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Problems

1.A liquid hydrocarbon A has a saturation pressure of 13.3 kPa at 10°C. Its density at 25°C is 0.80 g cm−3 and its molecular weight is 160. This is ail the information available on pure liquid A. An equimolar mixture of A in carbon disulfide at 10°C gives an equilibrium partial pressure of A equal to 8 kPa. Estimate the composition of the vapor that at 10°C is in equilibrium with an equimolar liquid solution of A in toluene, using the following data:

 Carbon disulfideToluene
Solubility parameters at 25°C (J cm−3)½20.518.2
Liquid molar volumes at 25°C (cm3 mol−1)61107
Saturation pressures at 10°C (kPa)1.7325.5


2.Consider a dilute isothermal solution of acetic acid in benzene. For the dilute region (say up to 5 mol % acid), draw schematically curves for versus x1 and versus x1 where subscript 1 refers to the acid. Briefly justify your schematic graphs with suitable explanations.
3.For distillation-column design, we need K factors (Ki = yi/xi). A liquid mixture at 50°C contains 30 mol % n-hexane and 70 mol % benzene. Calculate the K factors of n-hexane and benzene in this mixture. Assume that the pressure is sufficiently low to neglect gas-phase corrections and Poynting factors. At 50°C, pure-component vapor pressures are 0.533 bar for n-hexane and 0.380 bar for benzene.

At 25°C, the molar volumes and solubility parameters are:

 υL (cm3 mol−1)δ (J cm−3)½
n-Hexane13214.9
Benzene8918.8


4.Consider a solution of diethyl ether and pentachloroethane. Draw (schematically) a plot of g E versus x at constant temperature. Briefly justify your schematic graph with suitable explanations.
5.Liquids A and B when mixed form an azeotrope at 300 K and at a mole fraction xA = 0.5. It is desired to separate a mixture of A and B by distillation, and in order to break the azeotrope it is proposed to add a third liquid C into the mixture. Compute the relative volatility of A to B at 300 K when the ternary mixture contains 60 mol % C and equal molar amounts of A and B. Assume ideal gas behavior and assume that A, B, and C are nonreactive nonpolar substances. The data given below are all at 300 K.

 ABC
Liquid molar volume (cm3 mol−1)100100100
Solubility parameter(J cm−3)½14.316.418.4


6.A binary liquid mixture contains nonpolar components 1 and 2. The mixture is to be separated by ordinary distillation. To determine if this is feasible, it is necessary to know whether the mixture has an azeotrope. At 300 K the pure-component vapor pressures are and . The pure-component molar volumes are both 160 cm3 mol−1 and the solubility parameters are δ1 = 14.3 and δ2 = 17.4 (J cm−3)½. At 300 K, does this mixture have an azeotrope? If so, what is its composition? Assume the vapor phase is ideal.
7.At 380 K, an equimolar liquid mixture of A and B has a total pressure of 0.667 bar. Fluids A and B are simple nonpolar liquids having similar molar volumes. Pure-component vapor pressures (bar) are and .

If the equimolar mixture is cooled, partial miscibility (two liquid phases) results. Give an estimate of the (upper) critical solution temperature where partial miscibility begins. Explain and justify your method of calculation. Is your estimate likely to be high or low? Give an upper and lower bound of the expected (upper) critical solution temperature.

8.An equimolar liquid mixture of benzene and n-butane is fed to an isothermal flash tank operating at 50°C and 1 bar.

Find the compositions of the two streams leaving the flash tank. Assume that at 1 bar the gas is ideal. Assume also that for the liquid phase, the Scatchard-Hildebrand (regular-solution) equations are valid.

Data (all at 50°C) are as follows:

 Liquid density (g cm−3)Solubility parameter (J cm−3)½Vapor pressure (torr)
Benzene0.84518.8280
n-Butane0.54813.93620


9.Estimate the upper critical solution temperature for a binary system containing nonpolar liquids A and B.

Data at 25°C:

LiquidLiquid molar volume (cm3 mol−1)Solubility parameter (J cm−3)½
A12018
B18012


10.At 25°C, carbon disulfide (1) and perfluoro-n-heptane (2) are essentially totally immiscible. A small amount of cyclohexane (3) is added to this two-phase mixture. Estimate the distribution coefficient K for cyclohexane [K = x3 (in 1)/x3 (in 2)].

Pure component data:

LiquidLiquid molar volume (cm3 mol−1)Solubility parameter (J cm−3)½
Carbon disulfide6120.5
Cyclohexane10916.8
Perfluoro-n-heptane22612.3


11.Chemical engineers are fond of generalized plots. Show how you would prepare a generalized solubility parameter plot for nonpolar liquids based on Pitzer’s three-parameter theory of corresponding states.
12.At room temperature and atmospheric pressure:
  1. Give an order-of-magnitude estimate of for methanol dissolved in a large excess of isooctane.

  2. Give an order-of-magnitude estimate of the change in temperature when equal parts of cyclohexane and carbon disulfide are mixed adiabatically. Is ΔT positive or negative?

  3. Name two polar solvents that are likely to be very good and two others that are likely to be very poor for an extraction separation of hexane and hexene. Explain.

13.A dilute solution of picric acid in water is contacted with n-hexane. Consider the distribution of picric acid between the two solvents; assume that the acid exists as a monomer in both phases but that it ionizes partially in the aqueous phase. Show that the distribution of the acid should be described by an equation of the form


where cH is the concentration of picric acid in hexane, cw is the concentration of picric acid in water, and a and b are constants depending only on temperature.

14.Acetaldehyde forms a trimer (paraldehyde) in benzene solution; in excess water, acetaldehyde is completely solvated through hydrogen bonding. Experimental data are available on the distribution of acetaldehyde between benzene and water for small acetaldehyde concentrations. Show how these data should be plotted to yield a straight line, convenient for interpolation and (slight) extrapolation. (Use C for concentration, subscript A for acetaldehyde, and superscripts B and W for benzene phase and water phase, respectively.)
15.
  1. Dichloromethane, acetone, and methanol are strongly polar fluids; their molecules have appreciable dipole moments. At 25°C, the following activity coefficients (at infinite dilution) were measured by Smith et al. (1983, J. Chem. Eng. Data, 28; 412) in binary solutions:

     DichioromethaneAcetoneDichloromethaneMethanol
    γ0.590.532.9410.3


    These data show that binary mixtures of dichloromethane/acetone exhibit appreciable negative deviations from Raoult’s law. However, the data for binary mixtures of dichloromethane/methanol exhibit large positive deviations. Why is there such a striking difference between these two binary systems?

  2. At 50°C, we have data for the activity coefficient of nitroethane in benzene and in hexane. When the mole fraction of nitroethane is 0.05, is the activity coefficient of nitroethane larger in benzene or in hexane? Explain.

  3. Near room temperature, we want to dissolve a heavy, aromatic, coal-derived liquid in a volatile solvent. Two solvents are considered: methanol and chloroform. Which solvent is better; that is, in which solvent is the solute likely to be more soluble? Why?


  

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