Znd. Eng. Chem. Res. 1993,32, 594-599
594
Adiabatic Kinetic Studies of the Cytidine/Acetic Anhydride Reaction by Utilizing Temperature versus Time Data Joseph J o h n Shatynskit a n d D e r a n Hanesian* New Jersey Institute of Technology, Newark, New Jersey 07102
It is possible to predict the kinetics of a reaction by using temperature versus time data under adiabatic conditions. This method was used for the cytidine/acetic anhydride batch reaction using a Mettler RC1 reaction calorimeter. The authenticity of the experimental adiabatic system was verified by determining the kinetic parameters of a known reaction (hydrolysis of acetic anhydride) and comparing them to literature values. The cytidine/acetic anhydride reaction (unknown system) was subjected to the same adiabatic analysis, and the average experimental activation energy, heat of reaction, and In ko values were 13.3 f 0.2 kcal/g-mol, -10.5 f 0.1 kcal/g-mol, and 15.68 f 0.34 L/(g-molos), respectively. T o further verify the results for the unknown system, three isothermal runs were executed and samples were analyzed for concentration by high-pressure liquid chromatography (HPLC). The concentration-time data were analyzed, and an Arrhenius plot was constructed yielding an activation energy of 13.2 kcal/g-mol and a In ko value of 15.14 L/(g-mol-s). These isothermal runs agreed very well with the data obtained from the adiabatic runs. The reaction was second order. Introduction Temperature versus time curves of exothermic reactions are used instead of concentration versus time data to determine the order of reaction, the Arrhenius preexponential constant, and the activationenergy of two reactions under adiabatic conditions. The heat of reaction was also determined for each reaction. The first reaction is the hydrolysis of acetic anhydride (a known system) which is pseudo-first-orderunder given reaction conditions of excess water. readbn 1: hydrolysisd acetic anhydride
0
II
CHSC
>O
+
H20
CHIC
-
PCHSCOOH
II
0
The second reaction involves cytidine and acetic anhydride in N-methyl-2-pyrrolidone (NMP)to produce N-acetylcytidine (an unknown system): readion2: cytidine acetic anhydride
OH\“
“OH
cytidine MW243.2 ?HAC
MW 285.3 +
Current address: Hoffman La Roche, Nutley, N J 07110.
The latter reaction, similar to the formation of acetanilide from aniline, is used in the pharmaceutical industry to produce needed intermediates. Although concentration versus time analysis is not necessary for these kinetic studies, the integral method of analysis with concentration data will be usedfor the cytidinelaceticanhydride reaction system to further validate the results of this research. Theory of Homogeneous Reactions The rate at which the reaction proceeds at constant volume is expressed as the change in concentration of a reactant per unit time. There are many theories attempting to explain how chemical reactions occur. King (1964)states that molecules in liquid solutionsare in a constant state of motion. He describes the solution as numerous cages composed of many solvent molecules and particular molecule(s) of a reactant, “Holes” in the liquid exist and are large enough to accommodate a molecule. As the hole is filled by an adjacent molecule, it is observed that both the molecule and the hole physically move. This type of random motion occurs throughout the batch and describes diffusion in liquids. The homogeneous reactions cannot proceed faster than the rate at which the reactant molecules diffuse into the same “solvent cage”. Typically, the rates of reaction are considerably lower than the frequency of the reactant molecules diffusing into each other. The fact that not all collisionsof reactants result in a reaction is explained by the insufficient activation energy that those reactants possess. King summarizes by stating “During an encounter, the state in which reactant molecules are caged together, the bouncing of solvent molecules against the trapped reactants may or may not provide activation energy for the reaction to occur.* Morrison and Boyd (1983)describe reaction rate theory in slightly different terms. They state that in order for a chemical reaction to occur, the collisions must be of sufficient energy (Eact)and the right orientation. The orientation during collision is particularly important in the case of a relatively large molecule like cytidine. Activation energy is defined as the minimum energy required by a collision so that a reaction may occur. The
