David B. Greenberg1
Engineering Department United Stotes Naval Academy Annapolis, Maryland
Reaction Kinetics from Conductivity Data An apparatus for the student laboratory
In this paper a conductivity experiment in chemical reaction kinetics is described using an indicating type electrical instrument of simple circuit design. A set of calibration curves provides readings in terms of either solution resistance or concentration. The instrument is of sufficient versatility to be adaptable for both introduct,ory and physical chemistry courses. Conductrimetric methods for chemical kinetic studies have been well documented in the past (2,5 , 6, 9). In general, however, instrumentation requirements for such work are too complicated and expensive for consideration in an undergraduate chemist,ry program. Therefore an instrument was sought which would be relatively easy to assemble and operate, and readily calibrated to facilitate data reduction, so that a single laborat,ory period could serve for the whole experiment. To meet these requirements an adaptation of a voltage multiplying rectifier rircuit has been devised and successfully tested.
For a circuit of this nature it can be shown that the dc meter voltage, =
R, (RXX)E1
(1)
If S, the instrument sensitivity, is defined as the change
Figure 1. A circuit diagrom of the conductivity measuring in~rument. Part. Lirh
The
Inslrument
The instrument is composed of two basic component circnits, an ac conductivity cell circuit in parallel with a dc meter circuit. I n the cell circuit the cell (solution) resistance R. and a fixed control resistance R1 are in series with the 60 cycle ac power supply as shown in Figure 1. In the meter circuit, the multiplied ac cell voltage is rectified and displayed on the linear scale of a dc microammeter. Therefore, the output voltage Em, proportional to the voltage drop across the cell, provides a means of tracking the conductance changes within a reacting solution. Negligible current will be drawn by the meter provided that R,, the meter resistance, is large compared to both R,and R.. The circuit, a half wave vokage doubler (a), operates in the following manner. During the first negative half cycle of t,he voltage input, capacitor C1 is charged through rectifier 1 to the voltage El with the polarity as indicated. In the next positive half cycle this capacitor voltage and the source voltage add to charge capacitor C2 through rectifier 2. Capacitor C1 is discharged by a like amount a t the same time, its charge being restored during the following negative half cycle. As the process is continued, the charge added to C2from C1 is diminished until finally the charge on C2 approaches twice the peak value of El.
' Present address: Dept. of Chemical Engineering, Louisiana State University, Baton Rouge, La. 140
/
Journol o f Chemicol Educafion
1 1 2 2 1 1 1
6 K ohm, 1 w a n resistor, (RiL
R,1.
90K ohm, 1 wall resistor, 0.1 microfarad paper wound copocitars (C,,C J . crystal diodes, such ar Raytheon type i N 3 8 . variable outo-transformer, 1 amp., 0 - 1 4 0 volt output, such or Pawerstat type 2 PQ 10. dc microommeter, 2 0 0 microomp. movement, 3-31f2-in. dial, such or Simpron model 25-27. ac voltmeter, 0 - 1 5 0 v range, such or Simpron model 55-57. Hookup wire, mounting lugs, connectors, power card, and an 84". X 1 O-in. Moronite board.
in meter reading with respect to the fractional change in cell resistance, then
dE, R.
Therefore an expression for sensitivity in terms of resistance becomes:
An inspection of Figure 2 indicates that the instrument sensitivity is a maximum when the value of R, equals R,,and falls off relatively rapidly for either very small or very large values of R.. Although this imposes a serious limitation on the range of conductivity measurements for a particular value of resistance RE, the instrument is of sufficient accuracy to yield quantitative results for conductivity experiments where the 3 times value of R, varies within the range of about the value of R1.
Since the choice of an optimum value of R1 depends on the actual solution resistance, some experimentation is necessary in order to determine approximate initial and terminal values of R, for a particular conductivity study. R1may then be taken as a mean between these limits. The input voltage El should be chosen to yield a nearly full scale meter deflection a t this approximate maximum value of R,. Values of El above about 60 volts ac are to be avoided however, for the power dissipation requirements of the solution and the associated heating effects become excessive. A 3-in. diameter dc meter with a 200 microampere movement and a sensitivity of about 1000 ohms per volt will be more than adequate as a read-out meter. Generally, such meters have 50 to 75 dial divisions and offer an accuracy of better than 5% of the full scale reading. The value of R,, the meter resistance, is not critical but should be about 10 to 15 times the maximum value of R..
