Phase Rule for a Vapor System. For the system NH₃–water and only a vapor phase present, calculate the number of degrees of freedom. What variables can be fixed?

Boiling Point and Raoult's Law. For the system benzene–toluene, do as follows, using the data from Table 11.1-1:

Boiling-Point-Diagram Calculation. The vapor-pressure data are given below for the system hexane–octane:

Single-Stage Contact of Vapor–Liquid System. A mixture of 100 mol containing 60 mol % n-pentane and 40 mol % n-heptane is vaporized at 101.32 kPa abs pressure until 40 mol of vapor and 60 mol of liquid in equilibrium with each other are produced. This occurs in a single-stage system, and the vapor and liquid are kept in contact with each other until vaporization is complete. The equilibrium data are given in Example 11.3-2. Calculate the composition of the vapor and the liquid.

Relative Volatility of a Binary System. Using the equilibrium data for the n-pentane–n-heptane system given in Example 11.3-2, calculate the relative volatility for each concentration and plot α versus the liquid composition x_A.

Comparison of Differential and Flash Distillation. A mixture of 100 kg mol which contains 60 mol % n-pentane (A) and 40 mol % n-heptane (B) is vaporized at 101.32 kPa pressure under differential conditions until 40 kg mol are distilled. Use equilibrium data from Example 11.3-2.

Differential Distillation of Benzene–Toluene. A mixture containing 70 mol % benzene and 30 mol % toluene is distilled under differential conditions at 101.32 kPa (1 atm). A total of one-third of the moles in the feed is vaporized. Calculate the average composition of the distillate and the composition of the remaining liquid. Use equilibrium data from Table 11.1-1.

Steam Distillation of Ethylaniline. A mixture contains 100 kg of H₂O and 100 kg of ethylaniline (mol wt = 121.1 kg/kg mol), which is immiscible with water. A very slight amount of nonvolatile impurity is dissolved in the organic. To purify the ethylaniline, it is steam-distilled by bubbling saturated steam into the mixture at a total pressure of 101.32 kPa (1 atm). Determine the boiling point of the mixture and the composition of the vapor. The vapor pressure of each of the pure compounds is as follows (T1):

Steam Distillation of Benzene. A mixture of 50 g mol of liquid benzene and 50 g mol of water is boiling at 101.32 kPa pressure. Liquid benzene is immiscible in water. Determine the boiling point of the mixture and the composition of the vapor. Which component will first be removed completely from the still? Vapor-pressure data for the pure components are as follows:

Distillation Using McCabe–Thiele Method. A rectification column is fed 100 kg mol/h of a mixture of 50 mol % benzene and 50 mol % toluene at 101.32 kPa abs pressure. The feed is liquid at the boiling point. The distillate is to contain 90 mol % benzene and the bottoms 10 mol % benzene. The reflux ratio is 4.52:1. Calculate the kg mol/h distillate, kg mol/h bottoms, and the number of theoretical trays needed using the McCabe–Thiele method.

Rectification of a Heptane–Ethyl Benzene Mixture. A saturated liquid feed of 200 mol/h at the boiling point containing 42 mol % heptane and 58% ethyl benzene is to be fractionated at 101.32 kPa abs to give a distillate containing 97 mol % heptane and a bottoms containing 1.1 mol % heptane. The reflux ratio used is 2.5:1. Calculate the mol/h distillate, mol/h bottoms, theoretical number of trays, and the feed tray number. Equilibrium data are given below at 101.32 kPa abs pressure for the mole fraction n-heptane x_H and y_H:

Graphical Solution for Minimum Reflux Ratio and Total Reflux. For the rectification given in Problem 11.4-1, where an equimolar liquid feed of benzene and toluene is being distilled to give a distillate of composition x_D = 0.90 and a bottoms of composition x_W = 0.10, calculate the following using graphical methods:

Minimum Number of Theoretical Plates and Minimum Reflux Ratio. Determine the minimum reflux ratio R_m and the minimum number of theoretical plates at total reflux for the rectification of a mixture of heptane and ethyl benzene as given in Problem 11.4-2. Do this by using the graphical methods of McCabe–Thiele.

