Chemical Reactions Engineering Laboratory
Batch Reactor
Experiment 1
Nouran Shedid
130417
Abstract
A chemical reaction took place between Caustic Soda and Ethyl acetate to form Sodium
acetate and Ethanol. The aim of this experiment is to determine the order of this reaction and the
value of its rate constant in addition to the rate equation. This was successfully accomplished by
studying the reaction a bit at a time and observing the relation between the concentration of the
reactants and time. In the end, after establishing and studying several relationships, it was found
that this reaction is a second order reaction having a rate constant of 1.6215 M-1min-1.
Table of Contents
Abstract ........................................................................................................................................... 1
Introduction ..................................................................................................................................... 3
Reaction Kinetics ........................................................................................................................ 3
Methods for Calculating Reaction Kinetics ................................................................................ 4
Initial Rates Method ................................................................................................................ 4
Integrated Rate Law Method .................................................................................................. 6
Batch Reactors ............................................................................................................................ 7
Procedure ........................................................................................................................................ 9
Results ........................................................................................................................................... 10
Sources of Error ............................................................................................................................ 17
Conclusion .................................................................................................................................... 18
References ..................................................................................................................................... 19
Introduction
Reaction Kinetics
The kinetics of chemical reactions studies the rate at which any chemical process takes
place (Vallance, 2018). It can be represented by the amount of product formed in a certain time
interval or the amount of reactant consumed in a given time interval (Chemical Kinetics, 2018).
Reaction rates vary widely for different reactions ranging from reactions that can take place in
nanoseconds to others which can take up to decades to be completed. Geological processes are one
of the most famous examples for reactions that take such a long time to end. However, the most
common reactions usually consume a moderate amount of time that lies in the middle of this wide
range. Examples of these common reactions include the hydrolysis of bismuth (III) ion in a solution
having chloride in it to form the white BiOCl which takes numerous minutes, and the combustion
of hydrocarbons which is fairly rapid (Chemical Kinetics, 2018).
Most chemical processes can be broken down into a series of elementary steps or reactions.
Generally, elementary steps are classified into bimolecular steps and unimolecular steps. A
bimolecular step is one which takes place as a result of the reactive collision of two molecules. On
the other hand, a unimolecular step is usually an isomerization or dissociation reaction of a single
reactant molecule. When very high pressure is applied or present this is considered to be a special
case where three molecules collide simultaneously in what is known as a termolecular step.
However, this is a very rare case.
It is very important to note that most reactions which are written in a single equation are actually
made up of several elementary steps. However, only their net reaction was written to represent it
which is why it was written in a single equation or step. Generally elementary reactions are
perceived as a shift from an atomic or molecular state to another. These two states are separated
by what is known as a potential barrier. This barrier is demonstrated by the activation energy of
this process, which also determines its speed. If the thermal energy of the reactants is relatively
high that it can surmount the potential barrier represented by the activation energy, then this will
be a fast reaction. This takes place in processes having low potential barrier values. Alternatively,
when the potential barrier values are high, most reactants do not have the sufficient energy to
exceed that limit and hence, the reaction is rather slow. Potential barriers are the main reason the
rates of any reaction are temperature dependent (Vallance, 2018).
Methods for Calculating Reaction Kinetics
Several methods can be used in determining the rate law of any reaction. In this report, the
initial rates method and the integrated rate law method will be discussed.
Initial Rates Method
The rate equation for a bimolecular reaction usually looks like this:
There are two variables in this equation which are the concentration of the reactants, and the
powers q and p. The values of the concentration can be easily calculated knowing the number of
moles and the volume of the solution, or by using the relation between the molarity and volume.
