Effect Pulse

_______________________________________ CONTINUOUS STIRRED TANK REACTOR in SERIES

ABSTRACT

On 24th of August 2005, an experiment was conducted . Title of the experiment

was Continuous stirred tank reactor (CSTR) in series. Two experiments were

conducted. The first one is the effect of step change input which is a step-change

input would be introduced and the progression of the tracer will be monitored via

the conductivity measurements in all three reactors and the second one is the

effect of pulse input which is a pulse input would be introduced and the

progression of the tracer will be monitored via the conductivity measurements in

all three reactors too. Also we have to plot the graph of conductivity against time

for all three reactors to the both experiments.

1


INTRODUCTION

A stirred tank is the most fundamental of mixers and many common mixers from

the Brabender mixer used in lab to a cup of coffee with a spoon can be

considered a stirred tank under some set of approximation. Mixing in a stirred

tank is complicated and not well described (Middleman p. 340-348) although the

use of dimensionless numbers and comparison with literature accounts can lead

to some predictive capabilities. Often stirred tanks are used as industrial reactors

where a chemical component of a flow stream resides for some time in the tank

and then proceeds on to other steps in a chemical process. The residence time

distribution becomes a measure of the extent of a chemical reaction in this

situation. For mixing one can sometimes assume a constant rate of strain in the

stirred tank, Middleman p. 340-348, and the residence time distribution can then

be used under this approximation, as a measure of the extent of mixing. Dead

zones in a stirred tank for high viscosity fluids should be very familiar to anyone

who has worked in a kitchen mixing dough with a hand mixer.

Fluid motion in a stirred tank is confined to the immediate region of the

mixer blades for high viscosity fluids. In the simplest approximation that a uniform

extent of mixing occurs in the stirred tank, Middleman p. 301-306, this is called

the "perfect mixer". Consider a stream of butene in cyclohexane that is converted

to butene epoxide by reaction with a peroxide in a CSTR. The flow rate through

the tank is Q and the concentration of heptene is C0. The tank is at steady state

meaning the volumetric in-flow equals the volumetric out-flow. The tank volume is

V. The ratio of butene epoxide to butene is governed by the temperature, catalyst

concentration, effectiveness of the catalyst and the residence time in the reactor.

A master curve in terms of conversion at constant conditions as a function of

reaction time can easily be made in the lab.

2


Then a calculation of residence time distribution in the reactor can be

directly mapped, using the lab results, to conversion ratio for the desired product.

If the butene epoxide is to be used in a second CSTR to produce the final

product then this conversion ratio becomes the input concentration for the

second CSTR. Typically a synthetic chemical process will involve a number of

CSTR's joined in this way. Then we need to determine the residence time

distribution (RTD), f(t), for a perfect mixer to approximate the conversion for this

CSTR.

In order to determine the RTD, f(t), for the CSTR we consider a simpler

situation where a concentration C0 of a component in a flow stream Q flows into a

tank of volume V. At an instant of time all of the concentration C0 is tagged red so

that it can be distinguished from the other reactant in the stirred tank. We then

look for the red tagged reactant in the outflow stream to determine the residence

time of the reactant in the tank. The amount of tagged material the has left the

tank at time "t" is given by the cumulative residence time distribution function,

F(t), F(t)C0Q. This is related to the concentration of tagged material in the effluent

stream, QC(t),

so

Then F(t) is the response, efflux, of the system to a pulse of concentration in the

influx.A material balance for the CSTR under the assumption of perfect mixing

yields,

3


with the starting condition that the concentration of the tagged component in the

effluent is 0 at t = 0, C(t=0) = 0. The solution to this differential equation is, where

V/Q = t is a kind of time constant for the system. Under the assumption of perfect

mixing, this time constant is the mean residence time for the CSTR, t = V/Q. The

residence time distribution function is the derivative of the cumulative residence

time distribution function,

The function has a value at t = 0 of 1 t =Q/V which decays exponentially with

time. The function has a value at t = 0 because mixing is perfect, that is some

material is instantaneously in the effluent at the instant material is introduced to

the tank. Obviously this is not realistic. Nonetheless, the exponential

approximation for a CSTR is a common assumption both in polymer processing

and in the chemical process industry as a whole. It is widely used in a wide range

of scientific fields as for a first approximation for quantities such as residence

time in a lake or ocean or for an approximation of a drug or toxins residence in

the human body since it depends only on the system volume and rate of dilution.