0888-588519312632-0594$04.00/0 0 1993 American Chemical Society
Ind. Eng. Chem. Res., Vol. 32, No. 4, 1993 595 moving molecules provide the activation energy in the form of kinetic energy. The rate of a reaction can be represented by the following equation: rate = (collision frequency)(probability factor) (energy factor) rate = (z)(P)(e-Ead/"T) (1) The collision frequency, 2,depends on the concentration of the reactants, the system pressure, and the size of the particles and how fast they are moving. The probability factor, P, depends on the geometry of the particles and orientation at collision. The energy factor has the most pronounced effect on the reaction rate. It depends on the temperature and the activation energy. The term e-E=tIRT is the fraction of collisions that possess energy greater than Eact. From the previous equations, a small change in Ea&will greatly affect the reaction rate (i.e., the fraction of collisions with the necessary energy for a reaction to occur). Also, an increase in temperature will increase the kinetic energy of the particles and hence increase the collision frequency. Engineering texts (Fogler, 1986; Levenspiel, 1972) represent the rate equation empirically as:
for a bimolecular reaction A
heat generated = heat absorbed by reactor contents + heat transferred through reactor walls
(-mrxn)(-rA)v dt + Qstirrer dt = mcp d T + UA(AT, dt (5)
For an adiabatic system, no heat is transferred through the reactor walls. Also, the heat emitted by the stirrer in this study was negligible. Hence,
Separating variables gives (7)
-
For a second-order reaction of the cvtidinelacetic anhydride type (A B C D)
+
+
The material balance can be represented by
+ B, with
CBO - C B = CAO - CA The reaction rate constant is independent of the concentration of thereactanta. It depends on temperature and can also vary with different solvents and pressures.
Kinetics from Temperature vs Time Data It is well-known that the reaction rate rises with a temperature increase. The rate of temperature rise can be represented as the slope of the temperature vs time curve. A few studies were executed in the past to predict the kinetics of a reaction utilizing temperature vs time curves. Williams (1974) determined the kinetics and stoichiometry of the reaction between hydrogen peroxide and sodium thiosulfate. An adiabatic reactor was used with a thermocouple and strip-chart recorder. Glasser and Williams (1971) determined the kinetic parameters of the hydrolysis of acetic anhydride in dilute aqueous solutions. A vessel was placed in a constant-temperature bath, and the heat loss from the reactor was described mathematically. A thermistor was used for temperature readings. King and Glasser (1965) studied the kinetic parameters of the hydrolysis of acetic anhydride in dilute solutions. An adiabatic reactor was used in the experiments. The walls of the reactor were kept at the same temperature as the fluid by passing a high current through the reactor's walls. Temperature readings were taken by the use of thermocouples. Determining the Kinetic Parameters from the Energy and Mass Balances for an Adiabatic System For a constant-volume batch reactor,
Combining eqs 7, 9, 10, and 11,
In an adiabatic system, the conservation of energy dictates that the total temperature change be related to the initial concentration of reactant A for complete conversion by mcp(Tf- To)= -AH,,CAOV
(13)
Inserting eq 14 into eq 12 and multiplying both sides by
(Tf- To)/CAo
(15)
gives cBO
1
ddtT = ~ ~ ~ T f - T o ~ - ~ TA'-0 T o ) l [ - ( T f - T o ) - ( ~ - ~ o
where (4)
The energy balance can be established as
CB = CBO - (CAO - CAI
01
= kCAd(Tf- To)
(17)
For equimolar reactant concentrations (Le., CAO= CBO)