Hence, the unknown values now are the p and q values in addition to the value of the rate constant
k. The initial rates method is one of the ways which can be used to determine the value of these
unknowns. This method works through measuring the initial rate of the reaction (near t=0) for
several reactions having different reaction concentrations (Reaction Kinetics: Determining the
Rate Law, 2018). The values of the initial rate can be deduced from the concentration versus time
graphical representation whereas it equals negative the slope of the curve at time = 0 (Determining
Reaction Rates, 2018). By relating the values of these reactions together, the values of the rate
constant and the q and p powers can be deduced. This can be further explained using the following
example:
The rate law for the reaction between bromine and acetone is to be determined:
The rate law of this reaction has the following form:
The following values of initial rates will be used in calculating the reaction order for each
reactant, which are the p and q values:
Figure %: Initial rates data for the bromination of acetone
By looking into the numbers in the above table, it can be noticed that the concentration of acetone
is the same in both the first and second experiment, while that of bromine was doubled. However,
the reaction rate was not affected by the change in bromine concentration. Hence, it can be deduced
that the reaction is zero order with respect to bromine. This can also be proven mathematically by
relating the first and second rates as follows:
Similarly, we can relate the values of the first and third experiments to deduce that the reaction is
first order with respect to acetone. This is because doubling the concentration of acetone in the
third experiment lead to doubling the reaction rate as well which shows a direct relationship
between the rate and the reactant concentrations. Nevertheless, if the reaction rate was multiplied
by a different factor other than two when doubling the concentration of acetone, then the order of
the reaction in acetone would have been other than one. Usually the highest encountered order is
3. Lastly, the value of the rate constant can be calculated by adding the now known values of p
and q, concentrations, and the initial rate in the rate equation. All three equations should provide
the same value which is 1.64*10-4 s-1 in this case. Notice that the unit of the rate constant changes
by changing the overall order of reaction which is the sum of the individual reactant orders
(Reaction Kinetics: Determining the Rate Law, 2018).
Integrated Rate Law Method
Although the initial rates method is an easy and moderately accurate method for
determining the rate law, it has several disadvantages such as having to perform numerous
experiments. Another major disadvantage is that it does not produce accurate results for reactions
having high rates. Therefore, another method was developed to determine the rate law. This
method uses the values of concentration versus time as the reaction proceeds and compares them
to the mathematical estimates from the integrated rate laws. The strategy of assuming the order of
the reaction and plotting the data based on that assumption is used. The correctness of this
assumption is checked by inspecting the plotted graph. If it is linear, then the assumption was
correct. Otherwise, another order has to be assumed and the above steps should be refollowed.
Hence, the different forms of the integrated rate laws of the most common reaction orders which
are the zeroth, first, and second order will be discussed in the following section (Reaction Kinetics:
Determining the Rate Law, 2018).
Figure %: Integrated rate laws for reaction orders zero through two
The above laws ignored rate laws such as rate = k [A][B]. However, that does not mean that
integrated rate laws cannot be used in determining the rate law of such reactions. A certain method
is used in such cases. For example, for a system of second order that is made up of two components
and has a rate law of rate = k [A][B], the concentration of reactant B can be made so large when
compared to that of A such that the large concentration of B can be considered constant. With that
assumption made, the reaction can be deemed a first order reaction. In this case, a graph of Ln [A]
versus the time will produce a linear relationship meaning that this is a first order reaction in A. If
this reaction was second order in A, then a plot of 1/[A] versus the time would give the linear
relationship. The order of reactant B can be determined similarly by making the concentration of
A very large. For rate laws involving several components, the concentrations of all the reactants
should be made quite large except for the one of interest. This process should be repeated once for
each component in order to find the reaction order with respect to it (Reaction Kinetics:
Determining the Rate Law, 2018).
Batch Reactors
The batch reactor has two inlets at the top of its tank. The working principle of the batch
reactor is that the reactants are fed to the tank at the beginning of the process and then left to react
for a specific time period after being thoroughly mixed. The products are discharged at the end of
this time period or in other words, when the reaction is complete. When the reaction is going, no
material is added or removed from the tank meaning that the reaction inside is taking place
unsteadily. The compositions of the components inside the reactor are various with time. However,
the composition is uniform throughout the reactor at any time t (Batch Reactors, 2018).
