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Acid Neutralization reactor. Module 4: Acid neutralization reactor Lecture 3: Acid - base chemistry, pH and the equations for a CSTR for a reacting system. Mark J. McCready Chemical Engineering. Outline for today. Review: Feedback control of a chemical reactor - PowerPoint PPT Presentation
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Introduction to Engineering Systems Copyright ©2001, University of Notre Dame Module 4- Acid Neutralization Reactor Module 4: Acid neutralization reactor Lecture 3: Acid - base chemistry, pH and the equations for a CSTR for a reacting system Mark J. McCready Chemical Engineering Acid Neutralization reactor
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Page 1: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Module 4:Acid neutralization

reactorLecture 3:

Acid - base chemistry, pH and the equations for a CSTR for a

reacting system

Mark J. McCreadyChemical Engineering

Acid Neutralization

reactor

Page 2: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Outline for today

Review: Feedback control of a chemical reactor

Proportional and integral control pH and pH measurement

We will monitor progress of reaction this way pH is a design criterion for outlet stream

Weak acid chemistry and buffer solutions Acetic acid dissociation Neutralization reaction

Design equations for the chemical reactor

Page 3: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Control of a chemical reactor

The next few slides are a photo gallery showing the expected behavior of a chemical reactor with Proportional control

base flowrate is proportional to error in pH Integral control

flow rate of base is related to accumulated error in pH

Proportional and integral control together.

Page 4: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Control of a chemical reactor

Setpoint pH is supposed to be 5.

Just proportional control, base flowrate is proportional to error in pH

I should have stayed in

engineering

Page 5: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Control of a chemical reactor

Just proportional control, base flowrate is proportional to error in pH

Setpoint pH is supposed to be 5.We get a better setpoint by using less gain, but the response is slower

Page 6: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Control of a chemical reactor

(Just) integral control, flow rate of base is related to accumulated error in pH

Setpoint = pH of 5

Page 7: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Control of a chemical reactor

Proportional and integral control

Setpoint is 5.

Page 8: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Control of a chemical reactor

Setpoint is 5.

Proportional and integral control

Page 9: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Dissociation of water

You may recall that any aqueous solution (or “pure” water) contains hydronium and hydroxide ions because of the dissociation of water. This equilibrium relation is:

If the solution is neutral, the concentrations of the two ions are equal. If not, solution is either basic (more OH-) or acidic (more H3O

+)

2H2O H3O++OH −

Page 10: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Dissociation of water

We keep track of this dissociation using dissociation constants. For example:

At 25oC, the value for Kw is 1.01 X 10-14 mole2/l. At 100oC, the value for Kw is 5 X 10-13 mole2/l. Hydronium ion concentration of an aqueous solution is often

very important and thus it is useful to be able to measure and easily characterize it.

To do so we talk about pH (hydrogen potential) as

Kw = H3O

+[ ]OH −

[ ]

pH =−log10[H 3O+]

Page 11: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

How can we measure pH ?

Modern electrodes and electronics allow measurement of pH (except at extreme values) quite easily.

You could make mistakes, but these should be pretty small in this experiment

Electrolyte solutionKCl, pH=7Ag/AgCl reference cellspecial membraneglasspH meter6.5

Page 12: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Working principle of a pH

electrode If you place two solutions with different

chemical activities on opposite sides of a permeable membrane, an electrical potential will form that can be compared to a standard (i.e., known) voltage.

The way this is used for measurement is there will be a change in potential if the outside pH changes.

permeable membrane,special glassH3O+ activity=a1H3O+ activity=a2outsideinsidewire to pH meter

Page 13: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Workings of an electrode

The key to a pH electrode is a thin membrane of special glass. Glass is sensitive to H3O

+ ions, but not other singly charged ions.

pH is then determined from the potential between the pH electrode and a standard

reference electrode

Electrolyte solutionKCl, pH=7Ag/AgCl reference cell

Page 14: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Acid-Base Chemistry

In this project we will use a weak acid (acetic, “HAc”) and a strong base. The equilibrium relation is

The dissociation constant for acetic acid at room temperature is Ka = 1.75X 10-5

moles/liter.

HAc +H2O H3O++Ac−

Ka =

[H3O+][Ac−]

[HAc]

Page 15: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

pH of acid solution

If we want the pH of our acetic acid solution we start with the equilibrium relation

We want [H3O+] and we know Ka. Thus we need two more

equations to get [Ac-] and [HAc] We have available the mass balance for total acetate.

