CSTRs in Series
Gregory Naughton
This report is submitted to Dr. Adam St. Jean on 11/ 25 /2015
i
Table of Contents:
Table of Contents…………………………………………………………………………………………………... (ii)
List of Figures……………………………………………………………………………………………………….. (iii)
Abstract………………………………………………………………………………………………………………… (iv)
Introduction………………………………………………………………………………………………………….. (1)
Theory………………………………………………………………………………………………………………….. (1)
Description of Equipment……………………………………………………………………………………….(4)
Materials and Chemicals……………………………………………………………………………………….. (4)
Experimental procedure…………………………………………………………........................................... (5)
Analytical procedure.…….………………………………………………………........................................... (6)
Results………………………………………………………………………………………………………………….. (7)
Discussion…………………………………………………………………………………………………………….. (9)
Design Solution…………………………………………………………………………………………………….. (11)
Conclusions…………………………………………………………………………………………………………… (13)
Nomenclature……………………………………………………………………………………………………… (15)
Sample Calculations……………………………………………………………………………………………… (16)
Supplemental Data………………………………………………………..……………………………………….(17)
References……………………………………………………………………………………………………………. (19)
ii
List of Figures:
Figure 1: Experimental apparatus…………………………………………………………………………. (4)
Figure 2: Time of reaction to as a function of ln((1-X)/Xe)…………………………….……….. (7)
Figure 3: Conversion as a function of residence time…………………….……………………… (8)
Figure 4: Overall conversion as a function of average residence time. ….………………… (9)
Figure 5: Design problem…………………………………………………………..…..……………………… (10)
iii
Abstract
The objectives of the experiment were to determine the reaction rate constants and the
effects of residence time in a series of three CSTRs on conversion of Ph2- for reversible sodium
hydroxide and phenolphthalein reaction [1].
Ph2-+OH-⇌PhOH3[1]
An equal volume liquid mixture of 0.1M sodium hydroxide and 2X10-5 M phenolphthalein was
experimentally determined through a batch reaction to have forward and reverse reaction rate
constants (𝐾1′ and 𝐾2 ) of 6.10 X 10-4 s-1 and 1.90 X10-4s-1 respectively. The forward and reverse
rate constants are on the order of the same magnitude showing the reaction is highly reversible.
It was experimentally determined that an increase of residence time will increase the
overall conversion to Ph2-. At an average residence times per reactor of 321.96 seconds, 257.57
seconds, 214.64 seconds and 183.98 seconds, the overall conversion was 0.653±0.02,
0.397±0.003, 0.215±0.05 and 0.257±0.005 respectively. An average residence time of 321.96
seconds resulted in conversion increases of 64.5%, 202.6% and 153.9% for average residence
times of 257.57 seconds, 214.64 seconds and 183.98 seconds respectively. Experimental results
deviate from the expected conversion trend when comparing the conversion at an average
residence time of 214.64 seconds and 183.98 seconds. The conversion at 183.98 seconds was
19.1% greater. It was concluded that the system at an average residence time of 214.64 seconds
had not yet reached steady state when measurements used to calculate conversion were taken.
This conclusion is supported by the fact that the uncertainty for 214.64 seconds is 900% greater
than the uncertainty for 183.98 seconds.
It was found that a system of three 2.93 L CSTRS with an inlet flow rate of 20 l/h would
result in the desired conversion of 50%. CSTRs 1,2 and 3 would have overall conversions of
0.23, 0.385 and 0.5 respectively.
iv
Introduction
A CSTR is a stirred tank reactor operating at steady state with a continuous inlet and
outlet stream. CSTR in series is when more than one reactor is connected by the outlet stream of
one CSTR being the inlet feed stream of another CSTR [1]. CSTR usage in industry has both
advantages and disadvantages. A CSTR allows for good temperature control, low operating costs
and are easy to clean. A CSTR is also much easier to construct when compared to other reactor
types such as a PFR. The main disadvantage of CSTRs is they provide the lowest conversion per
unit volume of commercially utilized reactors [2]. In industry, CSTRs are primarily used in
homogeneous liquid-phased reactions where mixing is required [1]. For CSTR calculations, it is
assumed that the solution in the tank and in the exit stream is the same constant concentration
[1].
