Introduction to Chemical Engineering Thermodynamics

J. M. Smith, Hendrick C Van Ness, Michael Abbott, Hendrick Van Ness

Chapter 11 SOLUTION THERMODYNAMICS: THEORY - all with Video Answers

Educators

Chapter Questions

Problem 1

What is the change in entropy when $0.7 \mathrm{~m}^3$ of $\mathrm{CO}_2$ and $0.3 \mathrm{~m}^3$ of $\mathrm{N}_2$, each at 1 bar and $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$ blend to form a gas mixture at the same conditions? Assume ideal gases.

Amanda Hyde

Numerade Educator

02:05

Problem 2

A vessel, divided into two parts by a partition, contains $4 \mathrm{~mol}$ of nitrogen gas at $348.15 \mathrm{~K}$ $\left(75^{\circ} \mathrm{C}\right)$ and $30 \mathrm{bar}$ on one side and $2.5 \mathrm{~mol}$ of argon gas at $403.15 \mathrm{~K}\left(130^{\circ} \mathrm{C}\right)$ and $20 \mathrm{bar}$ on the other. If the partition is removed and the gases mix adiabatically and completely, what is the change in entropy? Assume nitrogen to be an ideal gas with $C_V=(5 / 2) R$ and argon to be an ideal gas with $C_V=(3 / 2) R$.

Penny Riley

Numerade Educator

01:02

Problem 3

A stream of nitrogen flowing at the rate of $2 \mathrm{~kg} \mathrm{~s}^{-1}$ and a stream of hydrogen flowing at the rate of $0.5 \mathrm{~kg} \mathrm{~s}^{-1} \mathrm{mix}$ adiabatically in a steady-flow process. If the gases are assumed ideal, what is the rate of entropy increase as a result of the process?

Hast Aggarwal

Numerade Educator

03:17

Problem 4

What is the ideal work for the separation of an equimolar mixture of methane and ethane at $448.15 \mathrm{~K}\left(175^{\circ} \mathrm{C}\right)$ and 3 bar in a steady-flow process into product streams of the pure gases at $308.15 \mathrm{~K}\left(35^{\circ} \mathrm{C}\right)$ and 1 bar if $T_\sigma=300 \mathrm{~K}$ ?

Hast Aggarwal

Numerade Educator

01:14

Problem 5

What is the work required for the separation of air ( $21-\mathrm{mol}-\%$ oxygen and $79-\mathrm{mol}-\%$ nitrogen) at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$ and 1 bar in a steady-flow process into product streams of pure oxygen and nitrogen, also at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$ and $1 \mathrm{bar}$, if the thermodynamic efficiency of the process is $5 \%$ and if $T_\sigma=300 \mathrm{~K}$ ?

Manik Pulyani

Numerade Educator

02:53

Problem 6

What is the partial molar temperature? What is the partial molar pressure? Express results in relation to the $T$ and $P$ of the mixture.

Willis James

Numerade Educator

03:01

Problem 7

Show that:
(a) The "partial molar mass" of a species in solution is equal to its molar mass.
(b) A partial specific property of a species in solution is obtained by division of the partial molar property by the molar mass of the species.

Dr. Satish Ingale

Numerade Educator

02:35

Problem 8

If the molar density of a binary mixture is given by the empirical expression:
$$
\rho=a_0+a_1 x_1+a_2 x_1^2
$$
find the corresponding expressions for $\bar{V}_1$ and $\bar{V}_2$.

Ajay Singhal

Numerade Educator

07:46

Problem 9

Fora ternary solution at constant $T$ and $P$, the compositiondependenceof molarproperty $M$ is given by:
$$
M=x_1 M_1+x_2 M_2+x_3 M_3+x_1 x_2 x_3 C
$$
where $M_1, M_2$, and $M_3$ are the values of $M$ for pure species 1,2 , and 3 , and $C$ is a parameter independent of composition. Determine expressions for $\bar{M}_1, \bar{M}_2$, and $\bar{M}_3$ by application of Eq. (11.7). As a partial check on your results, verify that they satisfy the summability relation, Eq. (11.11). For this correlating equation, what are the $\bar{M}_i$ at infinite dilution?

