EFFECT OF ULTRASOUND ON CHEIVIICAL REACTION RATE J. W . C H E N AND W A L T E R M. KALBACK1 School of Technology, Southern Illinois Unioersity, Carbondale, Ill.
The effect of ultrasound on hydrolysis of methyl acetate using hydrochloric acid as catalyst was studied in a batch reactor under isothermal condition. The reaction rate increased with increasing sonic amplitude. Varying freqiuency had only negligible effect. Arrhenius plots showed that ultrasonic vibration increased the frequency factor of the rate and that there was no effect on activation energy. Mechanical agitation and concentration of acid catalyst were also studied. There was no evidence that extra hydrogen ions were produced by ultrasonic vibration.
HE effect of ultrasound on chemical reaction rates has Treceived attention in recent years. T h e reactions studied (\\’eissler, 1951) include the iodine clock reaction, reaction betLveen calcium carbonate and hydrochloric acid, oxidation of potassium iodide arid ferrous sulfate. and others. I n all cases reaction rate increased during ultrasonic treatment. As a liquid reaction mixture is subjected to increasing ultrasonic intensity. a point is reached a t which cavitation occurs. This is the formation and violent collapse of millions of microscopic bubbles and results from local temperature and local pressure changes. Among proposed explanations for the increase in reaction rate by ultrasound art increase in mechanical agitation and mixing, rise in local temperatures and pressures because of cavitation. and increase in hydrogen ion concentration by sonic ionization of bvater. T h e present paper is concerned n i t h a systematic study of the effect of ultrasonic vibration on hydrolysis of methyl acetate Jvith hydrochloric acid as catalyst. The reaction rate was increased by increasin’: the ultrasonic intensity, but varying the ultrasonic frequency had no effect. Possible explanations for these results are given.
Kinetics
Acid-catalyzed h) drolysis of methyl acetate is given by the equation CHaCOOCH3
+ H20 + H +
kl’
CHaCOOH
+ C H 3 0 H + H + (A)
This is a typical second-order reversible reaction whose rate equation is:
-ddM/dt where -14 TI’ A E
= = = =
=
kl’iMTI’[H+]
concentra1:ion of concentrai.ion of concentraiion of concentrai ion of
- k*’AE[H+]
(1)
methyl acetate water acetic acid methanol
and kl’ and k?’ are rate constants for the forkyard and back\Yard reactions, respectively. If water is present in such excess that its concentration undergoes a negligible proportional change and if the reverse reaction is negligible, Equation 1 can be simplified to: 1 Present address, Department of Chemical Engineering, University of Colorado, Boulder, (2010.
-dM/dt
=
k1M
(2)
Equation 2 represents a pseudofirst-order reaction and k l = kl’TI’[H+]. I t can be used to study the kinetic behavior of the reaction during the reaction course. T h e apparent rate constant, k l , is a function of catalyst concentration and temperature. By Arrhenius‘ equation kl’
= s
exp(-E,/RT)
(3)
where s is the frequency factor and E , is the activation energy. Substituting Equation 3 into the expression of k l gives kl
=
sll’[H+] exp(-EE,,’RT)
(4)
By this equation, the apparent rate constant, k l , should be directly proportional to hydrogen ion concentration a t constant temperature and sound intensity, and change in k l can then be used to detect ivhether there is formation of hydrogen ion due to ultrasound or not. Experimental
Ultrasound was generated by a General Instrument Corp. ultrasonic generator \\ ith 23-kc. basic frequency and 350watt output. T h e treatment unit consisted of the generator and an ultrasonic tank with magnetostrictive transducers mounted on the bottom. The generator drew the power required from a 60-cycle source and converted it to useful ultrasonic output by alternate contraction and expansion of particular transducers a t their resonant frequencies. By frequency adjustment a t the generator the sound frequency could be varied in a narrow range around the 23-kc. base frequency. By a current adjustment the sound intensity could be varied from 200 to 800 ma., but the signal was too noisy for use above 530 ma. An 800-ml. borosilicate glass reaction vessel was clamped tightly to the base of the ultrasonic tank. The same vessel \vas used for all the experiments, to eliminate the effect of varying vessel wall thickness on sound energy. Constant temperature inside the reaction vessel \vas maintained by circulating xvater through the ultrasonic tank a t a rate about 4.2 liters per minute from an external constant temperature bath, to ensure that the heat generated by ultrasonic vibration was rapidly removed. Reaction temperature inside the vessel was periodically measured during each experiment; it was kept constant within 0.1’ C . IVhen it was needed, agitation was supplied by an electric mixer with a four-blade impeller. The reaction mixture consisted of 500 ml. of HC1 a t a given molarity and 25 ml. of methyl acetate. For analysis, 5 ml. of reaction mixture was titrated with standard sodium hydroxide; the volume required is given as V t a t any specified time t. The titer equivalent to complete hydrolysis is given as Vr. This quantity can be calculated by the following equation :
V,
=
V, * 500,’V,+ (5 X
lOOO/Sp)
VOL. 6
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(25/M,V8) MAY 1967
(5) 175
I * I.&
"T
-
f
5
1
10
3'
7.0
0.9
I
I
I
10
20
3J
I
I
I
I
I
40
50
60
70
BO
TIME M I N .