The purpose of the experiment was to determine the kinetic parameters 𝐾1𝐼 and 𝐾2 of
reaction [2].
Ph2-+OH-⇌PhOH3-
[2]
Another goal was to determine the effects of residence time on conversion. The
experimental apparatus consists of a series of 3 CSTRs with varying flowrates of 2x10-5M PH2and 0.1 M OH- as the feed stream. This apparatus provides data on effects of residence time on
conversion. A scaled down batch reactor was used to gather relevant kinetic parameters. A
UV/V spectrophotometry was used to evaluate concentrations of Ph2- in the reactors. It is
hypothesized that as residence time increases by decreasing the feed flow rate, conversion to Ph2will increase.
Theory
The phenolphthalein and sodium hydroxide undergo a twostep reaction scheme.
phenolphthalein (Ph) will rapidly react irreversibly with hydroxide ions (OH-) to produce Ph2and water. Ph2-is the quinoid form of phenolphthalein. Ph2-will then react with hydroxide ions to
produce the carbinol form of Phenolphthalein (PhOH3-). This reaction is the rate determining
step since it is a very slow reversible reaction. The quinoid form of phenolphthalein is a pink
color while the carbinol form of phenolphthalein is clear.
1
𝑃ℎ + 2𝑂𝐻 − → 𝑃ℎ2− + 2𝐻2 𝑂
𝑃ℎ2− + 𝑂𝐻 − ↔ 𝑃ℎ𝑂𝐻 3−
[1]
[2]
The overall rate law for the twostep reaction can be expressed below [1]. This overall rate
law is expressed by the reversible reaction [2] since it is the rate determining step. −𝑟𝐴 is the
overall reaction rate, 𝐾1 is the rate constant of the forward reaction, 𝐾2 is the rate constant of the
reverse reaction, 𝐶𝐴 is the concentration of Ph2, , 𝐶𝐵 is the concentration of the hydroxide ions
and 𝐶𝐶 is the concentration of PhOH3-.
−𝑟𝐴 = 𝐾1 (𝐶𝐴 𝐶𝐵 ) − 𝐾2 𝐶𝐶
[3]
Since the concentration of the hydroxide ions is much greater than any other of the
components concentrations, CB is considered a constant; this allows the rate law can be
simplified by being expressed as a pseudo first order reaction.
−𝑟𝐴 = 𝐶𝐴 𝑘1′ − 𝐶𝑐 𝑘2
[4]
Equation [4] can be written in terms of initial concentration of ph2- (CA0) and conversion
(x) [1].
−𝑟𝐴 = 𝐶𝐴0 (1 − 𝑋)𝑘1′ − 𝐶𝐴0 𝑋𝑘2
[5]
The general mole balance equation can be applied to describe the overall reaction rate in
terms of the differential equation of concentration and time [1].
𝑑𝐶𝐴
𝑑𝑡
= −𝑟𝐴
[6]
When the reaction is at equilibrium, the change in concentration with respect to time is 0.
By combining equations [5] and [6] when the reaction is at equilibrium, the equilibrium
conversion can be described as a function of the kinetic parameters 𝑘1′ and 𝐾2 .
𝑘′
1
𝑋𝑒 = (𝑘 ′ +𝑘
1
2)
[7]
Conversion can be derived as an expression of kinetic parameters and time [1].
𝑑𝑥
𝑑𝑡
= −𝐾1′ (1 − 𝑋) + 𝐾2 𝑋
[8]
Integrating equation [8], conversion as a function of time and rate constants can be solved.
𝑋
𝑙𝑛 (1 − 𝑋 ) = −𝑡(𝑘1′ + 𝑘2 )
𝑒
2
[9]
By graphing equation [8], the obtained slope of the graph is equal to 𝑘1′ + 𝑘2 . Through
use of equation [7], with the known equilibrium conversion, the rate constants for the pseudo
first order reaction can be solved.