Batch reactors have several applications. They are widely used in production on a small scale,
pharmaceutical industries, and in fermentation processes. Moreover, they are normally used when
liquid phase reactions having long residence times are taking place. Batch reactors are also
commonly used in the production of expensive products or those that are still in their
developmental stages. Like anything, batch reactors have advantages and disadvantages and
depending upon these pros and cons it is decided whether they will be used in a certain process or
not (Batch Reactors, 2018).
Batch reactors have several applications. They are widely used in production on a small scale,
pharmaceutical industries, and in fermentation processes. Moreover, they are normally used when
liquid phase reactions having long residence times are taking place. Batch reactors are also
commonly used in the production of expensive products or those that are still in their
developmental stages. Like anything, batch reactors have advantages and disadvantages and
depending on these pros and cons it is decided whether they will be used in a certain process or
not.
One of the most important advantages of batch reactors is that it can provide high conversions per
unit volume for a single batch. In addition, batch reactors are very flexible in terms of operation
as a single reactor can be used in the production of different products at different times. Moreover,
they are easy to clean which facilitates the previous point even more. Furthermore, batch reactors
are easily constructed and rarely require any auxiliary equipment.
On the other hand, batch reactors can be inconvenient in many ways as they have several
limitations. These limitations include lengthy idle times whereas the reactor cannot be used during
the time of charging the reactants or discharging the products leading to periods of zero production.
Batch reactors also require high labor and operating costs for every batch. They are also unsuitable
for non-homogenous reactions and large-scale production which limits their use and applications
widely. Lastly, the quality of the product is more variable as compared to that of the continuous
operation (Batch Reactors, 2018).
Procedure
1- Add 250mL of 0.1M NaOH and 250mL of 0.1M ethyl acetate to the reactor, mix them
thoroughly, and start the timer.
2- At time = 0, turn on the stirrer to ensure the homogeneity of the solution.
3- After 5 minutes, go through the following steps:
4- Using a pipette, withdraw a 10mL sample from the reaction mixture.
5- Add 15 mL of 0.1M HCl to this sample to quench it.
6- Supply the quenched sample with 2 drops of phenolphthalein as an indicator.
7- Titrate the quenched sample against NaOH of 0.1M concentration until the endpoint is
reached.