Rashmi Sinha

Numerade Educator

02:21

Problem 10

A pure-component pressure $p_i$ for species $\mathrm{i}$ in a gas mixture may be defined as the pressure that species $i$ would exert if it alone occupied the mixture volume. Thus,
$$
p_i \equiv \frac{y_i Z_i R T}{V}
$$
where $y_i$ is the mole fraction of species $i$ in the gas mixture, $Z_i$ is evaluated at $p_i$ and $\mathrm{T}$, and $\mathrm{V}$ is the molar volume of the gas mixture. Note that $p_i$ as defined here is not a partial pressure $y_i \mathrm{P}$, except for an ideal gas. Dalton's "law" of additive pressures states that the total pressure exerted by a gas mixture is equal to the sum of the pure-component pressures of its constituent species: $\mathrm{P}=\sum_i$ pi. Show that Dalton's "law" implies that $Z=\sum_i y_i Z_i$, where $Z_i$ is the compressibility factor of pure species i evaluated at the mixture temperature but at its pure-component pressure.

Sean Dougherty

Numerade Educator

05:47

Problem 11

If for a binary solution one starts with an expression for $\mathrm{M}$ ( or $M^R$ or $M^E$ ) as a function of $x_1$ and applies Eqs. (11.15) and (11.16) to find $\bar{M}_1$ and $\bar{M}_2$ (or $\bar{M}_1^R$ and $\bar{M}_2^R$ or $\bar{M}_1^E$ and $\bar{M}_2^E$ ) and then combines these expressions by Eq. (11.11), the initial expression for $\mathrm{M}$ is regenerated. On the other hand, if one starts with expressions for $\bar{M}_1$ and $\bar{M}_2$, combines them in accord with Eq. (11.11), and then applies Eqs. (11.15) and (11.16), the initial expressions for $\bar{M}_1$ and $\bar{M}_2$ are regenerated if and only if the initial expressions for these quantities meet a specific condition. What is the condition?

Ronald Prasad

Numerade Educator

17:42

Problem 12

With reference to Ex. 11.4,
(a) Apply Eq. (11.7) to Eq. (A) to verify Eqs. (B) and (C).
(b) Show that Eqs. (B) and (C) combinein accord with Eq. (11.11) to regenerate Eq. (A).
(c) Show that Eqs. (B) and (C) satisfy Eq. (11.14), the Gibbs/Duhem equation.
(d) Show that at constant $\mathrm{T}$ and $\mathrm{P}$,
$$
\left(d \bar{H}_1 / d x_1\right)_{x_1=1}=\left(d \bar{H}_2 / d x_1\right)_{x_1=0}=0
$$
(e) Plot values of $\mathrm{H}, \bar{H}_1$, and $\bar{H}_2$, calculated by Eqs. (A), (B), and (C), vs. $x_1$. Label points $H_1, H_2, \bar{H}_1^{\infty}$, and $\bar{H}_2^{\infty}$, and show their values.

Prachita Kush

Numerade Educator

07:46

Problem 13

The molar volume $\left(\mathrm{cm}^3 \mathrm{~mol}^{-1}\right)$ of a binary liquid mixture at $\mathrm{T}$ and $\mathrm{P}$ is given by:
$$
V=120 x_1+70 x_2+\left(15 x_1+8 x_2\right) x_1 x_2
$$
(a) Find expressions for the partial molar volumes of species 1 and 2 at $\mathrm{T}$ and $\mathrm{P}$.
(b) Show that when theseexpressionsare combined in accord with Eq. (11.11) the given equation for $\mathrm{V}$ is recovered.
(c) Show that these expressions satisfy Eq. (11.14), the Gibbs/Duhem equation.
(d) Show that $\left(d \bar{V}_1 / d x_1\right)_{x_1=1}=\left(d \bar{V}_2 / d x_1\right)_{x_1=0}=0$.
(e) Plot values of V, $\bar{V}_1$, and $\bar{V}_2$ calculated by the given equation for $\mathrm{V}$ and by the equations developed in (a) vs. $x_1$. Label points $V_1, V_2, \bar{V}_1^{\infty}$, and $\bar{V}_2^{\infty}$, and show their values.

