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Separation Process Principles

J. D. Seader, Ernest J. Henley

Chapter 4

Single Equilibrium Stages and Flash Calculations - all with Video Answers

Educators

Chapter Questions

06:48

Problem 1

Consider the equilibrium stage shown in Figure 4.35. Conduct a degrees-of-freedom analysis by performing the following steps:
(a) List and count the variables.
(b) Write and count the equations relating the variables.
(c) Calculate the degrees of freedom.
(d) List a reasonable set of design variables.

Abigail Martyr
Abigail Martyr
Numerade Educator
02:43

Problem 2

Can the following problems be solved uniquely?
(a) The feed streams to an adiabatic equilibrium stage consist of liquid and vapor streams of known composition, flow rate, temperature, and pressure. Given the stage (outlet) temperature and pressure, calculate the composition and amounts of equilibrium vapor and liquid leaving the stage.
(b) The same as part (a), except that the stage is not adiabatic.
(c) A multicomponent vapor of known temperature, pressure, and composition is to be partially condensed in a condenser. The outlet pressure of the condenser and the inlet cooling water temperature are fixed. Calculate the cooling water required.

Lottie Adams
Lottie Adams
Numerade Educator
00:57

Problem 3

Consider an adiabatic equilibrium flash. The variables are all as indicated in Figure 4.36.
(a) Determine the number of variables.
(b) Write all the independent equations that relate the variables.
(c) Determine the number of equations.
(d) Determine the number of degrees of freedom.
(e) What variables would you prefer to specify in order to solve a typical adiabatic flash problem?

David Collins
David Collins
Numerade Educator
06:08

Problem 4

Determine the number of degrees of freedom for a nonadiabatic equilibrium flash for one liquid feed, one vapor stream product, and two immiscible liquid stream products as shown in Figure $4.33$.

Jincy M Saji
Jincy M Saji
Numerade Educator
03:01

Problem 5

Consider the seven-phase equilibrium system shown in Fig ure 4.31. Assume that air consists of $\mathrm{N}_{2}, \mathrm{O}_{2}$, and argon. How many degrees of freedom are computed by the Gibbs phase rule? What variables might be specified to fix the system?

Mohammad Mehran
Mohammad Mehran
Numerade Educator
01:49

Problem 6

A liquid mixture containing $25 \mathrm{~mol} \%$ benzene and $75 \mathrm{~mol} \%$ ethyl alcohol, in which components are miscible in all proportions, is heated at a constant pressure of $1 \mathrm{~atm}(101.3 \mathrm{kPa}, 760$ torr $)$ from a temperature of $60^{\circ} \mathrm{C}$ to $90^{\circ} \mathrm{C}$. Using the following $T-x-y$ experimental data, perform calculations to determine the answers to parts (a) through (f).

Mahendra Rathore
Mahendra Rathore
Numerade Educator
01:43

Problem 7

Stearic acid is to be steam distilled at $200^{\circ} \mathrm{C}$ in a direct-fired still, heat-jacketed to prevent condensation. Steam is introduced into the molten acid in small bubbles, and the acid in the vapor leaving the still has a partial pressure equal to $70 \%$ of the vapor pressure of pure stearic acid at $200^{\circ} \mathrm{C}$. Plot the kilograms of acid distilled per kilogram of steam added as a function of total pressure from $101.3 \mathrm{kPa}$ down to $3.3 \mathrm{kPa}$ at $200^{\circ} \mathrm{C}$. The vapor pressure of stearic acid at $200^{\circ} \mathrm{C}$ is $0.40 \mathrm{kPa}$.

David Collins
David Collins
Numerade Educator
01:39

Problem 8

The relative volatility, $\alpha$, of benzene to toluene at $1 \mathrm{~atm}$ is $2.5$. Construct an $x-y$ diagram for this system at $1 \mathrm{~atm}$. Repeat the construction using vapor pressure data for benzene from Exercise $4.6$ and for toluene from the following table in conjunction with Raoult's and Dalton's laws. Also construct a $T-x-y$ diagram.
(a) A liquid containing $70 \mathrm{~mol} \%$ benzene and $30 \mathrm{~mol} \%$ toluene is heated in a container at $1 \mathrm{~atm}$ until $25 \mathrm{~mol} \%$ of the original liquid is evaporated. Determine the temperature. The phases are then separated mechanically, and the vapors condensed. Determine the composition of the condensed vapor and the liquid residue.
(b) Calculate and plot the $K$-values as a function of temperature at $1 \mathrm{~atm}$.

Lottie Adams
Lottie Adams
Numerade Educator
02:34

Problem 9

The vapor pressure of toluene is given in Exercise $4.8$, and that of $n$-heptane is given in the accompanying table.

Anand Jangid
Anand Jangid
Numerade Educator
02:05

Problem 10

Saturated-liquid feed, of $F=40 \mathrm{~mol} / \mathrm{h}$, containing $50 \mathrm{~mol} \%$ $\mathrm{A}$ and $\mathrm{B}$ is supplied continuously to the apparatus shown in Figure 4.37. The condensate from the condenser is split so that half of it is returned to the still pot.
(a) If heat is supplied at such a rate that $W=30 \mathrm{~mol} / \mathrm{h}$ and $\alpha=2$, as subsequently defined, what will be the composition of the overhead and the bottoms product?
(b) If the operation is changed so that no condensate is returned to the still pot and $W=3 D$ as before, what will be the composition of the products?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
16:21

