**12.33.** The solubility of nonpolar gases in liquid water is typically very low. Consider nitrogen in particular. Its solubility is characterized by the equilibrium mole fraction \( x_N \) of dissolved nitrogen in the liquid phase (with water mole fraction \( x_W = 1 - x_N \)) when the system is in equilibrium with a vapor phase (with corresponding mole fractions \( y_N \) and \( y_W \)). The mole fraction \( x_N \) is typically of the order \( 10^{-5} \). The vapor pressure of water at 300 K is \( P_W^{\text{vap}} = 3.5 \) kPa, and you can assume that the impact of its temperature dependence on solubility is relatively weak. Use ideal models in what follows. (a) At 1 bar and 300 K, estimate the mole fraction of water that is present in the vapor phase, \( y_W \). (b) Show that the solubility of nitrogen is given approximately by \[ x_N = C(T, P)(1 - y_W)P \] where \( C(T, P) \) is a constant that is independent of concentrations. Find an expression for \( C(T, P) \) in terms of standard and pure chemical potentials. (c) Do you expect the solubility to increase or decrease with temperature? Explain by finding the temperature dependence of \( C(T, P) \).
**12.33.** The solubility of nonpolar gases in liquid water is typically very low. Consider nitrogen in particular. Its solubility is characterized by the equilibrium mole fraction \( x_N \) of dissolved nitrogen in the liquid phase (with water mole fraction \( x_W = 1 - x_N \)) when the system is in equilibrium with a vapor phase (with corresponding mole fractions \( y_N \) and \( y_W \)). The mole fraction \( x_N \) is typically of the order \( 10^{-5} \). The vapor pressure of water at 300 K is \( P_W^{\text{vap}} = 3.5 \) kPa, and you can assume that the impact of its temperature dependence on solubility is relatively weak. Use ideal models in what follows. (a) At 1 bar and 300 K, estimate the mole fraction of water that is present in the vapor phase, \( y_W \). (b) Show that the solubility of nitrogen is given approximately by \[ x_N = C(T, P)(1 - y_W)P \] where \( C(T, P) \) is a constant that is independent of concentrations. Find an expression for \( C(T, P) \) in terms of standard and pure chemical potentials. (c) Do you expect the solubility to increase or decrease with temperature? Explain by finding the temperature dependence of \( C(T, P) \).
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
Related questions
Question
![**12.33.** The solubility of nonpolar gases in liquid water is typically very low. Consider nitrogen in particular. Its solubility is characterized by the equilibrium mole fraction \( x_N \) of dissolved nitrogen in the liquid phase (with water mole fraction \( x_W = 1 - x_N \)) when the system is in equilibrium with a vapor phase (with corresponding mole fractions \( y_N \) and \( y_W \)). The mole fraction \( x_N \) is typically of the order \( 10^{-5} \). The vapor pressure of water at 300 K is \( P_W^{\text{vap}} = 3.5 \) kPa, and you can assume that the impact of its temperature dependence on solubility is relatively weak. Use ideal models in what follows.
(a) At 1 bar and 300 K, estimate the mole fraction of water that is present in the vapor phase, \( y_W \).
(b) Show that the solubility of nitrogen is given approximately by
\[
x_N = C(T, P)(1 - y_W)P
\]
where \( C(T, P) \) is a constant that is independent of concentrations. Find an expression for \( C(T, P) \) in terms of standard and pure chemical potentials.
(c) Do you expect the solubility to increase or decrease with temperature? Explain by finding the temperature dependence of \( C(T, P) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F01979351-689f-4956-aa53-7abb3d3c26de%2F479af852-3760-43a9-ba26-54dbb5ce4f50%2Feeh228a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**12.33.** The solubility of nonpolar gases in liquid water is typically very low. Consider nitrogen in particular. Its solubility is characterized by the equilibrium mole fraction \( x_N \) of dissolved nitrogen in the liquid phase (with water mole fraction \( x_W = 1 - x_N \)) when the system is in equilibrium with a vapor phase (with corresponding mole fractions \( y_N \) and \( y_W \)). The mole fraction \( x_N \) is typically of the order \( 10^{-5} \). The vapor pressure of water at 300 K is \( P_W^{\text{vap}} = 3.5 \) kPa, and you can assume that the impact of its temperature dependence on solubility is relatively weak. Use ideal models in what follows.
(a) At 1 bar and 300 K, estimate the mole fraction of water that is present in the vapor phase, \( y_W \).
(b) Show that the solubility of nitrogen is given approximately by
\[
x_N = C(T, P)(1 - y_W)P
\]
where \( C(T, P) \) is a constant that is independent of concentrations. Find an expression for \( C(T, P) \) in terms of standard and pure chemical potentials.
(c) Do you expect the solubility to increase or decrease with temperature? Explain by finding the temperature dependence of \( C(T, P) \).
AI-Generated Solution
AI-generated content may present inaccurate or offensive content that does not represent bartleby’s views.
Unlock instant AI solutions
Tap the button
to generate a solution
Recommended textbooks for you
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Industrial Plastics: Theory and Applications
Chemical Engineering
ISBN:
9781285061238
Author:
Lokensgard, Erik
Publisher:
Delmar Cengage Learning
Unit Operations of Chemical Engineering
Chemical Engineering
ISBN:
9780072848236
Author:
Warren McCabe, Julian C. Smith, Peter Harriott
Publisher:
McGraw-Hill Companies, The