Rashmi Sinha

Numerade Educator

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Problem 14

For a particular binary liquid solution at constant $T$ and $P$, the molar enthalpies of mixtures are represented by the equation:
$$
H=x_1\left(a_1+b_1 x_1\right)+x_2\left(a_2+b_2 x_2\right)
$$
where the $a_i$ and $b_i$ are constants. Since the equation has the form of Eq. (11.11), it might be that $\bar{H}_i=a_i+b_i x_i$. Show whether this is true.

Rashmi Sinha

Numerade Educator

00:42

Problem 15

Analogous to the conventional partial property $\bar{M}_i$, one can define a constant- $\mathrm{T}, \mathrm{V}$ partial property $\widetilde{M}_i$ :
$$
\tilde{M}_i \equiv\left[\frac{\partial(n M)}{\partial n_i}\right]_{T, V, n_j}
$$
Show that $\tilde{M}_i$ and $\bar{M}_i$ are related by the equation:
$$
\tilde{M}_i=\bar{M}_i+\left(V-\bar{V}_i\right)\left(\frac{\partial M}{\partial V}\right)_{T, x}
$$
Demonstrate that the $\widetilde{M}_i$ satisfy a summability relation, $\mathrm{M}=\sum_i x_i \widetilde{M}_i$.

Linh Vu

Numerade Educator

Problem 16

From the following compressibility-factor data for $\mathrm{CO}_2$ at $423.15 \mathrm{~K}\left(150^{\circ} \mathrm{C}\right)$ prepare plots of the fugacity and fugacity coefficient of $\mathrm{CO} 2$ vs. P for pressures up to 500 bar. Compare results with those found from the generalized correlation represented by Eq. (11.65).
$$
\begin{array}{c|c||c|c}
\text { Phar } & \mathrm{Z} & \text { Phar } & \mathrm{Z} \\
\hline 10 & 0.985 & 100 & 0.869 \\
20 & 0.970 & 200 & 0.765 \\
40 & 0.942 & 300 & 0.762 \\
60 & 0.913 & 400 & 0.824 \\
80 & 0.885 & 500 & 0.910 \\
\hline
\end{array}
$$

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Problem 17

For $\mathrm{SO}_2$ at $600 \mathrm{~K}$ and $300 \mathrm{bar}$, determine good estimates of the fugacity and of $G^R / \mathrm{RT}$.

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01:46

Problem 18

Estimate the fugacity of isobutylene as a gas:
(a) At $553.15 \mathrm{~K}\left(280^{\circ} \mathrm{C}\right)$ and 20 bar; (b) At $553.15 \mathrm{~K}\left(280^{\circ} \mathrm{C}\right)$ and 100 bar.

Lottie Adams

Numerade Educator

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Problem 19

Estimate the fugacity of one of the following:
(a) Cyclopentane at $383.15 \mathrm{~K}\left(110^{\circ} \mathrm{C}\right)$ and 275 bar. At $383.15 \mathrm{~K}\left(110^{\circ} \mathrm{C}\right)$ the vapor pressure of cyclopentane is $5.267 \mathrm{bar}$.
(b) 1-Butene at $393.15 \mathrm{~K}\left(120^{\circ} \mathrm{C}\right)$ and 34 bar. At $393.15 \mathrm{~K}\left(120^{\circ} \mathrm{C}\right)$ the vapor pressure of 1 -butene is 25.83 bar.

