liquid phase reactor

A. SUMMARY

The topic investigated in this experiment was liquid phase chemical reactors with the

effect of temperature on reaction rate constant. This is significant in Chemical

Engineering because of the underlying importance it has in understanding how a

chemical reaction works (i.e. chemical kinetics). In addit ion, knowing

the kinetics of a reaction wil l help chemical engineers in optimum

reactor design.

The major objective of this lab was to find the reaction rate constant in a batch

stirred tank reactor for the saponification ethyl acetate with dilute sodium hydroxide.

Another objective was to study the effect of temperature on reaction rate constant,

and also to find the values of the rate constant and the Arrhenius parameters;

activation energy, Ea and pre-exponential factor, A).

In carrying out the experiment, a chemical reactor service unit fitted with batch

chemical reactor was used (see figure 1 for the diagram of the experimental set up).

From the experiment, some key results were obtained. One of such result was that

for any given chemical reaction, the reaction rate is temperature dependent. Thus,

an increase in temperature causes an increase in the reaction. Also, the conductivity

of the reactants decreases with time as the reactants loses their ions and become

less conductive. Another important finding was that as the concentration of the

hydroxide reduces, the reaction rate increases.

Going by the objectives of the lab, the Arrhenius parameters were estimated to be

197.87 and 501.625 kJ/mol respectively (i.e. the pre-exponential factor and

activation energy). In addition, the reaction rate constant (k) for the reactions were

estimated to be 0.0101 M-1s-1 at 25°C, 0.2853 M-1s-1 at 30°C and 0.0089 M-1s-1 at

40°C respectively.

From the experiment, it can be concluded that temperature plays a major part in

chemical kinetics (rate increases as temperature increases). Also, in a chemical

reaction, as the reactant (s) are been converted into products, the conductivity

changes. Finally, in homogenous (same phase) reaction that is second order overall

(first order in both components) like the one done in the lab, the concentration of the

reactants also affects the reaction rate.

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B. INTRODUCTION:

One of the major objectives of this lab was to find the reaction rate constant using a

batch stirred tank reactor for the saponification ethyl acetate with dilute sodium

hydroxide. Another objective was to study the effect of temperature on reaction rate

constant, and also to find the values of the rate constant and the Arrhenius

parameters; activation energy, Ea and pre-exponential factor, A). In the course of the

experiment, the effect of concentration of reactants on a homogenous reaction was

also considered.

One of the three types of reactors in chemical processes is the batch reactor. In this

type of reactor, the total feed is introduced at the beginning and no withdrawal is

made until the reaction has reached the degree of completion desired; hence it is a

closed system reactor. It differs from a continuous stirred tank reactor (CSTR) which

has material exchange taking place during the reaction.

For this experiment, a stirred tank batch reactor was used; meaning it has a stirrer to

ensure continuous mixing of the reactants to aid in a homogenous concentration

throughout the mixture. Another important thing to note about this type of reactor is

that it works with an unsteady process (that is all variables change with time).

Also, the mixture in the volume is assumed to be perfectly mixed (that is there will be

uniform concentrations). In addition, temperature will be uniform throughout the

reactor; however it may change with time (Basu, 2012). Also, batch reactors are

often used for liquid-phase reactions particularly when the required production is

small (Smith, 1981).

Generally, the mass balance for a stirred tank reactor can be written as:

Rate of change within the reactor = Input – Output – Loss by reaction. For any liquid

phase chemical reactor with a constant volume such as the batch stirred tank

reactor, this can be rearranged to give: Rate of change within the reactor = loss by

reaction.