Rectification Using a Partially Vaporized Feed. A total feed of 200 mol/h having an overall composition of 42 mol % heptane and 58 mol % ethyl benzene is to be fractionated at 101.3 kPa pressure to give a distillate containing 97 mol % heptane and a bottoms containing 1.1 mol % heptane. The feed enters the tower partially vaporized so that 40 mol % is liquid and 60 mol % vapor. Equilibrium data are given in Problem 11.4-2. Calculate the following:

Distillation Using a Vapor Feed. Repeat Problem 11.4-1 but use a feed that is saturated vapor at the dew point. Calculate the following:

Enriching Tower for Benzene–Toluene. An enriching tower is fed 100 kg mol/h of a saturated vapor feed containing 40 mol % benzene (A) and 60 mol % toluene (B) at 101.32 kPa abs. The distillate is to contain 90 mol % benzene. The reflux ratio is set at 4.0:1. Calculate the kg mol/h distillate D and bottoms W and their compositions. Also, calculate the number of theoretical plates required.

Stripping Tower. A liquid mixture containing 10 mol % n-heptane and 90 mol % n-octane is fed at its boiling point to the top of a stripping tower at 101.32 kPa abs. The bottoms are to contain 98 mol % n-octane. For every 3 mol of feed, 2 mol of vapor is withdrawn as product. Calculate the composition of the vapor and the number of theoretical plates required. The equilibrium data below are given as mole fraction n-heptane.

Stripping Tower and Direct Steam Injection. A liquid feed at the boiling point contains 3.3 mol % ethanol and 96.7 mol % water and enters the top tray of a stripping tower. Saturated steam is injected directly into liquid in the bottom of the tower. The overhead vapor which is withdrawn contains 99% of the alcohol in the feed. Assume equimolar overflow for this problem. Equilibrium data for mole fraction of alcohol are as follows at 101.32 kPa abs pressure (1 atm abs):

Murphree Efficiency and Actual Number of Trays. For the distillation of heptane and ethyl benzene in Problem 11.4-2, the Murphree tray efficiency is estimated as 0.55. Determine the actual number of trays needed by stepping off the trays using the tray efficiency of 0.55. Also, calculate the overall tray efficiency E_O.

Packing and Tray Efficiencies for Absorption Tower. An absorber in a petroleum refinery uses a lean oil to absorb butane from a natural gas stream. The composition of the key component butane in the gas phase is related to its composition in the liquid phase at equilibrium by y = mx = 0.7x. At the tower bottom, where the flows are largest, ρ_L = 57.9 lb_m/ft³ (927 kg/m³). At the average tower temperature, μ_L = 1.4 cp and the average molecular weight of the liquid is M_L = 245. Estimate the efficiency for a valve-tray tower and the HETP for Norton Intalox 2T structured packing.

Estimation of Tower Diameter of Sieve Tray. A distillation sieve-tray tower is being used to distill a hydrocarbon feed. The vapor flow rate at the tower bottom is 21 000 kg/hr and the liquid flow rate is 19 500 kg/hr. The density of the liquid ρ_L = 673 kg/m³ and ρ_V = 3.68 kg/m³. Assume a tray spacing of 24 in. (0.610 m). Calculate the tower diameter assuming the tower operates at 80% of flooding. Assume σ = 22.5 dyn/cm.

