# 6.21: Untitled Page 144

## Chapter 6

a

a

a

c

11

12

13

1

 

a

a

a

b

c

 21

22

23 

1

 2

 

a

a

a b

  c

(1)

31

32

33

 2

3

 

a

a

a

b

c

 41

42

43   3 

 4 

a

a

a

c

51

52

53 

 5 

If the 5  3 matrix is partitioned according to

(2)

indicate how Eq. 1 must be partitioned. Clearly indicate how the partitioned version of Eq. 1 leads to the detailed results associated with Eq. 1 that are given by

a b a b a b

c

(3a)

11 1

12 2

13 3

1

a b a b a b

c

(3b)

21 1

22 2

23 3

2

a b a b a b

c

(3c)

31 1

32 2

33 3

3

a b a b a b

c

(3d)

41 1

42 2

43 3

4

a b a b a b

c

(3e)

51 1

52 2

53 3

5

Section 6.3

6‐23. In Example 6.5, show how to obtain Eq. 3 beginning with the atomic matrix identified in Eq. 2.

6‐24. Show how to develop Eq. 6‐69 in terms of Eq. 6‐68 using the elementary row operations described in Sec. 6.2.5.

6‐25. Show how to obtain Eq. 6‐73 from Eq. 6‐72.

6‐26. When methane is partially combusted with oxygen, one finds the following molecular species: CH , O , CO , CO , H O and H . Determine the number 4

2

2

2

2

of independent stoichiometric reactions and comment on the restrictions concerning the choice of pivot and non‐pivot species.

Stoichiometry

267

Section 6.4

6‐27. Rucker et al. (1986) have studied the catalytic conversion of acetylene ( C H ) to form benzene ( C H ) along with hydrogen ( H ) and ethylene 2

2

6

6

2

( C H ). For this system, chose benzene and ethylene as the pivot species, 2

4

determine the rank of the atomic matrix, and apply the pivot theorem to determine the net rates of production of the non‐pivot species, R

and R

.

C2H2

H2

6‐28. The preparation of styrene ( C H ) and benzene ( C H ) from acetylene 8

8

6

6

( C H ) has been considered by Tanaka et al. (1955). and for this system a visual 2

2

representation of the atomic matrix is given by

Molecular Species  C H

C H

C H

2

2

6

6

8

8

carbon

 2

6

8 

oxygen

 2

6

8 

Determine the rank of the atomic matrix and use the pivot theorem to represent the rate of production of the non‐pivot species in terms of the rate of production of the pivot species.

6‐29. The reaction of acetylene ( C H ) with methanol ( CH OH ) to produce 2

2

3

methyl ether ( CH OC H ) is sometimes known as Reppe chemistry (Walter 3

2

3

Reppe, 1892‐1969). Determine the rank of the atomic matrix for this system.

Choose methyl ether as the pivot species and use the pivot theorem to represent the rates of production of the non‐pivot species in terms of the rate of production of the pivot species.

6‐30. Given a system containing the molecular species: CH , O , Cl , CH Cl , 4

2

2

3

HCl , H O and CO , determine the rank of the atomic matrix. Use the pivot 2

2

theorem to express the net rates of production of the non‐pivot species, CH , 4

O , Cl , CH Cl in terms of the net rates of production of the pivot species, 2

2

3

HCl , H O and CO .

2

2

6‐31. In this problem we consider the catalytic oxidation ( O ) of ethane ( C H ) 2

2

6

to produce ethylene ( C H ) and acetic acid ( CH COOH ) along with carbon 2

4

3

dioxide ( CO ), carbon monoxide ( CO ) and water ( H O ). This process has been 2

2

268