Chemical and Process Engineering 2022, 43 (2), 255–264
DOI: 10.24425/cpe.2022.140829

Use of isoperibolic reaction calorimeter for the studyof reaction kinetics of acetic anhydride hydrolysis
reaction: Effect of acetic anhydride and water ratio
Rajendra Kumar1∗ , Anurag Kumar Tiwari2
1 Council of Scientific and Industrial Research – National Chemical Laboratory, Chemical Engineeringand Process Development Division, Pune, India – 411008
2 Dr B R Ambedkar National Institute of Technology, Department of Chemical Engineering, Jalandhar,

Punjab, India – 144011
Reaction kinetics of acetic anhydride hydrolysis reaction is being studied at a fixed reaction temperature
and ambient pressure using an isoperibolic reaction calorimeter. Temperature versus time data alongwith heat and mass balance is used to determine the kinetics parameters i.e. activation energy andArrhenius coefficient. It has been studied with the varying volumetric ratio of acetic anhydride andwater; and kinetics parameters were compared and plotted for each ratio. Such a study has not been
done previously to determine the kinetics dependency on varying the acetic anhydride water ratio. As
the acetic anhydride hydrolysis reaction is exothermic in nature, the present study will help to decide
the safe and suitable operating conditions such as concentration and temperature for conducting thisreaction at plant scale. The kinetic data presented can be used further for the mathematical modelingand simulation of such exothermic hydrolysis reactions.
Keywords: acetic anhydride, water, reaction calorimeter, hydrolysis, kinetics

1. INTRODUCTION

Reaction calorimeter is an instrument which is widely used by scientists and engineers in chemical andpharmaceutical process development to measure the amount of thermal energy released or absorbed bya chemical or physical reaction. Reaction calorimeter allows the investigation of chemical processes underprocess-like conditions, providing a full set of information about the scalability and safety of the process.
The information obtained from the reaction calorimeter is essential for the safe transfer of a processfrom lab scale to plant scale. Basic principles and its use for process development and process safety
have been described by many researchers (Singh, 1997). Reaction kinetics of a reaction is an important∗ Corresponding author, e-mail: k.rajendra@ncl.res.in

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Presented at the International Chemical Engineering Conference 2021 (ICHEEC): 100 Glorious Years of Chemical
Engineering and Technology, held from September 16–19, 2021 at Dr B. R. Ambedkar National Institute of Technology,
Jalandhar, Punjab, India.
© 2022. The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY 4.0, https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution,and reproduction in any medium, provided the original author and source are credited.

R. Kumar, A.K. Tiwari, Chem. Process Eng., 2022, 43 (2), 255–264

information, which is used at various places such as process development, process scale-up, equipment
design, mathematical modelling and simulation, etc.
The traditional method to determine the reaction kinetics of a chemical reaction involves the measurementof concentration with respect to time, which requires continuous sampling and analysis. Apart fromusing the concentration data researchers have used other techniques such as conductivity measurement(Kralj, 2007), pH measurement (Wiseman et al., 2020), various spectroscopic methods such as Raman,
IR and NMR (Bell et al., 1998; Haji and Can, 2005; Susanne et al., 2012). Few researchers have used
the temperature versus time profile of the reaction to determine the reaction kinetics (Asiedu et al., 2013;
Hirota et al., 2010). These alternative techniques do not require sampling and offline analysis, becausea suitable in-situ probe or sensor captures the required data such as conductivity, pH, spectra or temperaturein real time. Captured information can be used to determine the reaction kinetics by analyzing the raw
data and using mathematical equations. These alternative techniques are suitable for the reactions wherecontinuous sampling and offline analysis is difficult due to process conditions.
If the kinetics of the reaction is not fully understood, then while conducting reaction, several serious issues
may arise, such as runaway which leads to high amount of pressure and thermal energy liberation resulting
into release of environmentally dangerous substances, serious equipment damage, and an explosion.
Unfortunately, for most important industrial reactions, there is limited knowledge about their kinetics andthermodynamics. Since several industrially important chemical reactions are moderately highly exothermic
such as hydrolysis, acid-base neutralization, esterification, hydrogenation, nitration etc.; it is possible toquantify their kinetics using the thermal data.
Acetic anhydride hydrolysis is a fast and moderate exothermic reaction which is very popular among
all the users of reaction calorimeter. It is most suitable exothermic reaction for the demonstration ofreaction calorimetry technique. The kinetics of acetic anhydride hydrolysis can be considered as first orderwith respect to acetic anhydride as well as with respect to water. It may also be noted that values ofkinetics parameters for acetic anhydride hydrolysis are not same from the different studies reported. They
dependent on various factors such as the user, type of instruments used, concentration, temperature, stirring
speed of the mixing, catalyst, solvent, etc. (Asiedu et al., 2013; Fritzler et al., 2014; Hirota et al., 2010;
Kralj, 2007). In this study an isoperibolic reaction calorimeter was used to determine the kinetics of theacetic anhydride hydrolysis reaction. “Isoperibolic” means the reaction mass is kept at a surrounding of
constant temperature, and then temperature changes during the reaction are studied using a thermocouple.
This technique is useful for very fast reactions and where kinetics information is not available. We havedemonstrated activation energy and Arrhenius coefficient determination of acetic anhydride hydrolysis
reaction using reaction calorimeter with varying volumetric ratios of acetic anhydride to water. This typeof study of reaction kinetics determination of acetic anhydride hydrolysis reaction has not been done with
low to high concentration of acetic anhydride in fixed water quantity or varying the acetic anhydride towater ratios as known to the authors.