Figure 1, Effect of sound intensity on chemical reaction rate at 25' C.
P
t
1.2 r
6.0-"
1
1
I
I
0
I
1
'
"
"
'
I
~ 1
1
7.57I IO
I
I
I
I
I
I
20
30
40
50
60
70
TIME
Figure 2.
1
80
MIN.
Experimental data at 35"
C.
/
i
7.0
0
0 MA, 450
I
Figure 3.
I
I
I
I
I
~
I
I
Experimental data at 45" C. Results and Discussion
where V , = total volume of reaction mixture, ml. V , = volume of standard NaOH solution required to neutralize 5 ml. of original HC1 solution, ml. N = normality of standard NaOH solution p = density of methyl acetate, grams per ml. M , = molecular weight of methyl acetate Thus the quantity of unhydrolyzed methyl acetate at time t is given by ( V , - V J . 176
I&EC FUNDAMENTALS
The integrated form of Equation 2 is In M / M o = -kit
(6)
where Mo is the initial methyl acetate concentration and is V') into proportional to VT. Substituting VT and ( V T Equation 6 gives the equation:
-
ln(V,
- VJ
= In V T
- kit
(7)
I.2r
'"1-
g 0.9 -I
, \ 70,
I 50
I
I 30
20
10
40
60
80
TIME MIN.
Figure 6.
Experimental data a t 35" C. and 450 ma.
-3.04r
i
b WITH
AGITAT1ON
-2.94
-2.92
?!WITHOUT AGITATION
20
10
0
50
40
30
60
TIME MIN.
Figure 7. Effect of mechanical agitation on chemical reaction rate
0 and 535 ma. resulted in a n increase in reaction rate, as evidenced by a decrease in slope. Data from a series of runs a t 25' C. and varying ultrasonic intensity, plotted as ki us. power level of sound generator, are given in Figure 4. There was a gradual increase in reaction rate a t low current setting, then a sharp rise a t about 530 ma. However, current setting measured in milliamperes may not indicate total sound energy supplied to the reaction mixture. Calorimetric data were taken for comparison. For this purpose, the reaction mixture was replaced by an equal volume of water, and ultrasonic vibration was applied a t known intensity without water either being fed into or being circulated through the ultrasonic tank. T h e rate of temperature rise was measured and calories of heat evolved per second were calculated. The results are plotted as k l us. calories per second in Figure 5. T h e straight line obtained indicates that the increase of reaction rate has linear relationship with the sound energy input (Barrett and Porter, 1941). T h e effect of varying ultrasonic frequency a t a constant intensity was studied a t 25' C. No effect on reaction rate was noted, This is in agreement with previous findings (Weissler, 1951), since cavitation is not highly sensitive to frequency. T o determine whether increase in reaction rate upon ultrasonic vibration is by the formation of hydrogen ions by ionization of water owing to ultrasound, a series of experiments was performed in 1.0, 0.5, and 0.251V hydrochloric acid a t 35' C . and 450 ma. of ultrasonic intensity. T h e results, shown in Figure 6, show that the apparent rate constants remained proportional to the catalyst concentration, and no increase above proportionality occurred at the lowest concentration. It is therefore unlikely that significant ionization of water occurred under ultrasonic vibration. The effect of agitation in the presence or absence of ultrasound a t 450 ma. is given in Figure 7 . Agitation had no effect on reaction rate under either condition and was not a factor in controlling the kinetic behavior. Kinetic data were taken over the temperature range between 0" and 45' C. From the Arrhenius equation,
0 450 M A .
0
L ' " ' ' 1 I38 3)t
32
Figure 8.
-
33
54
35
36
i7
Arrhenius plot
A plot of ln(VT V , ) us. t should yield a straight line with a negative slope of kl and a n intercept of In V T . T h e slope should be dependent on catalyst concentration, temperature, and ultrasonic effect. Plots of log(VT V,) us. time a t constant catalyst concentration a t 25", 35", and 45" C. are given in Figures 1, 2, and 3. T h e straight-line plots found indicate conformity to pseudofirst-order reaction. Increase in ultrasonic intensity between
-
In k l = -E,/RT
0
4-In S
(8)
a straight line should be obtained when In k l is plotted against 1/T. T h e slope of the line is related to the activation energy of the reaction and the intercept represents an apparent reaction frequency factor. Figure 8 shows that the plots a t no sound and at 450-ma. ultrasound have approximately the same slopes, indicating the same activation energy. The activation energy calculated was equal to 15.6 kcal. per gram-mole, which is in the same order of magnitude of the activation energies for chemical reactions in solution reported in the literature (Frost and Pearson, 1953). The intercepts were different, however. Thus the frequency factor of the rate constant is increased by ultrasonic vibration. T h e possible explanation for these findings is: According to the absolute rate theory, the reaction frequency factor is related to the vibratory motion of the reacting molecules. T h e effect of ultrasound may be to generate a tremendous local pressure gradient during cavitation which, in turn, may increase vibratory motion. Conclusions
T h e reaction rate in acid-catalyzed hydrolysis of methyl acetate between 0" and 45" C. was increased by ultrasoxiic vibration. T h e increase was proportional to ultrasonic inVOL. 6
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197
tensity as determined by calorimetric measurements and was not affected by frequency of the ultrasonic sound. No evidence was found that ultrasonic treatment generates extra hydrogen ions. T h e reaction rate was proportional to concentration of added acid even a t low acid concentrations. Agitation or mixing in the absence us. presence of ultrasound had no effect on reaction rate. Based on the experimental findings in this research, a possible explanation for the increase of reaction rate during ultrasonic treatment is proposed. The reaction frequency factor is sensitive to vibratory motion of the reacting molecules. Tremendous local pressure gradients accompanying the cavitation phenomenon were considered to provide the indicated increase in vibratory motion.