Rashmi Sinha

Numerade Educator

02:17

Problem 20

Justify the following equations:
$$
\begin{array}{ll}
\left(\frac{\partial \ln \hat{\phi}_i}{\partial P}\right)_{T_{, x}}=\frac{\bar{V}_i^R}{R T} & \left(\frac{\partial \ln \hat{\phi}_i}{\partial T}\right)_{P_{, x}}=-\frac{\bar{H}_i^R}{R T^2} \\
\frac{G^R}{R T}=\sum_i x_i \ln \hat{\phi}_i & \sum x_i d \ln \hat{\phi}_i=0 \quad \text { (const } T, P \text { ) }
\end{array}
$$

M Hassan Anwar

Numerade Educator

01:30

Problem 21

From data in the steam tables, determine a good estimate for $f / \mathrm{f}^{\text {sat }}$ for liquid water at $423.15 \mathrm{~K}\left(150^{\circ} \mathrm{C}\right)$ and $150 \mathrm{bar}$, where $f^{\text {sat }}$ is the fugacity of saturated liquid at 423.15 $\mathrm{K}\left(150^{\circ} \mathrm{C}\right)$.

Kratika Bhadauria

Numerade Educator

05:05

Problem 22

For one of the following, determine the ratio of the fugacity in the final state to that in the initial state for steam undergoing the isothermal change of state:
(a) From $9000 \mathrm{kPa}$ and $673.15 \mathrm{~K}\left(400^{\circ} \mathrm{C}\right)$ to $300 \mathrm{kPa}$.
(b) From $7000 \mathrm{kPa}$ and $700 \mathrm{~K}$ to $345 \mathrm{kPa}$.

Jordan Vanevery

Numerade Educator

01:05

Problem 23

Estimate the fugacity of one of the following liquids at its normal-boiling-pointtemperature and 200 bar:
(a) n-Pentane; (b) Isobutylene; (c) 1-Butene.

Narayan Hari

Numerade Educator

02:19

Problem 24

Assuming that Eq. (11.65) is valid for the vapor phase and that the molar volume of saturated liquid is given by Eq. (3.63), prepare plots of $f$ vs. $\mathrm{P}$ and of $\phi$ vs. $\mathrm{P}$ for one of the following:
(a) Chloroform at $473.15 \mathrm{~K}\left(200^{\circ} \mathrm{C}\right)$ for the pressure range from 0 to 40 bar. At 473.15 $\mathrm{K}\left(200^{\circ} \mathrm{C}\right)$ the vapor pressure of chloroform is 22.27 bar.
(b) Isobutane at $313.15 \mathrm{~K}\left(40^{\circ} \mathrm{C}\right)$ for the pressure range from 0 to 10 bar. At $313.15 \mathrm{~K}$ $\left(40^{\circ} \mathrm{C}\right)$ the vapor pressure of isobutane is 5.28 bar.

Adriano Chikande

Numerade Educator

Problem 25

For the system ethylene(1)/propylene(2) as a gas, estimate $\hat{f}_1, \hat{f}_2, \hat{\phi}_1$, and $\hat{\phi}_2$ at $T / t=423.15 \mathrm{~K}\left(150^{\circ} \mathrm{C}\right), \mathrm{P}=30 \mathrm{bar}$, and $y_1=0.35$ :
(a) Through application of Eqs. (11.59) and (11.60).
(b) Assuming that the mixture is an ideal solution.

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02:27

Problem 26

Rationalize the following expression, valid at sufficiently low pressures, for estimating the fugacity coefficient: $\ln \phi \approx Z-1$.