Problem 11

It is required to design a fractionation tower to operate at $101.3 \mathrm{kPa}$ to obtain a distillate consisting of $95 \mathrm{~mol} \%$ acetone (A) and $5 \mathrm{~mol} \%$ water, and a residue containing $1 \mathrm{~mol} \% \mathrm{~A}$. The feed liquid is at $125^{\circ} \mathrm{C}$ and $687 \mathrm{kPa}$ and contains $57 \mathrm{~mol} \% \mathrm{~A}$. The feed is introduced to the column through an expansion valve so that it enters the column partially vaporized at $60^{\circ} \mathrm{C}$. From the data below, determine the molar ratio of liquid to vapor in the partially vaporized feed. Enthalpy and equilibrium data are as follows:
Molar latent heat of $\mathrm{A}=29,750 \mathrm{~kJ} / \mathrm{kmol}$ (constant)
Molar latent heat of $\mathrm{H}_{2} \mathrm{O}=42,430 \mathrm{~kJ} / \mathrm{kmol}$ (constant)
Molar specific heat of $\mathrm{A}=134 \mathrm{~kJ} / \mathrm{kmol}-\mathrm{K}$ (constant)
Molar specific heat of $\mathrm{H}_{2} \mathrm{O}=75.3 \mathrm{~kJ} / \mathrm{kmol}-\mathrm{K}$ (constant)
Enthalpy of high-pressure, hot feed before adiabatic expansion $=0$
Enthalpies of feed phases after expansion: $h_{V}=27,200 \mathrm{~kJ} / \mathrm{kmol}$, $h_{L}=-5,270 \mathrm{~kJ} / \mathrm{kmol}$.

Chareen Guzman
Chareen Guzman
Numerade Educator
08:21

Problem 12

Using vapor pressure data from Exercises $4.6$ and $4.8$ and the enthalpy data provided below;
(a) Construct an $h-x-y$ diagram for the benzene-toluene system at $1 \mathrm{~atm}(101.3 \mathrm{kPa})$ based on the use of Raoult's and Dalton's laws.
(b) Calculate the energy required for 50 mol\% vaporization of a $30 \mathrm{~mol} \%$ liquid solution of benzene in toluene, initially at saturation temperature. If the vapor is then condensed, what is the heat load on the condenser in $\mathrm{kJ} / \mathrm{kg}$ of solution if the condensate is saturated and if it is subcooled by $10^{\circ} \mathrm{C}$ ?

Riaz Ahmad
Riaz Ahmad
Other Schools
08:21

Problem 13

Vapor-liquid equilibrium data at $101.3 \mathrm{kPa}$ are given for the chloroform-methanol system on p. 13-11 of Perry's Chemical Engineers' Handbook, 6 th ed. From these data, prepare plots like Figures $4.6 \mathrm{~b}$ and $4.6 \mathrm{c}$. From the plots, determine the azeotropic composition and temperature at $101.3 \mathrm{kPa}$. Is the azeotrope of the minimum- or maximum-boiling type?

Riaz Ahmad
Riaz Ahmad
Other Schools
08:21

Problem 14

Vapor-liquid equilibrium data at $101.3 \mathrm{kPa}$ are given for the water-formic acid system on p. 13-14 of Perry's Chemical Engineers' Handbook, 6 th ed. From these data, prepare plots like Figures $4.7 \mathrm{~b}$ and $4.7 \mathrm{c}$. From the plots, determine the azeotropic composition and temperature at $101.3 \mathrm{kPa}$. Is the azeotrope of the minimum- or maximum-boiling type?

Riaz Ahmad
Riaz Ahmad
Other Schools
04:39

Problem 15

Vapor-liquid equilibrium data for mixtures of water and isopropanol at $1 \mathrm{~atm}(101.3 \mathrm{kPa}, 760$ torr) are given below.
(a) Prepare $T-x-y$ and $x-y$ diagrams.
(b) When a solution containing $40 \mathrm{~mol} \%$ isopropanol is slowly vaporized, what will be the composition of the initial vapor formed?
(c) If this same $40 \%$ mixture is heated under equilibrium conditions until $75 \mathrm{~mol} \%$ has been vaporized, what will be the compositions of the vapor and liquid produced?

Bhumika Jayee
Bhumika Jayee
Numerade Educator
08:21

Problem 16

Using the $y-x$ and $T-y-x$ diagrams in Figures $4.3$ and $4.4$, determine the temperature, amounts, and compositions of the equilibrium vapor and liquid phases at $101 \mathrm{kPa}$ for the following conditions with a $100-\mathrm{kmol}$ mixture of $n \mathrm{C}_{6}(\mathrm{H})$ and $n \mathrm{C}_{8}(\mathrm{C})$.
(a) $z_{\mathrm{H}}=0.5, \Psi=V / F=0.2$
(b) $z_{\mathrm{H}}=0.4, y_{\mathrm{H}}=0.6$
(c) $z_{\mathrm{H}}=0.6, x_{\mathrm{C}}=0.7$
(d) $z_{\mathrm{H}}=0.5, \Psi=0$
(e) $z_{\mathrm{H}}=0.5, \Psi=1.0$
(f) $z_{\mathrm{H}}=0.5, T=200^{\circ} \mathrm{F}$

Riaz Ahmad
Riaz Ahmad
Other Schools
06:25

Problem 17

For a binary mixture of components 1 and 2 , show that the equilibrium phase compositions and amounts can be computed directly from the following reduced forms of Eqs. (5), (6), and (3) of Table $4.4$
$$
\begin{aligned}
x_{1} &=\left(1-K_{2}\right) /\left(K_{1}-K_{2}\right) \\
x_{2} &=1-x_{1} \\
y_{1} &=\left(K_{1} K_{2}-K_{1}\right) /\left(K_{2}-K_{1}\right) \\
y_{2} &=1-y_{1} \\
\Psi &=\frac{V}{F}=\frac{z_{1}\left[\left(K_{1}-K_{2}\right) /\left(1-K_{2}\right)\right]-1}{K_{1}-1}
\end{aligned}
$$

Shubham Kumar
Shubham Kumar
Numerade Educator
02:12

Problem 18

Consider the Rachford-Rice form of the flash equation,
$$
\sum_{i=1}^{c} \frac{z_{i}\left(1-K_{i}\right)}{1+(V / F)\left(K_{i}-1\right)}=0
$$
Under what conditions can this equation be satisfied?