The function can be modified for dead space using an effective volume rather

than the actual volume of the system. Alternatively, tracer studies can be used to

measure the mean residence time.

4


THEORY

Continuous Stirred Tank Reactors (CSTRs)

Figure 1

Type of Reactor Characteristics

Continuously Stirred

Tank Reactor (CSTR)

Run at steady state with continuous flow of reactants and

products; the feed assumes a uniform composition

throughout the reactor, exit stream has the same composition

as in the tank

Kinds of Phases

Present

Usage Advantages Disadvantages

1. Liquid phase

2. Gas-liquid rxns

3. Solid-liquid rxns

1.When

agitation is

required

2.Series

configurations

for different

1.Continuous operation

2.Good temperature control

3.Easily adapts to two

phase runs

1.Lowest

conversion per unit

volume

2. By-passing and

channeling

possible with poor

5


concentration

streams

4. Good control

5. Simplicity of construction

6.Low operating (labor) cost

7.Easy to clean

agitation

General Mole Balance Equation

Figure 2

Assumptions

1) Steady state therefore

2) Well mixed therefore rA is the same throughout the reactor

Rearranging the generation

6


In terms of conversion

Reactor Sizing

Given –rA as a function of conversion, –rA = f(X), one can size any type of reactor.

The volume of a CSTR can be represented as the shaded areas in the

Levenspiel Plot shown below:

Figure 3

Reactors in Series

Given –rA as a function of conversion, , –rA = f(X), one can also design any

sequence of reactors in series provided there are no side streams by defining the

overall conversion at any point.

7


Figure 4

Mole Balance on Reactor 1

Mole Balance on Reactor 2

8


Given –rA = f(X) the Levenspiel Plot can be used to find the reactor volume

Figure 5

For a PFR between two CSTRs

Figure 6

9


Given -rA = f (x), the Levenspiel Plot can be used to find the reactor volume

.

Figure 7

Tracer Analysis on the Transient Behaviors of Continuous

Stirred-Tank in Series.

Unlike the above, the tracer analysis will help to understand the transient

behaviors of the continuous stirred tank reactor in series by having a step input

or pulse of tracer component such as salts. The conductivity measurement will

indicate the progression of the tracer throughout the stirred tank in series.

CO

C1 C2 C3

Figure 8

10


dCi/ dt = (C1-1 – Ci ) / where = V/v and V = Tank Volume, v = volume flow

rate, and Ci= concentration in i thTank. The differential equations must be solved

simultaneously.

A real reactor will be modeled as a number of equality sized tanks-in-series.

Each tank behaves as an ideal CSTR. The number of tanks necessary, n (our

one parameter), is determined from the E(t) curve.

For n tanks in series, E(t) is,

E (t) = t n-1 e -t/ I

(0 - 1)/ In

Where, I = /n

It can be shown that

tm = = nI

In dimensionless from

= t / = t/I

n = t / I

E () = E (t) = n(n ) n-1 e -n

(n-1)

11


σө2 = σ2 = 0∞ ( t – τ )2 E (t) d τ

τ2 τ2

σө2 = σ2 = 0∞ ( Ө - 1 )2 E ( Ө) d Ө

τ2

Carrying out the integration for the n tanks in series E(t).

σө2 = σ 2 = 1

τ2 n

n = τ2

σ2

For a first order reaction,

X = 1 - 1 τi = τ

( 1 + τi k ) n n

For reactions other than first order and for multiple reactions, the sequential

equations must be solved.

Vi = V / n

Vi = vo ( CAo – CA1)

-rA1

Vi = vo ( CA1 – CA2)

-rA2

12


Vi = vo ( CA(n – 1) – CAn )

-rAn

Example

For a second order reaction with n = 3,

( V1 = V2 = V3 = V / 3 )

V3 = ( CAo – CA ) vo

kCA2

( τ1 = τ2 = τ3 )

τ3 = kCA2 + CA - CA = 0

CA1 = -1 + √ 1+ 4 τ3 k C Ao

2 τ3 k

Similarly,

CA2 = -1 + √ 1+ 4 τ3 k C A1

2 τ3 k

CA3 = -1 + √ 1+ 4 τ3 k C A2

2 τ3 k

X = 1 - (CA3 / CA0) , τ3 = τ / 3

Effect of Step Change in Input Concentration to the Concentration of Solute in

13


Stirred Tank Reactors in Series.