Thus for any given reaction in constant volume, the rate equation can be given as:

−dC A

dt=r A (1)

Where:

r A is the rate of disappearance of reactant ‘A’ among the reacting species

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C A is the concentration of reactant ‘A’ in the exit stream

t is the time in seconds it takes for reactant ‘A’ to disappear

For a bimolecular reaction like the one in the experiment; the saponification of ethyl

acetate with dilute sodium hydroxide which is given as:

NaOH+CH 3COOC 2H 5→CH 3COONa+C2H 5OH

The rate law for such reaction can be written as:

−r A=k C An CB

m (2)

Where:

k is the rate constant

n and m are appropriate powers based on experimental result

C A is the concentration of reactant ‘A’ in the exit stream

CB is the concentration of reactant ‘B’ in the exit stream

Generally several factors could influence the rate of a chemical reaction. Some of

these factors include:

(i) Temperature

(ii) Concentration (if homogenous)

(iii) State of reactants (that is if they are solid, liquid or gas)

(iv) Order of reaction

(v) Pressure

Out of the above mentioned factors, the effect of temperature on the reaction rate

was the one studied. Though, the effect of concentration was also observed because

the reaction that was studied was a homogenous reaction. The relationship between

reaction rate and temperature is explained by Arrhenius equation which is given as:

k=A∗e−EaRT

(3)

Where:

k is the reaction rate constant

R is the universal gas constant (8.314 J mol-1K-1)

T is temperature (K)

Ea is the activation energy (J mol-1)

A is Arrhenius constant or pre-exponential factor (s-1) for a first order reaction

By applying natural logarithm to both sides, equation (3) can be re-written as:

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¿k=¿ A−EaRT

(4)

From equation (4), a plot of ¿k against 1/T would yield a straight line graph from

which ‘A’ can be obtained as the intercept of the line at 1/T = 0. The activation

energy (Ea) can be obtained from the slope of the graph which is given as−EaRT

.

Thus if the slope, S =−EaRT

, then the activation energy can be estimated as:

Ea=−R∗slope (5)

It is noteworthy to mention here that reactions with low activation energy are

relatively temperature-insensitive while those with high activation energies are very

temperature sensitive. Therefore, any given reaction is much more temperature-

sensitive at a low temperature than at a high temperature (Levenspiel, 1999).

From the above, it shows that the reaction rate constant has to be obtained first

before applying Arrhenius equation to find the Arrhenius parameters. This can be

done by referring to reaction to be studied:

NaOH+CH 3COOC 2H 5→CH 3COONa+C2H 5OH

The rate of the reaction can be said to depend on the concentrations of both reactant

‘A’ (NaOH ¿and reactant ‘B’ (CH 3COOC 2H 5 ¿. The order of the reaction studied is

known to be first order with respect to both ‘A’, and ‘B’ , hence second order overall.

Thus by combining equation (1) and (2), an expression for the reaction rate constant

in terms of the concentration of A and B can be obtained as:

dC A

dt=kC ACB

(6)

Where:

All the parameters are as defined in equation (2)

If the initial concentration of reactant A (CA0) and reactant B (CB0) are made to be

equal, then equation (6) can be reduced to:

dC A

dt=kC A

2 (7)

Integrating equation (7) yields:

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kt= 1C A

− 1C A 0

(8)

Where:

k , t , C A and C A0are as defined before.

From equation (8), it can be seen that a graph of 1CA

against t will give a straight line

graph with slope equal to k (reaction rate constant) and intercept 1CA 0

For the experiment, to calculateC A, the conductivity of the one of the reactants; in

this case reactant ‘A’ (Sodium hydroxide) can be measured at various time intervals.

With this, the concentration of the hydroxide can be calculated as:

C A(t)=CA 0k (t )−k∞k 0−k∞

(9)

Where:

C A is the concentration of reactant ‘A’ in the exit stream at time t

C A0 is the initial concentration of NaOH

k (t ) is the conductivity of the solution at time t

k∞ is the conductivity of the solution at the end of reaction

k 0 is the initial conductivity at time t = 0

Note:

k 0 can be found by plotting a graph of the measured conductivity (k) against time and

extrapolating to t = 0.

k 0 can also be found from the same graph by extrapolating to large t.

