CHAPTER 9 PROBLEMS

I. CHAPTER 9 PROBLEMS

Problem I1 Consider a mixture of O 2 (1) and N 2 (2) at low temperatures in the form of a liquid mixture. You are asked to draw the T (K) vs. X and T vs. X k,l diagrams. Assume the following vapor pressure relations: ln (P sat bar) = A - B/(T in K +C) where A, B and C

are as follows: for O 2 : 8.273075661, 666.0593179, -9.69072568, respectively, and for N 2 : 6.394732229, 369.1680573, and -19.61997409, respectively. Use a spreadsheet program. Determine (a) X 1,e and X 1 for the equilibrium phases at 100 K and 100 kPa.

b) T and X 1 at 100 kPa and X 1,e = 0.4. (c) P and X 1 for T = - 170 C and X 1,e = 0.4. d) T and X 1,e for 100 kPa and X 1 = 0.4. e) P and X 1,e for –160ºC and X 1 = 0.4. f) The fraction of the system that is liquid, X 1,e , and X 1 at –160 °C and 100 kPa, when the

overall composition of the system is 21 mole percent of oxygen. Problem I2

Consider water in the atmosphere. Normally air is dissolved in liquid water. The nor- mal boiling point of water is 100ºC. Plot the mole fraction of X N2 and X O2 (given that

X N2 /X O2 = 3.76) vs. T. Assume that the mole fraction of H 2 O in liquid is close to unity so that mole fraction of water vapor in the gas mixture could be immediately deter- mined. The value of p O2 = 1 mm at –219ºC, 10 mm at -210.6, 40 mm at -204.1ºC, - 198.8ºC at 100mm, -188.8 ºCat 400 mm and -182.96ºC at 760 mm; p N2 = 1 mm at - 226.1ºC, 10 mm at -219.1ºC, 40 mm at -214.0ºC, -209.7ºC at 100mm, -200.9ºC at 400 mm and -195.8ºC at 760 mm. (First evaluate the constants A, B and C for the Cox

Antoine relation for N 2 and O 2 and then use spreadsheet.)

Problem I3 During the evaporative desalinization of sea water, salt water is first heated to its boiling point and then partially vaporized. The vapor, which is essentially pure water, is then condensed and collected to obtain water. If the entering sea water is initially

1.5 mol percent NaCl, determine the boiling temperature of the solution at 1 atm. ∆H v = 970 Btu/lb m and may be assumed constant. The vapor may be assumed to be ideal

and to have negligible density with respect to the liquid. List any assumptions you make.

Problem I4 The addition of glycol to water can lower the freezing point and, hence, more thermal energy can be stored in the mixture. Further the enthalpy of melting (h sm ) increases with a lowered freezing point. Plot a) the enthalpy of melting vs. glycol%, b) the freezing point vs. glycol concentration (upto 50% by weight) if the following data is

available: h sm = 334 kJ/kg at 273 K, c p,H2O( Ρ) =4.184 kJ/kg K, c p,H2O(s) = 2 kJ/kg K. As- sume the ideal solution model.

Problem I5 Find the partial pressure of benzene vapor for a mixture containing 30% benzene

(species 1) and 70% toluene (species 2) solution at 92 o

C, if the saturation vapor pres- sures of benzene and toluene at 92 o

C are 1078 torr and 432 torr. Problem I6

Consider a mixture of water (species 1) and ammonia (species 2). The vapor pressure relations are given as follows: ln P (bar) = 12.867 - 3063 /T (K) for ammonia; ln P

(bar) = 13.967 - 5205.2/T (K) for water. Plot P vs. X 1,e ,X 1 at 0ºC, 25ºC, 50ºC and T vs. X 1,e and X 1 at 0.5, 1, 10 bar.

Problem I7 The following is the composition of an acid which is vaporized and burnt in a hazard- ous waste plant: H 2 SO 4 : 92% by mass, Hydrocarbons: 4%, H 2 O: 4%. Lump hydrocar- bons with water. The vapor pressure relations are as follows: ln (p) = A - B/(T(K)+C), with p expressed in units of bar. The values of A, B and C are as follows: water:

11.9559, 3984.849, -39.4856, respectively; H 2 SO 4 : 8.346772, 4240.275, -119.155, re- spectively. Determine the vapor phase mole fraction of each component at a pressure of 1 bar at 100ºC. Assume an ideal solution. Will the vapor phase composition change

if N 2 is present in the vapor phase at 1 bar and 100ºC? If so, determine the value of this change. If p H2O and p H2SO4 at 270ºC for a strong acid are 0.335 bar and 0.0525 bar, respectively, determine the activity coefficients for the two species.

Problem I8 Justify if the ideal solution model is valid for a H 2 SO 4 and water liquid mixture.

Problem I9 Phase equilibrium is reached when the Gibbs energy has a minimum value at speci- fied values of temperature, pressure, and mass. One kg of water at 343 K water is poured into a cylinder of piston-cylinder-weight assembly. The space above water

initially contains 0.4 kg of dry air at 343 K and 100 kPa (c –1

pw = 4.184 kJ kg ). As wa- ter vaporizes the temperature of water drops and heat is added to maintain a constant water temperature. Consider values of p vapor in the range 0–0.9 bar in increments of

0.01 bar and determine G(p vapor ). Assume that water vapor and air behave as ideal gases.

Problem I10 a)

Obtain an expression for vapor pressure in air and vapor mixture just above the liquid surface of a lake which is at T. Assume that liquid is pure distilled water and pressure is P bar.

b) Derive the expression for mole fraction of vapor in the gas phase if gas phase is assumed to be an ideal gas mixture.

c) Determine p v and Y v at 30ºC and 0.9 bar. Problem I11

A methanol (component 1, 60% mole basis) and water (2, 40%) mixture at 60ºC ex- ists at a pressure P. Assume an ideal solution with p sat

1 = 625 mm of Hg and p 2 = 144 mm of Hg and determine the values of P, Y 1 , and Y 2 at equilibrium.

sat

Problem I12 Seven gmole of methanol (species 1 in both the liquid and vapor phases) and 3 gmole of water (species 2 as liquid and vapor) coexist in a piston cylinder assembly at 60ºC, and 433 kPa. With the values p sat

1 = 625 mm of Hg, p 2 = 144 mm of Hg, determine x 1 ,x 2 ,Y 1 , Y 2 , the vapor fraction or quality ¯w , and the moles of vapor of species 1

sat

and 2. Problem I13

Plot P vs. x H2O and P vs. Y H2O at T = 65 C for methanol and water solution. Assume ideal solution behavior.