Fasiha Binat Zafar
Fasiha Binat Zafar
Numerade Educator
02:50

Problem 19

A liquid containing $60 \mathrm{~mol} \%$ toluene and $40 \mathrm{~mol} \%$ benzene is continuously distilled in a single-equilibrium-stage unit at atmospheric pressure. What percent of benzene in the feed leaves in the vapor if $90 \%$ of the toluene entering in the feed leaves in the liquid? Assume a relative volatility of $2.3$ and obtain the solution graphically.

Lottie Adams
Lottie Adams
Numerade Educator
01:39

Problem 20

Solve Exercise $4.19$ by assuming an ideal solution and using vapor pressure data from Figure 2.4. Also determine the temperature.

Keenan Mintz
Keenan Mintz
University of Miami
01:21

Problem 21

A seven-component mixture is flashed at a specified temperature and pressure.
(a) Using the $K$-values and feed composition given below, make a plot of the Rachford-Rice flash function
$$
f\{\Psi\}=\sum_{i=1}^{C} \frac{z_{i}\left(1-K_{i}\right)}{1+\Psi\left(K_{i}-1\right)}
$$
at intervals of $\Psi$ of $0.1$, and from the plot estimate the correct root of $\Psi$.
(b) An alternative form of the flash function is
$$
f\{\Psi\}=\sum_{i=1}^{C} \frac{2_{i} K_{i}}{1+\Psi\left(K_{i}-1\right)}-1
$$
Make a plot of this equation also at intervals of $\Psi$ of $0.1$ and explain why the Rachford-Rice function is preferred.

Manik Pulyani
Manik Pulyani
Numerade Educator
02:00

Problem 22

One hundred kilomoles of a feed composed of $25 \mathrm{~mol} \%$ $n$-butane, $40 \mathrm{~mol} \% n$-pentane, and $35 \mathrm{~mol} \% n$-hexane are flashed at steady-state conditions. If $80 \%$ of the hexane is to be recovered in the liquid at $240^{\circ} \mathrm{F}$, what pressure is required, and what are the liquid and vapor compositions? Obtain $K$-values from Figure $2.8$.

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
06:19

Problem 23

An equimolar mixture of ethane, propane, $n$-butane, and $n$-pentane is subjected to a flash vaporization at $150^{\circ} \mathrm{F}$ and $205 \mathrm{psia}$. What are the expected amounts and compositions of the liquid and vapor products? Is it possible to recover $70 \%$ of the ethane in the vapor by a single-stage flash at other conditions without losing more than $5 \%$ of $n \mathrm{C}_{4}$ to the vapor? Obtain $K$-values from Figure $2.8$.

George Mckeown
George Mckeown
Numerade Educator
01:12

Problem 24

The system shown in Figure $4.38$ is used to cool the reactor effluent and separate the light gases from the heavier hydrocarbons. $K$-values for the components at 500 psia and $100^{\circ} \mathrm{F}$ are
$\begin{array}{lc}\text { Component } & \boldsymbol{K}_{i} \\ \mathrm{H}_{2} & 80 \\ \mathrm{CH}_{4} & 10 \\ \text { Benzene } & 0.010 \\ \text { Toluene } & 0.004\end{array}$
(a) Calculate the composition and flow rate of the vapor leaving the flash drum.
(b) Does the flow rate of liquid quench influence the result? Prove your answer analytically.

Manik Pulyani
Manik Pulyani
Numerade Educator
01:27

Problem 25

The mixture shown in Figure $4.39$ is partially condensed and separated into two phases. Calculate the amounts and compositions of the equilibrium phases, $V$ and $L$.

Ahmed Ali
Ahmed Ali
Numerade Educator
02:53

Problem 26

The following stream is at 200 psia and $200^{\circ} \mathrm{F}$. Determine whether it is a subcooled liquid or a superheated vapor, or whether it is partially vaporized, without making a flash calculation.
$\begin{array}{ccc}\text { Component } & \text { Ibmol/h } & \boldsymbol{K} \text {-value } \\ \mathrm{C}_{3} & 125 & 2.056 \\ n \mathrm{C}_{4} & 200 & 0.925 \\ n \mathrm{C}_{5} & 175 & 0.520\end{array}$

Keshav Singh
Keshav Singh
Numerade Educator
01:05

Problem 27

The overhead system for a distillation column is shown in Figure 4.40. The composition of the total distillates is indicated, with $10 \mathrm{~mol} \%$ of it being taken as vapor. Determine the pressure in the reflux drum, if the temperature is $100^{\circ} \mathrm{F}$. Use the following $K$-values by assuming that $K$ is inversely proportional to pressure.

Hast Aggarwal
Hast Aggarwal
Numerade Educator
00:21

Problem 28

Determine the phase condition of a stream having the following composition at $7.2^{\circ} \mathrm{C}$ and $2,620 \mathrm{kPa}$.
$\begin{array}{cc}\text { Component } & \mathbf{k m o l} / \mathbf{h} \\ \mathrm{N}_{2} & 1.0 \\ \mathrm{C}_{1} & 124.0 \\ \mathrm{C}_{2} & 87.6 \\ \mathrm{C}_{3} & 161.6 \\ n \mathrm{C}_{4} & 176.2 \\ n \mathrm{C}_{5} & 58.5 \\ n \mathrm{C}_{6} & 33.7\end{array}$
Perform the calculations with a computer simulation program using at least three different options for $K$-values. Does the choice of $K$-value method influence the results?