Corinne Costa

Numerade Educator

04:33

Problem 27

For the system methane(1)/ethane(2)/propane(3) as a gas, estimate $$\hat{f}_1, \hat{f}_2, \hat{f}_3, \hat{\phi}_1, \$ 2$$, and $\hat{\phi}_3$ at $T=373.15 \mathrm{~K}\left(100^{\circ} \mathrm{C}\right), \mathrm{P}=35 \mathrm{bar}, y_1=0.21$, and $y_2=0.43$ :
(a) Through application of Eq. (11.61).
(b) Assuming that the mixture is an ideal solution.

Eric Mockensturm

Numerade Educator

07:46

Problem 28

The excess Gibbs energy of a binary liquid mixture at $T$ and $P$ is given by:
$$
G^E / R T=\left(-2.6 x_1-1.8 x_2\right) x_1 x_2
$$
(a) Find expressions for $\ln \gamma_1$ and $\ln \gamma_2$ at $\mathrm{T}$ and $\mathrm{P}$.
(b) Show that when these expressionsare combined in accord with Eq. (11.95) the given equation for $G^E / R T$ is recovered.
(c) Show that these expressions satisfy Eq. (11.96), the Gibbs/Duhem equation.
(d) Show that $\left(\mathrm{d} \ln \gamma_1 / d x_1\right)_{x_1=1}=\left(\mathrm{d} \ln \gamma_2 / d x_1\right)_{x_1 \Rightarrow 0}=0$.
(e) Plot $\mathrm{G}^{\mathrm{E}} / R T, \ln \gamma_1$, and $\ln \gamma_2$ as calculated by the given equation for $G^E / R T$ and by the equations developed in (a) vs. $x_1$. Label points $\ln \gamma_1^{\infty}$ and $\ln \gamma_2^{\infty}$ and show their values.

Rashmi Sinha

Numerade Educator

02:19

Problem 29

Show that $\gamma_i=\hat{\phi}_i / \phi_i$.

Narayan Hari

Numerade Educator

21:52

Problem 30

Given below are values of $G^E / \mathrm{J} \mathrm{mol}^{-1}, H^E / \mathrm{J} \mathrm{mol}^{-1}$, and $C_P^E / \mathrm{J} \mathrm{mol}^{-1} \mathrm{~K}^{-1}$ for some equimolar binary liquid mixtures at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$. Estimate values of $G^E, H^E$, and $S^E$ at $328.15 \mathrm{~K}\left(55^{\circ} \mathrm{C}\right)$ for one of the equimolar mixtures by two procedures: (I) Use all the data; (II) Assume $C_P^E=0$. Compare and discuss your results for the two procedures.
(a) Acetonelchloroform: $G^E=-622, H^E=-1920, C_P^E=4.2$.
(b) Acetoneln-hexane: $G^E=1095, H^E=1595, C_P^E=3.3$.
(c) Benzene/isooctane: $G^E=407, H^E=984, C_P^E=-2.7$.
(d) Chloroform/ethanol: $G^E=632, H^E=-208, C_p^E=23.0$.
(e) Ethanolln-heptane: $G^E=1445, H^E=605, C_P^E=11.0$.
(f) Ethanol/water: $G^E=734, H^E=-416, C_P^E=11.0$.
(g) Ethyl acetateln-heptane: $G^E=759, H^E=1465, C_P^E=-8.0$.

Jennifer Stoner

Numerade Educator

Problem 31

The excess Gibbs energy of a particular ternary liquid mixture is represented by the empirical expression, with parameters $A_{12}, A_{13}$, and $A_{23}$ functions of $\mathrm{T}$ and $\mathrm{P}$ only:
$$
G^E / R T=A_{12} x_1 x_2+A_{13} x_1 x_3+A_{23} x_2 x_3
$$
(a) Determine the implied expressions for $\ln \gamma_1, \ln \gamma_2$, and $\ln \gamma_3$.
(b) Verify that your results for part (a) satisfy the summability relation, Eq. (11.95).
(c) For species 1 determine expressions (or values) for $\ln \gamma_1$ for the limiting cases: $x_1=0, x_1=1, x_2=0$, and $x_3=0$. What do these limiting cases represent?