Use of Enthalpy–Concentration Method to Distill an Ethanol–Water Solution. A mixture of 50 wt % ethanol and 50 wt % water which is saturated liquid at the boiling point is to be distilled at 101.3 kPa pressure to give a distillate containing 85 wt % ethanol and a bottoms containing 3 wt % ethanol. The feed rate is 453.6 kg/h and a reflux ratio of 1.5 is to be used. Use equilibrium and enthalpy data from Appendix A.3. Note that the data are given in wt fraction and kJ/kg. Use these consistent units in plotting the enthalpy–concentration data and equilibrium data. Do as follows:

Distillation of Ethanol–Water Solution Using Enthalpy–Concentration Method. Repeat Problem 11.6-1 but use a reflux ratio of 2.0 instead of 1.5.

Minimum Reflux and Theoretical Number of Trays. A feed of ethanol–water containing 60 wt % ethanol is to be distilled at 101.32 kPa pressure to give a distillate containing 85 wt % ethanol and a bottoms containing 2 wt % ethanol. The feed rate is 10 000 kg/h and its enthalpy is 116.3 kJ/kg (50 btu/lb_m). Use consistent units of kg/h, weight fraction, and kJ/kg.

Distillation of Benzene–Toluene Feed Using Enthalpy–Concentration Method. A liquid feed of 100 kg mol/h of benzene–toluene at the boiling point contains 55 mol % benzene and 45 mol % toluene. It is being distilled at 101.32 kPa pressure to give a distillate with x_D = 0.98 and a bottoms of x_W = 0.04. Using a reflux ratio of 1.3 times the minimum and the enthalpy-concentration method, do as follows:

Use of Enthalpy–Concentration Plot. For the system benzene–toluene do as follows:

Flash Vaporization of Multicomponent Feed. For the feed to the distillation tower of Example 11.7-1, calculate the following:

Boiling Point, Dew Point, and Flash Vaporization. Following is the composition of a liquid feed in mole fraction: n-butane (x_A = 0.35), n-pentane (x_B = 0.20), n-hexane (x_C = 0.25), n-heptane (x_D = 0.20). At a pressure of 405.3 kPa calculate the following.

Vaporization of Multicomponent Alcohol Mixture. The vapor-pressure data are given below for the following alcohols:

Total Reflux, Minimum Reflux, Number of Stages. The following feed of 100 mol/h at the boiling point and 405.3 kPa pressure is fed to a fractionating tower: n-butane (x_A = 0.40), n-pentane (x_B = 0.25), n-hexane (x_C = 0.20), n-heptane (x_D = 0.15). This feed is distilled so that 95% of the n-pentane is recovered in the distillate and 95% of the n-hexane in the bottoms. Calculate the following:

Shortcut Design of Multicomponent Distillation Tower. A feed of part liquid and part vapor (q = 0.30) at 405.4 kPa is fed at the rate of 1000 mol/h to a distillation tower. The overall composition of the feed is n-butane (x_A = 0.35), n-pentane (x_B = 0.30), n-hexane (x_C = 0.20), and n-heptane (x_D = 0.15). The feed is distilled so that 97% of the n-pentane is recovered in the distillate and 85% of the n-hexane in the bottoms. Calculate the following:

Distillation of Multicomponent Alcohol Mixture. A feed of 30 mol % methanol (A), 20% ethanol (B), 15% n-propanol (C), and 35% n-butanol (D) is distilled at 101.32 kPa abs pressure to give a distillate composition containing 95.0 mol % methanol and a residue composition containing 5.0% methanol and the other components as calculated. The feed is below the boiling point, so that q = 1.1. The operating reflux ratio is 3.0. Assume that Raoult's law applies and use vapor-pressure data from Problem 11.7-3. Calculate the following:

Shortcut Design Method for Distillation of Ternary Mixture. A liquid feed at its bubble point is to be distilled in a tray tower to produce the distillate and bottoms as follows: Feed, x_AF = 0.047, x_BF = 0.072, x_CF = 0.881; distillate, x_AD = 0.1260, x_BD = 0.1913, x_CD = 0.6827; bottoms, x_AW = 0, x_BW = 0.001, x_CW = 0.999. Average α values to use are α_A = 4.19, α_B = 1.58, α_C = 1.00.