596 Ind. Eng. Chem.
Res., Vol. 32, No. 4, 1993
d T = a ( T f - T)(Tf- T ) dt
-
=a(Tf- T)'
Hence
-
For a first-order reaction (A B),an analysis similar to the second-order case produces the following result dT/dt = k(Tf- T) = ko(Tf- T)e-E d R T
ln(-) dT/dt = I n k - - Eact Tf-T RT
(20) (21)
Objective The purpose of this experiment is to determine the kinetic parameters of the industrially important cytidine and acetic anhydride reaction in NMP by utilizing temperature vs time data under adiabatic conditions. The reliability of the equipment and method used in this study will be proven by comparing accepted literature values and the data obtained by the temperature versus time method described above for the known hydrolysis of acetic anhydride. Additionally, the integral method of analysis method using concentration data of the cytidine/ aceticanhydride reaction w i l l be applied to further support the experimental results. Experimental Section Chemicals Used. During the hydrolysis of acetic anhydride reaction, cerified American Chemical Society (ACS) grade acetic anhydride and deionized water were used. The materials used for thecytidine/aceticanhydride reaction were acetic anhydride (ACS grade) (Fisher Scientific), cytidine (99.7 % assay) (Somitomo), and N-methyl-2-pyrrolidone (NMP) (USP grade) (GAF). The solvents used for the high-performance liquid chromatography analysis of the latter reaction included acetonitrile (HPLC grade) (Fisher Scientific) and water (HPLC grade) (Fisher Scientific). Procedures. The details of all the experimental procedures for all experiments are listed in Shatynski (1991). The major divisions include AHm. of acetic anhydride/water, adiabatic studies of acetic anhydride/ water, AH- of cytidine/aceticanhydride,adiabatic studies of cytidine/acetic anhydride, AHH,i, of acetic anhydride/ NMP, and isothermal concentration studies of cytidine/ acetic anhydride. Equipment. Mettler Model RCl (Reaction Calorimeter). The RC1 reaction calorimeter is a computercontrolled 2-L, glass, batch reactor designed for isothermal and adiabatic operating conditions. The Mettler Model RC1 thermostat is shown as Figure 1,and details are given in Table I. During the experiments, process data were stored on a diskette at 10-s intervals. The following information was extracted from the Mettler RC1 manual (1987).
,a Figure 1. The Mettler Model RCl thermostat. Table I. Mettler Model RCI Thermostat Description 1. housing 2. cooling oil container (capacity ea. 5 L) 3. pump motor 4. displacement body 5. pump impellers of the heated circulation 6. pump impellers in cooling oil container I. connection for electrical heating 8. stepper-motor regulated control valve 9. level sensors for detection of the oil level 10. PtlW cooling oil temperature, T, 11. PtlW jacket temperature, T, 12. PtlW T, safety, T,8 13.Safety valve 14. stirrer motor 15. double jacketed reaction vessel or reador 16. PtlW reactor contents, T., and PtlOO T. safety, T, 11. calibration heating 18. external coolant connection 19. oil drain cock 20. drain cock of glass reaction "easel
(a) General Description. The 2-L glass reactor (Figure 1,Table I, item 15) uses a thermostat for temperature control. Specifically, silicone oil is pumped through the double jacket of the reactor in a closed circulation system so that heat transfer can occur. The oil can be heated electrically (Figure 1, Table I, item 5 ) or cooled by subjecting it to an external coolant (Figure 1, Table I, item 18). Jacket (Tj)and reactor (T,) temperatures are measured using probes (Figure 1,Table I, items 11and 16, respectively). Agitation is controlled using a stirrer motor (Figure 1,Table I, item 14). Calibration is accomplished using a calibration probe (Figure 1, Table I, item 17). ( b ) Basic Concept of Measuring Heat Flow.
Boow= UA(T,- Tj) (22) The term UA in this study is determined by calibration. The Calibration probe emits a known amount of electrical
Ind. Eng. Chem. Res., Vol. 32, No. 4, 1993 597 Table 11. AHrxnExperimental Results and Published Results for Hydrolysis of Acetic Anhydride Shatynski (1991);average of four runs -14.4f 0.2 -14.6 Dyne (1967) Conn (1942) -14.1 Glasser and Williams (1971) -14.3 published average -14.3 f 0.3
energy into the system, and hence, Q is known. The reactor (T,)and jacket (Tj)temperatures are recorded, and thus, U A can be calculated for the system. ( c ) Energy Balance of the System. The energy balance for the calorimeter is given by the reaction heat flow (Qr) = measured heat flow (Qf) + accumulated heat (Qa) + heat losses (Q1)
-5 97 -5 96.