8- Tabulate the consumed volume of NaOH.
9- Determine the amount of HCl that was used in neutralizing the unreacted caustic soda in
the quenched sample by calculating the unreacted moles of HCl.
10- Repeat steps [4-9] every 5 minutes.
Results
We added 250 mL of 0.1 M NaOH and 250 mL of 0.1 M CH3COOC2H5. We will use these values
to calculate the initial concentration of the solution at time = 0.
First,
𝑛𝑁𝑎𝑂𝐻 = 𝐶𝑁𝑎𝑂𝐻 ∗ 𝑉𝑁𝑎𝑂𝐻
Hence,
𝑛𝑁𝑎𝑂𝐻 = 0.1 ∗ 250 ∗ 10−3 = 0.025 𝑚𝑜𝑙𝑒𝑠
Similarly,
𝑛𝐶𝐻3𝐶𝑂𝑂𝐶2𝐻5 = 𝐶𝐶𝐻3𝐶𝑂𝑂𝐶2𝐻5 ∗ 𝑉𝐶𝐻3𝐶𝑂𝑂𝐶2𝐻5
Hence,
𝑛𝐶𝐻3𝐶𝑂𝑂𝐶2𝐻5 = 0.1 ∗ 250 ∗ 10−3 = 0.025 𝑚𝑜𝑙𝑒𝑠
Then,
𝑛𝑡𝑜𝑡𝑎𝑙 = 𝑛𝑁𝑎𝑂𝐻 + 𝑛𝐶𝐻3𝐶𝑂𝑂𝐶2𝐻5
𝑛𝑡𝑜𝑡𝑎𝑙 = 0.025 + 0.025 = 0.05 𝑚𝑜𝑙𝑒𝑠
Hence,
𝐶𝑖𝑛𝑖𝑡𝑖𝑎𝑙 =
𝑛𝑡𝑜𝑡𝑎𝑙
0.05
=
= 0.1 𝑀
𝑉𝑡𝑜𝑡𝑎𝑙 (250 + 250) ∗ 10−3
To calculate the concentration of the solution at different time intervals, we will go through the
following steps:
𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝑢𝑛𝑟𝑒𝑎𝑐𝑡𝑒𝑑 𝐻𝐶𝑙 = 𝑉𝑇𝑖𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝐶𝑁𝑎𝑂𝐻
𝑇𝑜𝑡𝑎𝑙 𝑛𝑜. 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝐻𝐶𝑙 = 𝑣𝑜𝑙.∗ 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛
= 15 ∗ 10−3 ∗ 0.1
= 1.5 ∗ 10−3 𝑚𝑜𝑙𝑒𝑠
Hence,
𝑛𝑜. 𝑜𝑓 𝑟𝑒𝑎𝑐𝑡𝑒𝑑 𝐻𝐶𝑙 𝑚𝑜𝑙𝑒𝑠 = 𝑇𝑜𝑡𝑎𝑙 𝑛𝑜. 𝑜𝑓 𝐻𝐶𝑙 𝑚𝑜𝑙𝑒𝑠 − 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝑢𝑛𝑟𝑒𝑎𝑐𝑡𝑒𝑑 𝐻𝐶𝑙
= 𝑛𝑜. 𝑜𝑓 𝑢𝑛𝑟𝑒𝑎𝑐𝑡𝑒𝑑 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝑁𝑎𝑂𝐻
𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 =
Time (min.)
Vtitration (mL)
𝑛𝑜. 𝑜𝑓 𝑢𝑛𝑟𝑒𝑎𝑐𝑡𝑒𝑑 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝑁𝑎𝑂𝐻
𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑆𝑎𝑚𝑝𝑙𝑒 (0.01𝐿)
Unreacted HCl
Unreacted NaOH
Concentration
(mol)
(mol)
(M)
0
__
__
__
0.1
5
11.8
1.18*10-3
3.2*10-4
0.032
10
12.4
1.24*10-3
2.6*10-4
0.026
15
23.3
2.33*10-3
-8.3*10-4
-0.083
20
12.8
1.28*10-3
2.2*10-4
0.022
25
12.5
1.25*10-3
2.5*10-4
0.025
Draw the relation between (CA) and (t) and comment on your results
Zero Order Reaction
0,12
Concentration (M)
0,1
y = -0.0033x + 0.0736
R² = 0.5722
0,08
0,06
0,04
0,02
0
0
5
10
15
20
25
Time (min.)
Comment
As expected, the concentration of the reactants decreases by increasing the time. This
means that they are being consumed and that the reaction is taking place forming Sodium acetate
and Ethanol. However, the decrease in concentration is not steady (R2 = 0.5722) with time meaning
that this is not a zero-order reaction. To identify the order of this reaction, we will study the
following relations graphically.
a) The Relation between ln
𝐶𝑁𝑎𝑂𝐻.𝐼𝑛𝑖𝑡𝑖𝑎𝑙
𝐶𝑁𝑎𝑂𝐻.𝑎𝑛𝑦 𝑡𝑖𝑚𝑒
Vs. Time
We will construct a graph using the following data:
𝐶𝐼𝑛𝑖𝑡𝑖𝑎𝑙
𝐶𝑎𝑛𝑦 𝑡𝑖𝑚𝑒
Time (Sec.)
Concentration (M)
0
𝐶𝑖𝑛𝑖𝑡𝑖𝑎𝑙 = 0.1
0
5
0.032
-1.139
10
0.026
-1.347
20
0.022
-1.514
ln
First Order Reaction
0
-0,2 0
5
10
15
y = -0.066x - 0.4222
R² = 0.6794
-0,4
Ln[Ci/Ct]
-0,6
-0,8
-1
-1,2
-1,4
-1,6
-1,8
-2
20
Time (min.)
