# 5.19: Untitled Page 116

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## Chapter 5

5‐10. Given the general representations for the chemical potentials ( )

(

*G T , p, y , y , * etc.) *, *

( )

(

*F T , p, x , x , * etc.)

(1)

*A gas*

*A*

*B*

*A liquid*

*A*

*B*

make use of Eq. 5‐24 to develop Henry’s law given by Eqs. 5‐31 and 5‐32. Use a Taylor series expansion for

(see Problem 5‐31) to obtain

*A, gas*

2

*G*

*G*

2

( )

*G*

( *y *)

( *y *) *..... *

(2)

*A gas*

*y *0

*A*

2

*A*

*A*

*y*

*A y *0

*yA*

*A*

*y *0

*A*

Since the chemical potential of species *A* is zero when there is no species *A* present, this simplifies to

2

*G*

*G*

2

( )

( *y *)

( *y *) *..... *

(3)

*A gas*

*A*

2

*A*

*y*

*A y*

0

*y*

*A*

*A*

*y *0

*A*

Restricting this development to dilute solutions of species *A*, we can impose *y * 1 in order to express the chemical potential in the gas phase as *A*

*G*

( )

( *y *)

*A gas*

*A*

(4)

*yA y *0

*A*

Develop a similar representation for the liquid phase and show how these special representations for the chemical potential lead to Henry’s law given by Eq. 5‐31.

*Section* 5.4

5‐11. An equi‐molar mixture of ethanol and ethyl ether is kept in a closed container at 103 KPa and 95 C. The temperature of the container is slowly reduced to the dew point of the mixture. Determine:

(a) What is the dew point temperature of the mixture?

(b) What is the pressure of the container at the dew point temperature of the mixture?

(c) What is the composition of the first drop of liquid at the dew point?

5‐12. A liquid mixture of n‐hexane (mole fraction equal to 0.32) and n‐heptane is heated until it begins boiling. Find the bubble point at *p* = 760 mm Hg. What are the mole fractions in the vapor when the mixture begins to boil?

*Two‐Phase Systems* & *Equilibrium Stages* 213

5‐13. A vapor mixture of benzene and toluene is slowly cooled inside a constant volume vessel. Initially the pressure inside the vessel is 300 mm Hg and the temperature is 70 C. As the vessel is cooled, the pressure inside the vessel decreases. Assume the vapor behaves like an ideal gas and take the dew point of the mixture to be 60 C. What is the mole fraction of benzene in the initial vapor mixture?

5‐14. Given Eq. 5‐36 as the definition of the point humidity, explore the possible definitions for the area averaged humidity and the volume averaged humidity.

Refer to Example 5.6 for guidance.

5‐15. Derive Eq. 5‐37 from Eq. 5‐36.

5‐16. Consider a day when the percent relative humidity is 70%, the temperature is 80 F and the barometric pressure is 1 atm. What is the humidity, mole fraction of water in the air, and dew point of the air?

5‐17. A mole of air is sampled from the atmosphere when the atmospheric pressure is 765 mm Hg, the temperature is 25 C, and relative humidity is 75%.

The sample of air is placed inside a closed container and heated to 135 C and then compressed to 2 atm. What are the relative humidity, the humidity, and the mole fraction of water in the compressed air?

5‐18. A humidifier is used to introduce moisture into air supplied to an office building during winter days. Outside air at atmospheric pressure and 5 C is introduced into the heating system at a rate of 100 m3/min, on a dry air basis. The relative humidity of the outside air is 95%, and the heating system delivers warm air into the building at 20 C. How much water must be introduced into the warm air, in kg/min, the keep the relative humidity inside the building at 75%?

5‐19. The modified mass fraction, , is defined by

*A*

*B* *N*1

*A*

*A*

*B*

*B*1

Use this definition to develop relations analogous to Eqs. 5‐40 and 5‐42.