# 7.40: Untitled Page 185

## Chapter 7

determine the composition of the stream leaving the furnace. The percent of excess air is defined as:

 molar flow 

 molar rate of

rate of oxygen

consumption of oxygen 

percent of

 entering

 owing to reaction

 

 100

excess air 

 molar rate of

consumption of oxygen

 owing

to reaction

7‐20. A fuel composed entirely of methane and nitrogen is burned with excess air. The dry flue gas composition in volume percent is: CO ,7.5%, O ,7%, and 2

2

the remainder nitrogen. Determine the composition of the fuel gas and the percentage of excess air as defined in Problem 7‐19.

7‐21. In this problem we consider the production of sulfuric acid illustrated in Figure 7.21. The mass flow rate of the dilute sulfuric acid stream is specified as Figure 7.21. Sulfuric acid production

Material Balances for Complex Systems

347

m

  100 lb / h and we are asked to determine the mass flow rate of the pure 1

m

sulfur trioxide stream, m

 . As is often the custom with liquid systems the 2

percentages given in Figure 7.21 refer to mass fractions, thus we sire

de

to

roduce

p

a final product in which the mass fraction of sulfuric acid is 0.98.

7‐22. In Example 7.3 use elementary row operations to obtain Eq. 10 om fr

Eq. 9,

nd

a

apply the pivot theorem to Eq. 10 to verify that Eqs. 11 are correct.

Section 7.3

7‐23. Given ( x ) , ( x ) and any three molar flow rates for the splitter illustrated A 1

A 2

in Figure 7.4, demonstrate that the compositions and total molar flow rates of all the streams are determined. For the three specified molar flow rates, use either species molar flow rates, or total molar flow rates, or a combination of both.

7‐24. Given any three total molar flow rates and any two species molar flow rates for the splitter illustrated in Figure 7.4, demonstrate that the compositions and total molar flow rates of all the streams are determined. If the directions of the streams in Figure 7.4 are reversed we obtain a mixer as illustrated in Figure 7‐6.

Show that six specifications are needed to completely determine a mixer with ree

th

input streams, i.e., S  3 .

7‐25. Given ( x ) , ( x ) , M

M

 , MM , and any species molar flow rate for A 1

B 1

3

2

4

2

the splitter illustrated in Figure 7.4, demonstrate that the compositions and total molar flow rates of all the streams are determined.

7‐26. Show how Eq. 6 is obtained from Eq. 5 in Example 7.5 using the concepts discussed in Sec. 6.2.5.

7‐27. In the catalytic converter shown in Figure 7.27, a reaction of the form A  products takes place. The product is completely separated from the stream leaving the reactor, and pure A is recycled via stream #5. A certain fraction,  , of species A that enters the reactor is converted to product, and we express this idea s

a

( x ) M

 (1  ) M

A 3

3

2

348