Shazia Naz
Shazia Naz
Numerade Educator
02:50

Problem 29

A liquid mixture consisting of $100 \mathrm{kmol}$ of $60 \mathrm{~mol} \%$ benzene, $25 \mathrm{~mol} \%$ toluene, and $15 \mathrm{~mol} \%$ o-xylene is flashed at $1 \mathrm{~atm}$ and $100^{\circ} \mathrm{C}$.
(a) Compute the amounts of liquid and vapor products and their composition.
(b) Repeat the calculation at $100^{\circ} \mathrm{C}$ and $2 \mathrm{~atm}$.
(c) Repeat the calculation at $105^{\circ} \mathrm{C}$ and $0.1$ atm.
(d) Repeat the calculation at $150^{\circ} \mathrm{C}$ and $1 \mathrm{~atm}$.
Assume ideal solutions and use the vapor pressure curves of Figure $2.4$ for benzene and toluene. For $o$-xylene, draw a vapor pressure line that goes through the points $\left(100.2^{\circ} \mathrm{C}, 200\right.$ torr) and $\left(144^{\circ} \mathrm{C}, 760\right.$ torr $)$.

Lottie Adams
Lottie Adams
Numerade Educator
04:52

Problem 30

Prove that the vapor leaving an equilibrium flash is at its dew point and that the liquid leaving an equilibrium flash is at its bubble point.

Ronald Prasad
Ronald Prasad
Numerade Educator
06:19

Problem 31

The following mixture is introduced into a distillation column as saturated liquid at $1.72 \mathrm{MPa}$. Calculate the bubble-point temperature using the $K$-values of Figure $2.8$.
$\begin{array}{lr}\text { Compound } & \mathrm{kmol} / \mathbf{h} \\ \text { Ethane } & 1.5 \\ \text { Propane } & 10.0 \\ n \text {-Butane } & 18.5 \\ n \text {-Pentane } & 17.5 \\ n \text {-Hexane } & 3.5\end{array}$

George Mckeown
George Mckeown
Numerade Educator
03:32

Problem 32

An equimolar solution of benzene and toluene is totally evaporated at a constant temperature of $90^{\circ} \mathrm{C}$. What are the pressures at the beginning and end of the vaporization process? Assume an ideal solution and use the vapor pressure curves of Figure 2.4.

Shazia Naz
Shazia Naz
Numerade Educator
02:24

Problem 33

The following equations are given by Sebastiani and Lacquaniti [Chem. Eng. Sci., 22, 1155 (1967)] for the liquid-phase activity coefficients of the water (W)-acetic acid (A) system.
$$
\begin{aligned}
\log \gamma_{\mathrm{W}} &=x_{\mathrm{A}}^{2}\left[A+B\left(4 x_{\mathrm{W}}-1\right)+C\left(x_{\mathrm{W}}-x_{\mathrm{A}}\right)\left(6 x_{\mathrm{W}}-1\right)\right] \\
\log \gamma_{\mathrm{A}} &=x_{\mathrm{W}}^{2}\left[A+B\left(4 x_{\mathrm{W}}-3\right)+C\left(x_{\mathrm{W}}-x_{\mathrm{A}}\right)\left(6 x_{\mathrm{W}}-5\right)\right] \\
A &=0.1182+\frac{64.24}{T(\mathrm{~K})} \\
B &=0.1735-\frac{43.27}{T(\mathrm{~K})} \\
C &=0.1081
\end{aligned}
$$
Find the dew point and bubble point of a mixture of composition $x_{W}=0.5, x_{A}=0.5$ at 1 atm. Flash the mixture at a temperature halfway between the dew point and the bubble point.

Penny Riley
Penny Riley
Numerade Educator
02:24

Problem 34

Find the bubble-point and dew-point temperatures of a mixture of $0.4$ mole fraction toluene (1) and $0.6$ mole fraction $n$-butanol (2) at $101.3 \mathrm{kPa}$. The $K$-values can be calculated from (2-72), the modified Raoult's law, using vapor-pressure data, and $\gamma_{1}$ and $\gamma_{2}$ from the van Laar equation of Table $2.9$ with $A_{12}=0.855$ and $A_{21}=1.306$. If the same mixture is flashed at a temperature midway between the bubble point and dew point, and $101.3 \mathrm{kPa}$, what fraction is vaporized, and what are the compositions of the two phases?

Penny Riley
Penny Riley
Numerade Educator
19:02

Problem 35

(a) For a liquid solution having a molar composition of ethyl acetate (A) of $80 \%$ and ethyl alcohol (E) of $20 \%$, calculate the bubble-point temperature at $101.3 \mathrm{kPa}$ and the composition of the corresponding vapor using $(2-72)$ with vapor pressure data and the van Laar equation of Table $2.9$ with $A_{\mathrm{AE}}=0.855, A_{\mathrm{EA}}=0.753$.
(b) Find the dew point of the mixture.
(c) Does the mixture form an azeotrope? If so, predict the temperature and composition.

Chareen Guzman
Chareen Guzman
Numerade Educator
03:35

Problem 36

A binary solution at $107^{\circ} \mathrm{C}$ contains $50 \mathrm{~mol} \%$ water $(\mathrm{W})$ and $50 \mathrm{~mol} \%$ formic acid (F). Using (2-72) with vapor pressure data and the van Laar equation of Table $2.9$ with $A_{W F}=-0.2935$ and $A_{\mathrm{FW}}=-0.2757$, compute:
(a) The bubble-point pressure.
(b) The dew-point pressure.
Also determine whether the mixture forms a maximum- or minimum-boiling azeotrope. If so, predict the azeotropic pressure at $107^{\circ} \mathrm{C}$ and the azeotropic composition.