Experimentally, conversion information was obtained by converting transmittance
readings into absorbance data and then converting absorbance into conversion. Transmittance
was converted into absorption through the use of Beers Law. A is absorbance, %T is percent
transmittance [3].
𝐴 = 2 − (𝑙𝑜𝑔10 )(%𝑇)
[10]
Absorbance can then be calculated into concentration through equation [11]. ∈ is molar
absorptivity, b is path length and c is concentration. Solving for c, the concentration for every
transmittance reading is able to be calculated. The concentration obtained is the concentration of
Ph2-[3].
𝐴 =∈ 𝑏𝑐
[11]
The conversion of Ph2- experimentally in the series of reactors was calculated through
equation [12]. CAi is the concentration of Ph2- measured at any given time, CA0 is the initial
concentration of Ph2-[1].
𝐶
𝑋 = 1 − 𝐶 𝐴𝑖
[12]
𝐴0
Residence time is the amount of a time a particular particle is expected to remain in a
certain reactor. 𝑉̇ is volumetric flowrate and V is volume of the reactor and 𝜏 is the residence
time . At constant volume, residence time will increase with an increase in flow rate [1].
𝜏=
𝑉
𝑉̇
[13]
Triplicate data was taken at each of the three reactors in series at steady state and each
time interval while constructing time versus conversion graph. Due to triplicate data, standard
deviation was able to be used for all uncertainty.
3
Materials and Methods
-Description of Equipment
Figure 1: flow diagram of the experimental apparatus consisting of 3 CSTRs in series. C A is the concentration of Ph2and X is the conversion of Ph2-.
The experimental CSTRs in series apparatus consisted of 3 equal volume 1000 ml Pyrex
beakers. The experimental working volumes of the CSTRs were found to be 905ml, 933ml and
845ml for CSTRs 1,2 and 3 respectively. Each of the three beakers was agitated with Talboys
engineering 40W mixers. The impeller used in mixing was a pitched, 3 bladed design. The
NaOH and phenolphthalein solutions enter at the top of CSTR 1 in two separate streams. Each
stream enters at the same volumetric flowrate. Model number 714405-05 Cole-Parmer
Instrument Company pumps were used to pump the solutions from the Carboy storage tanks to
the series of reactors. A valve at the bottom of each CSTR allows for steady state transmittance
data to be observed in each reactor. A Thermo Scientific Spectronic 20D+ with an uncertainty of
±0.1% was used to obtain transmittance data throughout the reaction.
-Materials and Chemicals
Water
Tap water from the University of New Hampshire was used when preparing the 0.1M
NaOH solution. The tap water was observed to be slightly basic because it turned pink in the
presence of phenolphthalein which indicates a basic solution. The purity of the tap water was not
determined, however standard tap water normally contains between 300 to 400 ppm of
contamination [4]. Distilled water was used in the preparation of the 0.00002M phenolphthalein
4
solution. The purity of the distilled water was not determined, however standard distilled water
normally contains 1ppm of contamination [4].
Phenolphthalein
The phenolphthalein used experimentally was a solution of 1% phenolphthalein and 99%
ethanol. The chemical was produced by Fisher Scientific and it has purity greater than or equal to
95%. Phenolphthalein is a known carcinogenic so latex gloves and safety glasses were worn at
all times to avoid skin and eye contact. This solution, due to the presence of alcohol is flammable
and slightly explosive. Excessive contact may also cause genetic and organ defects.
Sodium Hydroxide
The sodium hydroxide used during experimentation was produced by the Sigma
Chemical Company. It had purity greater than or equal to 95%. Sodium hydroxide is extremely
corrosive in the case of skin or eye contact. Latex gloves were worn at all times when handling
this chemical. Sodium hydroxide is also toxic to consume or inhale.