The rationale for calculating the concentration of the hydroxide by evaluating

conductivity is that the degree of conversion of reactants affects the conductivity of

the reactant contents, so that recording the conductivity with respect to time helps to

calculate the amount of conversion (Denbihh and Turner, 1971).

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C. EXPERIMENTAL EQUIPMENT

The major equipment used in the experiment was a chemical reactor service unit

fitted with batch chemical reactor. A diagram of the experimental set up is shown in

figure 1. Other equipment used include; thermostatic bath to control the temperature

stability of the two reactants to be added in at any time, 1 litre glass flasks containing

the reactants, conductivity meter to measure the conductivity of the solution,

stopwatch and stock solutions of 0.1M solution of sodium hydroxide and 0.1M of

ethyl acetate.

A batch reactor is one of the three types of reactors in chemical processes. It is

similar to the continuous stirred tank reactor in the sense that the mixture in the

volume is stirred but unlike the continuous stirred tank reactor where there is a

continuous supply of feed while products are continually removed, in the case of the

batch reactor; there is no inflow or outflow of material. The total feed is introduced at

the beginning and no withdrawal is made until the reaction has reached the degree

of completion desired.

This type of reactor is mostly used for liquid-phase chemical reactions, especially on

a small scale. Thus when used for liquid-phase reactions, the reactor volume does

not change significantly with the extent of reaction. For a gas-phase reaction, it may

be constant pressure sometimes. In addition, since the mixture in the tank is

assumed to be perfectly mixed, there will be uniform concentrations, and

temperature will also be uniform throughout the reactor; however with time it may

change. See figure 1 and 2 for a schematic diagram of a batch stirred tank reactor

and the experimental set-up respectively. The picture of the experimental set up is

also shown in figure 3.

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Figure 1: Schematic diagram of a batch stirred tank reactor

Source: http://www.rpi.edu/dept/chem-eng/Biotech-Environ/IMMOB/stirredt.htm

Figure 2: Schematic diagram of the experimental set up

Stirrer

Reactant components

Figure 3: Diagram of the experimental set-up

D. EXPERIMENTAL PROCEDURE AND OBSERVATIONS

For safety reasons safety goggles and protective gloves were worn

during the course of the experiment advised to wear safety goggles and

protective gloves. After this, 0.1M sodium hydroxide and 0.1 M ethyl acetate

were provided to run the experiment. Then the reaction temperature was set to 25°C

on the thermostatic bath.

Then the two 1 l i tre f lasks were fi l led to the mark with sodium hydroxide

solution and ethyl acetate solution respectively and placed in a bath.

The reaction temperature was then set on the reactor control panel.

After this, the conductivity meter was set and the probe end was placed

in the bath to get to get to the reaction temperature. The flasks were

also allowed to reach the reaction temperature.

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Conductivity probe

Reaction vessel

Conductivity meter

Temperature probe

Ethyl acetate NaoH

Temperature adjuster

The 1 l i tre of sodium hydroxide solution was added to the reactor,

fol lowed by the 1 l i tre of ethyl acetate solution, and the clock was

started when ca. 50% of ethyl acetate solution was added. After wait ing

for about 30 seconds, ca. 200ml was withdrawn and the conductivity

was measured, and then the sample was returned to the reactor while

the probe was returned to the bath.

The conductivity readings were taken every 30 seconds for about 10

minutes. It was then allowed to run for further 20 minutes and the

readings were taken after every 3 minutes.

The experiment was then repeated for reaction temperatures of 30°C

and 40°C. Some observations were then made, one of which was that

with t ime the conductivity of the solution decreases. This could be as a

result of loses of ions in the solution, thereby making it less conductive.