Each plate is silver-soldered to one end of a 6-in. length of No. 14 copper wire. The wires, mounted through holes drilled into a No. 10'/r rubber stopper, are positioned so that each electrode plate edge is about in. from the bottom when the stopper is firmly placed in a 100-ml Pyrex beaker. A short length of glass rod, cemeuted to the wires just above the electrodes, acts as a brace to prevent accidental changing of the electrode geometry. A thermometer (-15°C to +50°C) and a small glass funnel are also mounted in holes drilled through the stopper. Both wires, the soldered faces of the electrodes, and the bottom of the stopper are insulated by means of an epoxy resin, commercially available in paste form. The cell constant has been determined to be 1.28 using a standardized 0.01000M KC1 solution. The Reaction
A reaction was sought which would be sufficiently swift so that a number of determinations could be made in a single laboratory period, yet slow enough to enable the student to obtain quantitative results from his data. A reaction which meets these requirements is the decomposition of acetic anhydride in a hydroxylic solvent. The reaction is quite rapid in pure water, whereas in a less polar solvent, for example in alcohol, the rate decreases more than one hundred fold. Therefore, a small quantity of alcohol added to the reactant will retard the rate to a practical level as well as promote complete dissolution of the anhydride i r ~water. Acetic anhydride decomposes in water according to the following overall reaction: (CH,CO),O
i
0
i
I
1 1 1111
I
LOR,
O.IR,
CELL RESISTANCE. R,
I
I I i i I I IOR,
, OHUS
Figure 2. A plat of t h e relative instrument sensitivity versus cell resistance in terms of the control resistance R,.
For the rate of reaction experiment t o be described below the working values of R. have been established as 11K ohms and 0.5K ohms respectively. Therefore a one-watt 6Kohm resistor will suffice for R1, and 90K ohms for R,. Since the current and power requirements of the circuit are low, selenium rectifiers, crystal diodes, or vacuum tube diodes may be used with equal facility. Capacitance values for C1 and C2 are about 0.1 microfarads. Larger values tend to increase the time constant of the circuit which results in an overdamping of the meter, while values much lower will cause excessive pointer vibration from the rectified ripple voltage. Ei, the voltage input t o the instrument, should be controlled by a variable auto-transformer or divider circuit (see any standard electronics text) if the 60 cycle, 110 volt ac supply t o the laboratory cannot he monitored. I n this case a transformer has been used. These components are most conveniently mounted on an 8-in. X 10-in. piece of masonite or plywood as illustrated in Figure 3.
+ H20
-
2CHsCOOH
(4)
The acetic acid formed immediately undergoes an ionization st,ep CHICOOH
+ H 2 0 = C H S O O - + HaO+
(5)
The hydronium ion thus produced bccomes the primary contributor to electrical conductivity in the solution. Therefore, the progress of the reaction can be followed by observing the conductance change of the solution due to the increase in the [H,O+]. I t has been suggested that the rat,e controlling step involves the
The Electrode Assembly
The electrodes consist of pieces of sheet platinum 0.010 in. thick and approximately 0.40 cm' in area.
Figure 3. A photograph of the instrument and ossocioted equipment.