Adriano Chikande
Adriano Chikande
Numerade Educator
03:15

Problem 37

For a mixture consisting of 45 mol\% $n$-hexane, 25 mol\% $n$-heptane, and $30 \mathrm{~mol} \% n$-octane at $1 \mathrm{~atm}$, use a simulation computer program to:
(a) Find the bubble- and dew-point temperatures.
(b) Find the flash temperature, and the compositions and relative amounts of the liquid and vapor products if the mixture is subjected to a flash distillation at 1 atm so that $50 \mathrm{~mol} \%$ of the feed is vaporized.
(c) Find how much of the octane is taken off as vapor if $90 \%$ of the hexane is taken off as vapor.
Repeat parts (a) and (b) at $5 \mathrm{~atm}$ and $0.5 \mathrm{~atm}$.

Lottie Adams
Lottie Adams
Numerade Educator
04:26

Problem 38

In Figure $4.41,150 \mathrm{kmol} / \mathrm{h}$ of a saturated liquid, $L_{1}$, at $758 \mathrm{kPa}$, of molar composition, propane $10 \%, n$-butane $40 \%$, and $n$-pentane $50 \%$, enters the reboiler from stage 1 . What are the compositions and amounts of $V_{B}$ and $B$ ? What is $Q_{R}$, the reboiler duty? Use a simulation computer program to find the answers.

Sima Sarker
Sima Sarker
Numerade Educator
03:15

Problem 39

(a) Find the bubble-point temperature of the following mixture at 50 psia, using $K$-values from Figure $2.8$ or Figure $2.9$.
$\begin{array}{lc}\text { Component } & z_{i} \\ \text { Methane } & 0.005 \\ \text { Ethane } & 0.595 \\ n \text {-Butane } & 0.400\end{array}$
(b) Find the temperature that results in $25 \%$ vaporization at this pressure. Determine the corresponding liquid and vapor compositions.

Lottie Adams
Lottie Adams
Numerade Educator
04:28

Problem 40

As shown in Figure 4.42, a hydrocarbon mixture is heated and expanded before entering a distillation column. Calculate, using a simulation computer program, the mole percent vapor phase and vapor and liquid phase mole fractions at each of the three locations indicated by a pressure specification.

Aadit Sharma
Aadit Sharma
Numerade Educator
01:03

Problem 41

Streams entering stage $F$ of a distillation column are shown in Figure 4.43. What is the temperature of stage $F$ and the compositions and amounts of streams $V_{F}$ and $L_{F}$ if the pressure is $785 \mathrm{kPa}$ for all streams? Use a simulation computer program to obtain the answers.

Hast Aggarwal
Hast Aggarwal
Numerade Educator
00:55

Problem 42

Flash adiabatically, across a valve, a stream composed of the six hydrocarbons given below. The feed upstream of the valve is at $250^{\circ} \mathrm{F}$ and $500 \mathrm{psia}$. The pressure downstream of the valve is 300 psia.
$\begin{array}{cc}\text { Component } & z_{i} \\ \mathrm{C}_{2} \mathrm{H}_{4} & 0.02 \\ \mathrm{C}_{2} \mathrm{H}_{6} & 0.03 \\ \mathrm{C}_{3} \mathrm{H}_{6} & 0.05 \\ \mathrm{C}_{3} \mathrm{H}_{8} & 0.10 \\ i \mathrm{C}_{4} & 0.20 \\ n \mathrm{C}_{4} & 0.60\end{array}$
Compute using a simulation computer program:
(a) The phase condition upstream of the valve.
(b) The temperature downstream of the valve.
(c) The molar fraction vaporized downstream of the valve.
(d) The mole fraction compositions of the vapor and liquid phases downstream of the valve.

Hast Aggarwal
Hast Aggarwal
Numerade Educator
02:46

Problem 43

Propose a detailed algorithm like Figure 4.19a and Table 4.4 for a flash where the percent vaporized and the flash pressure are to be specified.

Adriano Chikande
Adriano Chikande
Numerade Educator
01:03

Problem 44

Determine algorithms for carrying out the following flash calculations, assuming that expressions for $K$-values and enthalpies are available.
$$
\begin{array}{lr}
\text { Given } & \text { Find } \\
h_{F}, P & \Psi, T \\
h_{F}, T & \Psi, P \\
h_{F}, \Psi & T, P \\
\Psi, T & h_{F}, P \\
\Psi, P & h_{F}, T \\
T, P & h_{F}, \Psi
\end{array}
$$

Hast Aggarwal
Hast Aggarwal
Numerade Educator
13:30

Problem 45

A feed of $13,500 \mathrm{~kg} / \mathrm{h}$ consists of $8 \mathrm{wt} \%$ acetic acid (B) in water (A). The removal of the acetic acid is to be accomplished by liquid-liquid extraction at $25^{\circ} \mathrm{C}$. The raffinate is to contain only $1 \mathrm{wt} \%$ acetic acid. The following four solvents, with accompanying distribution coefficients in mass-fraction units, are being considered. Water and each solvent (C) can be considered immiscible. For each solvent, estimate the kilograms required per hour if a single equilibrium stage is used.
$\begin{array}{cc}\text { Solvent } & \boldsymbol{K}_{D} \\ \text { Methyl acetate } & 1.273 \\ \text { sopropyl ether } & 0.429 \\ \text { Heptadecanol } & 0.312 \\ \text { Chloroform } & 0.178\end{array}$

Chareen Guzman
Chareen Guzman
Numerade Educator
15:31

Problem 46

Forty-five kilograms of a solution containing 30 wt $\$$ ethylene glycol in water is to be extracted with furfural. Using Figures 4.14a and 4.14e, calculate:
(a) The minimum quantity of solvent.
(b) The maximum quantity of solvent.
(c) The weights of solvent-free extract and raffinate for $45 \mathrm{~kg}$ solvent, and the percent glycol extracted.
(d) The maximum possible purity of glycol in the finished extract and the maximum purity of water in the raffinate for one equilibrium stage.