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01:00

Problem 32

The data in Table 11.2 are experimental values of $V^E$ for binary liquid mixtures of 1,3-dioxolane(1) and isooctane(2) at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$ and $1 \mathrm{~atm}$.
(a) Determine from the data numerical values of parametersa, b, and $\mathrm{c}$ in the correlating equation:
$$
\mathrm{V}^E=x_1 x_2\left(a+b x_1+c x_1^2\right)
$$
(b) Determine from the results of part (a) the maximum value of $V^E$. At what value of $x_1$ does this occur?
(c) Determine from the results of part (a) expressions for $\bar{V}_1^E$ and $\bar{V}_2^E$. Prepare a plot of these quantities vs. $x_1$, and discuss its features.
Table 11.2 Excess Volumes for 1,3-Dioxane(1)/Isooctane(2) at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$
R. Francesconi et al., Int. DATA Ser., Ser. A, vol. 25, no. 3, p. 229, 1997.
$$
\begin{array}{c|c||c|c}
x_1 & V^E / 10^{-3} \mathrm{~cm}^3 \mathrm{~mol}^{-1} & x_1 & V^E / 10^{-3} \mathrm{~cm}^3 \mathrm{~mol}^{-1} \\
\hline 0.02715 & 87.5 & 0.69984 & 276.4 \\
0.09329 & 265.6 & 0.72792 & 252.9 \\
0.17490 & 417.4 & 0.77514 & 190.7 \\
0.32760 & 534.5 & 0.79243 & 178.1 \\
0.40244 & 531.7 & 0.82954 & 138.4 \\
0.56689 & 421.1 & 0.86835 & 98.4 \\
0.63128 & 347.1 & 0.93287 & 37.6 \\
0.66233 & 321.7 & 0.98233 & 10.0 \\
\hline
\end{array}
$$

Manik Pulyani

Numerade Educator

03:54

Problem 33

For an equimolar vapor mixture of propane(1) and $n$-pentane $(2)$ at $348.15 \mathrm{~K}\left(75^{\circ} \mathrm{C}\right)$ and 2 bar, estimate $Z, H^R$, and $S^R$. Second virial coefficients, in $\mathrm{cm}^3 \mathrm{~mol}^{-1}$.
$$
\begin{array}{lccc}
\hline T / t\left(\mathrm{~K} /{ }^{\circ} \mathrm{C}\right) & B_{11} & \mathrm{~B} 22 & B_{12} \\
\hline 323.15(50) & -331 & -980 & -558 \\
348.15(75) & -276 & -809 & -466 \\
373.15(100) & -235 & -684 & -399 \\
\hline
\end{array}
$$
Equations $(3.37),(6.54),(6.55)$, and (11.58) are pertinent.

Dominique Jan Tan

Numerade Educator

05:27

Problem 34

Use the data of $\mathrm{Pb} \cdot 11.33$ to determine $\hat{\phi}_1$ and $\hat{\phi}_2$ as functions of composition for binary vapor mixtures of propane $(1)$ and $n$-pentane $(2)$ at $348.15 \mathrm{~K}\left(75^{\circ} \mathrm{C}\right)$ and 2 bar. Plot the results on a single graph. Discuss the features of this plot.

Kyle Gassaway

Numerade Educator

01:53

Problem 35

For a binary gas mixture described by Eqs. (3.37) and (11.58), prove that:
$$
\begin{array}{ll}
G^E=\delta_{12} P y_1 y_2 & S^E=-\frac{d \delta_{12}}{d T} P y_1 y_2 \\
H^E=\left(\delta_{12}-T \frac{d \delta_{12}}{d T}\right) P y_1 y_2 & C_P^E=-T \frac{d^2 \delta_{12}}{d T^2} P y_1 y_2
\end{array}
$$
See also Eq. (11.84), and note that $\delta_{12}=2 B_{12}-B_{11}-B_{22}$.