2. METHODOLOGY
The details of equations and methodologies used for the reaction kinetics determination using the isoperibolic reaction calorimeter have been described in various reported research papers (Asiedu et al., 2013;
Fritzler et al., 2014; Garcia et al., 2021; Hirota et al., 2010; Salahudeen et al., 2020). The hydrolysis
reaction of acetic anhydride can be represented as(CH3 CO)2 O + H2 O → 2CH3 COOH

(1)

This reaction can be considered as first order with respect to each reagent.

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Use of isoperibolic reaction calorimeter for the study of reaction kinetics of acetic anhydride hydrolysis reaction . . .

Considering this reaction to be in batch mode and in liquid phase, mass and energy balance equations are
given by:d 𝑋𝐴
= (−𝑟 𝐴)𝑉d𝑡d𝑇𝑟
= (−𝑟 𝐴)𝑉 (−Δ𝐻) − 𝑈 𝐴(𝑇𝑟 − 𝑇 𝑗 )
𝑚𝐶 𝑃
d𝑡
𝑁 𝐴0

(2)
(3)

Here acetic anhydride (𝐴) is considered to be the limiting reactant, 𝑁 𝐴0 is the initial number of moles ofacetic anhydride, 𝑉 is the effective volume of the reactor used for the reaction, d𝑇𝑟 /d𝑡 is the rate of changeof the temperature of the reaction mass.
For heat balance it is assumed that there is negligible thermal effect due to dosing and stirring and there is
negligible heat exchange from the atmosphere.
Here 𝑚𝐶 𝑃 in Eq. (3) accounts for the total heat capacity of the∑︁
system; which has two parts, first is(𝑚𝐶 𝑃 )reactor which is for the empty reactor and stirrer, second is
𝑚 𝑗 𝐶 𝑝 𝑗 which is for the chemical𝑗components (acetic anhydride, water and acetic acid), 𝑗 is the number of chemical components in thereactor.
∑︁
𝑚𝐶 𝑃 = (𝑚𝐶 𝑃 )reactor +𝑚 𝑗𝐶𝑝 𝑗
(4)𝑗

The Δ𝐻 is the molar heat of the acetic anhydride hydrolysis reaction, it has to be obtained by isothermal
reaction calorimeter experiment. Δ𝐻 is fixed for the reaction irrespective of concentration and ratio. UA
and 𝑚𝐶 𝑃 can be obtained by doing the calibration of the reaction mass using the calibration heater fromreaction calorimeter.
Considering hydrolysis of acetic anhydride as second order kinetics, the rate law of the reaction can be
represented as:(−𝑟 𝐴) = 𝑘𝐶 𝐴𝐶𝑊(5)
where 𝑘 is the rate constant, which is temperature-dependent according to the Arrhenius equation:𝐸
𝑘 = 𝑘 0 exp −
𝑅𝑇𝑟

