by a potentiometric technique, and utilizes the fact that, if the sensing electrode responds to the concen- tration of a reactant and if the reaction is first order (or pseudo first order) in that reactant, then the emf will be linear with time. The electrode used is a bromine elec- trode which is used in a manner based upon that de- scribed by Bell and Ramsden.l

The reactions used are oxidation of formate and oxalate by bromine

R. H. Smith Mocquorie university North Ryde, N.S.W.,

21 13, Australia

HCOO- + Br, + C02 + H' + 2Br-

A Kinetic Experiment Using Potentiometric

Determination of Reactant concentration

I t is very easy to convince students that there are sever- al possible mechanisms for each of these reactions and that all of them look chemically reasonable: for example, for the formate reaction some possible rate determining steps (preceded by the necessary rapid pre-equilibria) are

mechanistically. A pair of kinetically indistinguishable mechanisms can also be included if desired.

In order to simplify kinetic analysis the initial concen- trations of HCOOH, H+, and Br- are made much greater than that of bromine and hence remain essentially con- stant throughout the reaction. Thus a generalized rate law

Rate = ~ [ H C O O H I ' [ H ' ~ [ B ~ - ~ [ B ~ ~

simplifies to

Rate = kn[BrJ"

where k,, the pseudo nth order rate constant, is given by

By determining which function of [BIZ] is linear with time ([Brz], log @rz], l/[Brz] etc.) one can determine n and hence a value for k, from that experiment. Alternatively if all the proposed mechanisms lead to rate laws which are first-order in bromine we can take as our working hypoth- esis that

Rate = kdBr,l

and simply test whether or not this is true. Then by repeating the experimeht with a different (but

still excessive) initial concentration of formic acid and seeing how k , changes as [HCOOH] is altered, a value of a is obtained. Similarly b and c are determined.

The experiment has been used in two different ways: first as a normal class experiment with students working in pairs, in which form it has usually been possible to per-

Br- + HBr + CO* + (1)

'02

By having to derive the rate law implied by each of sever- al proposed mechanisms, students are easily persuaded that a determination of the rate law will lead to elimina- tion of many of the possibilities, and thus before starting the experiment they can see how i t will he of value

Figure 1. The thermostatted reaction vessel. A, Saturated calomel elec-

1 Bell, R. P., and Ramsden, E. N., J. Chem. Soc., 161 (1958). trode: 6, platinum electrode; C, magnetic stirrer; D, thermostatting water

Smith, R. H.,A,ut. J. Chem., 25,2503 (1972). inlet.

Volume 50, Number 6, June 7973 / 441

form the minimum number of experiments (usually 4-6) to distinguish between the four mechanisms just de- scribed in about 6-9 hr (including time for processing re- sults), providing stock solutions of the reagents are avail- able. Formate was the only reductant used in this form of the experiment.

Secondly the experiment has been used i n a more ex- tended form a s a "project" of about 25 hr duration for pairs of students: both oxalate and formate have been used a s the reductant i n this form. Such pairs of students (formate t o one pair, oxalate t o the other) have been able to establish the rate laws more thoroughly in this time and for the formate reaction (which is considerably sim- pler t o study) the activation energy bas also been mea- sured (using three temperatures). T h e fact t ha t these ap- parently similar reactions have different rate laws2 has been the cause of keen competition between pairs of stu- dents (who assume the reactions have analogous rate laws) as they try t o prove the correctness of their particu- lar rate laws.

Since the time to perform the actual kinetic experiment is not great (10-20 min), one set of apparatus per pair of students is adequate.

Experimental

The apparatus, shown in Figure 1, consists of a thermostatted reaction vessel sitting upon a magnetic stirrer. The vessel is made with a B55 standard socket at the top into which fits the lid (made from a B55 cone) whieh carries a platinum wire electrode and a commercial saturated calomel electrode (electrical cannec- tion via a sintered glass plug).

The vessel used for the oxalate reaction is painted black to ea- clude light completely: for formate a transparent vessel is used since the normal levels of laboratory light do not affect the rate. The formate reaction is thus much better for a normal student experiment since the student can see what is occurring.