When a step change of solute concentration is introduced at the feed of

tank 1, the tank in series will experience a transient behavior as of Figure 8

below. The response will be dependent on the residence time of each reactor in

series.

figure 9a: step change input. Figure 9b: transient

response of tank in series

to the step input.

14


Effect of Pulse in Input Concentration to the Concentration of solute in Stirred

Tank in Series.

When a pulse input of solute concentration is introduced at the feed of

tank 1, the transient behavior will be different than the step change input due to

the diminishing concentration from the input after pulsing.

figure 10a: pulse input. Figure 10b: Transient response of tank in

series to the pulse input.

OBJECTIVE

To determine;

15


The effect of step changes in input concentration of solute.

The effect of pulse or residence time in input concentration of solute

curve.

APPARATUS

1. Distillation water

2. Sodium Chloride

3. Continuous reactor in series

4. Stirrer system

5. Feed tanks

6. Waste tank

7. Dead time coil

8. Computerize system

16


APPARATUS DISCRIPTION

Figure 11

Before operating the unit, we must familiarize ourselves with the unit. Please

refer to figure 1 to understand the process. The unit consists of the followings:

Reactors

Three reactors made of borosilicate glass, each having approximately 2 liters

capacity. Each reactor is fitted with variable speed stirred mounted on the top

plate. Temperature and conductivity sensors are provided for each reactor. Flows

between vessels are by gravity. Overflow tubes are provided for the 2nd and 3rd

reactor.

17


Stirred System

Variable speed stirred system with digital display consisting of a motor and a

shaft with impellers made of stainless steel. Speed adjustment by means of a

speed controller knob on each stirrer.

Feed Tanks

Two 15-L cylindrical tanks made of stainless steels are provided with the unit.

Each tank has a feed pump to transfer the liquid from feed tank to the reactors.

Each tank is fitted with a level switch to protect the pumps from dry on.

Waste Tank

A rectangular 50-L waste tank made of stainless steel is provided at the bottom

of the equipment.

Dead Time Coil

Material: 3/8” stainless steel tubing

Volume: approx. 200 ml

Instrumentations

1) Flow meter

Range: 0 to 500 ml/min

Output: 0 to 5 VCD

Display: LCD digital display

2) Conductivity Meter

Sensor Range: 0 to 200 mS/cm

No. of sensors: 4 (CT1, CT2, CT3, CT4)

Output: 4 to 20 mA

Display: conductivity controller with digital display for each sensor

mounted on the control panel.

18


3) Temperature Sensor

No. Of sensors: 3 (TT1, TT2, TT3)

Sensor type: RTD

4) Data Acquisition System

The Data Acquisition System consists of a personal computer, ADC

modules and instrumentations for measuring the process parameters. A

flow meter with 0 to 5 VCD output signal is supplied for feed flow rate

measurement. Conductivity sensors with controller are provided for

monitoring the tracer concentration in each reactor. The ADC modules into

digital signals will convert all analog signals from the sensors before being

sent to the personal computer for display and manipulation.

Equipment Description

The system consists of three agitated, glass reactor vessels connected in series,

two feed tanks, two variable through put feed pumps, variable speed agitators,

fixed height overflow, and an electrical conductivity meter. Two feed systems are

provided. Each feed system consists of a feed tank, a variable speed pump, and

a mixer (tee-type) at the first tank inlet. The feeds flow through each tank where a

constant liquid holdup (steady-state operation).

Chemicals

The conductive component with be potassium chloride at low concentrations.

19


EXPERIMENTAL PROCEDURES

Experiment A: The effect of Step Change

In this experiment a step change input would be introduced and the

progression of the tracer will be monitored via the conductivity measurement in

all the three reactors.

1. The two of three tanks (tank 1 and tank 2) was filled up with 20L feeds

deionized water.

2. 300 g of sodium chloride in tank 1 was dissolved. Make sure the salts

dissolve entirely and the solution is homogenous.

3. The three way valve (V3) was setting to position 2 so that the deionized

water from tank 2 will flow into reactor 1.

4. The pump 2 is switch on to fill up all three reactors with deionized water.

5. The flow rate (Fl1) was set to 150 ml/min by adjusting the needles valve

(V4). Do not use too high flow rate to avoid the over flow. Make sure no air

bubbles trapped in the piping. The stirrers 1, 2 and 3 were switch on.