6 99
-
-600 601
-
2
-6003 4 O2003316
0 003322
0 003330
0 003326
0 003334
0 003338
0 003342
lIT,(’K)
Figure 2. Adiabatic hydrolysis of acetic anhydride. Table 111. Experimental Activation Energies and In ko Values for Hydrolysis of Acetic Anhydride
=Crimi
+
= UA(T,- T j ) mep,$
+ Q1
(23)
( d ) Temperature Control Modes. The reactor was controlled in three modes: 1. T , Mode: The temperature of the reactor (T,) is fixed or ramped. The jacket temperature (Tj)is adjusted to achieve the desired T,. 2. Tj Mode: The temperature of the jacket (Tj)is kept constant or ramped. 3. Adiabatic Mode: The temperature of the batch is solely dependent on the reaction profile. The jacket temperature, Tj, is manipulated so that any heat emitted due to a reaction is conserved in the system. Thus, the RC1 acta as an adiabatic reactor. In the adiabatic mode, two adiabatic points must be set (at the batch temperature before and after the reaction). The Mettler manual defines the adiabatic control parameters as follows: “An adiabatic point is defined as the value of ( T , - Tj) for one temperature point of the reactor temperature. Two adiabatic points define a linear equation; the resulting parameters of this linear function, offset and slope, are utilized as constants in the adiabatic control algorithm.” The adiabatic temperature rise is found by
ATad= AHrxnlmcp (24) The high-performance liquid ( e ) HPLC Equipment. chromatography (HPLC) instrument used in this experiment was a Hewlett Packard Model 1050. A variablewavelength UV detector was used, but was set at a fixed 254 nm. The column was a Zorbsax NH2,250-mm X 4.6mm i.d. Acetonitrile and water (75:25 vlv) were used as the mobile phase. The flow rate was set to 1.0 mL/min. Actually, two Model 1050 instruments were used. All of the above information is applicable to both systems. However, one system had a computer-controlled integrator while the other had an ordinary integrator.
Results and Discussion Hydrolysis of Acetic Anhydride Reaction: Heat of Reaction Studies. The average of four experimental values for the heat of reaction of the hydrolysis of acetic anhydride is tabulated in Table I1 and is compared with published data. The agreement between measured and published data is very good.
Shatynski (1991); average of four runs Dyne (1967) Rivett and Sidgwick (1910) Marmers (1965) Marek (1954) Glasser and Williams (1971) King and Glasser (1965) Bisio and Kabel (1985) published average
activation energy (kcal/g-mol) 11.2f 0.5
In ko L/(g-mol-s) 12.74k 0.94
11.8 10.3 16.4 13.8 10.8 9.5 11.1 12.0 f 2.4
11.94 9.93 12.8 11.56 f 1.47
Table IV. AH,,,, Experimental Results for the Cytidine/ Acetic Anhydride Reaction
mole ratio (cytidine:acetic anhydride) 1.0:1.2 1.O:l.O 1.0:0.60
AH,,, (kcal/g-mol) -10.5 -10.5 -10.6
Adiabatic Kinetic Analysis. For the pseudo-firstorder hydrolysis of acetic anhydride, Figure 2 shows a typical graph given by eq 21. Correlation coefficients were in the range between 0.987 and 0.996. The activation energies and the preexponential factors for four experimental runs of the hydrolysis of acetic anhydride are shown in Table I11together with published data. The agreement between experimental and measured data is good. For this reaction any heat of mixing of acetic anhydride and water is assumed to be a part of the heat of reaction. The reaction is very rapid. Cytidine1Acetic Anhydride Reaction in NMP. Since the experimental method and equipment were proven satisfactory, measurements were made on the unknown biochemical reaction involving cytidine and acetic anhydride in NMP. Heat of Reaction. Measurements for the heat of reaction were made at various mole ratios of cytidine to acetic anhydride. The data are shown in Table IV. Within the range of mole ratios studied, the heat of reaction is constant. Adiabatic Kinetic Analysis. Using second-order kinetics for the cytidinetacetic anhydride reaction in N W , the measured data are correlated in Figure 3 by eq 19. The correlation coefficients for all runs made ranged from 0.996 to 0.997. These data were also subjected to first-order kinetics using eq 21. A correlation coefficient of 0.962 was obtained. Despite the high values of the correlation coefficients in both Figures 2 and 3, there is a tendency
Ind. Eng. Chem. Res., Vol. 32, No. 4, 1993
I:
\
-8.18
a19-8.20
-8.21
!