Nomenclature concentration of acetic acid
A
=
E E,
= concentration of methanol = activation energy
= concentration of hydrogen ion [H+l k I t and kz’ = forward and backward rate constants, respectively ki = apparent rate constant = concentration of methyl acetate M
M O M
W
N
= initial concentration of methyl acetate = molecular weight of methyl acetate = =
S
S V.
= = =
VT
= =
Vt
V Z
W
=
P
=
normality of standard N a O H solution frequency factor empirical frequency factor = sW [ H + ] total volume of reaction mixture ml. of standard N a O H solution required to neutralize 5.0 ml. of reaction mixture a t time t titer equivalent to complete hydrolysis ml. of standard N a O H solution required to neutralize 5.0 ml. of original HCl solution concentration of water density of methyl acetate
literature Cited Babikov, O., “Ultrasonics and Its Industrial Applications,” Consultants Bbreau Enterprises, New York, 1960. Barrett, E., Porter, C., J . A m . Chem. Sot. 63, 3434 (1941). Frost, A., Pearson, R., “Kinetics and Mechanism,” Wiley, New York, 1953. Weissler, A., A.I.Ch.E. J . 47, 22 (1951). RECEIVED for review June 23, 1966 ACCEPTEDJanuary 9, 1967 Division of Industrial and Engineering Chemistry, 151st Meeting, ACS, Pittsburgh, Pa., March 1966.
SURFACE CHEMICAL KINETICSAND GAS-PHASE DIFFUSION IN THE GERMANIUM-IODINE R EACT IO M DONALD R. OLANDER Inorganic Materials Research Division, Lawrence Radiation Laboratory and bepartment of Nuclear Engineering, CollPge of Engineering, Unioersity of California, Berkeley, Calif. The reaction of gaseous iodine and a rotating disk of germanium was studied in the temperature range 280” to 460” C. A clear demarcation between reaction-limited and diffusion-limited regions was observed. In the reaction-limited region, the rate was proportional to the square root of the iodine concentration and exhibited an activation energy of 31 kcal. per mole. In the diffusion-limited region, the rate was practically independent of temperature. The slight increase in rate at the highest temperature studied was attributed to the decomposition of Gel4 into Gel2 in the boundary layer.
temperature inorganic reactions in which a gas and a solid combine to form gaseous reaction products have important practical applications. The reaction of uranium tetrafluoride with fluorine to produce volatile uranium hexafluoride is a basic step in the preparation of uranium for isotopic separation in a gaseous diffusion plant (4). The oxidation of the refractory metals, which is used in gas-cooled nuclear reactors and in aircraft engines, are also in this class. Molybdenum, tantalum, niobium, and tungsten all form oxides with melting or boiling points below the melting point of the parent metal. At temperatures where the oxide is volatile, no protective coating of the metal substrate is present to prevent catastrophic corrosion (9). Many of the familiar vapor deposition processes, such as the deposition of titanium from the tetraiodide and of iron from iron carbonyl ( 3 ) ,fall in the same category. Tungsten coating by hydrogen reduction of WF6 has been investigated IGH
(5)* Combinations of gas-solid reactions and diffusional transport are used to grow large germanium single crystals (6). At the 178
IBEC F U N D A M E N T A L S
hot end of a sealed tube, raw germanium is vaporized by reaction with gaseous Geld to produce GeI2, which then diffuses to the cold end of the tube and deposits germanium by decomposition. The transport rate in the iodine system was adequately described by a pure molecular diffusion model, but when bromine was substituted for iodine, some evidence of a surface kinetic restriction was noted. T h e germanium-iodine system was chosen for this kinetic study for several reasons. The principal iodide of germanium is volatile a t reasonably low temperatures, thus facilitating the design of the apparatus. Neither the reactants nor the products are particularly corrosive, eliminating the need for special materials of construction and elaborate safety precautions. The reactants can be obtained in high purity in the desired form and the thermodynamics and important species involved are known.
Thermodynamics of Ge-h System This system has been studied thermodynamically by Lever
(7), whose results we quote here. I n our experiments, the