-Experimental Procedures
The first step in the experiment was to determine the kinetic parameters (K1 and K2) of
the phenolphthalein and sodium hydroxide reaction. 1L of 2x10-5M phenolphthalein solution
and 50 ml of 0.1M NaOH solution were prepared. The UV/V spectrometer was then calibrated
with 100% transmittance set for light passing through 0.1M NaOH and 0% transmittance set for
when no light was passing through the system. Three 3 ml samples of equal volume 0.1M NaOH
and 2x10-5M phenolphthalein were mixed and their respective transmittance reading was
measured every 90 seconds for a total of 45 minutes. Each of the three samples were staggered
by 30 seconds before starting, this allowed for triplicate data for each 90 second time interval.
The three samples were put away to react for a week. It was assumed that the reaction was at
equilibrium after a week, the transmittance readings of the three equilibrium samples were then
measured.
The two Cole-Parmer Instrument Company pumps were calibrated to relate flow meter
setting to volumetric flowrate. The time it took each pump to fill a 60ml container at flow meter
5
settings of 40, 80 and 120 was recorded. A pump Calibration curve was then created. By using a
linear line of regression, correlations between pump setting and flowrate were determined.
The effect of residence time in a series of CSTRs on the conversion to Ph2- was evaluated
through the experimental apparatus depicted in figure 1. Four total flow rates of 35L/h, 30L/h,
25L/h and 20L/h were tested; each flowrate contained a 1 to 1 volumetric ratio of 0.1M NaOH
and 2X10-5M phenolphthalein. At the beginning of each test, 15L of both 0.1M NaOH and
2X10-5M were prepared. This provided enough solution for the reaction to reach steady state.
The outlet stream from reactor 3 had its transmittance evaluated through UV/V spectrometry
every 2 minutes. The process continued until there was only negligible change in the
transmittance of the outlet stream, signifying steady state. The transmittance of reactors 1,2 and 3
was measured once the reaction had reached steady state. Lastly, the volume of each CSTR was
measured.
-Analytical Procedures
UV/V spectrometry was used to measure the transmittance of the sample solution of the
phenolphthalein and sodium hydroxide reaction. The spectrometer was set so 100%
transmittance was when light passed through a sample of 0.1M NaOH and 0% was set when the
when no light as passed through the transmittance sensors. Transmittance is defined as the
percentage of light that is absorbed by a given sample.
6
Results
0
500
Time (seconds)
1000
1500
2000
0
ln((1-X)/Xe)
-0.5
-1
-1.5
y = -0.0008x
R² = 0.9611
-2
-2.5
Figure 2: Elapsed Time of reaction as a function of ln((1-X)/Xe). Each sample was composed of a 1:1 volumetric
amount of 0.1M NaOH and 2X10-5M Phenolphthalein. Transmittance values for three samples were measured in
90 second intervals for duration of 45 minutes. Due to triplicate data points standard deviation was used to
represent the uncertainty.
In figure [2] a linear line of regression was used to relate Time of reaction to
ln((1-X)/Xe). As shown by the R2 value of 0.96, there is a strong linear correlation between
reaction time and ln((1-X)/Xe). The equilibrium conversion (Xe) for the reversible
Phenolphthalein and sodium hydroxide reaction was experimentally determined to be
0.7623±0.0008. The slope of the linear line of regression is -0.0008. Through the use of
equations [7] and [8], with the use of the linear regression slope, the forward and reverse reaction
rate constants (𝐾1′ and 𝐾2 ) were determined to be 6.10 X 10-4 s-1 and 1.90 X10-4s-1 respectively.
7
0.8
0.7
Conversion
0.6
0.5
0.4
0.3
0.2
0.1
0
150
200
250
300
350
residence time (seconds)
Figure 3: Conversion of Ph2- as a function of residence time. (X) represents a flowrate of 17.5L/h, ( ▪) represents
15L/h, (−) represents 12.5L/h and (•) represents 10L/h. Each of the three data points per flowrate represent the
total overall conversion exiting each of the three reactors. Red represents the conversion at CSTR 1, Green
represents the conversion at CSTR 2 and black represents the conversion at CSTR 3. Due to triplicate data points,
standard deviation was used to represent the uncertainty.