(6)

In Eq. (5), the molar concentrations of acetic anhydride (𝐶 𝐴) and water (𝐶𝑊 ) may be written in terms ofthe conversion of the acetic anhydride as follows:
𝐶 𝐴 = 𝐶 𝐴0 (1 − 𝑋 𝐴)
𝐶 𝐴0 𝑋 𝐴𝐶𝑊 = 𝐶𝑊0 1 −
𝐶𝑊0

(7)
(8)

𝑇𝑟 is the reactor temperature which is measured and recorded in real time using a temperature sensor.
By combining the mass and energy balances and integrating the resulting equation from time 𝑡 = 0 to 𝑡 = 𝑡
and assuming that the conversion of acetic anhydride is 100% at the end of the experiment, conversion
formula can be obtained. The conversion of acetic anhydride is given by the following relationship:∫𝑡(𝑚𝐶 𝑃 ) 𝑇 𝑓 − 𝑇𝑖 + 𝑈 𝐴
𝑋 𝐴𝑖 = 𝑋 𝐴 𝑓 −
𝑇𝑟 − 𝑇 𝑗 d𝑡0

𝑁 𝐴0 (−Δ𝐻)(9)Here 𝑋 𝐴𝑖 is the conversion at a given point, and 𝑋 𝐴 𝑓 is the final conversion.
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The integral part of above equation is calculated for each interval of time using trapezoidal rule:∫𝑏𝑓 (𝑥) d𝑥 =Δ𝑥
[ 𝑓 (𝑥 0 ) + 2 𝑓 (𝑥 1 ) + 2 𝑓 (𝑥 2 ) + . . . + 2 𝑓 (𝑥 𝑛 )]
2

(10)

𝑎

Hence, the values of experimental conversion are obtained starting from the time of completion of reaction.
With the known values of 𝑚𝐶 𝑃 , UA, Δ𝐻 and d𝑇𝑟 /d𝑡, the rate of reaction can be determined at each data
point experimentally by rearranging the thermal balance as follows:(𝑚𝐶 𝑃 )𝑟(−𝑟 𝐴) =d𝑇𝑟+ 𝑈 𝐴 𝑇𝑟 − 𝑇 𝑗d𝑡
𝑉 (−Δ𝐻)(11)

Once (−𝑟 𝐴) is determined, the values of the rate constant at each point can be calculated from Eq. (5) as:𝑘=(−𝑟 𝐴)𝐶 𝐴𝐶𝑊(12)

where 𝐶 𝐴 and 𝐶𝑊 are calculated from Eqs. (7) and (8), respectively.
Finally, the values of the 𝐸 and ln 𝑘 0 are obtained respectively, from the intercept and the slope of thestraight line plot of ln 𝑘 versus 1/𝑇𝑟 :𝐸
ln 𝑘 = ln 𝑘 0 −(13)
𝑅𝑇𝑟
In the result section, the values of ln 𝑘 0 will be reported instead of 𝑘 0 .

3. EXPERIMENTAL SECTION
Distilled water prepared at NCL lab and high purity Acetic Anhydride from Thomas Baker Mumbai wasused for conducting the hydrolysis experiments. A similar model of reaction calorimeter from HEL UK
was used (Fig. 1) for conducting the experiments. This reaction calorimeter consists of 1 liter Borosilicate
glass reactor and 1 liter SS316 metal reactor in the same unit with interchangeable option. Out of these2 available reactors, the glass reactor which had vacuumed double jacket for least heat loss into theatmosphere was used for this study. This reaction calorimeter was connected with a high-end Julabo A45
circulator which is used to heat or cool the reaction mass or reactor jacket with temperature range of–40 to 250 ◦ C. A Heidolph made overhead motor and PTFE stirrer was connected with the reactor whichis capable to stir the reaction mass at suitable RPM. Separate temperature sensors were connected withthe reactor and jacket for the monitoring and recording of the reaction mass temperature (𝑇𝑟 ) and jacket
temperature (𝑇 𝑗 ) accurately to two decimal places. The reactor was also integrated with a ProMinent delta
pump and Sartorius weighing balance for the controlled addition of reagent into the reactor.
This reaction calorimeter is fully automatic which runs through the WinISO software from the computer.
All the process parameters such as temperature, RPM, reactor temperature, jacket temperature, torque, etc.
can be monitored and recorded in real time. After the completion of experiments the recorded data is being
analyzed by in-build iQ software to determine various parameters such as Δ𝐻, UA, and 𝑚𝐶 𝑃 . The obtained
parameters from the reaction calorimeter, temperature time profile, heat and mass balance equations areused for the reaction kinetics determination.
For Δ𝐻 calculation heat flow method of reaction calorimeter was used. UA and 𝑚𝐶 𝑃 were determinedby various calibration experiments using the calibration heater. Calibration experiments were performed258