Volume 39, Number 3, Morch 1962
/
141
severance of a carbon-oxygen bond in the anhydride molecule, followed by rapid combination with the hydroxylic solvent (4, 5, 9). The reaction mechanism is thus represented as: HlO (CHaC0)zO +CHaCOOslow CH&OO-
+ CHaCO+ + H1O
-
+ CHICO+
fast
ZCHSOOH
(6)
To determine the initial solution resistance Ro a plot of R. versus time must be extrapolated back to zero time. I t often will be found however, that Ro is much greater than R m , hence equation (18) can be further modified under these circumstances, eliminating R~entirely,to yield
(7)
If the [H,O] is maintained large compared to the anhydride concentration, to be written as [Ac20], then the reaction approaches first order with respect to the [AcZO]. Therefore, the rate equation becomes:
where k is the first order rate constant. Integrating between the limits, initial anhydride concentration [AcpOIoat time zero, and [Ac20]at any time later,
Since the solution resistance R, is a function of the hydronium ion concentration,
Here Ro represents the initial solution resistance and +, a constant, is a function of the ionic mobilities. From equation (5) the ionization constant for acetic acid is approximately:
From equation (18) or (19) the student may obtain the rate constant k as the absolute value of the slope of the straight line plot of the left member versus time. For the sophisticated student with some background in physical chemistry, the foregoing analysis offers little more than a routine challenge. He should be able to handle the normal laboratory techniques and the mathematical interpretation with a minimum of direction. I n the course of a laboratory period such a student can make a number of determinations to study the effect of such parameters as initial anhydride concentration and temperature on the rate of reaction. From these latter runs, a graph of the Arrhenius equation would be used to evaluate the activation energy. On the other hand, for a beginning student whose knowledge of physical chemistry and whose mathematical acumen is limited, such an approach might foster more confusion than insight. Therefore, in order for this student to derive the maximum benefit from the experiment, an instrument calibrated t o read concentration values directly (Fig. 4) would be more suitable. I n this case, however, the integrated rate expression, equation (9), would be employed to determine the rate constant:
Solving equation (11) for [H30+]and substituting back in equation (10)
From equation (4) : [AcOH] = 2 [[AsOl0 - [Ar20]I
(13)
Therefore equation (12) may be rewritten as
The terminal resistance of the solut,ionR ,is
The constant 4 may be eliminated between equations (14) and (15),
Solving equation (16) for the concentration terms Figure 4. Calibration curves of acetic acid concentration as o fundion of meter reading far on input voltage of 50 v ac.
Therefore the rate equation in terms of resistances may be obtained by subst,ituting for the concentration from equation (14) back into equation (9) and rearranging.
Insfrumenf Calibration
Where
In order to calibrate the instrument in terms of concentration, it is first necessary t o establish a graph of temperature versus meter reading for a series of
142
B = [(R,/R=)-112
1 Journal of Chemical Education
standardized acetic acid solutions ranging in composition from about 1.000 M to 0.005 M. Approximately 100 ml of each solution is required. To exactly 50 ml of each acetic acid sampl? add 1.00 ml of absolute alcohol. This quantity of alcohol, which aids the dissolution of the anhydride in water a t the onset of the reaction, will require that a concentration correction be made for each sample. Using a water bath to adjust the solution temperatures (ice water a t the lower temperatures), obtain meter readings at about 8'C intervals from 10 to 50°C for all of the solutions. It would be best to check each reading twice, once as the solution temperature rises, and again as it descends through each temperature point. Swirl the solutions gently as the readings are taken to be sure that thermal equilibrium has been established. From the data a series of constant composition curves are prepared of temperature versus meter reading. Draw smooth curves through the plotted points. Using t,he data of this primary graph, the concent,ration-meter reading calibration is constructed as a crossplot of the data for temperature intervals of 5'C, as indicated in Figure 4. From this graph and equation (13), the experimental data are converted to read in terms of anhydride concentrations for use with the integrated rate expression, equation (9). Subsequent calibrations for a number of instruments are prepared using this data as a reference. The only other information required is an accurate determination of the cell constant for each instrument. Thus, from the relationship
The last column indicates the length of time for which each reaction was followed. Table 1:
Run no.
AGO (ml)
A Typical Set of Runs
[Ae201 (moles/ liter)
HzO (ml)
Temp. avg. ("C)
Time (min)
Results
Values of the reaction rate constant can he determined graphically using either equation (9) or (19). The plotted experimental data are shown in Figure 5.