Four flowrates, 10L/h, 12.5L/h, 15L/h and 17.5L/h with equal volume amounts of 0.1M
sodium hydroxide and 2X10-5M phenolphthalein were fed into a series of three CSTRs. Flow
rate is directly related to the residence time in CSTRs. The working volume of CSTRs 1,2 and 3
was measured to be 0.905L, 0.933L and 0.845 L respectively. Figure [3] generally follows the
expected trend that an increase of residence time will increase conversion to Ph2- . The total
conversion at CSTR 3 with a flowrate of 10L/h, resulting in a residence time of 304.2 seconds is
0.653±0.02 while the total conversion at CSTR 3 at a flow rate of 17.5L/h with a residence time
of 173.8 seconds has a conversion of 0.2572±0.005. The reduced residence time will result in a
conversion 153.9 % greater.
8
0.8
0.7
Conversion
0.6
0.5
0.4
0.3
0.2
0.1
0
321.96
257.57
214.64
183.98
residence time (seconds)
Figure 4: Average residence time in each of the 3 CSTRs and the subsequent total overall conversion. Due to
triplicate data points standard deviation was used to represent the uncertainty.
At average residence times per reactor of 321.96 seconds, 257.57 seconds, 214.64
seconds and 183.98 seconds, the overall conversion was 0.653±0.02, 0.397±0.003, 0.215±0.05
and 0.257±0.005 respectively. An average residence time of 321.96 seconds resulted in a
conversion increase of 64.5%, 202.6% and 153.9% for average residence times of 257.57
seconds, 214.64 seconds and 183.98 seconds respectively.
Depicted in both figures [3] and [4], a flow rate of 17.5L/h with an average residence time
of 183.98 seconds per reactor and a flow rate of 15L/h with an average residence time of 214.64
seconds deviate from the expected trend. An average residence time of 214.64 seconds resulted
in a 19.1% increase in conversion. The overall uncertainty of the flowrate of 15L/h is ±.05; this
uncertainty is 250% greater than the next largest experimental uncertainty of ±0.02 and 900%
greater than the uncertainty at 17.5L/h.
Discussion
Reaction [2], composed of a 1:1 volumetric amount of 0.1M NaOH and 2X10-5M
Phenolphthalein has an experimentally calculated forward rate constant of 6.10 X 10-4 s-1 and
reverse rate constant of 1.90 X10-4 s-1. The forward and reverse rate constants are on the order of
the same magnitude showing the reaction is highly reversible. Literature values for the reaction
with a 1:1 volumetric composition and initial concentrations of 0.0017M sodium hydroxide and
9
5.95X10-6M phenolphthalein suggest the forward rate constant is 7.511X10-3s-1 and the reverse
rate constant is 1.149-4s-1 [5]. It is assumed the literature rate constants, although having
different initial concentrations, relate to the experimental rate constants because NaOH is 5
magnitudes greater than phenolphthalein in both the experimental and literature apparatuses. A
much larger concentration means both the experimental and literature reaction can be assumed to
be pseudo first order. Literature values and experimental values both agree that reaction [2]
favors the product, the carbinol form of phenolphthalein due to a larger K1 value. Through
observations, the reaction faded in color with time; this further confirms that the forward reaction
is favored because the carbinol form of phenolphthalein is colorless. Both literature and rate
constant values were for the reaction at room temperature 298K± 4K. The difference between
literature values and experimental values could possibly be due to different initial concentrations
of sodium hydroxide and phenolphthalein. Another possibility is the experimental samples used
in calculations had not reached equilibrium. Ideally equilibrium should be measured after an
infinite amount of time. For practicality, samples were assumed at steady state after a week of
reacting. One last possible source of error could be from the fact that experimental sample were
only measured for transmittance for 45 minutes compared to 100 minutes for the literature
samples. More data points could change the slope of the time versus ln((1-X)/Xe figure. The
slope was used to quantify the rate constant values.
Another goal of the experiment was to determine the effects of residence time on
conversion to Ph2- in a series of 3 CSTRs. It was hypothesized that an increased residence time
would increase overall conversion. Figures [3] and [4] both show that an increase of residence
time will increase the overall conversion to Ph2-. At an average residence time of 321.96 seconds
conversion is higher than an average residence time of 214.64 seconds. Likewise, the average
residence time of 257.57 has a greater conversion than average residence times of 214.64
seconds and 183.98 seconds.
