CPP Lecture 6 - Material balances involving reactions.pdf

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1. Chemical Engineering
Process Principles
Material Balances involving reactions

2. Objectives of this section
•Carry out a degree-of-freedom analysis for processes involving
chemical reaction(s)
•Formulate and solve material balances using (a) species balance and
(b) element balances
•Decide when element balances can be used as material balances
•Understand how the extend of reaction is determined for a process,
and how to apply it in material balance problems
•Understand the meaning of stack gas, flue gas, Orsat analysis, dry
basis, wet basis, theoretical air (oxygen), and excess air (oxygen), and
employ these concepts in combustion problems

3. Species Mole Balance
•Processes Involving a Single Reaction
•Material balance for a species include generation and consumption
terms when chemical reactions occur in a system. In terms of moles
of species ??????, a material balance for a general system is:
•Generation and consumption terms are more conveniently
represented in terms of moles because reactions are usually written
in terms of molar ratios.

4. Species Mole Balance
�����
�� ?????? ��
??????
2 ??????�
�ℎ�
�??????����
−
�����
�� ?????? ��
??????
1 ??????�
�ℎ�
�??????����
−
����� �� ??????
�����??????��
�ℎ�
�??????����
����� ��
?????? ����??????��
�ℎ�
�??????����
����� �� ??????
���������
�??????
�����??????��
����� �� ??????
��������
�?????? �����??????��
+
−
=

5. Species Mole Balance
Processes Involving a Single Reaction (Example)
N
2 and H
2 reacts to form NH
3 in a gas phase
Steady-state, open system operating for a fixed interval so that the
terms will be zero on the left-hand side of the equal sign in the material
balance
The measured values for the flows in gram moles

6. Species Mole Balance
Processes Involving a Single Reaction (Example)
N
2 and H
2 reacts to form NH
3 in a gas phase
For this simple example you can calculate by inspection or by the material
balance equation a value in gram moles for the generation and-or
consumptions for each of the three species in the reaction:
NH
3: 6 – 0 = 6 g mol (product generated)
H
2: 9 – 18 = -9 g mol (reactant consumed)
N
2: 12 – 15 = -3 g mol (reactant consumed)

7. Species Mole Balance
Processes Involving a Single Reaction (Example)
Because of the stoichiometry of the chemical reaction equation
N
2 + 3 H
2 → 2 NH
3
The three respective generation and consumption terms are related. For example,
given the value for the generation of NH
3, you can calculate the values for the
consumption of H
2 and N
2 using the reaction equation. The ratio of hydrogen to
nitrogen consumed in the reactants and maintained in the product ammonia is
always 3 to 1. Thus, you cannot specify more than one value of the N
2 and H
2 pair
left over from the reaction without introducing a redundant or possibly an
inconsistent specification. In general, if you specify the value of the generation or
consumption of one species in a reaction, you are able to calculate the values of
the other species from a solo reaction equation.

8. Species Mole Balance
Processes Involving a Single Reaction (Example)
N
2 + 3 H
2 → 2 NH
3
??????=
�
??????
���
− �
??????
??????�
�
??????
i = 1,…,N
For the NH
3 reaction : ??????
????????????
3
=2; ??????
??????
2
=−3; ??????
??????
2
=−1

9. Species Mole Balance
Processes Involving a Single Reaction (Example)
N
2 + 3 H
2 → 2 NH
3
And the extent of reaction calculated via any of the species is:
??????=
�
????????????
3
���
− �
????????????
3
??????�
�
????????????
3
=
6−0
2
= 3
??????=
�
??????
2
���
− �
??????
2
??????�
�
??????
2
=
9−18
−3
= 3
??????=
�
??????
2
���
− �
??????
2
??????�
�
??????
2
=
15−12
1
= 3

10. Species Mole Balance
Processes Involving a Single Reaction (Example)
•You can conclude for the case of a single chemical reaction that the
specification of the extent of reaction provides one independent
quantity that will determine all the values of the generation and
consumption terms for the various species in the respective
implementation of the material balance equation because the molar
ratios of the reactants and products are fixed by the solo
independent chemical reaction equation.

11. Species Mole Balance
Processes Involving a Single Reaction (Example)
The three species balance corresponding to the process are listed below
based on the extent of reaction equation and equation directly derived from
the material balance equation for an open, steady state process:
The term ??????
??????ξ corresponds to the moles of species i generated or consumed

12. Species Mole Balance
Processes Involving a Single Reaction (Example)
In general, you can write one material balance equation for each species
present in the system. If equation (5.8) is applied to each species that reacts
in a steady-state system, the resulting set of material balances will contain
an additional variable, namely, the extent of reaction, ξ. For a species that
does not react, ??????
?????? =. 0

13. Species Mole Balance
Frequently asked questions
1.Does it make any difference how the chemical reaction is written as long
as the equation is balanced? No. For example, write the decomposition
of ammonia as
NH
3 → ½ N
2 + 3/2 H
2
Calculating ξ given that zero moles of NH
3 are introduced into a reactor and
that 6 moles exit. Then:
Ξ =
6−0
−1
=−6
The material balance for NH
3 is just
6 – 0 = (-1)(16) = 6

14. Species Mole Balance
Frequently asked questions
•??????
�ξ which is used in each species material balance, remains unchanged
regardless of the size of the stoichiometric coefficients in a chemical
reaction equation
•If the chemical reaction equation is multiplied by a factor of 2, so that the
stoichiometric coefficient are each twice their previous value, ξ will
decrease by a factor of 2
2.The negative sign in front of ξ signifies that the chemical reaction
equation was written to represent a direction that is the reverse of the
one in which the reaction actually proceeds as

15. Species Mole Balance
Frequently asked questions
•f is the fraction conversion of the limiting reactant

16. Question 1 (Himmelblau & Riggs, 2012)
The chlorination of methane occurs by the following reaction:
CH
4 + Cl
2 → CH
3Cl + HCl
You are asked to determine the product composition if the conversion
of the limiting reactant is 67%, and the feed composition in mole
percent is 40% CH
4, 50% Cl
2, and 10% N
2.