Ronald Prasad
Ronald Prasad
Numerade Educator
01:06

Problem 47

Prove that, in a triangular diagram, where each vertex represents a pure component, the composition of the system at any point inside the triangle is proportional to the length of the respective perpendicular drawn from the point to the side of the triangle opposite the vertex in question. It is not necessary to assume a special case (i.e., a right or equilateral triangle).

Raj Bala
Raj Bala
Numerade Educator
05:02

Problem 48

A mixture of chloroform $\left(\mathrm{CHCl}_{3}\right)$ and acetic acid at $18^{\circ} \mathrm{C}$ and $1 \mathrm{~atm}(101.3 \mathrm{kPa})$ is to be extracted with water to recover the acid.
(a) Forty-five kilograms of a mixture containing $35 \mathrm{wt} \% \mathrm{CHCl}_{3}$ and $65 \mathrm{wt} \%$ acid is treated with $22.75 \mathrm{~kg}$ of water at $18^{\circ} \mathrm{C}$ in a simple one-stage batch extraction. What are the compositions and weights of the raffinate and extract layers produced?
(b) If the raffinate layer from the above treatment is extracted again with one-half its weight of water, what will be the compositions and weights of the new layers?
(c) If all the water is removed from this final raffinate layer, what will its composition be?
Solve this exercise using the following equilibrium data to construct one or more of the types of diagrams in Figure $4.14$.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
05:15

Problem 49

Isopropyl ether (E) is used to separate acetic acid (A) from water (W). The liquid-liquid equilibrium data at $25^{\circ} \mathrm{C}$ and $1 \mathrm{~atm}$ (a) One hundred kilograms of a $30 \mathrm{wt} \% \mathrm{~A}-\mathrm{W}$ solution is contacted with $120 \mathrm{~kg}$ of ether in an equilibrium stage. What are the compositions and weights of the resulting extract and raffinate? What would be the concentration of acid in the (ether-rich) extract if all the ether were removed?
(b) A mixture containing $52 \mathrm{~kg} \mathrm{~A}$ and $48 \mathrm{~kg} \mathrm{~W}$ is contacted with $40 \mathrm{~kg}$ of $\mathrm{E}$. What are the extract and raffinate compositions and quantities?

Ronald Prasad
Ronald Prasad
Numerade Educator
07:29

Problem 50

Diethylene glycol (DEG) is used as a solvent in the UDEX liquid-liquid extraction process [H.W. Grote, Chem Eng. Progr., $\mathbf{5 4}$ (8), 43 (1958)] to separate paraffins from aromatics. If $280 \mathrm{lbmol} / \mathrm{h}$ of $42.86 \mathrm{~mol} \% n$-hexane, $28.57 \mathrm{~mol} \% n$-heptane, $17.86 \mathrm{~mol} \%$ benzene, and $10.71 \mathrm{~mol} \%$ toluene is contacted with $500 \mathrm{lbmol} / \mathrm{h}$ of $90 \mathrm{~mol} \%$ aqueous DEG at $325^{\circ} \mathrm{F}$ and $300 \mathrm{psia}$, calculate, using a simulation computer program and the UNIFAC L/L method for estimating liquid-phase activity coefficients, the flow rates and molar compositions of the resulting two liquid phases. Is DEG more selective for the paraffins or the aromatics?

Chareen Guzman
Chareen Guzman
Numerade Educator
03:22

Problem 51

A feed of $110 \mathrm{lbmol} / \mathrm{h}$ includes 5,3 , and $2 \mathrm{lbmol} / \mathrm{h}$, respectively, of formic acid, acetic acid, and propionic acid in water. If the acids are extracted in a single equilibrium stage with $100 \mathrm{lbmol} / \mathrm{h}$ of ethyl acetate (EA), calculate with a simulation computer program using the UNIFAC method, flow rates and molar compositions of the resulting two liquid phases. What is the order of selectivity of EA for the three organic acids?
4.52 Repeat Example $4.9$ for $200,000 \mathrm{~kg} / \mathrm{h}$ of hexane.

Lottie Adams
Lottie Adams
Numerade Educator
06:02

Problem 52

Repeat Example $4.9$ for $200,000 \mathrm{~kg} / \mathrm{h}$ of hexane.

Farnaz Mohseni
Farnaz Mohseni
Numerade Educator
02:08

Problem 53

Water is to be used in a single equilibrium stage to dissolve $1,350 \mathrm{~kg} / \mathrm{h}$ of $\mathrm{Na}_{2} \mathrm{CO}_{3}$ from $3,750 \mathrm{~kg} / \mathrm{h}$ of a solid, where the balance is an insoluble oxide. If $4,000 \mathrm{~kg} / \mathrm{h}$ of water is used and the underflow from the stage is $40 \mathrm{wt} \%$ solvent on a solute-free basis, compute the flow rates and compositions of the overflow and the underflow.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
01:16

Problem 54

Repeat Exercise $4.53$ if the residence time is only sufficient to leach $80 \%$ of the carbonate.

AG
Ankit Gupta
Numerade Educator
07:58

Problem 55

A total of $6,000 \mathrm{lb} / \mathrm{h}$ of a liquid solution of $40 \mathrm{wt} \%$ benzene in naphthalene at $50^{\circ} \mathrm{C}$ is cooled to $15^{\circ} \mathrm{C}$. Assuming that equilibrium is achieved, use Figure $4.23$ to determine the amount of crystals formed, and the flow rate and composition of the mother liquor. Are the crystals benzene or naphthalene?

