# 5.25: Untitled Page 122

- Page ID
- 18255

## Chapter 5

5‐33. Derive the form of the solid phase mass balance given by Eq. 11 in Example 5.8.

5‐34. In this problem we wish to complete the analysis given in Example 5.8 in order to determine the total molar flow rate of fresh air entering the dryer. To accomplish this we must first derive the macroscopic mole balance for air which can then be applied to the dryer illustrated in Example 5.8.

Part I. Consider air to consist of nitrogen and oxygen and determine under what conditions the mole balances for these two components can be added to obtain the special form

*d*

*c*

*dV *

*c*

*dA * 0

**v n**

(1)

*air*

*air*

*dt V*

*A*

in which *c*

*c*

*c *. Begin the analysis with the macroscopic mole balances *air*

N2

O2

given by

*d*

*c dV *

*c ***v ** **n ** *dA *

*R dV*

(2)

*A*

*A A*

*A*

*dt V*

*A*

*V*

*d*

*c dV *

*c ***v ** **n ** *dA *

*R dV*

(3)

*B*

*B B*

*dt*

*B*

*V*

*A*

*V*

and identify the simplifications that are necessary in order to obtain Eq. 1.

Part II. Use Eq. 1 to determine the *molar flow* rate of the incoming air indicated by *M*

in Eq. 5 of Example 5.8. Clearly identify the process equilibrium relation 2

that must be imposed in order to solve this problem.

*Section* 5.6

5‐35. A sequential analysis of the multi‐stage extraction process illustrated in Figure 5‐10 led to the relation between ( *y *) and ( *y *) *A * 1

*A N* given by Eq. 5‐90.

1

That result was based on the special condition given by ( *x *) 0 . In this *A * o

problem you are asked to develop a general form of Eq. 5‐90 that is applicable for any value of ( *x *) .

*A * o

*Two‐Phase Systems* & *Equilibrium Stages* 225

5‐36. In Example 5.9 what value of *M*

can be used instead of *M*

30 kmol/h so

that the exit condition of ( *y *) 0 001

*. *

is satisfied exactly?

*A * 1

5‐37. In Example 5.9 an implicit equation for the absorption factor was given by 2

3

4

5

6

1 *A * *A * *A * *A * *A * *A*

20 *. * 0

The solution for *A * can be obtained by the methods described in Appendix B.

Use at least one of the following methods to determine the value of the absorption coefficient:

a). The bi‐section method

b). The false position method

c). Newton’s method

d). Picard’s method

e). Wegstein’s method

5‐38. Point #2 in Figure 5‐15 is represented by an equation given in Sec. 5.6.1.

Identify the equation.

5‐39. Point #3 in Figure 5‐15 is represented by an equation given in Sec. 5.6.1.

Identify the equation.

5‐40. Point #4 in Figure 5‐15 is represented by an equation given in Sec. 5.6.1.

Identify the equation.

5‐41. Point #5 in Figure 5‐15 is represented by an equation given in Sec. 5.6.1.

Identify the equation.

5‐42. In Example 5.10 the ‐phase mole fraction entering the *th* *N * stage was listed

as ( *x *) 0 00386

*. *

. Indicate how this mole fraction was determined and verify

*A N*

that the molar flow rate of acetone leaving in the liquid stream remains unchanged because of the change in *M*

.

5‐43. Verify that ( *x *) 0 00386

*. *

for the conditions associated with Figure 5.10b

*A N*

in Example 5.10.