25
Comment
It is obvious from the from the graph that there is a negative correlation between ln 𝐶
𝐶𝐼𝑛𝑖𝑡𝑖𝑎𝑙
𝑎𝑛𝑦 𝑡𝑖𝑚𝑒
2
and the time. In addition, the value of R increased and became closer to one when comparing it
to the prior graph. However, the relation is non-linear, is closer to a curve than a straight line, and
varies greatly from the trendline, meaning that this reaction is not a first order reaction.
b) The Relation between
1
𝐶𝐴.𝑡
and Time
We will construct a graph using the following data:
1
𝐶𝐴.𝑡
Time (Sec.)
Concentration (M)
0
0.1
10
5
0.032
31.25
10
0.026
38.46
20
0.022
45.45
(M-1)
Second Order Reaction
60
1/C (M-1)
50
40
30
20
y = 1.6215x + 17.102
R² = 0.8156
10
0
0
5
10
15
Time (min.)
20
25
Comment
It is obvious from the graph that the direct relation between the reciprocal of the
concentration and the time is linear. In addition, when compared to the above 2 graphs, this one is
the most fit and closest to its trendline. It also has the highest value of R2 from the three above
graphs which is equal to 0.8156 and is very close to 1. The deviation of the curve from the straight
line can be due to certain sources of error which will be discussed below. Hence, from the above
three graphs we can deduce that this is a second order reaction. We can get the slope of this
line using its equation which is:
y = 1.6215x + 17.102
The slope of this line is represented by the coefficient of X which is equal to 1.6215. The following
rate equation for second order reactions tells us that this slope is equal to the rate constant. Hence,
the rate constant of this reaction is equal to 1.6215 M-1min-1.
Rate Equation:
1
𝐶𝑡
−
1
𝐶𝑖𝑛𝑖𝑡𝑖𝑎𝑙
= 𝑘𝑡
Sources of Error
1- The conditions under which the reaction took place were not taken into consideration. For
example, variation in temperature.
2- The stirrer was not working all the time in which the reaction was taking place.
3- The concentrations of the used solutions were not accurately prepared.
4- The volumes used were not accurately measured.
5- Titration was stopped not exactly at the end point due to human error.
6- The samples were not taken at accurate and equal time intervals.
7- Human error when making the calculations required to construct the graphs.
Conclusion
In this experiment, a chemical reaction took place between caustic soda and ethyl
acetate. The aim of this experiment was the determination of the order of this reaction in addition
to the value of its rate constant and rate law. This objective was reached by following a series of
steps each having its own purpose. First, the reactants were added to the tank and were left to react.
A sample was taken at time intervals of 5 minutes and quenched using a solution of HCl.
Subsequently, a phenolphthalein indicator was added to this quenched sample and it was titrated
against a solution Sodium Hydroxide. The volume obtained from this titration process was used in
calculating the amount of unreacted NaOH in the first sample. This was repeated several times
until several readings of concentration versus time were obtained. These readings were used in
establishing the graphical relationships that show a linear relationship for each of the zeroth, first,
and second order reactions. for this reaction, the only graph that showed a linear relationship was
that of the second order. The value of the rate constant for this reaction is equivalent to the slope
of the straight line resulting from the graphical relation between the reciprocal of concentration
and time. It was found to be 1.6215 M-1min-1.
References
Batch Reactors. (2018). Retrieved from University of Michigan:
http://umich.edu/~elements/asyLearn/bits/batch/index.htm
Chemical Kinetics. (2018). Retrieved from behrend.psu.edu:
http://chemistry.bd.psu.edu/jircitano/kinetics.html
Determining Reaction Rates. (2018). Retrieved from Purdue Science - Department of Chemistry:
https://www.chem.purdue.edu/gchelp/howtosolveit/Kinetics/CalculatingRates.html
Reaction Kinetics: Determining the Rate Law. (2018). Retrieved from Spark Notes Chemistry:
http://www.sparknotes.com/chemistry/kinetics/ratelaws/section2/
Vallance, C. (2018). Reaction Kinetics. Retrieved from Vallance Group - Department of
Chemistry - University of Oxford:
http://vallance.chem.ox.ac.uk/pdfs/KineticsLectureNotes.pdf