Dominique Jan Tan
Dominique Jan Tan
Numerade Educator
01:04

Problem 56

Repeat Example 4.10, except determine the temperature necessary to crystallize $80 \%$ of the naphthalene.

Dominador Tan
Dominador Tan
Numerade Educator
03:58

Problem 57

A total of $10,000 \mathrm{~kg} / \mathrm{h}$ of a $10 \mathrm{wt} \%$ liquid solution of naphthalene in benzene is cooled from $30^{\circ} \mathrm{C}$ to $0^{\circ} \mathrm{C}$. Assuming that equilibrium is achieved, determine the amount of crystals formed and the composition and flow rate of the mother liquid. Are the crystals benzene or naphthalene? Use Figure $4.23$.

Adriano Chikande
Adriano Chikande
Numerade Educator
00:55

Problem 58

Repeat Example 4.11, except let the original solution be $20 \mathrm{wt} \% \mathrm{Na}_{2} \mathrm{SO}_{4}$.

Harshit Mawandia
Harshit Mawandia
Numerade Educator
01:45

Problem 59

At $20^{\circ} \mathrm{C}, 1,000 \mathrm{~kg}$ of a mixture of $50 \mathrm{wt} \% \mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}$ and 50 wt\% $\mathrm{Na}_{2} \mathrm{SO}_{4}$ crystals exists. How many kilograms of water must be added to just completely dissolve the crystals if the temperature is kept at $20^{\circ} \mathrm{C}$ and equilibrium is maintained? Use Figure $4.24$.

Will Li
Will Li
Numerade Educator
03:21

Problem 60

Repeat Example 4.12, except determine the grams of activated carbon to achieve:
(a) $75 \%$ adsorption of phenol.
(b) $90 \%$ adsorption of phenol.
(c) $98 \%$ adsorption of phenol.

Madi Sousa
Madi Sousa
Numerade Educator
06:24

Problem 61

A colored substance (B) is to be removed from a mineral oil by adsorption with clay particles at $25^{\circ} \mathrm{C}$. The original oil has a color index of 200 units/ $100 \mathrm{~kg}$ oil, while the decolorized oil must have an index of only 20 units/ $100 \mathrm{~kg}$ oil. The following experimental adsorption equilibrium data have been measured in a laboratory:
$\begin{array}{cccccc}c_{\mathrm{B}} \text {, color units/ } & 200 & 100 & 60 & 40 & 10 \\ 100 \mathrm{~kg} \text { oil } & & & & & \\ q_{\mathrm{B}} \text {, color units/ } & 10 & 7.0 & 5.4 & 4.4 & 2.2 \\ 100 \mathrm{~kg} \text { clay } & & & & & \end{array}$
(a) Fit the data to the Freundlich equation.
(b) Compute the kilograms of clay needed to treat $500 \mathrm{~kg}$ of oil if one equilibrium contact is used.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:39

Problem 62

Vapor-liquid equilibrium data in mole fractions for the system acetone-air-water at 1 atm (101.3 kPa) are as follows:
$\begin{array}{lllllll}y, \text { acetone in air: } & 0.004 & 0.008 & 0.014 & 0.017 & 0.019 & 0.020 \\ x, \text { acetone in water: } & 0.002 & 0.004 & 0.006 & 0.008 & 0.010 & 0.012\end{array}$
(a) Plot the data as (1) a graph of moles acetone per mole air versus moles acetone per mole water, (2) partial pressure of acetone versus g acetone per $g$ water, and (3) $y$ versus $x$.
(b) If 20 moles of gas containing $0.015$ mole fraction acetone is brought into contact with 15 moles of water in an equilibrium stage, what would be the composition of the discharge streams? Solve graphically. For both parts, neglect partitioning of water and air.

Manik Pulyani
Manik Pulyani
Numerade Educator
06:47

Problem 63

It has been proposed that oxygen be separated from nitrogen by absorbing and desorbing air in water. Pressures from $101.3$ to $10,130 \mathrm{kPa}$ and temperatures between 0 and $100^{\circ} \mathrm{C}$ are to be used.
(a) Devise a workable scheme for doing the separation assuming the air is $79 \mathrm{~mol} \% \mathrm{~N}_{2}$ and $21 \mathrm{~mol} \% \mathrm{O}_{2}$.
(b) Henry's law constants for $\mathrm{O}_{2}$ and $\mathrm{N}_{2}$ are given in Figure $4.27 .$ How many batch absorption steps would be necessary to make $90 \mathrm{~mol} \%$ pure oxygen? What yield of oxygen (based on total amount of oxygen feed) would be obtained?

Kevin Zaborsky
Kevin Zaborsky
Numerade Educator
04:45

Problem 64

A vapor mixture having equal volumes of $\mathrm{NH}_{3}$ and $\mathrm{N}_{2}$ is to be contacted at $20^{\circ} \mathrm{C}$ and $1 \mathrm{~atm}$ ( 760 torr) with water to absorb a portion of the $\mathrm{NH}_{3}$. If $14 \mathrm{~m}^{3}$ of this mixture is brought into contact with $10 \mathrm{~m}^{3}$ of water and if equilibrium is attained, calculate the percent of the ammonia originally in the gas that will be absorbed. Both temperature and total pressure will be maintained constant during the absorption. The partial pressure of $\mathrm{NH}_{3}$ over water at $20^{\circ} \mathrm{C}$ is as follows:
$$
\begin{array}{cc}
\begin{array}{l}
\text { Partial Pressure } \\
\text { of } \mathrm{NH}_{3} \text { in Air, torr }
\end{array} & \begin{array}{c}
\text { Grams of Dissolved } \\
\mathrm{NH}_{3} / \mathbf{1 0 0} \mathbf{~ g} \text { of } \mathbf{~}_{2} \mathbf{~} \mathbf{O}
\end{array} \\
470 & 40 \\
298 & 30 \\
227 & 25 \\
166 & 20 \\
114 & 15 \\
69.6 & 10 \\
50.0 & 7.5 \\
31.7 & 5.0 \\
24.9 & 4.0 \\
18.2 & 3.0 \\
15.0 & 2.5 \\
12.0 & 2.0
\end{array}
$$