The platinum electrode needs occasional cleaning. This is most simolv done bv heatine the wire to red heat for about a minute at the'bknnine-of eachhav of the exoeriment. The reaction mix- ture nnmt bestirred at a un~f<rrm genrlc rate throughout.

'fhc ronvrntiunal d~agram rtprcsentlng the gel\nnir cell set up hy this exprrinwnr is ahvwn in Flgurc 2. and , t i e m / E rs thus given by

If bromide concentration is sufficiently large so that it changes negligibly during an experiment, then we can write

RT E = constant + ln[Br,]

In addition, if the reaction is pseudo first-order, then, as will be shown below

IdBr,] = constant - k,t ( 5)

so that E is linear with time and k, can he calculated from the slope

Figure 2. Wiring diagram for measuring emf. V.T.V.M. is vacuum tube volt meter.

Under typical conditions ([BIZ], = 1 to 5 X 10-8 M, P r - ] = 0.020 to 0.50 M) E has a value of approximately 0.8 V, and for consumption of 90% of the initial bromine, E changes by 29.5 mV. In order to measure this change sufficiently accurately (*0.3 mV), the emf of the cell is opposed by a constant (though adjust- able) potential and the difference hetween the two (adjusted ini- tially to he less than 100 mV) is measured on a vacuum tube voltmeter as shown in Figure 2. Occasionally a digital voltmeter has been used with equal success. It is found most accurate to note the time (on a stopwatch) at whieh the needle of the meter passes over each 1 mV graduation. Readings are continued until the total change in emf exceeds 30 mV. The constant potential is obtained from a pair of alkaline dry cells across a 1 kohm potenti- ometer.

For the formic acid reaction a convenient set of stack solutions to provide is [BPS] = 0.030 M, [HCOOH] = 0.40 M, [HCl] = 2.0 M, [NaBr] = 1.0 M, and a suitable set of conditions for the first experiment (giving a half life of nearly 4 min at 298'K) is [Brr] = 0.0030 M, [HCOOH] = 0.10 M, [HtJ = 0.10 M, [Brr] = 0.10 M. The experiment is performed by diluting appropriate volumes of HCOOH and HCI to 50 ml in one volumetric flask and pouring this into the reaction vessel to equilibrate, then by diluting bro- mine and bromide in a second volumetric flask and equilibrating thls in the water bath. Finally this solution is rapidly poured into the reaction vessel, the watch started, potentiometer adjusted, and readings taken: readings can usually be commenced within 30-50 see after mixing. E is plotted against time and the linearity of the d o t establishes the order in bromine. Order in the other reactants is then determined by halving and/or doubling each [HCOOH], [H+], [Br-] in turn and repeating the experiment.

For the oxalate reaction a convenient set of initial conditions (giving a half life of 5 min at 298'K) is [Brz] = 0.0030 M, [ H C d - ] = 0.080 M. [CzOi-] = 0.020 M, [Br-] = 0.075 M (using 0.50 M a s stock bromide solution). Oxalate, hydrogen oxa- late mixtures are made by addingHC1 to K2C2O4 solution^.

Results and Discussion

The use of a relatively high bromide concentration ( to simplify interpretation of emf data) means t ha t tribrom- ide formation

Br, + B F 4 Br,-

must be considered. Hence

[Brpla = [Br21(1 + K,[Br-1) (7)

where [Brz], is total analytical concentration of hromine ([BIZ] + [Br3-] in acid solution) and where Kt i s the for- mation constant for tribromide.

In terms of hromine the rate of reaction is expressed a s -d[Br~],/dt in order to be equal to the other expressions for rate of reaction, which for the formic acid reaction are -d[HCOOH]/dt and d[COz]/dt. Since the simple mecha-

I I I I *u 'm 8W

TIME (eec)

Figure 3. Experimental curves (obtained by students) for the farmate. bromine reaction at 298% [Brr]., = 0.0030 M. [Br-] = 0.100 M. a. [HCOOH] = 0.200 M. [H+J = 0.100 M; b, [HCOOH] = 0.100 M, [H+] = 0.100 M; c, [HCOOH] = 0.100 M. [H+] = 0.200M.