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Use of isoperibolic reaction calorimeter for the study of reaction kinetics of acetic anhydride hydrolysis reaction . . .

Fig. 1. Reaction calorimeter used for the experiments

before and after addition of acetic anhydride to determine UA and 𝑚𝐶 𝑝 ; and average value was used for the
kinetics calculation for each experiments. Temperature time profiles of all the acetic anhydride hydrolysis
experiments were captured at isoperibolic mode of the reaction calorimeter at fixed jacket temperatureof 35 ◦ C.
Temperature controlled heat transfer oil was circulated through the jacket of the reactor. The oil temperature
was controlled to maintain the desired temperature of the water in the reactor. When both the reactor
temperature as well as jacket temperature reached 35 ◦ C, acetic anhydride was added suddenly to thereactor vessel. Stirrer RPM was kept constant at 400 for all the experiments during addition and reaction.
The reaction calorimeter constantly measured the 𝑇𝑟 , 𝑇 𝑗 and d𝑇𝑟 /d𝑡 after each 2 seconds. As the reaction
proceeded, temperature-time profiles for the reaction were obtained. A total of 9 experiments with varying
volumetric ratios of acetic anhydride and water; 1:2 (run 1), 1:3 (run 2), 1:4 (run 3), 1:5 (run 4), 1:6 (run5), 1:7 (run 6), 1:8 (run 7), 1:9 (run 8), 1:10 (run 9) were conducted for this study.

4. RESULTS AND DISCUSSION
A reaction calorimeter was used to determine the kinetic parameters of a reaction using temperature-time
profiles. Figure 2 represents the temperature versus time data for different volumetric ratios of acetic
anhydride to water. From the temperature time profile, the peak shows the 100% conversion of acetic
anhydride to acetic acid. The absolute amount of heat released by the reaction is proportional to theamount of acetic anhydride taken. Hence temperature peak is highest for run 1 and lowest for run 9.
Similarly, reaction time also decreases from run 1 to run 9; reaction time is inversely proportional to theamount of acetic anhydride used.
Molar heat of reaction Δ𝐻 was determined to be 56.1 kJ/mol, which is in agreement with several otherreported values (Asiedu et al., 2013; Fritzler et al., 2014; Hirota et al., 2010). Values of UA and 𝑚𝐶 𝑃 aredependent on the quantity of reaction mass, hence they are different for all the runs. UA and 𝑚𝐶 𝑃 were
determined separately for each experiments and are represented in Figures 3 and 4. It is observed that UAand 𝑚𝐶 𝑃 both decreased from run 1 to run 9 as the amount of acetic anhydride decreased with respect tothe fixed quantity of water. With the known values of UA, Δ𝐻 and 𝑚𝐶 𝑃 for all the runs, conversions at
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Fig. 2. Temperature-time profile for all the runs

Fig. 3. 𝑈 𝐴 variation for all the runs

Fig. 4. 𝑚𝐶 𝑝 variation for all the runs

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Use of isoperibolic reaction calorimeter for the study of reaction kinetics of acetic anhydride hydrolysis reaction . . .

each point were calculated using Eq. (9). It was in reverse manner starting from the last point assuming
100% conversion at the completion of the reaction. Figure 5 depicts conversion-time data for all the runs.
Initial conversion of acetic anhydride at the start of the reaction or time 𝑡 = 0 for each run is shown in
Fig. 6, it varies from zero to 10% for run 1 to run 9. It indicates that initial conversion is highly dependent
on the quantity of acetic anhydride used. Lowest initial conversion for run 1 means that more quantity ofreagent makes it difficult to start the reaction.

