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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
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.
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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