442 /Journal of Chemical Education

nisms that we can write (e.g., (1)-(4) above) imply that the reaction is first order in molecular bromine, we can postulate that the rate law is

where f is some function (depending upon which is the correct mechanism) of [HCOOH], [Hf], [Br-1. This equa- tion cannot be integrated until the same variable appears on both sides: thus eqn. (7) is used to convert it to

By writing k, for f / ( l + KJ3-1) and integrating we ob- tain eqn. (5) ahove. Even mechanisms (1) and (2) imply that the pseudo first-order rate constant, k,, shows some dependence upon bromide concentration.

Experimental emf versus time curves are convincingly linear as the typical examples presented in Figure 3 clear- ly show. This linearity confirms that the reaction is in- deed pseudo first-order.

Student Results for Bromine Oxidation of Formate

[Bml.. = 0.0030M; temperature, 298'K.

The table presents k, values obtained by one pair of students working for two 3-hr sessions and spending a third session processing data and preparing a report. They confirm the rate law

and give kl = (7.8 i 0.6) x lo-?-' a t 298°K. This value agrees reasonably well with the most recent literature value,2 (7.5 i: 0.2) X 10-3s-1. While three bromide con- centrations may not really he enough to establish the ahove dependence exactly, they are sufficient to distin- guish between that dependence and the only other one emerging from the proposed mechanisms, namely rate in- versely proportional to [Br-] (1 + K,[Br-]).

Figures 4 and 5 show results for bromide dependence for the formate and oxalate reactions obtained by pairs of students performing the experiments as more prolonged project type exercises (about 25 hr each): they quite clear- ly demonstrate the different bromide dependencies. For the oxalate reaction the complete rate law is

with kz = 0.015 s-1 a t ionic strength 0.50 M and 0.019 s-1 a t 0.20 M2, both a t 29S°K. The student value of kz is in reasonable agreement with this, particularly considering that kz (unlike kl) is dependent upon ionic strength.

Instructions for Students

Rather than detail the necessary theory for students, a set of instructions and questions is provided with the aim of leading the students towards the necessary equations, etc. First the student is asked to derive the rate law im- plied by each of several proposed mechanisms, then to calculate for a given set of initial conditions the percent- age change in [H+], [HCOOH], and P I - ] as the reaction goes to completion and thus to establish that they remain

- ar 0.e

CBfl Figure 4. Student results showing the dependence of the pseudo first- order rate constant. k,, upon [Br-] for the formate, bromine reaction at 298°K. [HCOOH] = [H+] = 0.100 M. This clearly demonstrates the validity of eqn. (8) and the intercept gives k , = 0.0077 s-'.

Figure 5. Student results showing the dependence of the pseudo first order rate constant, kg, upon [ B r ] for the axalate. bromine reaction at 298'K. [Cz012-] = 0.020 M. [HC204-1 = 0.080 M. This demonstrates the validity of eqn. (91 and the intercept bives k l = 0.020 s-'.

approximately constant. The next group of questions leads to the derivation of eqns. (5) and (61, followed by calcula- tion of the initial emf of the cell and of the change in emf for 90% reaction: this establishes the precision required in measuring changes in emf.

A complete account of the experimental procedure is then given for performing the experiment once. Students are then instructed to design and perform the subsequent experiments.

Conclusion

Students usually obtain good results with this experi- ment and even when weaker students make a poor job of their first attempt, i t only takes 30-40 min to repeat the run and this is usually much more successful. The experi- ment virtually minimizes the amount of data processing associated with a kinetics experiment and thus allows the emphasis to be placed upon determination of the com- plete rate law and upon selection of a mechanism. It has been used at Macquarie University for three successive years now and really does seem to he giving students in- sight into the interrelation of kinetics and mechanism.

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