A study on the effect of residence time on conversion of Phenylalanine in a
phenylalanine and high temperature water reaction is assumed to follow the same conversion
trend as the experimental reaction. At a water temperature of 280oC, conversion was found to be
0.60, 0.66, 0.70 and 0.73 for residence times of 90 minutes, 120 minutes, 150 minutes and 180
minutes respectively [6]. The literature conversion increasing with residence time further
confirms the hypothesis and adds validity to the observed experimental trend.
10
Experimental data deviates from the expected conversion trend when comparing the
conversion at a flowrates of 15l/h and 17.5 L/h. 17.5L/h experimentally had a higher conversion.
As shown from the large relative error associated with the 15L/h flowrate, it is very likely that it
had not yet reached steady state when transmittance measurements were taken.
The knowledge that conversion will increase with a decreased flow rate, resulting in a
higher residence time is very significant to industrial processes. A higher conversion results in a
more cost efficient process. The minimum flowrate that will provide the desired amount of yield
will be the ideal settings in a CSTR apparatus. Another way to increase residence time is to
increase the volume of each reactor; conversion is a function of reactor volume [1].
Conversion will increase with increased residence time because the mixture will remain
in each reactor longer which allows more reactant to be converted to product, increasing
conversion. This can be explained through equation [14] where x is conversion, 𝜏 is residence
time, k is the rate constant and n is the number of reactors in series [1].
1
𝑋 = 1 − (1+𝜏𝑘)𝑛
[14]
As n and 𝜏 increase the overall conversion in the CSTR will also increase.
Possible sources of error in calculations of conversion could be from the assumption that
the solution in the tank and in the exit stream are the same constant value and that the tank is
perfectly mixed. It is also possible that the sample that was measured for its transmittance could
have been taken from a dead zone. A dead zone is an almost stagnant region in a reactor where
little reaction takes place [1]. To further improve the experiment the reactors should have been
reacted for a longer period of time to ensure steady state was reached. All calculations were
made with the assumption that this was an ideal system, to further improve accuracy; a non-ideal
system should be considered.
Design Solution
A stabilizer for latex blends enters a series of CSTRs at a flow rate of 20 l/h with a 50%
conversion. It is assumed that the stabilizer process can be directly modeled after reaction [2],
which involves the reaction of phenolphthalein and sodium hydroxide. It was assumed that there
11
were three CSTRs in series. A series of three CSTRs was chosen because the experimental
apparatus consisted of three reactors.
It is assumed that the inlet feed stream was a 1:1 volumetric ratio of 2X10-5M Ph2solution and 0.1M OH- solution. The initial concentration of Ph2- (𝐶𝐴0 ) can be solved.
𝐶𝐴0
2𝑋10−5 𝑚𝑜𝑙 10𝐿
(
)(
)
𝐿
ℎ
=
= 1𝑋10−5 𝑀
20𝐿
ℎ
The initial molar flowrate of the PH2- (𝐹𝐴0 ) can be solved by equation [15]. 𝐶𝐴0 is the
initial concentration of Ph2- and 𝑣𝑜 is the initial volumetric flow rate of the feed [1].
𝐹𝐴0 = 𝐶𝐴0 𝑣𝑜
𝐹𝐴0
[15]
1𝑋10−5 𝑚𝑜𝑙 20𝐿
ℎ
𝑚𝑜𝑙
=(
)(
) = 5.55𝑋10−8
)(
𝐿
ℎ
3600𝑠
𝑠
The rate of disappearance of Ph2- (−𝑟𝐴 ) is defined by equation [4]. 𝑘1′ and 𝑘2 were
experimentally determined and found to be 6.10 X10-4 sec-1 and 1.90X10-4sec-1 respectively.
−𝑟𝐴 = 𝐶𝐴 𝑘1′ − 𝐶𝑐 𝑘2
[4]
Setting 𝐶𝐴 = (1 − 𝑥)𝐶𝐴0 and 𝐶𝑐 = 𝐶𝐴0 𝑋, the rate of disappearance of Ph2- is able to be
evaluated through equation [5].