6. The deionized water was continued pumped for about 10 minute until the

conductivity readings for all three reactors are stable at low values.

7. The values of conductivity were recorded at t0.

8. T he pump 2 was switch off after 5 minutes. The valve (V3) was switch to

position 1 and the pump 1 was switch on. The timer was started.

9. The conductivity values for each reactor were recorded every three

minutes.

10. Record the conductivity values were continued until reading for the three

reactors were closed to the starting value recorded.

11. Pump 2 was switch off and the valve (V4) was closed.

12. All liquids in reactors were drained by opening valves V5 and V6.

Experiment 2: The effect of pulse input.

20


In this experiment a pulse input would be introduced and the progression

of the tracer will be monitored via the conductivity measurements in all three

reactors.

1. The two of three tanks (tank 1 and tank 2) was filled up with 20L feeds

deionized water.

2. 300 g of sodium chloride in tank 1 was dissolved. Make sure the salts

dissolve entirely and the solution is homogenous.

3. The three way valve (V3) was setting to position 2 so that the deionized

water from tank 2 will flow into reactor 1.

4. The pump 2 is switch on to fill up all three reactors with deionized water.

5. The flow rate (Fl1) was set to 150 ml/min by adjusting the needles valve

(V4). Do not use too high flow rate to avoid the over flow. Make sure no air

bubbles trapped in the piping. The stirrers 1, 2 and 3 were switch on.

6. The deionized water was continued pumped for about 10 minute until the

conductivity readings for all three reactors are stable at low values.

7. The values of conductivity were recorded at t0.

8. Switch off pump 2 after 5 minutes. The valve (V3) was switch to position 1

and switch on pump 1. The timer was started.

9. Let the pump 1 to operate for 5 minute, and then switch off pump 1.

Switch the three ways valve (V3) back to position 2. The pump 2 was

switch on.

10. The conductivity values for each reactor were recorded every three

minutes.

11. Record the conductivity values were continued until reading for the three

reactors were closed to the starting value recorded.

12. Pump 2 was switch off and the valve (V4) was closed.

13. All liquids in reactors were drained by opening valves V5 and V6.

21


RESULTS

Experiment 1: The effect of step change input.

FT: 139.8 ml / min TT1: 25.5 oC TT2: 25.4 oC TT3 25.3 oC

Time (min) QT1(mS/cm) QT2(mS/cm) QT3(mS/cm)0 0.0126 0.0389 0.06863 1.3219 0.1109 0.00006 2.1260 0.6421 0.00009 2.6304 0.8866 0.194612 3.0477 1.3243 0.355615 3.3034 1.9302 0.633218 3.5090 2.2321 1.051721 3.6304 2.5395 1.237424 3.7146 2.8006 1.614727 3.5343 3.0621 1.829930 3.8813 3.2544 2.074133 3.9561 3.4134 2.375236 4.0157 3.4241 2.627939 3.9349 3.5468 2.699642 3.8083 3.5900 2.911545 4.0114 3.7752 2.995748 4.0294 3.7211 3.171651 3.9380 3.7843 3.238954 4.0201 3.8207 3.347257 3.9122 3.8028 3.223360 4.0844 3.7139 3.345463 4.0220 3.8698 3.517766 4.1531 3.9130 3.388269 4.1140 3.9109 3.449772 4.0197 3.9402 3.508675 4.0778 3.8673 3.474278 4.0297 3.9166 3.684081 3.9986 3.8304 3.586784 4.1068 3.9662 3.5754

88.1 4.0198 3.8499 3.5305

22


Experiment 2: The effect of pulse input.

FT: 0.2 ml / min TT1: 24.9 oC TT2: 24.9 oC TT3 24.8 oC

Time (min) QT1(mS/cm) QT2(mS/cm) QT3(mS/cm)0 1.3767 0.3259 0.22623 1.4100 0.6906 0.28226 1.1217 0.8530 0.31499 0.8780 0.8989 0.487712 0.6144 0.8570 0.563415 0.4597 0.7494 0.621118 0.3506 0.7071 0.710521 0.2307 0.6185 0.656024 0.1596 0.4772 0.573427 0.1578 0.4298 0.571630 0.0934 0.3096 0.563133 0.1610 0.2545 0.425436 0.0319 0.2005 0.390539 0.0513 0.2184 0.347742 0.0596 0.1412 0.318445 0.0056 0.0925 0.291448 0.0011 0.1384 0.184751 0.0553 0.0898 0.236554 0.0000 0.0377 0.130957 0.0515 0.0229 0.148660 0.0636 0.0367 0.144563 0.0185 0.0173 0.080466 0.0000 0.0000 0.122369 0.0094 0.0669 0.064472 0.0000 0.0315 0.067375 0.0395 0.0000 0.051878 0.0663 0.0000 0.0561

GRAPH: EXPERIMENT 1

23


Graph 1

24


GRAPH: EXPERIMENT 2

Graph 2

SAMPLE OF CALCULATION

25


No sample of calculation involve.