Adriano Chikande
Adriano Chikande
Numerade Educator
01:03

Problem 65

Repeat Example $4.15$ for temperatures corresponding to the following vapor pressures for solid PA:
(a) $0.7$ torr
(b) $0.4$ torr
(c) $0.1$ torr
Plot the percent recovery of PA versus the solid vapor pressure for the range from $0.1$ torr to $1.0$ torr.

Crystal Wang
Crystal Wang
Numerade Educator
01:50

Problem 66

Nitrogen at 760 torr and $300^{\circ} \mathrm{C}$ contains $10 \mathrm{~mol} \%$ anthraquinone (A). If this gas is cooled to $200^{\circ} \mathrm{C}$, calculate the percent desublimation of A. Vapor pressure data for solid A are as follows:
$\begin{array}{lcccl}\mathrm{T},{ }^{\circ} \mathrm{C}: & 190.0 & 234.2 & 264.3 & 285.0 \\ \text { Vapor pressure, torr: } & 1 & 10 & 40 & 100\end{array}$
These data can be fitted to the Antoine equation (2-39) using the first three constants.

CA
Chi-Chung Ai
Numerade Educator
11:01

Problem 67

At $25^{\circ} \mathrm{C}$ and $101 \mathrm{kPa}, 2 \mathrm{~mol}$ of a gas containing $35 \mathrm{~mol} \%$ propylene in propane is equilibrated with $0.1 \mathrm{~kg}$ of silica gel adsorbent. Using the equilibrium data of Figure $4.30$, calculate the moles and composition of the gas adsorbed and the equilibrium composition of the gas not adsorbed.

Jincy M Saji
Jincy M Saji
Numerade Educator
06:24

Problem 68

A gas containing 50 mol\% propylene in propane is to be separated with silica gel having the equilibrium properties shown in Figure $4.30$. The final products are to be $90 \mathrm{~mol} \%$ propylene and $75 \mathrm{~mol} \%$ propane. If $1,000 \mathrm{lb}$ of silica gel/lbmol of feed gas or less is used, can the desired separation be made in one equilibrium stage? If not, what separation can be achieved?
Section $4.10$

Ronald Prasad
Ronald Prasad
Numerade Educator
06:02

Problem 69

Repeat Example 4.17 for $90 \%$ evaporation of the water.

Farnaz Mohseni
Farnaz Mohseni
Numerade Educator
04:16

Problem 70

A $5,000-\mathrm{kg} / \mathrm{h}$ aqueous solution of $20 \mathrm{wt} \% \mathrm{Na}_{2} \mathrm{SO}_{4}$ is fed to an evaporative crystallizer operating at $60^{\circ} \mathrm{C}$. Equilibrium data are given in Figure $4.24$. If $80 \%$ of the $\mathrm{Na}_{2} \mathrm{SO}_{4}$ is to be crystallized, calculate:
(a) The kilograms of water that must be evaporated per hour
(b) The crystallizer pressure in torr

Ronald Prasad
Ronald Prasad
Numerade Educator
02:24

Problem 71

Calculate the dew-point pressure, secondary dew-point pressure, and bubble-point pressure of the following mixtures at $50^{\circ} \mathrm{C}$, assuming that the liquid aromatics and water are mutually insoluble:
(a) $50 \mathrm{~mol} \%$ benzene and $50 \mathrm{~mol} \%$ water.
(b) $50 \mathrm{~mol} \%$ toluene and $50 \mathrm{~mol} \%$ water.
(c) 40 mol $\%$ benzene, 40 mol\% toluene, and 20 mol $\$$ water.

Penny Riley
Penny Riley
Numerade Educator
01:07

Problem 72

Repeat Exercise 4.71, except compute temperatures for a pressure of $2 \mathrm{~atm}$.

Mayukh Banik
Mayukh Banik
Numerade Educator
02:50

Problem 73

A liquid containing $30 \mathrm{~mol} \%$ toluene, $40 \mathrm{~mol} \%$ ethylbenzene, and $30 \mathrm{~mol}$ ? water is subjected to a continuous, flash distillation at a total pressure of $0.5 \mathrm{~atm}$. Assuming that mixtures of ethylbenzene and toluene obey Raoult's law and that the hydrocarbons are completely immiscible in water and vice versa, calculate the temperature and composition of the vapor phase at the bubblepoint temperature.

Lottie Adams
Lottie Adams
Numerade Educator
06:24

Problem 74

As shown in Figure $4.8$, water (W) and $n$-butanol (B) can form a three-phase system at $101 \mathrm{kPa}$. For a mixture of overall composition of $60 \mathrm{~mol} \% \mathrm{~W}$ and $40 \mathrm{~mol} \% \mathrm{~B}$, use a simulation computer program and the UNIFAC method to estimate:
(a) Dew-point temperature and composition of the first drop of liquid.
(b) Bubble-point temperature and composition of the first bubble of vapor.
(c) Compositions and relative amounts of all three phases for $50 \mathrm{~mol} \%$ vaporization.

James Kiss
James Kiss
Numerade Educator
01:55

Problem 75

Repeat Example $4.19$ for a temperature of $25^{\circ} \mathrm{C}$. Are the changes significant?

Manik Pulyani
Manik Pulyani
Numerade Educator