.
.
-8.21.
Figure 5. Arrhenius plot for the cytidine/aceticanhydride reaction.
was a AHmix of -0.44 kcal/g-mol. This value is small compared to the measured heat of reaction and can be neglected.
f 0
2
4
6
8
10
12
14
18
Tlme ( Seconds; In Thousand# )
Figure 4. Isothermalreactionof cytidme/acetic anhydride/correlated with second-order kinetics.
for both curves to flex downward with increasing slope at low temperatures. One possible explanation for these first few points following start-up (low temperatures) is that the temperature versus time curve is less accurate at startup, causing a lower than true value for dT/dt and thus causing the dependent variable to be lower than expected. The activation energies and preexponential factors for the experimental runs of the cytidine/acetic anhydride in NMP reaction were determined, and the average activation energy was 13.3 i 0.2 kcal/g-mol. The average value for In ko,the natural logarithm of the preexponential factor, was 15.68 f 0.34, where ko has units of L/(g-mo1.s). Concentration vs Time Data by HPLC Method. Figure 4 shows the inverse of the concentration of cytidine vs time at isothermal conditions at 40,50, and 60 "C for a second-order reaction. The concentration data were calculated by subjecting the samples to HPLC analysis. Details of the method and data for runs are given by Shatynski (1991). From the three isothermal runs at 40,50, and 60 "C, the Arrheniua plot was constructed and is shown as Figure 5. The rate constants used in the Arrhenius plot were derived from the slope of the plots of Figure 4 which represent isothermal runs. The correlation coefficients for the isothermal plots ranged from 0.995 to 0,998. The data fit second-order kinetic models. The Arrhenius plot yielded an activation energy of 13.2 kcal/g-mol and a In ko value of 15.14 L/(g-mobs). These values agree very well with the values obtained by the adiabatic studies described above. In one run, the heat of mixing was calculated by determining the enthalpy change when0.4668 mol of acetic anhydride were added to 13.50 mol of NMP. The result
Conclusion The validity of the procedures used in the adiabatic studies was proven by comparing the experimental kinetic results of the hydrolysis of acetic anhydride reaction to published values. Thus, the method could then be applied, with confidence, to an unknown system. Temperatures can be measured easily to determine the kinetics of reactions. The cytidine/acetic anhydride reaction in NMP (unknown system) follows second-order kinetics. The activation energy is approximately 13.3 f 0.2kcal/g-mol. The average In ko value is approximately 15.41 f 0.27 L/(gmol-s). The heat of reaction for the cytidine/acetic anhydride reaction in NMP is approximately -10.5 i 0.1 kcal/g-mol. The heat of mixing between acetic anhydride (0.4668 mol) and NMP (13.50mol) is approximately -0.44 kcal/g-mol. Acknowledgment The authors are indebted to the Hoffmann-LaRoche Company for allowing the cytidine/acetic anhydride in NMP system to be studied, for the use of their Mettler RC1 system, and for publication of the M.S. Thesis of J.J.S. Nomenclature A = heat exchange area, m2 CA = concentration of component