E. RESULTS AND CALCULATIONS

The results (both experimental and calculated, and extrapolated results) obtained in

the experiment are shown in table 1- 4 below. The graphs are shown in figures 3 - 9

Table 1: Measured conductivity values at different reaction temperatures

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t (s)Conductivity, k @ 25°C (S/m)

Conductivity, k @ 30°C (S/m)

Conductivity, k @ 40°C (S/m)

30 1.511 0.601 1.69860 1.398 0.544 1.51190 1.308 0.498 1.386

120 1.246 0.462 1.304150 1.188 0.431 1.246180 1.140 0.407 1.199210 1.100 0.387 1.161240 1.066 0.37 1.13270 1.037 0.355 1.105300 1.011 0.343 1.084330 0.988 3.33 1.065360 0.968 0.324 1.049390 0.950 0.317 1.035420 0.934 0.31 1.022450 0.918 0.305 1.011480 0.906 0.3 1.001510 0.893 0.296 0.984540 0.882 0.292 0.976570 0.871 0.289 0.969600 0.862 0.287 0.955780 0.818 0.276 0.936960 0.787 0.271 0.9131140 0.765 0.268 0.8961320 0.748 0.266 0.8821500 0.735 0.265 0.87

Table 2: Calculated hydroxide concentration CA at different temperatures

t (s) CA @ 25°C CA @ 30°C CA @ 40°C

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30 0.1250 0.1383 0.132260 0.1156 0.0710 0.117790 0.1082 0.0593 0.1079

120 0.1031 0.0501 0.1015150 0.0983 0.0422 0.0970180 0.0943 0.0361 0.0934210 0.0910 0.0310 0.0904240 0.0882 0.0267 0.0880270 0.0858 0.0229 0.0860300 0.0836 0.0198 0.0844330 0.0817 0.0173 0.0829360 0.0801 0.0150 0.0817390 0.0786 0.0132 0.0806420 0.0773 0.0115 0.0796450 0.0759 0.0102 0.0787480 0.0749 0.0089 0.0779510 0.0739 0.0079 0.0766540 0.0730 0.0069 0.0760570 0.0720 0.0061 0.0754600 0.0713 0.0056 0.0744780 0.0677 0.0028 0.0729960 0.0651 0.0015 0.0711

1140 0.0633 0.0008 0.06981320 0.0619 0.0003 0.06871500 0.0608 0.000 0.0677

Table 3: Calculated reciprocal of hydroxide concentration (1/CA) at different

temperatures.

t (s) 1/CA @ 25°C 1/CA @ 30°C 1/CA @ 40°C30 8.001 7.231 7.564

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60 8.648 14.086 8.50090 9.243 16.867 9.266

120 9.703 19.949 9.849150 10.177 23.675 10.307180 10.605 27.676 10.711210 10.991 32.213 11.062240 11.341 37.429 11.365270 11.659 43.667 11.623300 11.958 50.385 11.848330 12.237 57.794 12.059360 12.490 66.610 12.243390 12.726 75.577 12.409420 12.944 87.333 12.567450 13.170 98.250 12.703480 13.344 112.286 12.830510 13.539 126.774 13.052540 13.707 145.556 13.159570 13.881 163.750 13.254600 14.026 178.636 13.448780 14.780 357.273 13.721960 15.362 655.000 14.0671140 15.804 1310.000 14.3341320 16.163 3930.000 14.5611500 0.000 0.000 0.000

Initial conductivity,k0

@ 25°C (S/m)


@ 30°C (S/m)


@ 40°C (S/m)

Conductivity at end of

reaction, k∞

@ 25°C (S/m)

Conductivity at end of reaction, k∞

@ 30°C (S/m)

Conductivity at end of

reaction, k∞

@ 40°C (S/m)

1.209 0.4346 1.2843 0 0 0

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Table 4: Extrapolated data

k0 was extrapolated to t = 0 from a graph of measured k against t in figure 4, 5 and 6

k∞ was extrapolated to large t from a graph of measured k against t in figure in figure

4, 5 and 6.

Table 5: Reaction rate constants at different temperatures

Reaction rate constant, k@ 30°C ( M-1s-1 )



0.0101 0.2853 0.0089

These values were obtained from figures 7, 8 and 9.