We can also be pretty sure that all of the [H3O+] comes from

the acetic acid (it is not from the little that would be present

in pure water) so that (each Ac- must have an H3O

+)

Ka =

[H3O+][Ac−]

[HAc] HAc +H2O H3O

+ +Ac−⎛ ⎝

⎞ ⎠

cHAc =[Ac−]+[HAc]

[Ac−]=[H3O+]

(cHAc

is the concentration you made up)

Page 16: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

pH calculation

We have three equations that we can combine

Ka =

[H3O+][Ac−]

[HAc] cHAc =[Ac−]+[HAc] [Ac−]=[H3O

+]

Ka =[H3O

+][Ac−]

cHAc −[Ac−]

Ka =[H3O

+][H3O+]

cHAc −[H3O+]

Ka =

[H3O+]2

cHA −[H3O+] [H3O

+]2 +Ka[H3O+]−KacHA =0

[H3O

+]=−Ka + Ka

2+4KacHA

2

Page 17: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

pH calculation

We have three equations that we can combine

Ka =

[H3O+][Ac−]

[HAc] cHAc =[Ac−]+[HAc] [Ac−]=[H3O

+]

Ka =[H3O

+][Ac−]

cHAc −[Ac−]

Ka =[H3O

+][H3O+]

cHAc −[H3O+]

Ka =

[H3O+]2

cHA −[H3O+] [H3O

+]2 +Ka[H3O+]−KacHA =0

[H3O

+]=−Ka + Ka

2+4KacHA

2

Page 18: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

pH calculation

We have three equations that we can combine

Ka =

[H3O+][Ac−]

[HAc] cHAc =[Ac−]+[HAc] [Ac−]=[H3O

+]

Ka =[H3O

+][Ac−]

cHAc −[Ac−]

Ka =[H3O

+][H3O+]

cHAc −[H3O+]

Ka =

[H3O+]2

cHA −[H3O+] [H3O

+]2 +Ka[H3O+]−KacHA =0

[H3O

+]=−Ka + Ka

2+4KacHA

2

Page 19: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

pH numbers

We can put in numbers Ka = 1.75X 10-5 moles/liter, cHAc = 1

mole/liter

[H3O

+]=−Ka + Ka

2+4KacHAc

2

[H3O

+]=−1.75X10−5 + (1.75X10−5)2 +4(1.75X10−5)(1)

2

[H3O+]=0.0042moles / liter

pH =−

log(0.0042)log(10)

pH =2.38

Page 20: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

An Aside

So, you don’t like lectures !!! If you have come to all of them, so far you have been to

about 26 lectures, there are 6 remaining.

You would have been to 81% of the total classes so far..

19%

81%

remaining

done

0 5 10 15 20 25 30

remaining

done

Page 21: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Buffer solutions

Once you begin to titrate the acetic acid with sodium hydroxide, you begin producing sodium acetate and water.

The presence of both a weak acid and its “conjugate base” (i.e., sodium acetate) constitutes a “buffer solution”. It is called this because it resists changes in pH caused by the addition of a strong base or pure water.

Page 22: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

pH of buffer solutions

Calculation of pH for buffer solutions is even easier than for just a weak acid.

We have the same relation,

Suppose we know the acid concentration: 1 moles/liter and the acetate concentration: 0.5 mole/liter

We would expect that [Ac-] = 0.5 and [HAc]=1,

Ka =

[H3O+][Ac−]

[HAc]

Ka =

[H3O+][.5]

[1] [H3O

+]=1.75X10−5 [1][.5]

pH =−log10(3.5X10−5)=4.5

Page 23: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Batch titration

How can we model a simple batch titration? We will take fixed volume of acid and add

base until the solution is neutralized.

Mass Balance equations -- of course!

2

Base in

HAc

Page 24: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

RecallRecall Mass Balances

General mass balance equation for a fixed control volume Rate of Accumulation = Rate In - Rate Out + Production by reaction- Consumption by reaction

Overall

Component mass (mole) balance

dρVdt

=∑jqj ρj

masstime

⎝ ⎜

⎠ ⎟

dciVdt

=∑jqjc j i −riV

molestime

⎝ ⎜

⎠ ⎟

j - density of stream j, (mass/length3 )qj -- volumetric flow rate of stream j, (length3 /time)V -- active volume of reactor,(length3)

cji-- molar concentration of species i in stream j, (moles/ length3 )ri -- molar reaction rate per volume (moles/ (length3 -time))

Page 25: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Model equations for batch titration

We will consider a tank of acetic acid to which we will add NaOH. Let’s look at our mass balance equations

dV

dt=q2

dVcHAc

dt=−rHAcV

dVcAc−

dt=r

Ac−V

Total volume

Acetic acid

Ka =

[H3O+][Ac−]

[HAc]

Acetate ions

None flows in, just reacts with each OH- that shows up

There is no flow in, all of the acetate comes from neutralized

HAc

[H3O

+] =Ka[HAc]

[Ac−]

In addition to the mass balance equations, we have the equilibrium relation.