A, g-mol/L or kg-mol/m3 Cg = concentration of component B, g-moVL or kg-mol/m3 cp = heat capacity of batch, cal/(g.OC) or kJ/(kg°C) cp,l = specific heat of batch, cal/(g."C) or kJ/(kp"C) cp,2= specific heat of dosedmaterial, cal/(g."C) or kJ/(kg."C) E,,, = activation energy, kcal/g-mol or kJ/kg-mol AH, = heat of reaction, kcal/g-mol or kJ/kg-mol AHi = heat of reaction for reaction i, kcal/g-molor kJ/kg-mol k = specificreaction rate constant, s-l for first-order reaction or L/ (g-mo1.s) or m3/(kg-mol.s) for second-order reaction ko = preexponentialfactor, 8-1for first-order reaction or L/(gmo1.s) or m3/(kg-mol-s)for second-order reaction m = mass of batch, g or kg N , = mol of component A, g-mol or kg-mol goow= heat flow,kcal/s or kJ/s Qstirrer = heat generated by agitator, kcal/s or kJ/s -PA = rate of disappearance of component A, g-mol/(L.s) or kg-mol/(m3.s) ri = rate of reaction i, g-mol/s or kg-mol/s R = gas constant, kcal/(kg-mol.K) or kJ/(kg-mo1.K)
Ind. Eng. Chem. Res., Vol. 32, No. 4, 1993 599 Zr,AHi = reaction heat flows of all reactions occurring concurrently and any phase changes (i.e., evaporation, crystallization, mixing), W t = time, s T = absolute temperature, K T,= temperature of batch, OC Tj = temperature of jacket, "C U = heat-transfer coefficient, kcal/(s.m2-"C)or kJ/(s.m2."C) UA = heat flux,cal/(s."C) or kJ/(s."C) V = volume of reactor, L or m3 NMP = N-methyl-2-pyrrolidone
Glasser, David; Williams, Donald F. The Study of Liquid-Phase Kinetics Using Temperature as a Measured Variable. Znd. Eng. Chem. Fundam. 1971,10 (3), 516-519. King, Edward L. How Chemical Reactions Occur; W. A. Benjamin: New York, 1964; pp 5-70. King, R. P. Estimation of Parameters in Systems Defined by Differential Equations. S. Afr. J. Sci. 1967, March, 91-96. King, R. P.; Glasser D. The Use of the Adiabatic Calorimetar for Reaction Rate Studies. S. Afr. Znd. Chem. 1965, Jan, 12-15. Levenspiel, 0.ChemicalReaction Engineering, 2nd ed.; Wiley: New York, 1972. Marek, J. Chem. L i t y 1954,48,168; Collect. Czech. Chem Commun.
Subscripts 0 = initial condition f = final condition
Marmers, H. Ph.D. Dissertation, University of Birmingham, Birmingham, England, 1965. Mettler Operating Instructions for RC1 Reaction Calorimeter, May
Literature Cited
Morrison, Robert; Boyd, Robert Organic Chemistry, 4th ed.; Allyn and Bacon: Boston, 1983. Rivett, A. C. D.: Sidgwick, N. V. J. Chem. SOC.1910,97,732. Shatynski, J. J. M.S. Thesis, New Jersey Institute of Technology, Newark, NJ, 1991. Williams,R. D. Indirect Measurement of Reaction Rate. Chem.Eng. Educ. 1974, Winter, 28-30.
Bisio, Attilio; Kabel, Robert L. Scaleup of Chemical Processes; Wiley: New York, 1985; pp 136-138. Cohen, W. C.; Spencer, J. L. Determination of Chemical Kinetics by Calorimetry. Chem. Eng. Prog. 1962,58 (12), 40-41. Conn, J. B.; Kistiakowsky,G. B.; Roberta, R. M.; Smith, E. A. J.Am. Chem. SOC.1942,64,1747. Dyne, S. R.; Glasser, D.; King, R. P. Rev. Sci. Znstrum. 1967,38,209. Fogler, H. Scott Elements of Chemical Reaction Engineering; Prentice Hall: Englewood Cliffs, NJ, 1986.
1954, 19, 621.
1987.
Received for reuiew July 6, 1992 Reuised manuscript received December 4, 1992 Accepted December 23, 1992