−𝑟𝐴 = 𝑘1′ (1 − 𝑥)𝐶𝐴0 − 𝑘2 𝐶𝐴0 𝑥
CSTR 1
CSTR 2
[5]
CSTR 3
Figure 5: A levenspiel plot is able to be implemented by constructing a curve of
Each of the three rectangles represents the volume of one of the CSTRs[1].
12
𝐹𝐴0
−𝑟𝑎
as a function of conversion.
It was assumed that each CTSR had the same volume. This assumption was made
because in industrial processes it is highly likely that each reactor will be the same size. Each
reactor was found to have a volume of 2.93m3. CSTRs 1,2 and 3 will have conversions of 0.23,
0.385 and 0.5 respectively.
Conclusions

2X10-5 M phenolphthalein was experimentally determined through a batch reaction to
have forward and reverse reaction rate constants (𝐾1′ and 𝐾2 ) of 6.10 X 10-4 s-1 and 1.90
X10-4s-1 respectively.

An increase of residence time will increase the overall conversion to Ph2-. At average
residence times per reactor of 321.96 seconds, 257.57 seconds, 214.64 seconds and
183.98 seconds, the overall conversion was 0.653±0.02, 0.397±0.003, 0.215±0.05 and
0.257±0.005 respectively. An average residence time of 321.96 seconds resulted in a
conversion increase of 64.5%, 202.6% and 153.9% for average residence times of 257.57
seconds, 214.64 seconds and 183.98 seconds respectively.

Experimental results deviate from the expected conversion trend when comparing the
conversion at an average residence time of 214.64 seconds and 183.98 seconds. The
conversion at 183.98 seconds was 19.1% greater. It was concluded that the system at an
average residence time of 214.64 seconds had not yet reached steady state when
measurements used to calculate conversion were taken. This conclusion is supported by
the fact that the uncertainty for 214.64 seconds is 900% greater than the uncertainty for
183.98 seconds
13

A system of three, 2.93 L CSTRS with an inlet flow rate of 20 l/h would result in the
desired conversion of 50%. CSTRs 1,2 and 3 would have overall conversions of 0.23,
0.385 and 0.5 respectively
14
Appendices:
A. Nomenclature
A Absorbance
b path length
CA concentration of species A
CA0 initial concentration of species A
CB concentration of species B
Cc concentration of species C
c concentration
𝒅𝑪𝑨
𝒅𝒕
change in concentration with respect to time
𝑭𝑨𝟎 initial molar flow rate of species A
V volume
𝑽̇ volumetric flow rate
K1 rate constant of forward reaction
𝑲′𝟏 rate constant of pseudo first order forward reaction
K2 rate constant of reverse reaction
n number of CSTRs in series
−𝒓𝑨 Overall reaction rate- disappearance of species A
t time
T transmittance
X conversion
Xe equilibrium conversion
∈ is molar absorptivity, b is path length
τ residence time
15
B. Sample Calculations
Conversion of transmittance to absorbance at 10L/h at CSTR 3 with transmittance measured to
be 78.73%.
𝐴 = 2 − (𝑙𝑜𝑔10 )(%𝑇) = 2 − (𝑙𝑜𝑔10 )(78.73) = 0.104
Absorbance can we calculated into concentration (c).
𝐴 =∈ 𝑏𝑐
𝑀
0.104 = (30,000 𝑐𝑚) (1𝑐𝑚)𝑐
Solving for c, the concentration is determined to be 3.46X10-6M
With concentration determined, conversion can be solved for.
𝐶
𝑋 = 1 − 𝐶 𝐴𝑖
𝐴0
𝑋 =1−
3.46𝑥10−6 𝑀
1𝑥10−5 𝑀
= 0.653
Residence time for CSTR 1 at 12.5L/h can be calculated through equation [14].