DISCUSSIONS

The Continuous Flow Stirred Tank Reactor (CSTR) is probably the easiest way

to transfer a batch process to a continuous one since all engineering and scale-

up data can be used from the batch process. The very broad residence time

distribution (RTD) profile however can pose some sever complications, therefore

the pitfalls are mentioned first

A minor problem is that the lower volumetric reaction rate results in a lower

productivity, this can easily be compensated by the reduction of waiting times

(filling, heating, cooling, emptying of the batch reactor) and a more constant

product quality. The effect on the selectivity of reactions can either be good or

bad. In the case of production of homogeneous copolymers for example, the

CSTR can be an ideal reactor since composition drift is absent during steady

state operation. The main reason that a series of CSTRs is not suited for the

entire emulsion polymerisation process is that the first stage of the process, the

particle nucleation, is very sensitive towards residence time distribution.

First of all, compared to the batch process, the steady state operation results in

more constant product properties, an improved energy consumption (the heat of

reaction can be used to heat feed streams) and a higher productivity through the

reduction of inactive periods (filling, heating, cooling, emptying). The control over

local mixing independently from net flow is one of the key advantages compared

to a traditional tubular reactor.

The ideal mixing in a single vessel can, besides all the negative effects

mentioned above, also have its positive effects. For the production of

homogeneous copolymers, the steady state concentrations in each CSTR make

it a lot easier to calculate and feed additional monomer streams to each CSTR

compared to the time-based addition profile for the semi-batch process. Because

26


no backmixing is possible from downstream CSTRs, the reaction conditions can

be changed sharply in subsequent reactors, without having a (negative) effect on

the reactors upstream.

In the first experiment of the effect of step change, the values of the conductivity

for those three stirrers were recorded in each three minutes. From the graph we

can see that the concentration of the deionized water was increasing with time.

The concentration of the tank 1 is higher than the others. This is because; the

300 g of sodium chloride was dissolved firstly in tank 1. Then, the deionized

water that was dissolved to the sodium in tank 1 was pumped to other one by

one which was full with deionized water. Though the concentration is uniform in

each reactor, nevertheless there are changes in concentration as fluid moves on

from 1st reactor to others. After 93 minutes, the concentration in the 3 reactors

becomes stable which is equivalent for each reactor. The resulted was shown in

graph 1.

In the second experiment, the purpose on running this experiment was to

determine the concentration response to pulse change. Same as before, the

conductivity was recorded for those reactors in each 3 minutes. From the graph,

we can see that the concentration of the deionized water was increasing with

time. After 87 minute mixing, the concentration reading of the three stirrers

reached a stable at low value which is equivalent for each stirrer.

This situation above is one of the draw back of using cstr in series if compared to

single STR. Although the series STR requires a lower reactor volumes but it take

longer to reach the conversion and it also requires more stirrer than the single

STR.

27


CONCLUSIONS

From the graph and observation, it can be concluding that;

o Both first experiment and second experiment has the graph pattern as the

standard graph (figure 9 and 10).

o For the first experiment, it takes more time to achieving equilibrium in

concentration which rather it can be said that the concentration on the

reactor are directly proportional with time .

o Time measuring very important because it is can affect the conductivity.

RECOMMENDATIONS

During the experiment there are some problem occur, so these is the list of the

recommendation that can be considered if we want to produce better results;

o Firstly all the basic procedure and maintenance must be followed.

o Secondly, the instrument must have certain program which can

automatically record every 3 minutes.

o The time for doing the experiment must be extended because it takes time

to achieved equivalent data.

28


REFERENCES

i. Levenspiel Octave, Department of Chemical Engineering Oregon State

University, Chemical Reaction Engineering Third Edition, John Wiley &

Sons, 1999.

ii. Schmidt, Lanny D., The Engineering of Chemical Reactions. New York:

Oxford University Press, 1998.