0 200 400 600 800 1000 1200 1400 16000.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1.600

f(x) = − 0.000432987654320987 x + 1.20903407407407

Time, t (seconds)

Mea

sure

d co

nduc

tivity

, k (S

/m)

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Figure 4: Graph of conductivity against time at reaction temperature of 25 °C

0 200 400 600 800 1000 1200 1400 16000.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

f(x) = − 0.000172329218106996 x + 0.434598024691358

time, t (seconds)

Mea

sure

d Co

nduc

tivity

, k (S

/m)


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0 200 400 600 800 1000 1200 1400 16000.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1.600

1.800

f(x) = − 0.000393218106995884 x + 1.28426469135802

time, t (seconds)

Mea

sure

d Co

nduc

tivity

, k (S

/m)


0 100 200 300 400 500 600 7000

2

4

6

8

10

12

14

16

f(x) = 0.0100635628274733 x + 8.54951503276483

time, t (seconds)

1/CA

(M)

Figure 7: Graph of 1/CA against time at reaction temperature of 25 °C

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0 100 200 300 400 500 600 7000

20

40

60

80

100

120

140

160

180

200

f(x) = 0.285281895218509 x − 20.5766175931413

time, t (seconds)

1/CA (M)


0 100 200 300 400 500 600 7000.000

2.000

4.000

6.000

8.000

10.000

12.000

14.000

16.000

f(x) = 0.00892611933035733 x + 8.67920958875541

time, t (seconds)

Mea

sure

d co

nduc

tivity

, k (S

/m)


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0.00329

0.0033

0.00331

0.00332

0.00333

0.00334

0.00335

0.00336

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

f(x) = − 60334.5561617578 x + 197.869733707811

Series2Linear (Series2)

1/T (K)

In k

Figure 10: Graph of In (k) against 1/T showing the effect of temperature on reaction

rate constant.

Note: When plotting the graph of ln (k) against 1/T, the value of the reaction rate

constant (k) gotten when the reaction temperature was 40 °C as shown in figure 9

was not used. This was because from the readings gotten from the experimental as

shown in table 1, an experimental error was suspected to have occurred thereby

giving wrong readings. This error could possibly be in the reading of the conductivity

meter.

SAMPLE CALCULATIONS:

(A) Sample calculation for the concentration of the hydroxide.

Hydroxide concentration at 25°C in 30 seconds.

Using equation (9) C A(t)=CA 0k (t )−k∞k 0−k∞

When CA0 = 0.1 M, k (t) = 1.511 S/m, k∞ = 0, k0 = 1.209

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∴C A( t)=0.11.511−01.209−0 = 0.1250 M

→ 1/CA = 1/0.1250 = 8.001

Using same procedure, the hydroxide concentration (CA) and its reciprocal (1/CA) at

30°C and 40°C at various time intervals were also calculated.

(B) Calculation of Arrhenius parameters (A and Ea)

From equation (4): ¿(k )=¿ A−EaRT

A graph of In (k) against 1/T as shown in figure 8 will yields a straight line with

intercept ‘A’

∴ Arrhenius parameter (A) = 197.87

Activation energy (Ea):

From equation (5): Ea=−R∗slope

Where slope in figure 8 = - 60335, R = 8.314 *10-3 kJ mol K-1

∴ Ea=−60335 ¿8.314 *10-3) = 501.625 kJ/mol = 501625.19 J/mol

F. DISCUSSION OF RESULTS:

From the results obtained in the experiment, it shows that reaction rate is dependent

on temperature, through the dependence of reaction rate constant on ‘k’ on

temperature ‘T’. This can be seen from figure 9 where a plot of In (k) against 1/T

gave a straight line graph. This can also be seen from table 1 where at a

temperature of 25 °C, the reaction rate constant was 0.010 M-1s-1, while at 30 °C it

was 0.2853 M-1s-1 . At 40 °C, the reaction rate constant was 0.0089 M-1s-1.