Fig. 5. Conversion-time data for all the runs

Fig. 6. Initial conversion for all the runs

Figure 7 shows the plots between ln 𝑘 vs. 1/𝑇𝑟 . By fitting these curves into a straight line, slope andintercept values are used to determine the reaction kinetics parameters 𝐸 and ln 𝑘 0 . The values of 𝐸
and ln 𝑘 0 obtained are plotted in Figure 8 and Figure 9 against each run. It is observed that activationenergy and ln 𝑘 0 are almost constant while decreasing the acetic anhydride concentration with respect tofixed quantity of water. It depicts that the activation energy which is the minimum energy required by theacetic anhydride and water system for the hydrolysis and formation of acetic acid does not change whilechange in the reagent concentration. It is quite expected that it should not change, as activation energy is
an independent value and does not depend on parameters such as concentration, temperature, etc; it can
only change if we use a catalyst in the reaction.
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Fig. 7. ln 𝑘 vs. 1/𝑇𝑟 for all the runs

Fig. 8. Activation energy for all the runs

Fig. 9. ln 𝑘 0 for all the runs

5. CONCLUSIONSThis work shows the effect on reaction kinetics of acetic anhydride hydrolysis reaction by varying the ratioof acetic anhydride to water using isoperibolic reaction calorimeter at a fixed temperature of 35 ◦ C. Heretemperature time data from the experiments were used for the kinetics determination. The values of Δ𝐻

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Use of isoperibolic reaction calorimeter for the study of reaction kinetics of acetic anhydride hydrolysis reaction . . .

were fixed for all the experiments, and UA and 𝑚𝐶 𝑃 were determined separately for each reaction. Kinetics
parameters 𝐸 and ln 𝑘 0 were determined for each ratio. It was found that 𝐸 and ln 𝑘 0 does not change withrespect to the quantity of acetic anhydride used with the fixed quantity of water. The values of 𝐸 and ln 𝑘 0
were found to be almost constant while acetic anhydride concentration was maximum and then it gradually
decreases to minimum from run 1 to run 9. Data also shows that temperature peak was highest for run 1
and lowest for run 9. Complete reaction conversion took maximum time for run 1 and minimum for run 9.
The study also indicates that the amount of absolute heat generated is dependent on the amount of acetic
anhydride used, however molar heat is independent of amount used. The presented data and study may be
helpful to design the acetic anhydride hydrolysis reaction system in a safe and easy to handle manner. It
will also be helpful to decide the safe concentration and temperature limits as per the available cooling
capacity for the production of acetic acid using acetic anhydride hydrolysis process.
Authors would like to thank Ravi Pohankar, intern student from MANIT Bhopal and Vaibhavi Zanzad,
intern student from VIT Pune for helping to conduct the experiments and data analysis.

SYMBOLS

𝐶𝐴
𝐶𝑊
𝑚𝐶 𝑃
𝐸
𝑘
𝑘0
𝑁 𝐴0
𝑁𝑊 0
𝑅
(−𝑟 𝐴)
𝑇𝑗
𝑇𝑟
UA
𝑉
𝑋𝐴
Δ𝐻

concentration of acetic anhydride, mol/l
concentration of water, mol/l
total heat capacity of reactor and components, J/K
activation energy, kJ/mol
specific reaction rate constant, l/mol s
arrhenius coefficient, l/mol s
initial moles of acetic anhydride, molinitial moles of water, molideal gas constant, J/(mol·K)
rate of disappearance of acetic anhydride, mol/(l·s)
jacket temperature, K
reactor temperature, K
product of heat transfer coefficient and used reactor area, J/K
volume of reacting fluid, lconversion of acetic anhydridemolar heat of hydrolysis of acetic anhydride, kJ/mol

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Received 16 February 2022
Received in revised form 22 March 2022
Accepted 6 April 2022

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