Manik Pulyani

Numerade Educator

Problem 36

The data in Table 11.3 are experimental values of $H^E$ for binary liquid mixtures of 1,2-dichloroethane $(1)$ and dimethyl carbonate $(2)$ at $313.15 \mathrm{~K}\left(40^{\circ} \mathrm{C}\right)$ and $1 \mathrm{~atm}$.
(a) Determine from the data numerical values of parameters a, b, and $c$ in the correlating equation:
$$
H^E=x_1 x_2\left(a+b x_1+c x_1^2\right)
$$
(b) Determine from the results of part (a) the minimum value of $H^E$. At what value of $x_1$ does this occur?
(c) Determine from the results of part (a) expressions for $\bar{H}_1^E$ and $\bar{H}_2^E$. Prepare a plot of these quantities vs. $x_1$, and discuss its features.
Table 11.3 $\boldsymbol{H}^{\boldsymbol{E}}$ Values for 1,2-Dichloroethane(1)/
Dimethyl Carbonate(2) at $313.15 \mathrm{~K}\left(40^{\circ} \mathrm{C}\right)$
R. Francesconi et al., Int. DATA Ser., Ser. A, vol. 25, no. 3, p. 225,1997 .
$$
\begin{array}{c|c||c|c}
x_1 & H^E / \mathrm{J} \mathrm{mol}^{-1} & x_1 & H^E / \mathrm{J} \mathrm{mol}^{-1} \\
\hline 0.0426 & -23.3 & 0.5163 & -204.2 \\
0.0817 & -45.7 & 0.6156 & -191.7 \\
0.1177 & -66.5 & 0.6810 & -174.1 \\
0.1510 & -86.6 & 0.7621 & -141.0 \\
0.2107 & -118.2 & 0.8181 & -116.8 \\
0.2624 & -144.6 & 0.8650 & -85.6 \\
0.3472 & -176.6 & 0.9276 & -43.5 \\
0.4158 & -195.7 & 0.9624 & -22.6 \\
\hline
\end{array}
$$

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07:04

Problem 37

Make use of Eqs. (3.37), (3.61), (3.62), (6.53), (6.54), (6.55), (6.80), (6.81), (11.58), and (11.66)-(11.71), to estimate $\mathrm{V}, H^R, S^R$, and $\mathrm{G}^{\mathrm{R}}$ for one of the following binary vapor mixtures:
(a) Acetone(1)/1,3-butadiene(2) with mole fractions $y_1=0.28$ and $y_2=0.72$ at $\mathrm{T}=$ $333.15 \mathrm{~K}\left(60^{\circ} \mathrm{C}\right)$ and $P=170 \mathrm{kPa}$.
(b) Acetonitrile(1)/diethyl ether(2) with mole fractions $y_1=0.37$ and $y_2=0.63$ at $\mathrm{T}=323.15 \mathrm{~K}\left(50^{\circ} \mathrm{C}\right)$ and $\mathrm{P}=120 \mathrm{kPa}$.
(c) Methylchloride(1)/ethyl chloride(2) with mole fractions $y_1=0.45$ and $y_2=0.55$ at $\mathrm{T}=298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$ and $P=100 \mathrm{Wa}$.
(d) Nitrogen(1)/ammonia(2) with mole fractions $y_1=0.83$ and $y_2=0.17$ at $\mathrm{T}=$ $293.15 \mathrm{~K}\left(20^{\circ} \mathrm{C}\right)$ and $\mathrm{P}=300 \mathrm{kPa}$.
(e) Sulfur dioxide(1)/ethylene(2) with mole fractions $y_1=0.32$ and $y_2=0.68$ at $\mathrm{T}=$ $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$ and $\mathrm{P}=420 \mathrm{kPa}$.

Theodore Donnell

Numerade Educator