17. Species In (mols) Reacted (mols)
(??????ξ)
Product (mols)Composition
(%)
CH
4 40 −ξ 13.2
Cl
2 50 −ξ 23.2
CH
3Cl 0 ξ 26.8
HCl 0 ξ 26.8
N
2 10 0 10
ξ
CH
4
,�????????????=
0−40
−1
=40
ξ
Cl
2
,�????????????=
0−50
−1
=50
ξ=
(−0.67)×40
−1
=26.8

18. Question 1

19. Question 1

20. Question 1

21. Question 1

22. Processes Involving Multiple Reactions
Do you just include a ξ
?????? for every reaction
•Usually the answer is yes, but more precisely the answer is no!
•You should include in the species material balances only the ξs associated
with a (nonunique) set of independent chemical reactions called the
minimal set
•Minimal set: Smallest set of chemical reaction equations that can be
assembled so as to include all of the species involved in the process

23. Processes Involving Multiple Reactions
Example
C + O
2 → CO
2
C + 1/2O
2 → CO
CO + 1/2O
2 → CO
2
By inspection you can see that if you subtract the second equation from the
first one, you obtain the third equation. Only two of the three equations are
independent; hence the minimal set will be composed of any two of the
three equations.

24. Processes Involving Multiple Reactions
Generally for component i:
•�
�
���
=�
�
��
+σ
�=1
�
??????
��ξ
�
Where ??????
�� is the stoichiometric coefficient of species I in reaction j in the
minimal reaction set
ξ
� is the extent of reaction for the jth reaction in which component i is
present in the minimal set R is the number of independent chemical
reaction equations (the size of the minimal set)
The total moles N exiting the reactor are
??????=෍
�=1
ሶ�
�
�
���
=෍
�=1
ሶ�
�
�
��
+෍
�=1
ሶ�
෍
�=1
�
??????
��ξ
�
Where S is the number of species in the system

25. Question 2 (Himmelblau & Riggs, 2012)
Material Balances Involving two Ongoing Reactions
Formaldehyde (CH
2O) is produced industrially by the catalytic oxidation of
methanol (CH
3OH) by the following reaction:
CH
3OH + 1/2 O
2 → CH
2O + H
2O (1)
Unfortunately, under the conditions used to produce formaldehyde at a
profitable rate, a significant portion of the formaldehyde can react with
oxygen to produce CO and H
2O:
CH
2O + 1/2O
2 → CO +H
2O (2)
Assume that methanol and twice the stoichiometric amount of air needed
for complete oxidation of the CH3OH are fed to the reactor, that 90%
conversation of the methanol results, and that a 75% yield of formaldehyde
occurs (based on the theoretical production of CH2O by Reaction (1)).
Determine the composition of the product gas leaving the reactor.

26. Question 2
Material Balances Involving two Ongoing Reactions

27. Question 2
Material Balances Involving two Ongoing Reactions

28. Question 2
Material Balances Involving two Ongoing Reactions

29. Question 2
Material Balances Involving two Ongoing Reactions

30. Question 2
Material Balances Involving two Ongoing Reactions

31. Question 2
Material Balances Involving two Ongoing Reactions

32. Question 3 (Himmelblau & Riggs, 2012)
Analysis of a Bioreactor
A bioreactor is a vessel in which biological reactions are carried out involving
enzymes, microorganisms, and/or animal and plant cells. In the anaerobic (in the
absence of oxygen) fermentation of grain, the yeast Saccharomyces cervisiae
digest glucose (C6H12O6) from plants to form the products ethanol (C2H5OH) and
propenoic acid (C2H3CO2H) by the following overall reactions:
Reaction 1: C6H12O6 → 2C2H5OH + 2CO2
Reaction 2: C6H12O6 → 2C2H3CO2H + 2H20
In a process, a tank is initially charged with 4000 kg of a 12% solution of glucose in
water. After fermentation, 120 kg of CO2 have been produced and 90 kg of
unreacted glucose remain in the broth. What are the weight (mass) percents of
ethanol and propenoic acid in the broth at the end of the fermentation process?
Assume that none of the glucose is retained by the microorganisms.

33. Question 3
Analysis of a Bioreactor

34. Question 3
Analysis of a Bioreactor

35. Question 3
Analysis of a Bioreactor

36. Question 3
Analysis of a Bioreactor

37. Question 3
Analysis of a Bioreactor

38. Question 3
Analysis of a Bioreactor

39. Reference
Himmelblau, D. M., & Riggs, J. B. (2012). Basic principles and
calculations in chemical engineering. Michigan: Prendice hall.