(where R is the solution resistance, K is the ccll constant, and subscripts u and c represent the uncalibrated and calihratedi nstruments, respectively) additional calibrations can be determined. The Experiment
When the bath and solvent have been adjusted to the desired temperature, 1.00 ml of absolute alcohol is added to a measured quantity of anhydride in a 100-ml beaker. With the electrodes firmly in place and the whole assembly supported by the ringstand, the beaker (cell) is submerged in the bath about half way. Then a pre-determined amount of distilled water is added to the reactant through the funnel. Commence timing when about half of the solvent has been charged. Temperatures and meter readings should be taken at 30second intervals or oftener for the first two minutes and every minute or two thereafter. Temperature control can be maintained to within a few tenths of a degree by raising or lowering the beaker and periodically swirling the solution. The reaction should be followed until about 15 readings have been recorded, or for approximately 10 to 20 min. depending on the reaction temperature. Since the reaction will be incomplete a t this time, set the solution aside for an additional 45 min. before obtaining a terminal reading. In Table 1 are shown five typical runs that were performed in a single laboratory period; these runs may he used as a guide for the design of other experiments. I n all cases the total reactant volume was 51.0 ml.
TIME,
MIN.
Figure 5. A sample plot of experimental data for the determination of the rate constant urine equation (9).
These calculated k's are compared with the experimental values of Banks, et al., (1) in Table 2, for the decomposition of acetic anhydride in aqueous solution. As can be seen, the overall agreement between the computed k values for this report are well within experimental tolerances. Those obtained from equation (15) average about 6% greater than the k's from equation (6). Therefore, the assumption that the ratio R = / R o is negligible, made in the derivation of Table 2:
Run no.
Temp. avg. ('C)
A Comparison of the Resulfs k Calculated (min.-1) Em. ( 9 ) Em. (19)
k Lit.* (min-1)
Volume 39, Number 3, March 1962
1 143
equation (Is), appears justified. Literature values on the other hand are generally 10% to 15% larger in most cases. This is to be expected however, for in the runs presented here, the introduction of a small quantity of alcohol with the reactant would tend to reduce the reaction rate by a measurable amount. The activation energy for the reaction is 11,400 cal/mole as calculated from the slope of the Arrhenius plot (In k versus l/T). This compares favorably with the values obtained by Wilhelm and Cleland ( l o ) ,and Banks, et al. (1). . Although the conductivity measuring instrument described in this paper has been designed primarily for the decomposition of acetic anhydride reaction, it can with suitable modification be used t o follow many other reactions of this general nature. Two other reactions well adapted to this method are the saponification of ct,hyl acetate (3) and the hydrolysis of tertiary bulyl chloride (3). Acknowledgment
The author wishes to express his appreciation to
144
/
Journal of Chemical Educofion
Professors Neustadt and Leydorf of the Science Department of the U. S. Naval Academy for their help with the circuitry. Literature Cited (1) BANKS,E. N., ET AL.,Can. J . Res., 28B, 669 (1950). (2) CAESICK,J. P. AND PATTERSON,A,, JR.,J. CHEM.EDUC., 37,242 (1960). (3) DANIELS,3. M., ET AL., "Experimental Physical Chemistry," 5th ed., McGraw-Hill Book Co., Inc., New York, 1956, p. 130. (4)GOLD,V., AND JEFFERSON,E. O., J . c h m . Soc., 1409, 1416 (1953). ( 5 ) HINE, J., "Physieal Organic Chemistry," McGrmv-Hill Book Co., Inc., New York, 1956, p. 301. (6) MAEON,S. F., AND LAMER,J., J . Am. Chem. Soc., 61, 692 (1939). M., J . C h a . Soc., 101, 1708 (7) ORTON,K.J . P. AND JONES, 11912). (8) h he ~ a d i oAmatuer's Handbook," 1946 ed., The American Radio Relay League, West Hartford, Conn., 1946, p. 183. (9) RIVEIT, A. C. D. AND SIDGWICK,N. V., J . Chern. Soc., 97,732 (1910). F. A., A. I. Ch. E. Jow., (10) WILAELM, R. H. AND CLELAND, 2,403 (1956).