Thus reaction rate increases with an increase in temperature. This is because as

temperature increases, the reactants will acquire a lot of kinetic energy; hence there

will be more collision between the reacting molecules. In addition, this temperature

rise will also bring the reaction closer to its activation energy which is the minimum

amount of energy needed for a chemical reaction to occur.

It is noteworthy to mention here that even though there is suppose to be an

increasing trend in the reaction rate with time, at 40 °C there was a decrease. The

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reason could be because of an experimental error. This could be due to the readings

of the conductivity meter.

Thus when a graph of In (k) was plotted against 1/T to estimate the Arrhenius

parameters, the values of the reaction rate constant (k) obtained when the

temperature was 40 °C was not used so as to obtain a straight line (linear) graph.

From figures 3, 4 and 5, it shows that conductivity decreases with time. This is could

be due to loses of some ions. This can also explain why at the start, only sodium

hydroxide would contribute to the conductivity. As reaction proceeds, sodium acetate

would start forming after consumption of sodium hydroxide resulting in different

conductivity results (Fogler, 1999).

Hence in the experiment carried out, there was a reduction in the concentration of

the hydroxide (NaOH) at various time intervals. The reason for this could be that

since it is a batch reactor, the reactants would be converted into products while

remaining in the reactor since there is no inflow or outflow; thus as the reactants are

been converted into products, there would be less and less reactant and more and

more products.

It can then been inferred that close to time t = 0, there would be a lot of reactant and

little product while close to time = infinity, there would be more product and less

reactant (Missen et al, 1999).

Finally, this goes to show that for a second order reaction (first order in each reacting

components) like the saponification of ethyl acetate with dilute sodium hydroxide, the

reaction rate is also dependent on one or both of the reactants concentrations; in this

case that of the sodium hydroxide. For the reaction studied in this experiment, a

decrease in one of the reactant concentrations; in this case sodium hydroxide

causes and increase in the reaction rate. This is in line with the collision theory.

G. CONCLUSIONS:

From the experiment, the following conclusions can be drawn.

(i) The rate of a chemical reaction is temperature dependent. It increases

with an increase in temperature and vice versa.

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(ii) In a batch reactor, since there is no inflow or outflow, the reactants

concentration reduces with time.

(iii) For an overall second order reaction (first order in both components) like

the one that was done in the lab, the reaction rate is also dependent on

the concentration of the reactants unlike a zero order reaction that is

independent of the concentrations of the reactants.

(iv) Conductivity of a solution reduces with time as the solution loses it ions

and become less conductive.

Nomenclature

Symbols Units Meaning

A Arrhenius parameter (pre-exponential factor)

CA M exit concentration of reactant ‘A’ in the exit stream

CA0 Minput concentration of ‘A’ in the

input stream

CB M concentration of reactant ‘B’ in the exit stream

Ea kJ/mol Arrhenius parameter (activation energy)

k M-1s-1 Reaction rate constant

k S/mConductivity of solution at various time intervals

k0 S/m initial conductivity at time t = 0

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k∞ S/m conductivity of the solution at

the end of reaction

mOrder of reaction of reactant

component ‘A’

nOrder of reaction of reactant

component ‘B’

T °C Reaction temperature

References:

Denbihh, K. G., and Turner, J. C. R. (1971) Chemical Reactor Theory. 2nd ed.

Cambridge: Cambridge University Press.

Fogler, H.S. (1999) Elements of Chemical Reaction Engineering. 3rd ed .New Jersey:

Prentice Hall.

Levenspiel, O. (1999) Chemical Reaction Engineering. 3rd ed. New York: John

Wiley & Sons, Inc.,

Missen, R. W., Charles, A. M. and Bradley, A. S (1999) Introduction to Chemical

Reaction Engineering and Kinetics. 3rd ed. New York: John Wiley & Sons, Inc.,

Smith, J.M. (1981) Chemical Engineering Kinetics. 3rd ed .New York: McGraw-Hill.

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liquid phase reactor

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