29


APPENDICES

CE 442

DESIGN EXAMPLE

- Application of Chemical Reactor Theory -

A chemical manufacturing facility is planning on a product modification that will result in a change in wastewater character. Of significance is the anticipated presence of phenol, an organic chemical that has not been treated by the company's wastewater treatment facility. Consequently, the ability of the existing facility to “treat” phenol is in question. In order to predict the existing reactor performance, kinetic and dispersion information is needed. Reaction kinetic data have been collected for the chemical destruction of phenol through batch reactor tests (Table 1).

Table 1. Batch reactor reaction kinetic data.Time(min)

Phenol(mg/L)

0 10010 5520 2230 840 560 0.8280 0.15

The phenol-bearing wastewater flow is projected to be 0.45 MGD with an anticipated phenol concentration of 95 mg/L. The reactor ( a chemical oxidation process) has a total liquid volume of 25,000 gal. (L=35 ft., W=12 ft., H=8 ft.). A reactor dispersion analysis has been performed by injecting an impulse of non-reactive material into the reactor feed stream. The flow rate was monitored during the dispersion study and was determined to be 0.45 MGD. The reactor dye trace data are presented in Table 2. The phenol discharge permit limit has been set at 0.1 mg/L by the state regulatory board. Estimate the effluent concentration of phenol based on the available information. Determine what might be done to meet the discharge limit. It would be desirable to maintain the existing reactor due to obvious economic reasons. However, any reasonable design option may be considered. Justify your final design recommendation. Show all calculations in a clear and concise fashion. State all assumptions that you make in the design process. It should be assumed that the kinetic relationship (Table 1) are fixed and cannot be altered. That is, the reaction kinetic data represents optimum conditions.

Table 2. Field scale reactor dispersion data.t

(min)Conc(mg/L)

0 044.75 0.2346 0.32

30


46.92 0.3648 0.8248.5 1.2449 2.1549.33 2.6150 2.9850.75 2.9351.67 2.9852.75 2.8954 2.8456 2.8958 2.8460 2.5262 2.5264 1.9266 1.7968 1.670 1.3375 1.2879 1.1483 1.198 0.41113 0.39128 0.27

31


SolutionThe solution approach is based on utilizing the kinetic information (Table 1) and dispersion information (Table 2) to estimate existing reactor performance and to develop alternatives for upgrading the treatment process. The solution approach is presented below. 1. determine reaction rate and order,

2. determine the normalized variance (

2

= 2/tbar2),

3. determine the number (N) of CSTR's in series that simulates the calculated dispersion (

2

= 1/N),3. estimate the existing reactor effluent concentration, and4. develop alternative reactor design modifications. Reaction rate constant and order. Reaction rate and order is determined using the data in Table 1 of the problem statement. The general rate expression (equation 1) is applied in the analysis process.

(1) nkCdt

dC

wherek = reaction rate constantn = reaction order

After assuming a reaction order, equation 1 is integrated and algebraically manipulated such that a general straight line relationship (equation 2) is developed.

(2) bmxy

For example, if we assume n=0, the following solution applies.

ktCC

dtkdC

kdtdC

kkCdt

dC

t

tC

C

t

0

0

0

0

Equation 3 is a straight line relationship and indicates that if the reaction data is truly zero order, a plot of C t vs. t would result in a straight line. If, however, the data is not linear, another order must be assumed and the process repeated. For example, assuming n=1 yields the following solution to equation 1.

32

(3) 0CktCt


ktCC

dtkC

dC

kdtC

dC

kCdt

dC

t

tC

C

t

0

0

lnln

0

The result of performing these operations on the kinetic data is presented in Figure 1.

Figure 1. C and ln(C) vs. time for the rate data from Table 1.

The data in Figure 1 indicate that a zero (n=0) order assumption does not result in a linear relationship (C vs. t data is non-linear). ln(C) vs. t, however, does fall on a straight line. The reaction rate is therefore first order with the slope equal to k = 0.08 min-1.

33

Kinetic Data

y = -0.0819x + 4.7085

0

20

40

60

80

100

120

0 20 40 60 80 100

Time (min)

C (

mg

/L)

-3

-2

-1

0

1

2

3

4

5

6

Ln

(C)

C

Ln(C)

0lnCktLnC t

Documents

Effect Pulse