Ĝex derive the following equations at constant T and Example 6: For binary mixture, if @M RT P: d (Ĝex X2 dx2 RT Ĝex Iny1 RT d Ĝex X1 dx1 Ĝex Iny2 = RT RT
Ĝex derive the following equations at constant T and Example 6: For binary mixture, if @M RT P: d (Ĝex X2 dx2 RT Ĝex Iny1 RT d Ĝex X1 dx1 Ĝex Iny2 = RT RT
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
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![**Example 6:** For a binary mixture, if
\[
\hat{\phi}_M = \frac{\hat{G}^{ex}}{RT}
\]
derive the following equations at constant T and P:
\[
\ln \gamma_1 = \frac{\hat{G}^{ex}}{RT} - x_2 \frac{d}{dx_2} \left( \frac{\hat{G}^{ex}}{RT} \right),
\]
\[
\ln \gamma_2 = \frac{\hat{G}^{ex}}{RT} - x_1 \frac{d}{dx_1} \left( \frac{\hat{G}^{ex}}{RT} \right)
\]
This derivation involves applying the principles of thermodynamics to determine the activity coefficients (\(\gamma_1\) and \(\gamma_2\)) in a binary mixture. The equations make use of the excess Gibbs free energy (\(\hat{G}^{ex}\)) and its dependence on the mole fractions (\(x_1\) and \(x_2\)).
Note: There are no graphs or diagrams included with this example.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58e30080-5af3-43c1-bb19-7e2f27cfd9f6%2F76e3951b-990f-43f6-89d0-8e196af8a3b0%2F6vg2ka_processed.png&w=3840&q=75)
Transcribed Image Text:**Example 6:** For a binary mixture, if
\[
\hat{\phi}_M = \frac{\hat{G}^{ex}}{RT}
\]
derive the following equations at constant T and P:
\[
\ln \gamma_1 = \frac{\hat{G}^{ex}}{RT} - x_2 \frac{d}{dx_2} \left( \frac{\hat{G}^{ex}}{RT} \right),
\]
\[
\ln \gamma_2 = \frac{\hat{G}^{ex}}{RT} - x_1 \frac{d}{dx_1} \left( \frac{\hat{G}^{ex}}{RT} \right)
\]
This derivation involves applying the principles of thermodynamics to determine the activity coefficients (\(\gamma_1\) and \(\gamma_2\)) in a binary mixture. The equations make use of the excess Gibbs free energy (\(\hat{G}^{ex}\)) and its dependence on the mole fractions (\(x_1\) and \(x_2\)).
Note: There are no graphs or diagrams included with this example.
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