2

Page 26: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

batch titration (cont.)

The problem is, what are the reaction terms? Let’s do a mass balance for OH-. We can see that it comes in

by our inlet stream and it will all react away until all of the acid is used up. Further, the concentration of OH- in the reactor will be almost 0 (solution is acidic) until the acid is used up.

For every mole of OH- used up we must react one mole of H

3O+. Thus we use up one mole of HAc.

We likewise make a mole of Acetate,

dVcOH−

dt=0=q2c2OH − −rOH −V q2c2OH − =rOH −V

rHAV =rOH −V =q2c2OH −

rA−V =rOH −V =q2c2OH −

Page 27: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

batch titration (cont.)

The problem is, what are the reaction terms? Let’s do a mass balance for OH-. We can see that it comes in

by our inlet stream and it will all react away until all of the acid is used up. Further, the concentration of OH- in the reactor will be almost 0 (solution is acidic) until the acid is used up.

For every mole of OH- used up we must react one mole of H

3O+. Thus we use up one mole of HAc.

We likewise make a mole of Acetate,

dVcOH−

dt=0=q2c2OH − −rOH −V q2c2OH − =rOH −V

rHAV =rOH −V =q2c2OH −

rA−V =rOH −V =q2c2OH −

Page 28: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Model equations for batch titration

Thus our equations become:

dVdt

=q2

dVcHAc

dt=−q2c2OH −

dVcAc−

dt=q2c2OH −

Total volume

Acetic acid

Acetate ions

We have substituted for the reaction term !!!

[H3O

+] =Ka[HAc]

[Ac−]

We then obtain the concentration of H3O+ from the equilibrium relation.

We have substituted for reaction term !!!

2

Page 29: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Titration curve

If we take 50 ml of 0.1M HAc and add 0.1 M NaOH. Here is the result

Page 30: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Yikes, they won’t go Yikes, they won’t go away!!away!!

General mass balance equation for a fixed control volume Rate of Accumulation = Rate In - Rate Out + Production by reaction- Consumption by reaction

Overall

Component mass (mole) balance

dρVdt

=∑jqj ρj

masstime

⎝ ⎜

⎠ ⎟

dciVdt

=∑jqjc j i −riV

molestime

⎝ ⎜

⎠ ⎟

j - density of stream j, (mass/length3 )qj -- volumetric flow rate of stream j, (length3 /time)V -- active volume of reactor,(length3)

cji-- molar concentration of species i in stream j, (moles/ length3 )ri -- molar reaction rate per volume (moles/ (length3 -time))

Page 31: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Model equations for flowing

system Now consider our stirred tank, neutralization reactor:

dVdt

=q1 +q2 −q3

dVc3HAc

dt=q1c1HAc −q3c3HAc −rHAcV

dVc3Ac−

dt=−q3c3Ac− +r

Ac−V

Total volume

Acetic acid

Ka =

[H3O+][Ac−]

[HAc]

Acetate ions

In addition to the mass balance equations, we again have the equilibrium relation.

3

3

21 NaOH

HAc

Page 32: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Flowing system model (cont.)

Again, we don’t yet know the reaction terms. What are they?

Again we do a mass balance for OH-. We can see that it comes in by our inlet stream and it will all react away until all of the acid is used up. Further, the concentration of OH- in the reactor will be almost 0 (solution is acidic) until the acid is used up.

For every mole of OH- used up we must react one mole of H

3O+. Thus we use up one mole of HAc. So we again get:

We likewise make a mole of Acetate,

dVcOH−

dt=0=q2c2OH − −rOH −V q2c2OH − =rOH −V

rHAV =rOH −V =q2c2OH −

rA−V =rOH −V =q2c2OH −

Page 33: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Model equations for flowing

system Now consider our stirred tank, neutralization reactor:

dVdt

=q1 +q2 −q3

dVc3HAc

dt=q1c1HAc −q3c3HAc −q2c2OH −

dVc3Ac−

dt=−q3c3Ac− +q2c2OH −

Total volume

Acetic acid

Ka =

[H3O+][Ac−]

[HAc]

Acetate ions

In addition to the mass balance equations, we again have the equilibrium relation.