𝑉
0.905𝐿
𝜏 = 𝑉̇ =
𝐿
ℎ
12.5
= 0.0724ℎ
Calculation of forward and reverse rate constants through use of slope of time vs ln((1-X)/Xe).
m= -0.0008= 𝑘1′ + 𝑘2
The equilibrium conversion was experimentally determined.
𝑘′
1
𝑋𝑒 = (𝑘 ′ +𝑘
1
2)
𝑘′
1
0.763 = −0.0008
16
𝑘1′ =6.10 X 10-4 s-1
-0.0008= 6.10 𝑋 10−4 𝑠 −1 + 𝑘2
K2=1.90 X10-4s-1
C. Supplemental Data
7
Flow Rate (ml/s)
6
5
4
3
y = 0.0541x
R² = 0.9925
2
1
0
0
20
40
60
80
100
120
140
Pump Setting
Figure 6: Calibration for NaOH pump. Linear line of regression used to relate pump setting to flow rate.
7
Flow Rate (ml/s)
6
5
4
3
y = 0.0504x
R² = 0.8334
2
1
0
0
20
40
60
80
100
120
140
Pump Setting
Figure 7: Calibration for phenylalanine pump. Linear line of regression used to relate pump setting to flow rate.
17
Table 1: uncertainty associated with graph of time vs ln(1-X/Xe)
time
ln(1-X/Xe)
0
90
180
270
360
450
540
630
720
810
900
990
1080
1170
0
-0.0231329
-0.0750677
-0.1811403
-0.2419712
-0.2943248
-0.3999879
-0.5504592
-0.5788882
-0.5590194
-0.6349487
-0.7344391
-0.6978451
-0.7300256
error
0
0.04943165
0.0618443
0.06448913
0.06864842
0.02132692
0.04027106
0.09631671
0.02331727
0.06710209
0.04503123
0.03893472
0.14135766
0.04757511
time
1260
1350
1440
1500
1560
1620
1680
1740
1800
1860
1920
1980
2040
ln(1-X/Xe)
-0.9284748
-0.8901943
-0.9650071
-1.0333143
-1.3363111
-1.363536
-1.4406768
-1.3872377
-1.5492382
-1.6227281
-1.6235082
-1.6909847
-1.8245149
error
0.04917602
0.13948792
0.1033075
0.21460222
0.17413911
0.12587277
0.22565388
0.12532747
0.1526354
0.20554787
0.4346981
0.38704399
0.21392415
Table 2: uncertainty values for conversion to Ph2-. Uncertainty was determined through standard deviation.
CSTR 1
10L/h
12.5L/h
15L/h
17.5L/h
Average
conversion
uncertainty
Average
conversion
uncertainty
Average
conversion
uncertainty
Average
conversion
uncertainty
CSTR 2
CSTR 3
0.56928 0.580844 0.65373
0.011926 0.022573 0.023944
0.274903 0.361447 0.397015
0.004778 0.005191 0.002537
0.114369 0.164895 0.215886
0.056834 0.06218 0.047583
0.19291 0.229546 0.257276
0.020469 0.017328 0.005591
18
References
[1] H. Fogler, Ed., Elements of Chemical Reaction Engineering. NJ: Prentice-Hall, 2006.
[2] Continuous Stirred Tank Reactors (CSTRs). Available:
http://www.umich.edu/~elements/5e/asyLearn/bits/cstr/index.htm.
[3] Beer's Law. Available: http://teaching.shu.ac.uk/hwb/chemistry/tutorials/molspec/beers1.htm.
[4] (5/2/2011). What is the difference between distilled and purified water?.
Available: http://www.endlesswaters.com/distilled-or-purified-water.
[5] K. Y. Tam and F. T. Chau, Simultaneous multiwavelength study of the reaction of
phenolphthalein with sodium hydroxide, Journal of Automatic Chemistry, Vol. 14, No. 5, pp.
157-162.
[6] Shujauddin Changi, Adam J. Matzger, Phillip E. Savage, Kinetics and pathways for an algal
phospholipid (1,2-dioleoyl-sn-glycero-3-phosphocholine) in high-temperature (175–350 °C)
water, Green Chemistry, 2012, 14, 10, 2856
19