The excess Gibbs energy of a binary liquid mixture at T and P is: GE X₁X₂ (−2.6x₁ — 1.8x₂) RT a. Find expressions for In y₁ and In y₂ at T and P. b. Show that when these expressions are combined in accord GE with the summability relation = Σ₁ x¡ In y₁, the given GE/RT equation is recovered. RT c. Show also that these satisfy the Gibbs/Duhem equation Σ₁ x¡d In y₁ = 0 at constant T and P. d In d. Show that (₁) (dIn y₂) = 0. = = X₁=1 X1=0 e. Plot GE/RT, GE/x₁x₂RT, In Y₁, and In Y₂ from the given equation and developed expressions in (a) as functions of X₁. Label the points In y and In y2, and solve for their actual values.
The excess Gibbs energy of a binary liquid mixture at T and P is: GE X₁X₂ (−2.6x₁ — 1.8x₂) RT a. Find expressions for In y₁ and In y₂ at T and P. b. Show that when these expressions are combined in accord GE with the summability relation = Σ₁ x¡ In y₁, the given GE/RT equation is recovered. RT c. Show also that these satisfy the Gibbs/Duhem equation Σ₁ x¡d In y₁ = 0 at constant T and P. d In d. Show that (₁) (dIn y₂) = 0. = = X₁=1 X1=0 e. Plot GE/RT, GE/x₁x₂RT, In Y₁, and In Y₂ from the given equation and developed expressions in (a) as functions of X₁. Label the points In y and In y2, and solve for their actual values.
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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Transcribed Image Text:The excess Gibbs energy of a binary liquid mixture at T and P is:
GE
= X₁X₂ (-2.6x₁ - 1.8x₂)
RT
a. Find expressions for In y₁ and In y2 at T and P.
b. Show that when these expressions are combined in accord
GE
with the summability relation
Σ₁x₁ Iny₁, the given GE/RT
RT
equation is recovered.
c. Show also that these satisfy the Gibbs/Duhem equation
Σ₁ x¡d Iny₁ = 0 at constant T and P.
d. Show that (₁)
(din y₂) = 0.
dx₁
=
=
X₁=1
X₁=0
e. Plot GE/RT, GE/x₁x₂RT, In Y₁, and In y₂ from the given equation
and developed expressions in (a) as functions of X₁. Label the
points In y and In y, and solve for their actual values.
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