3

3

21

Substituted reaction terms

Page 34: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Matlab code to solve the equations

%titration_cstr.m %this m file solves the "titration" problem for a stirred tank with %two input streams %The volume can remain constant or vary depending upon the initial conditions. % q1 = 10/1000; %acid flow rate in l/s c1 = .85; %acid concentration in moles/liter q2 = 10/1000; %base flow rate in l/s c2 = .55;%base concentration in moles/liter

q3(1) = q1 + q2;% initial exit flow rate

v(1) =1; %initial volume Vmax = 1; %maximum volume ka = 1.75 *10^-5;%dissociation constant for acetic acid ch(1) = (-ka+sqrt(ka^2+ 4*c1*ka))/2;%initial H3O+ concentration ph(1) = -log(ch(1))/log(10); %initial pH

t(1) = 0; %set the initial time to 0 cv1(1) = .85; %initial concentration*volume for the acetic acid cv2(1) = 0; %initial concentration * volume for the acetate. index = 3000;% number of time steps to take dt = .1; %

Page 35: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Matlab code to solve these

equations (pg2) % here is the loop for i=1:index t(i + 1) = t(i) + dt; %advance the time counter v(i + 1) = v(i) + (q1 + q2 - q3(i))*dt; %get a new volume with Euler int. if v(i + 1) < Vmax %check to see if overflowing q3(i + 1) = 0; %if not, don't change flow rate else q3(i + 1) = q1 + q2 ; %if so, set outlet flow equal to inflow end %find the new V*c1 using Euler integration cv1(i + 1) = cv1(i) + (q1*c1 - q2*c2 - q3(i)*cv1(i)/v(i))*dt; %find the new V*c2 using Euler integration cv2(i + 1) = cv2(i) + ( q2*c2 - q3(i)*cv2(i)/v(i))*dt; ch(i + 1) = ka*cv1(i + 1) /cv2(i + 1) ; %calculate the new H3O+

concentration ph(i + 1) = -log(ch(i + 1))/log(10); %calculate the pH

end

Page 36: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Model equations for flowing

system

Some results For tank initially filled with HAc q

1 = 10 ml/s, c

1=0.85 mole/l

q2= 3 ml/s, c

2=0.55 mole/l

3

3

21

V=.3, 1, 5 liters

4.4

Page 37: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Model equations for flowing

system

Some results For tank initially filled with HAc q

1 = 10 ml/s, c

1=0.85 mole/l

q2= 10 ml/s, c

2=0.55 mole/l

3

3

21

V=.3, 1, 5 liters

5.0

Page 38: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Recap pH

We keep track of this dissociation using dissociation constants. For example:

At 25oC, the value for Kw is 1.01 X 10-14 mole2/l. At 100oC, the value for Kw is 5 X 10-13 mole2/l. Hydronium ion concentration of an aqueous solution is often

very important and thus it is useful to be able to measure and easily characterize it.

To do so we talk about pH (hydrogen potential) as

Kw = H3O

+[ ]OH −

[ ]

pH =−log10[H 3O+]

Page 39: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

recap pH electrode

If you place two solutions with different chemical activities on opposite sides of a permeable membrane, an electrical potential will form that can be compared to a standard (i.e., known) voltage.

The way this is used for measurement is there will be a change in potential if the outside pH changes.

permeable membrane,special glassH3O+ activity=a1H3O+ activity=a2outsideinsidewire to pH meter

Page 40: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Recap:Reaction terms

To get the reaction terms for Ac- and Hac, we do a mass balance for OH- and determine that there will never be a significant amount of OH- present thus:

Rate of OH- reaction is the rate at which it flows in This is also the rate at

which HAc reacts away and the rate at which Ac- is produced!

rHAV =rOH −V =q2c2OH −

rA−V =rOH −V =q2c2OH −

Page 41: Acid Neutralization reactor

Introduction to Engineering Systems

Copyright ©2001, University of Notre Dame

Module 4- Acid Neutralization Reactor

Recap:model equations

for flowing system

Now consider our stirred tank, neutralization reactor:

dVdt

=q1 +q2 −q3

dVc3HAc

dt=q1c1HAc −q3c3HAc −q2c2OH −

dVc3Ac−

dt=−q3c3Ac− +q2c2OH −

Total volume

Acetic acid

Ka =

[H3O+][Ac−]

[HAc]

Acetate ions

In addition to the mass balance equations, we again have the equilibrium relation.

3

3

21

Substituted reaction terms


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